**Previous months:**

2007 - 0703(2)

2008 - 0812(1)

2009 - 0907(1) - 0908(3) - 0909(1) - 0910(2)

2010 - 1001(3) - 1002(1) - 1003(1) - 1006(13) - 1007(2) - 1009(2) - 1010(3) - 1011(1) - 1012(5)

2011 - 1101(4) - 1102(4) - 1103(3) - 1104(1) - 1105(3) - 1106(2) - 1107(2) - 1108(4) - 1109(2) - 1110(1) - 1111(10) - 1112(2)

2012 - 1201(3) - 1202(2) - 1203(6) - 1204(3) - 1205(5) - 1206(8) - 1207(4) - 1208(4) - 1209(2) - 1210(2) - 1211(4) - 1212(7)

2013 - 1301(8) - 1302(7) - 1303(7) - 1304(5) - 1305(27) - 1306(6) - 1307(8) - 1308(7) - 1309(7) - 1310(9) - 1311(12) - 1312(2)

2014 - 1401(10) - 1402(8) - 1403(16) - 1404(11) - 1405(8) - 1406(6) - 1407(4) - 1408(9) - 1409(7) - 1410(6) - 1411(7) - 1412(8)

2015 - 1501(11) - 1502(11) - 1503(9) - 1504(10) - 1505(12) - 1506(9) - 1507(8) - 1508(10) - 1509(4) - 1510(19) - 1511(11) - 1512(8)

2016 - 1601(7) - 1602(9) - 1603(9) - 1604(6) - 1605(14) - 1606(11) - 1607(5) - 1608(13) - 1609(17) - 1610(17) - 1611(7) - 1612(23)

2017 - 1701(9) - 1702(9) - 1703(5) - 1704(10) - 1705(18) - 1706(9) - 1707(14) - 1708(16) - 1709(6) - 1710(16) - 1711(11) - 1712(8)

2018 - 1801(16) - 1802(10)

Any replacements are listed further down

[728] **viXra:1802.0355 [pdf]**
*submitted on 2018-02-24 12:29:27*

**Authors:** Robert A. Herrmann

**Comments:** 32 Pages.

The methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmology, the General Grand Unification Model (GGU-model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from certain observable entities, which are physical processes and mental procedures that we use to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is applied to it an ultra-logic-system is *-deduced. Another application of an hyper-algorithm yields a hyperfinite instruction paradigm that is hyper-deduced in the in the required sequential order. It is shown that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patten and Wheeler participator universe requirements. In this version, the participator process portion of the GGU-model is significantly altered from the original process presented and a correction is made to an equation and its applications. A specific data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. This set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A process is introduced that leads, when applied, to the individual developmental of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields, all physical-systems are produced. In this refinement, the page 11 statement, in the original version of this paper on quantum theory, is completely modified and the previous statement is now essentially incorrect.

**Category:** Mathematical Physics

[727] **viXra:1802.0310 [pdf]**
*submitted on 2018-02-21 18:46:48*

**Authors:** Yongsop Ri, Namhyok Ri, Jonggwang Pak, Iljin Kim, Zhihua Chen –Department of Mechanics Enineering, Kim Il Sung University, Pyongyang, DPR of Korea - School of Civil Engineering, Tianjin University, Tianjin 300072, PR of Chi

**Comments:** 21 Pages.

The topology optimization using the homogenization method is to find optimal layout of microstructures which satisfies design demand in the neighborhood of an arbitrary point in a given design domain. The homogenization approach is to compute proper mechanical properties of those microstructures in terms of integral averaging by accepting the periodicity assumption and characteristic function.
In this paper, we described a stiffness homogenization theory that is able to avoid the complication of the homogenization approach and reduce the computation cost by considering the topology optimization process in consistence with the finite element analysis. The method can be applied more flexibly to individual or simultaneous optimization of the topology, shape, size and material layout. We discussed a stiffness homogenization during meshing the space structure with different kinds of elements in detail. An optimal criterion for the minimum weight design problem, as one of typical optimization design problems, was derived and the computational algorithm was presented. Numerical results of an example were compared with previous methods, which show the validation of the method.

**Category:** Mathematical Physics

[726] **viXra:1802.0239 [pdf]**
*submitted on 2018-02-18 13:58:51*

**Authors:** Alexander I.Dubinyansky, Pavel Churlyaev.

**Comments:** 6 Pages. dubinyansky@mail.ru http://universe100.narod.ru/ http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html (English)

Development of the mathematical model of the elastic universe. The spins of the loks (0,0), (1,0) and (1,1) are calculated. Assumptions are made regarding other loks. Further conclusions were drawn on the identification of elementary particles in a set of loks.

**Category:** Mathematical Physics

[725] **viXra:1802.0231 [pdf]**
*submitted on 2018-02-19 00:43:55*

**Authors:** Jack Bidnik

**Comments:** 6 Pages.

Electrostatics, Gravity, and Galactic Force © US 2015
by Jack Bidnik
This paper is a continuation of my paper entitled Gravitational Forces Revisited (GFR), http://vixra.org/abs/1707.0128 and may be considered as Chapter 2 of the concepts developed in that paper.
Two corollaries of the derivation of Gs in GFR are elaborated here to show that the formula can be extended to include both the smallest and the largest masses and spaces. The same formula can give both the electrostatic force of the Hydrogen atom and also the force which counteracts the centrifugal force of large galaxies. I believe this development nullifies the most basic motive for postulating dark matter, which is that the gravitational force at such high speeds could not hold the galaxy together. Examples are given for galaxies of various size.
The paper starts with continuing analysis of the mathematical conclusion in GFR that the derived force Ft is equivalent to the centripetal force of the orbit vo2/r. This analysis is perhaps superfluous since there is no other acceleration present radially than the one derived for Ft , but I present various looks at the math to dispel any nagging doubts.
Another set of doubts to be dispelled involves the idea of frames of motion. It suffices to point out that when one uses the reduced mass, it is the equivalent of the motion of either mass in the frame of the other, since it is the equivalent of one mass being stationary.

**Category:** Mathematical Physics

[724] **viXra:1802.0207 [pdf]**
*submitted on 2018-02-16 06:19:14*

**Authors:** Alexander I. Dubinyansky, Pavel Churlyaev.

**Comments:** 7 Pages. dubinyansky@mail.ru http://universe100.narod.ru/ http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html (English)

Development of the mathematical model of the elastic universe. The energy of the loks (0,0), (1,0) and (1,1) are calculated. Assumptions are made regarding other loks. The first conclusions on the identification of elementary particles in a set of loks are made.

**Category:** Mathematical Physics

[723] **viXra:1802.0183 [pdf]**
*submitted on 2018-02-15 07:40:11*

**Authors:** Renzun Lian

**Comments:** 5 Pages.

Traditionally, all working modes of a perfect electric conductor are classified into resonant modes, inductive modes, and capacitive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the resonant modes are alternatively classified into intrinsically resonant modes and non-intrinsically resonant modes, and the intrinsically resonant modes are further classified into non-radiative intrinsically resonant modes and radiative intrinsically resonant modes. Based on the modal expansion corresponding to this new modal classification, an alternative modal decomposition method is proposed. In addition, it is also proved that: all intrinsically resonant modes and all non-radiative intrinsically resonant modes constitute linear spaces respectively, but all resonant modes and all radiative intrinsically resonant modes cannot constitute spaces respectively.

**Category:** Mathematical Physics

[722] **viXra:1802.0114 [pdf]**
*submitted on 2018-02-11 01:51:57*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 2 Pages.

A no-brainer.

**Category:** Mathematical Physics

[721] **viXra:1802.0109 [pdf]**
*submitted on 2018-02-10 02:51:25*

**Authors:** Antoine Balan

**Comments:** 2 pages, written in french

The KdV equations are generalized over differentiable manifolds. The equations are integrable.

**Category:** Mathematical Physics

[720] **viXra:1802.0055 [pdf]**
*submitted on 2018-02-05 20:46:50*

**Authors:** Vu B Ho

**Comments:** 9 Pages.

In this work we show that, as in the case of Dirac equation, it is possible to formulate Maxwell field equations of electromagnetism from a general system of linear first order partial differential equations. A prominent feature that emerges from formulating Dirac and Maxwell field equations from a general system of linear first order partial differential equations is that the field equations must be formed in such a way that the functions that represent the system also obey a wave equation. This type of mathematical duality may be related to the wave-particle duality in quantum physics.

**Category:** Mathematical Physics

[719] **viXra:1802.0016 [pdf]**
*submitted on 2018-02-02 23:39:32*

**Authors:** Durgadas Datta.

**Comments:** 7 Pages. A paper for CERN .

The meaning of fine tuning and emergent gravitation.

**Category:** Mathematical Physics

[718] **viXra:1801.0417 [pdf]**
*submitted on 2018-01-30 09:07:40*

**Authors:** Peter Bissonnet

**Comments:** 11 Pages.

The author used to think that the only representation of prime numbers, etc. was the prime number double helix
representation. However, in 2011, the author published a paper which puzzled him and it eventually dawned upon him that
there was more than one representation of prime numbers. The second representation will be referred to as the hyperbolic
representation. The third representation will be called the parabolic representation and is related to the hyperbolic
representation. The fourth representation is the triangular representation and is related to the hyperbolic representation.
Both of the primary representations, the double helix and the hyperbolic both reject that 2 and 3 are prime numbers. The
hyperbolic representation is shown to be related to Lorentz-like transformations.

**Category:** Mathematical Physics

[717] **viXra:1801.0287 [pdf]**
*submitted on 2018-01-23 04:40:36*

**Authors:** Renzun Lian

**Comments:** 15 Pages.

In this paper, we generalize Huygens' principle (HP), extinction theorem (ET), and Franz-Harrington formulation (FHF) in two parts. In Part I, the traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment; the traditional FHF of homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system and then to piecewise inhomogeneous anisotropic lossy material system; the traditional HP, ET, and FHF of simply connected material system are generalized to multiply connected system and then to non-connected system; the traditional FHF of external scattering field and internal total field are generalized to internal scattering field and internal incident field. In Part I, it is proved that the generalized HP (GHP) and generalized ET (GET) are equivalent to each other; the GHP, GET, and generalized FHF (GFHF) satisfy so-called topological additivity, i.e., the GHP/GET/GFHF of whole electromagnetic (EM) system equals to the superposition of the GHP/GET/GFHF corresponding to all sub-systems. In this Part II, the above results obtained in previous Part I, which focuses on the EM system constructed by material bodies, are further generalized to the metal-material combined EM system in inhomogeneous anisotropic lossy environment, and traditional surface equivalence principle is generalized to line-surface equivalence principle.

**Category:** Mathematical Physics

[716] **viXra:1801.0268 [pdf]**
*submitted on 2018-01-22 00:27:33*

**Authors:** Miroslav Súkeník, Jozef Šima

**Comments:** 3 Pages. No comment

The paper covers applicability areas of the Euler – Mascheroni constant in General Theory of Relativity and Quantum Theory.

**Category:** Mathematical Physics

[715] **viXra:1801.0267 [pdf]**
*submitted on 2018-01-22 01:55:25*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 4 Pages. dubinyansky@mail.ru

A formula is obtained that relates the mass (energy) of a lok (1,0) with the parameters of the elasticity of a Gukuum.

**Category:** Mathematical Physics

[714] **viXra:1801.0266 [pdf]**
*submitted on 2018-01-21 04:53:30*

**Authors:** Renzun Lian

**Comments:** 19 Pages.

Huygens' principle (HP), extinction theorem (ET), and Franz's / Franz-Harrington formulation (FHF, which is a mathematical expression of surface equivalence principle) are the important components of electromagnetic (EM) theory, and they are generalized from the following aspects.
1) Traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment. 2) Traditional FHF for homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system in this Part I, and will be further generalized to metal-material combined system in future Part II. 3) The Huygens' surface in traditional HP and ET is a single closed surface. In Part I, it is generalized to the "Huygens' surface" which is constructed by multiple closed surfaces. In Part II, it will be further generalized to the "Huygens' boundary" which includes some lines and open surfaces. 4) For a material body, traditional FHF has only ability to express the external scattering field and the internal total field (the summation of scattering and incident fields) in terms of the equivalent sources on material boundary, and it is generalized to formulating the internal scattering and incident fields in this paper.
In addition, the relationships among HP, ET, and FHF are studied, and it is proved that HP and ET are equivalent to each other.

**Category:** Mathematical Physics

[713] **viXra:1801.0258 [pdf]**
*submitted on 2018-01-20 09:33:26*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 6 Pages. dubinyansky@mail.ru

A theoretical calculation is made of the total energy of the wave vortex in a vacuum, for the general case.

**Category:** Mathematical Physics

[712] **viXra:1801.0240 [pdf]**
*submitted on 2018-01-19 10:26:34*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 9 Pages. dubinyansky@mail.ru

Some solutions of the wave equation in gukuum, possibly creating the whole variety of matter.

**Category:** Mathematical Physics

[711] **viXra:1801.0232 [pdf]**
*submitted on 2018-01-18 05:29:53*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 8 Pages. Details on the site http://universe100.narod.ru/

The beginning of a more rigorous exposition of the theory of the elastic universe.

**Category:** Mathematical Physics

[710] **viXra:1801.0197 [pdf]**
*submitted on 2018-01-16 05:17:24*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 5 Pages. Russian: http://universe100.narod.ru/ English: http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html dubinyansky@mail.ru

In the wave vortices, the energy is capable of winding itself onto itself and at the same time being redistributed.

**Category:** Mathematical Physics

[709] **viXra:1801.0163 [pdf]**
*submitted on 2018-01-15 04:26:21*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 7 Pages. site http://universe100.narod.ru/index.html

The hypothesis is stated that the whole variety of the material world, the whole variety of elementary particles, the whole variety of physics, can be explained by localized solutions of the three-dimensional wave equation in the elastic continuum.

**Category:** Mathematical Physics

[708] **viXra:1801.0162 [pdf]**
*submitted on 2018-01-14 05:28:47*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 1 Page. Details on the site http://universe100.narod.ru/

The universe is a solid elastic continuum - gukuum. This continuum does not contain any numerical parameters or constraints.
All visible and invisible objects of the universe, from large to small, are wave objects in this continuum.
All the wave objects in the gukuum are described by the letter specification of the elasticity parameters of the solid body and the three-dimensional wave equation.
The nonlinearity that exists in the universe is explained by the law of "winding the linear solution on itself." As a result of such winding, or layering, the linear solution becomes non-linear and creates the entire variety of the material world.

**Category:** Mathematical Physics

[707] **viXra:1801.0079 [pdf]**
*submitted on 2018-01-07 05:41:04*

**Authors:** Ricardo Gil

**Comments:** 1 Page. All these items are off the shelf items. Try them and upload a comment with results.

The objective of this paper is to suggest that bullet with a watch battery on it(superglue them on) will have reduced mass and travel more efficiently. Place them in a conventional revolver and in a conventional shot gun.(single or double barrel)

**Category:** Mathematical Physics

[706] **viXra:1801.0066 [pdf]**
*submitted on 2018-01-06 10:25:14*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages.

This paper is an appendix to the article "From Bernoulli to Laplace and Beyond"
(refenced below), and discusses different aspects of it: electromagnetism, field tensors,
general relativity, and probability.

**Category:** Mathematical Physics

[705] **viXra:1801.0047 [pdf]**
*submitted on 2018-01-04 20:41:10*

**Authors:** YiMing Xia

**Comments:** 17 Pages. 1.A new split-full node notion is presented and a novel technique is proposed to construct a simple and clear basic full node shape function for a triangular plate-bending element.

A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis functions are built out of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by means of extending the shape function triangle domain for a split node at the zero coordinates to the hexagon area enclosing the zero coordinates. As a result, a new split-full node notion is presented and a novel rational MRA concept together with the resolution level (RL) is constituted for the element. Via practical examples, it is found that the traditional triangular plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated. The continuous full node shape function unveils secrets behind assembling artificially of node-related items in global matrix formation by the conventional FEM.

**Category:** Mathematical Physics

[704] **viXra:1801.0036 [pdf]**
*submitted on 2018-01-03 16:51:21*

**Authors:** Ricardo Gil

**Comments:** 3 Pages. MIT unknowingly has a dark matter quantum computer. This is the topological computer Krysta Svore is working on at Microsoft but Peter Shor at MIT has unknowingly achieved the dark matter quantum computer that has time reversal. Ref: Hooft,Wilzek.MIT.

The purpose of these 5 papers(paragraphs) is to share my thoughts on Dark Matter, Dark Energy and my observation on Light Theory with respect to different gravities.

**Category:** Mathematical Physics

[703] **viXra:1801.0025 [pdf]**
*submitted on 2018-01-03 09:38:11*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Retracted & now republished: Fixed forgotten factor i.

Reviewing Laplace's equation of gravitation from the perspective of D. Bernoulli, known as Poisson-equation, it will be shown that Laplace's equation tacitly assumes the temperature T of the mass system to be approximately 0 degrees of Kelvin.
For temperatures greater zero, the gravitational field will have to be given an additive correctional field.
Now, temperature is intimately related to the heat, and heat is known to be radiated as an electromagnetic field.
It is shown to take two things in order to get at the gravitational field in the low temperature limit:
the total square energy density of the source in space-time and a (massless) field, which expresses the equivalence of inert and gravitational mass/energy in a quadratic, Lorentz-invariant form.
This field not only necessarily must include electromagnetic interaction, it also will be seen to behave like it.

**Category:** Mathematical Physics

[702] **viXra:1712.0663 [pdf]**
*submitted on 2017-12-29 15:54:44*

**Authors:** Vu B Ho

**Comments:** 7 Pages.

In this work we discuss the possibility to formulate gravity as a coupling of two electromagnetic fields of equal magnitude but opposite direction.

**Category:** Mathematical Physics

[701] **viXra:1712.0598 [pdf]**
*submitted on 2017-12-25 14:56:26*

**Authors:** Jonathan Tooker

**Comments:** 284 Pages. The Persian Stitch is one thing and Chaos Monkey typesetter malware is quite another.

In lieu of an abstract each chapter in this book has a description of its contents.

**Category:** Mathematical Physics

[700] **viXra:1712.0594 [pdf]**
*submitted on 2017-12-24 19:34:26*

**Authors:** Harry Watson

**Comments:** 2 Pages.

We make the following Ansatz for the mass ratio of the neutron to the electron:
m_n /m_e is approx (4pi)(4pi-1/pi)(4pi-2/pi) +ln(4pi) = 1838.682763
where m_n is the neutron rest mass and m_e is the electron rest mass. The CODATA value is 1838.68366158. The neutron decays into a proton and an electron. If ln(4pi) is the neutron-proton mass difference, then m_p/m_e is (4pi)(4pi-1/pi)(4pi-2/pi), where m_p is the proton rest mass.
harry.watson@att.net

**Category:** Mathematical Physics

[699] **viXra:1712.0419 [pdf]**
*submitted on 2017-12-12 13:58:40*

**Authors:** Nikola Samardzija

**Comments:** 16 Pages. This review paper was written in 2014, and since has raised quite a few eyebrows in academia. The simplicity of the globotoroid model is far reaching, and alters some central themes in mathematics and sciences - Namely, the singularity based theories.

Mathematical models can give us invaluable insights into natural phenomena, and as such play an important role in science. The intent of this paper is to give a high-level overview of a simple continuous dynamical model that offers an insight into a qualitative behavior seldom reported or discussed. This model has no equilibrium or singular points, yet its phase space unveils four distinct topological features: a limit cycle, a torus, a sphere and a wormhole. Each of these features results from model solutions that can be periodic, quasi-periodic and chaotic, which collectively form a space-time structure referred to as the globotoroid. The model generalizes the energy behavior of many processes of interest, and consequently is reshaping contemporary systems theory to fit more completely with different natural phenomena. Specifically, the globotoroid is the simplest 3-dimensional dynamic model that exposes the concept of the wormhole, which embodies an important energy behavior throughout our universe. The fields of science that may benefit from this modeling approach are many, including physics, cosmology, biology, chemistry, engineering, cognitive sciences, economics, politics, and business and finance. This is demonstrated by reviewing some well-known phenomena in natural and social sciences.

**Category:** Mathematical Physics

[698] **viXra:1712.0404 [pdf]**
*submitted on 2017-12-13 03:42:44*

**Authors:** Vu B Ho

**Comments:** 12 Pages.

In this work, we discuss a method to derive Dirac equation and other equations, such as the Cauchy-Riemann equations, from a general system of linear first order partial differential equations, with the hope that when studied more thoroughly the general system may provide deeper insights into geometrical and topological structures of quantum particles and fields.

**Category:** Mathematical Physics

[697] **viXra:1712.0399 [pdf]**
*submitted on 2017-12-12 03:53:52*

**Authors:** D. K. K. Adjaï, J. Akande, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 3 pages

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear two-point boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared to be a special case of a more general equation. As a result, various initial and boundary value problems may be solved explicitly and exactly.

**Category:** Mathematical Physics

[696] **viXra:1712.0364 [pdf]**
*submitted on 2017-12-10 07:52:18*

**Authors:** J. Akande, Y. J. F. Kpomahou, D. K. K. Adjaï, L. H. Koudahoun, M. D. Monsia

**Comments:** 3 pages

This paper shows, for the first time, that the mathematical pendulum and generalized mathematical pendulum initial and boundary value problems may be computed from the explicit and exact general solution to the corresponding differential equation in a straightforward fashion by a direct method.

**Category:** Mathematical Physics

[695] **viXra:1712.0149 [pdf]**
*submitted on 2017-12-06 10:01:43*

**Authors:** L. H. Koudahoun, J. Akande, D. K. K. Adjaï, Y. J. F. Kpomahou, M. Nonti, M. D. Monsia

**Comments:** 13 pages

A generalized Bratu equation is established in the framework of Sundman transformation. The well-known exact solution to the Bratu boundary value problem is deduced from the obtained explicit and exact general solution which may be also used to compute the exact solution to Bratu type initial and boundary value problems.

**Category:** Mathematical Physics

[694] **viXra:1712.0082 [pdf]**
*submitted on 2017-12-04 05:04:28*

**Authors:** Dmitri Martila

**Comments:** 3 Pages.

Derived the integral of motion for perfect fluid. It reduces the number of valid equations of state: must be p=0.

**Category:** Mathematical Physics

[693] **viXra:1711.0468 [pdf]**
*submitted on 2017-11-28 12:24:15*

**Authors:** Richard L Amoroso, Peter Rowlands, Louis H Kauffman

**Comments:** 11 Pages. Paper from VIII international symposium honoring mathematical physicist Jean-Pierre Vigier

We make a preliminary exploratory study of higher dimensional (HD) orthogonal forms of the quaternion algebra in order to explore
putative novel Nilpotent/Idempotent/Dirac symmetry properties. Stage-1 transforms the dual quaternion algebra in a manner that
extends the standard anticommutative 3-form, i, j, k into a 5D/6D triplet. Each is a copy of the others and each is self-commutative
and believed to represent spin or different orientations of a 3-cube. The triplet represents a copy of the original that contains no new
information other than rotational perspective and maps back to the original quaternion vertex or to a second point in a line element. In
Stage-2 we attempt to break the inherent quaternionic property of algebraic closure by stereographic projection of the Argand plane
onto rotating Riemann 4-spheres. Finally, we explore the properties of various topological symmetries in order to study
anticommutative - commutative cycles in the periodic rotational motions of the quaternion algebra in additional HD dualities.

**Category:** Mathematical Physics

[692] **viXra:1711.0459 [pdf]**
*submitted on 2017-11-29 03:16:37*

**Authors:** Christopher Goddard

**Comments:** 21 Pages.

I sketch roughly how an Alcubierre drive could work, by examining exotic geometries consisting of soliton solutions to the dynamics of space filling curves. I also briefly consider how remote sensing might work for obstacle avoidance concerning a craft travelling through space via a 'wormhole wave'. Finally I look into how one might adopt remote sensing ideas to build intrasolar wormhole networks, as well as extrasolar jump gates.

**Category:** Mathematical Physics

[691] **viXra:1711.0446 [pdf]**
*submitted on 2017-11-28 03:18:52*

**Authors:** Vu B Ho

**Comments:** 18 Pages.

In this work, we will investigate possible spacetime structures of massless particles by formulating Dirac equation in a six-dimensional spatial-temporal continuum in both pseudo-Euclidean and Euclidean metrics. We show that the state of a massless particle flows as an irrotational and incompressible fluid in steady fluid dynamics in the sense that all spatial and temporal components of the wavefunction of a massless particle can be described by Laplace equation. Furthermore, we also show that the six components of the wavefunction are coupled in pairs to form two-dimensional subspaces and this result may suggest why quantum particles possess an intrinsic spin angular momentum that takes half-integral values.

**Category:** Mathematical Physics

[690] **viXra:1711.0435 [pdf]**
*submitted on 2017-11-26 15:20:30*

**Authors:** Dan Visser

**Comments:** 23 Pages.

This article breaks with the inviolability of the quantum-unit. It ‘crumbles’ (or cuts up, or refines) the quantum-vacuum. That also crumbles the constant vacuum-energy-density, or dark energy. It offers a new definition for dark energy. New dark energy does no longer belong to the Big Bang-universe: New dark energy is part of a rotating-hologram universe. Such a universe has the shape of a Double Torus, which has an inner-torus that rotates while an outer-torus represents the ‘crumble of the vacuum’ with time below the Planck-scale. The ‘vacuum-crumbling’ implies a ‘new ‘building-stone’ for vacuum:Tdan . This is a new (rotating) energy-tensor, which has two states , one for above and one for below the Planck-scale. The ‘beauty’ is the dimension of the tensor remains unchanged in those two states! Hence, the quantum-Planck-unit is transparent for migration. That makes the Big Bang-universe no longer a fundamental universe. The Big Bang-universe is emerged (or induced) by rotation of the hologram-universe. This means the Big Bang-universe will exist in every place of the rotating hologram-universe implying: parallel universes ‘outside’ a Big Bang-universe are a nonissue. Parallel universes exist embedded in the rotating hologram-universe. Thereby the origin of the ‘old Big Bang-universe’ is no longer relevant. A new definition of age of the universe lies in the cycle-duration of one cycle, although rotation goes on eternally. Continuously the origin is recalculated. Seemingly the Big Bang-universe is materialized above the Planck-scale and dé-materializes below the Planck-scale, however, such a perspective is reciprocal facing the transparent frontier. Against all expectations my formulas show that one can migrate from one to the other parallel-universe. Locally that is interpreted as ‘change’, but on larger scales it is called traveling through time without space. Because there is extra time (or refined time in the crumble of vacuum), which affects relativistic time that can make traveling faster than traveling through space with the speed of light. There is no horizon between the physics of the ‘soul’ and the physics of ‘materialization’ including the other way around.

**Category:** Mathematical Physics

[689] **viXra:1711.0395 [pdf]**
*submitted on 2017-11-24 05:57:12*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Making an intuitive assumption, and using the completeness of the position and momentum eigenstates, along with the postulates of quantum mechanics, we provide a geometric presentation of the position and momentum representations in quantum mechanics, in the hope of offering a perspective complementary to those given in standard textbooks.

**Category:** Mathematical Physics

[688] **viXra:1711.0365 [pdf]**
*submitted on 2017-11-21 01:59:25*

**Authors:** Giuliano Bettini

**Comments:** 19 Pages. in Italian

Starting from the 32 crystal classes, we find a complete classification scheme of the same with only 5 bits, and at least in part the meaning of the various bits.
There is no inverse demonstration, ie only 5 bits must generate all 32 crystalline classes in nature.
However, the proposed classification seems to invoke a logical process of formation of the various classes, doing this way:
the matter first aggregates without any symmetry, then it adopts various rotation symmetries (no symmetry, binary, ternary, etc., simple or composite) and then adds to each symmetry of rotation the additional symmetries c (center), m (planes) or c + m together

**Category:** Mathematical Physics

[687] **viXra:1711.0348 [pdf]**
*submitted on 2017-11-17 14:12:41*

**Authors:** Gary D. Simpson

**Comments:** 9 Pages.

This essay discusses the meaning and role of the term “fundamental” as it applies to Math and Physics. The importance of Lagrange’s Four Squares Theorem is also discussed. It is argued that the vacuum is a 5-D Quantum-Space-Time and that the vacuum is fundamental.

**Category:** Mathematical Physics

[686] **viXra:1711.0272 [pdf]**
*submitted on 2017-11-10 13:59:02*

**Authors:** Dmitri Martila

**Comments:** 4 Pages.

Do Stokes and Gauss's theorems from Vector Analyses hold also in curved spacetime (or in the curved coordinates of a flat manifold)? These theorems (especially the Gauss's or the "Divergence" theorem) are ones of the utmost importance, especially for theoretical astrophysics. My opinion is in the file. Can you tell me what journal will accept this "nonsense"?

**Category:** Mathematical Physics

[685] **viXra:1711.0270 [pdf]**
*submitted on 2017-11-10 17:28:55*

**Authors:** David Njeru kathuri

**Comments:** 62 Pages.

This publication is about a theory that tries to scientifically prove that under certain conditions, fire is a portal that can be used in teleportation of matter.
The document also tries to give an alternative to General Relativity in the most scientifically precise way that leaves no room for doubt. This is done by giving a testable alternative theory of what the past & future is and its relation to gravity.

**Category:** Mathematical Physics

[684] **viXra:1711.0260 [pdf]**
*submitted on 2017-11-09 07:17:38*

**Authors:** Spiros Konstantogiannis

**Comments:** 42 Pages.

Quasi-exactly solvable symmetrized sextic oscillators have been proposed and studied by Quesne, who categorized them based on the parity – natural or unnatural – of their known eigenfunction [2]. Herein, we examine the quasi-exact solvability of symmetrized sextic oscillators using a quotient-polynomial approach [3, 4, 5], which, in this case, opens up the possibility to construct non-analytic sextic oscillators from analytic quotient polynomials, and thus to distinguish the oscillators resulting from analytic quotient polynomials from those resulting from non-analytic quotient polynomials. We analyze the cases n=0 and n=1, and we show that the results are in agreement with those of Quesne [2]. In the case n=2, we construct sextic oscillators using only analytic quotient polynomials, and focusing on the non-analytic oscillators whose known eigenfunction is of unnatural parity, we register a relation between the coefficients of the two non-analytic terms of the exponential polynomial, which then we generalize to the higher cases n=3 and n=4, to construct new non-analytic sextic oscillators whose known eigenfunction is of unnatural parity.

**Category:** Mathematical Physics

[683] **viXra:1711.0201 [pdf]**
*submitted on 2017-11-06 03:26:57*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 5 Pages.

The occurrence of infinite values in physical equations, such as singularity in the description of black holes, is a painstaking problem that causes many theories to break down and/or being incapable of describing extreme events. Different methods, such as re-normalization, have been used in the assessment of physical observables in order to erase the undesirable infinity. Here we propose a novel technique, based on geometrical considerations, that allows removal of infinity and achievement of physical theories void of such a problem. We compare finite quantities to curved lines endowed in positive-curvature manifolds, and intractable infinity to a straight line. In order to restore the equations and erase the straight line of infinity, we project the quantities onto curved lines endowed in negative-curvature manifolds.

**Category:** Mathematical Physics

[682] **viXra:1710.0346 [pdf]**
*submitted on 2017-10-31 09:40:52*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 13 Pages. This paper has not been submitted to a journal. Your comments are welcome

Borges has a rare ability to put wild ideas into detective stories with reporting style. At least that is the impression that we got on his short stories. In particular, one of his short story is worthnoting: Tlon, Uqbar, Orbis Tertius. The story told us about a mysterious country called Uqbar, in apparently an unofficial reprint of Encyclopedia Britannica. It also tells about Tlon, a mysterious planet, created purely by imaginative minds. While this story clearly criticizes Berkeley view and may be not related to our daily reality, a reinterpretation of this story leads us to a long standing discourse in the philosophy of science: to how extent the entire modern physics follow such a Berkeley-antirealism tendency? This paper is intended to bring this subject into our attention. We will also discuss shortly on the antirealism in certain trends in theoretical physics and cosmology.

**Category:** Mathematical Physics

[681] **viXra:1710.0233 [pdf]**
*submitted on 2017-10-20 23:29:29*

**Authors:** Paris S. Miles-Brenden

**Comments:** 60 Pages. Grand Unified Theory of Electromagnetism Updated

The proposal of this thesis formulation is that of the development, design, and creation of a `Light Gyroscope' which is the formulation of a method to bal- ance light on a point with all such other light in existence; as an emanation of di erence between light and darkness; for which there is a balance between complete physical form and nonphysical formlessness; from that of a non-dual relation of physical electrical component design of general form of an in nite cascade of quarter wave re ectors of nite dimension and volume; of the nature for which an in nite cascade non related to that of the quadrature condition of elliptic function is met with a dual to an in nite cascade of ordinary elliptic operator solutions as their dual sine wave harmonic functions of free extension in space, time, and quanti able moment of temporal singular event structure; for which there exists an in nitely encompassed volumetric space of in nite dimension by co-parallelism of electricity and magnetism of no form other than topological nature; with in nite depth of four fold relation.

**Category:** Mathematical Physics

[680] **viXra:1710.0219 [pdf]**
*submitted on 2017-10-17 19:41:10*

**Authors:** Huai-Yi Xie

**Comments:** 115 Pages.

In this paper, we have derived planar multilayer dyadic Green’s functions by Fourier expansion method and have checked its correctness by comparing results for reflected electric fields from dipole emissions near such structures available in previous literature. Furthermore, we show how these dyadic Green’s functions can be applied to calculate reflected fields from a dipole source with arbitrary orientations. We believe our formulation will be powerful in the modeling of molecular fluorescence near these structures.

**Category:** Mathematical Physics

[679] **viXra:1710.0198 [pdf]**
*submitted on 2017-10-15 23:37:12*

**Authors:** Hongbing Zhang

**Comments:** 30 Pages.

The geometric significance of complex numbers is well known, such as the meaning of imaginary unit i is to rotate a vector with pi/2, etc. In this article, we will try to find some intuitive geometric significances of Pauli matrices, split-complex numbers, SU(2), SO(3), and their relations, and some other operators often used in quantum physics, including a new method to lead to the spinor-space and Dirac equation.

**Category:** Mathematical Physics

[678] **viXra:1710.0197 [pdf]**
*submitted on 2017-10-15 23:42:10*

**Authors:** Hongbing Zhang

**Comments:** 7 Pages.

In history, the problem of Johann Bernoulli's Brachistochrone Curve (BBC) was assumed the case that the force of gravity on the falling body is constant, for example, the case of near the surface of the Earth. In this article, we will propose and solve a new problem of the General Brachistochrone Curve (GBC), in case of the body falling in a large space of Newton gravity field, or in stronger Newton gravity field, in which the force of gravity is inversely proportional to the square of the height above the center of the star or planet.

**Category:** Mathematical Physics

[677] **viXra:1710.0196 [pdf]**
*submitted on 2017-10-15 23:46:11*

**Authors:** Hongbing Zhang

**Comments:** 6 Pages.

The metric tensor of Minkowski space-time, the electromagnetic field tensor, etc., are usually represented by 4x4 matrices in many textbooks, but in this paper we will demonstrate that this form of matrix-representation is unreasonable. We will introduce more reasonable rules of matrix-form for representing any (p,q)-type tensor.

**Category:** Mathematical Physics

[676] **viXra:1710.0155 [pdf]**
*submitted on 2017-10-13 16:20:37*

**Authors:** Antoine Balan

**Comments:** 2 pages, written in french

Here are introduced KdV type equations following the stationary solution which is the Weierstrass fonction of an elliptic curve.

**Category:** Mathematical Physics

[675] **viXra:1710.0119 [pdf]**
*submitted on 2017-10-10 20:58:30*

**Authors:** Harry Watson

**Comments:** 2 Pages.

Let Q denote a function from the nonnegative integers into the real numbers, such that: Q(0) = 1.000000509157;
Q(1) = Q(0) * (4pi));
Q(2) = Q(0) * (4pi) * (4pi-1/pi);
Q(3) = Q(0) * (4pi) * (4pi-1/pi) * (4pi-2/pi);
Q(4) = Q(0) * (4pi) * (4pi-1/pi) * (4pi-2/pi) * (4pi-3/pi);
Q(5) = Q(0) * (4pi) * (4pi-1/pi) * (4pi-2/pi) * (4pi-3/pi) * (4pi-4/pi).
Consider Q(3) = 1836.15267389 and Q(5)=240773.8273. Q(3) is the CODATA value for the ratio of the proton mass to the electron mass. Q(5) approximates the mass ratio of the Higgs Boson to the electron. (The value of Q(5)/Q(3) is 131.1295246. If the CODATA value for the mass ratio of the proton to the electron is revised, it will only have to be changed in Q(0). The approximation Q(5)/Q(3) is compared with changing values of the mass ratio of the Higgs Boson to the proton.
harry.watson@att.net

**Category:** Mathematical Physics

[674] **viXra:1710.0106 [pdf]**
*submitted on 2017-10-09 08:46:09*

**Authors:** Markos Georgallides

**Comments:** 89 Pages.

The Geometrical Inversion Mechanism .
In article is presented the Algebraic and Geometric Solution , and the Geometrical
Construction of all the n-Regular Polygons . The Method , is the Geometrical - Inversion on three circles , of the Alternate Interior angles of the Mechanism , where Extrema ( maximum or minimum Magnitude between two Positions which are the vertices of any two Sequent-Regular-Even-Polygons ) is expressed in this closed and bounded - interval , as the Inflection or Deflection of Coupler curves , and as the local maximum or minimum between the two Points , and which is their critical point .

**Category:** Mathematical Physics

[673] **viXra:1710.0102 [pdf]**
*submitted on 2017-10-09 13:58:58*

**Authors:** Louai Hassan Elzein Bashier

**Comments:** 22 Pages.

This paper is prepared to show the synthesis of the Newtonian mechanical
force and its counter part the inertial force. It is shows that the Newtonian
mechanical force splits into two counter forces when it is act upon a rigid
body. The paper is also shows the derivation of the momentum and the
kinetic energy that occur due to the presence of the inertial force.

**Category:** Mathematical Physics

[672] **viXra:1710.0084 [pdf]**
*submitted on 2017-10-08 01:22:16*

**Authors:** Moises Dominguez-Espinosa

**Comments:** 5 Pages.

There is a paradigm in Quantum Mechanics that explains quantization through normal vibration modes called Eigenstates that arise from Schrödinger wave equation. In this contribution we propose an alternative methodology of quantization by using basic concepts of mechanics and chaos from which a Toy Model is built.

**Category:** Mathematical Physics

[671] **viXra:1710.0076 [pdf]**
*submitted on 2017-10-07 09:38:09*

**Authors:** Vito R. D'Angelo

**Comments:** 3 Pages.

From a mathematical perspective, the key to the universe lies at the central tenet of Pythagorean thought - that the universe can be explained by pure numbers, i.e. dimensionless ratios. A Planck constants hierarchy is created that postulates an undiscovered Planck constant - the Planck circumference, symbol (P). The Planck constants hierarchy produces dimensionless ratios, that allow for the first time the theoretical calculation of constants, e.g. the Planck momentum, Planck mass and Planck energy constants.

**Category:** Mathematical Physics

[670] **viXra:1710.0074 [pdf]**
*submitted on 2017-10-07 13:09:06*

**Authors:** L. H. Koudahoun, J. Akande, D.K.K. Adjaï, Y.J.F. Kpomahou, M. D. Monsia

**Comments:** 16 pages

This work exhibits a generalized Painlevé-Gambier XVII equation and its applications in physics.

**Category:** Mathematical Physics

[669] **viXra:1710.0061 [pdf]**
*submitted on 2017-10-05 10:26:57*

**Authors:** Andrei P. Kirilyuk

**Comments:** 10 pages, 15 eqs, 15 refs; Paper presented at the FQXi essay contest 2016-2017, http://fqxi.org/community/forum/topic/2774

Based on the unreduced, non-perturbative solution to arbitrary interaction problem, we show that any interaction process underlying real system dynamics and object properties gives rise to irreversible time flow, universally specified evolution purpose and meaningful intentions at higher levels of universally defined dynamic complexity. The new mathematics of real-world complexity contains thus well-specified intrinsic teleology due to its rigorously derived extension with respect to usual, “goal-free” and “mindless” theory. We outline major aspects and applications of that extended, naturally teleological and causally complete science framework, including critically important problem solutions.

**Category:** Mathematical Physics

[668] **viXra:1710.0014 [pdf]**
*submitted on 2017-10-01 11:18:40*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages.

We describe a fluid motion in three dimensions with rectangular, cylindrical and spherical coordinates.

**Category:** Mathematical Physics

[667] **viXra:1710.0011 [pdf]**
*submitted on 2017-10-01 07:55:47*

**Authors:** Spiros Konstantogiannis

**Comments:** 28 Pages.

The quasi-exact solvability of symmetrized quartic anharmonic oscillators has been studied first by Znojil [2] and then by Quesne [3]. In this work, we examine the solvability of these models using, as basic parameter, the energy-dependent, constant (i.e. position-independent) term of a quotient polynomial. We examine the cases n=0 and n=1, and we show that our results are in agreement with those of Quesne. For n=2, following a different path from that of Znojil, we derive the cubic equation that our parameter satisfies and for the case it has a root at zero, we follow the zero root to obtain an even-parity, ground-state wave function and an odd-parity, third-excited-state wave function. As in the case of the sextic anharmonic oscillator [6], the straightforwardness and transparency of the analysis demonstrates the eligibility of the quotient polynomial as a solvability tool of polynomial oscillators.

**Category:** Mathematical Physics

[666] **viXra:1709.0356 [pdf]**
*submitted on 2017-09-23 12:39:53*

**Authors:** Paris Samuel Miles-Brenden

**Comments:** 10 Pages. relativity, time, theory, everything, equivalence, wave, equation

Be ready for a 10 page compendium of the principles by which time operates with that of the relativistic theory in duplicity of reconcilation between either end of the wave equation. This theory incorporates the ideal of time and space transformation in very general form under entirely compatible principles and only two general equations for that of the theory of everything together. There is a rough synthesis of what is required then to understand the transformations of time; that of a theory second only to Albert Einstein's theory of special and general relativity; without contradiction.

**Category:** Mathematical Physics

[665] **viXra:1709.0332 [pdf]**
*submitted on 2017-09-23 11:15:52*

**Authors:** Christopher L. Andreadis

**Comments:** 15 Pages. A though experiment rooted in non-linear time.

This is a calibration procedure that is prefaced by a set of premises that led up to said procedure. It deals with the possibility that "cause preceded by effect" is greater than null at the macroscopic scale.

**Category:** Mathematical Physics

[664] **viXra:1709.0330 [pdf]**
*submitted on 2017-09-22 15:05:15*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages.

Usually, physics students don't like thermodynamics: it is incomprehensible.
They commonly get told to get used to it. Later on, as an expert, they'll find that the thermodynamic calculations come with surprises: sometimes evil, sometimes good. That can mean only
one thing: The theory is inconsistent. In here, it will be shown where that is.

**Category:** Mathematical Physics

[663] **viXra:1709.0329 [pdf]**
*submitted on 2017-09-22 23:43:46*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

In this work, we discuss the possibility to formulate a temporal electromagnetic field that can be produced by a temporal system, such as a temporal hydrogen atom in the temporal continuum. We also show that a temporal electromagnetic field can manifest itself not only in the temporal continuum but also in the spatial space.

**Category:** Mathematical Physics

[662] **viXra:1709.0321 [pdf]**
*submitted on 2017-09-21 06:08:47*

**Authors:** Vu B Ho

**Comments:** 12 Pages.

In our previous works on possible relationship between Schrödinger wavefunctions and spacetime structures of quantum particles we suggested that a Ricci scalar curvature for a particular quantum state of a quantum system could be constructed using the Schrödinger wavefunctions as mathematical objects. In this work we will extend our discussions by suggesting possible line elements that can be used to construct relativistic spacetime structures of a hydrogen atom. We also discuss the possibility to use a covariant Ricci flow as evolution equations to describe the dynamics of the hydrogen atom geometric structures.

**Category:** Mathematical Physics

[661] **viXra:1709.0029 [pdf]**
*submitted on 2017-09-03 04:28:49*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Among the one-dimensional, smooth and real polynomial potentials, the sextic anharmonic oscillator is the only one than can be quasi-exactly solved [6, 7], in the sense that it is expressed in terms of a non-negative integer n and for every value of n, we can find n+1 energies and the respective eigenfunctions in closed form. In this work, we use, as basic parameter, the constant term of a quotient polynomial [3], to quasi-exactly solve the sextic anharmonic oscillator and demonstrate that the new parameter is a preferential one to study the system, as it makes the analysis straightforward and transparent.

**Category:** Mathematical Physics

[660] **viXra:1708.0445 [pdf]**
*submitted on 2017-08-29 05:42:34*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 5 Pages. This paper has not been submitted to a journal. Your comments are welcome

While it is known that Euclid’s five axioms include a proposition that a line consists at
least of two points, modern geometry avoid consistently any discussion on the precise
definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean
geometry: how many points are there in a line segment? – from discrete space viewpoint.
In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete
gravitational theories.

**Category:** Mathematical Physics

[659] **viXra:1708.0424 [pdf]**
*submitted on 2017-08-29 02:39:21*

**Authors:** Vu B Ho

**Comments:** 5 Pages.

In this work, we discuss the possibility to formulate a covariant Ricci flow so that it satisfies the principle of relativity and therefore can be applied to all coordinate systems defined on a Riemannian manifold. Since the investigation may be considered to be in the domain of pure mathematics, which is outside our field of physical investigations, therefore there may be errors in mathematical arguments that we are unable to foresee.

**Category:** Mathematical Physics

[658] **viXra:1708.0406 [pdf]**
*submitted on 2017-08-28 04:39:26*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 6 Pages. In French.

From the equations of the problem of $n$ body, we consider that $t$ is a function of the variables $(x_k,y_k,z_k)_{k=1,n}$. We write a new formulation of the equations of the $n$ body problem.

**Category:** Mathematical Physics

[657] **viXra:1708.0328 [pdf]**
*submitted on 2017-08-24 06:50:21*

**Authors:** Spiros Konstantogiannis

**Comments:** 17 Pages.

Making use of the Bethe ansatz, we introduce a quotient polynomial and we show that the presence of intermediate terms in the quotient polynomial, i.e. terms other than the constant and the leading one, constitutes a non-solvability condition for the respective potential. In this context, both the exact solvability of the quantum harmonic oscillator and the quasi-exact solvability of the sextic anharmonic oscillator stem naturally from the quotient polynomial, as in the first case, it is an energy-dependent constant, while in the second case, it is a second-degree binomial with no linear term. In all other cases, the quotient polynomial has at least one intermediate term, the presence of which makes the respective potentials non-solvable.

**Category:** Mathematical Physics

[656] **viXra:1708.0254 [pdf]**
*submitted on 2017-08-21 21:54:53*

**Authors:** Robert B. Easter

**Comments:** 24 pages. Written as an invited extended paper, extending the 10-page conference paper Double Conformal Geometric Algebra (ICNPAA 2016), for possible later submission to the journal Mathematics in Engineering, Science and Aerospace (MESA).

The G(4,8) Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra that extends the concepts introduced with the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the G(1,3) Space-Time Algebra (STA). Two G(2,4) Conformal Space-Time subalgebras (CSTA) provide spacetime entities for points, hypercones, hyperplanes, hyperpseudospheres (and their intersections) and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion. G(4,8) DCSTA is a doubling product of two orthogonal G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new 2-vector entities for general (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime surface entities that use the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in hyperpseudospheres. An operation for the directed non-uniform scaling (anisotropic dilation) of the 2-vector general quadric entities is defined using the boost operator and a spatial projection. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the Thomas-Wigner rotation and length contraction of special relativity. DCSTA is an algebra for computing with general quadrics and their inversive geometry in spacetime. For applications or testing, G(4,8) DCSTA can be computed using various software packages, such as the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[655] **viXra:1708.0226 [pdf]**
*submitted on 2017-08-18 17:46:16*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

Investigations into the nature of the principle of least action have shown that there is an intrinsic relationship between geometrical and topological methods and the variational principle in classical mechanics. In this work, we follow and extend this kind of mathematical analysis into the domain of quantum mechanics. First, we show that the identification of the momentum of a quantum particle with the de Broglie wavelength in 2-dimensional space would lead to an interesting feature; namely the action principle δS=0 would be satisfied not only by the stationary path, corresponding to the classical motion, but also by any path. Thereupon the Bohr quantum condition possesses a topological character in the sense that the principal quantum number n is identified with the winding number, which is used to represent the fundamental group of paths. We extend our discussions into 3-dimensional space and show that the charge of a particle also possesses a topological character and is quantised and classified by the homotopy group of closed surfaces. We then discuss the possibility to extend our discussions into spaces with higher dimensions and show that there exist physical quantities that can be quantised by the higher homotopy groups. Finally we note that if Einstein’s field equations of general relativity are derived from Hilbert’s action through the principle of least action then for the case of n=2 the field equations are satisfied by any metric if the energy-momentum tensor is identified with the metric tensor, similar to the case when the momentum of a particle is identified with the curvature of the particle’s path.

**Category:** Mathematical Physics

[654] **viXra:1708.0198 [pdf]**
*submitted on 2017-08-17 01:42:13*

**Authors:** Vu B Ho

**Comments:** 24 Pages.

In this work we discuss the possibility of reconciling quantum mechanics with classical mechanics by formulating a temporal dynamics, which is a dynamics caused by the rate of change of time with respect to distance. First, we show that a temporal dynamics can be derived from the time dilation formula in Einstein’s theory of special relativity. Then we show that a short-lived time-dependent force derived from a dynamical equation that is obtained from the temporal dynamics in a 1-dimensional temporal manifold can be used to describe Bohr’s postulates of quantum radiation and quantum transition between stable orbits in terms of classical dynamics and differential geometry. We extend our discussions on formulating a temporal dynamics to a 3-dimensional temporal manifold. With this generalisation we are able to demonstrate that a sub-quantum dynamics is a classical dynamics.

**Category:** Mathematical Physics

[653] **viXra:1708.0197 [pdf]**
*submitted on 2017-08-17 01:50:44*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

In this work we discuss the possibility of combining the Coulomb potential with the Yukawa’s potential to form a mixed potential and then investigate whether this combination can be used to explain why the electron does not radiate when it manifests in the form of circular motions around the nucleus. We show that the mixed Coulomb-Yukawa potential can yield stationary orbits with zero net force, therefore if the electron moves around the nucleus in these orbits it will not radiate according to classical electrodynamics. We also show that in these stationary orbits, the kinetic energy of the electron is converted into potential energy, therefore the radiation process of a hydrogen-like atom does not related to the transition of the electron as a classical particle between the energy levels. The radial distribution functions of the wave equation determine the energy density rather than the electron density at a distance r along a given direction from the nucleus. It is shown in the appendix that the mixed potential used in this work can be derived from Einstein’s general theory of relativity by choosing a suitable energy-momentum tensor. Even though such derivation is not essential in our discussions, it shows that there is a possible connection between general relativity and quantum physics at the quantum level.

**Category:** Mathematical Physics

[652] **viXra:1708.0196 [pdf]**
*submitted on 2017-08-17 01:54:09*

**Authors:** Vu B Ho

**Comments:** 15 Pages.

In this work we develop a theory of temporal relativity, which includes a temporal special relativity and a temporal general relativity, on the basis of a generalised Newtonian temporal dynamics. We then show that a temporal relativity can be used to study the dynamics of quantum radiation of an elementary particle from a quantum system.

**Category:** Mathematical Physics

[651] **viXra:1708.0192 [pdf]**
*submitted on 2017-08-17 03:51:07*

**Authors:** Vu B Ho

**Comments:** 18 Pages.

In this work we propose a covariant formulation for the gravitational field and derive equations that can be used to construct the spacetime structures for short-lived and stable quantum particles. We also show that Schrödinger wavefunctions can be used to construct spacetime structures for the quantum states of a quantum system, such as the hydrogen atom. Even though our discussions in this work are focused on the microscopic objects, the results obtained can be applied equally to the macroscopic phenomena.

**Category:** Mathematical Physics

[650] **viXra:1708.0184 [pdf]**
*submitted on 2017-08-16 10:47:23*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 10 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[649] **viXra:1708.0166 [pdf]**
*submitted on 2017-08-15 06:49:15*

**Authors:** Spiros Konstantogiannis

**Comments:** 50 Pages.

Exactly solvable rational extensions of the harmonic oscillator have been constructed as supersymmetric partner potentials of the harmonic oscillator [1] as well as using the so-called prepotential approach [2]. In this work, we use the factorization property of the energy eigenfunctions of the harmonic oscillator and a simple integrability condition to construct and examine series of regular and singular rational extensions of the harmonic oscillator with two known eigenstates, one of which is the ground state. Special emphasis is given to the interrelation between the special zeros of the wave function, the poles of the potential, and the excitation of the non-ground state. In the last section, we analyze specific examples.

**Category:** Mathematical Physics

[648] **viXra:1708.0147 [pdf]**
*submitted on 2017-08-13 21:51:40*

**Authors:** Harry Watson

**Comments:** 1 Page.

Abstract: Consider the product
(4pi)(4pi-1/pi)(4pi-2/pi)(pi-2/pi)(4pi-4/pi).
The product of the first three terms is 1836.15.
The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15.
We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13$.

**Category:** Mathematical Physics

[647] **viXra:1708.0031 [pdf]**
*submitted on 2017-08-03 09:30:29*

**Authors:** Hideki Mutoh

**Comments:** 5 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[646] **viXra:1708.0011 [pdf]**
*submitted on 2017-08-02 04:28:15*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more general case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics

[645] **viXra:1707.0301 [pdf]**
*submitted on 2017-07-23 12:42:25*

**Authors:** Jean C.Dutailly

**Comments:** 405 Pages.

This book proposes a review and, on important points, a new formulation of the main concepts of Theoretical Physics. Rather than offering an interpretation based on exotic physical assumptions (additional dimension, new particle,
cosmological phenomenon,...) or a brand new abstract mathematical formalism, it proceeds to a systematic review of the main concepts of Physics,
as Physicists have always understood them : space, time, material body, force fields, momentum, energy... and proposes the right mathematical objects to deal with them, chosen among well grounded mathematical theories. Proceeding
this way, the reader will have a comprehensive, consistent and rigorous understanding of the main topics of the Physics of the XXI° century, together with many tools to do practical computations.
After a short introduction about the meaning of Theories in Physics, a new interpretation of the main axioms of Quantum Mechanics is proposed. It is proven that these axioms come actually from the way mathematical models are expressed, and this leads to theorems which validate most of the usual
computations and provide safe and clear conditions for their use, as it is shown in the rest of the book.
Relativity is introduced through the construct of the Geometry of General Relativity, from 5 propositions and the use of tetrads and fiber bundles, which provide tools to deal with practical problems, such as deformable solids. A review of the concept of motion leads to associate a frame to all material bodies, whatever their scale, and to the representation of motion in
Clifford Algebras. Momenta, translational and rotational, are then represented by spinors, which provide a clear explanation for the spin and the existence of anti-particles.
The force fields are introduced through connections, in the framework of gauge theories, which is here extended to the gravitational field. It shows that this field has actually a rotational and a transversal component, which are masked under the usual treatment by the metric and the Levy-Civita connection. A thorough attention is given to the topic of the propagation of fields with new and important results.
The general theory of lagrangians in the application of the Principle of Least Action is reviewed, and two general models, incorporating all particles and fields are explored, and used for the introduction of the concepts of currents
and energy-momentum tensor. Precise guidelines are given to find solutions for the equations representing a system in the most general case.
The topic of the last chapter is discontinuous processes. The phenomenon of collision is studied, and we show that bosons can be understood as
discontinuities in the fields.

**Category:** Mathematical Physics

[644] **viXra:1707.0296 [pdf]**
*submitted on 2017-07-22 15:52:25*

**Authors:** Sayan Nag

**Comments:** 6 Pages.

“Art attracts us only by what it reveals of our most secret self.”- Alfred North Whitehead
The basic building blocks upon which the natural world is built are Fractals. Recognizing these patterns in Nature is essential-because of these patterns Nature is so aesthetically pleasing. We try to find these patterns everywhere instinctively. In our work we look forward to find the fractality in Abstract art-the paintings of the renowned artist Jackson Pollock using a novel approach of 2D-Multifractal Detrended Fluctuation Analysis in his paintings.

**Category:** Mathematical Physics

[643] **viXra:1707.0284 [pdf]**
*submitted on 2017-07-21 09:18:46*

**Authors:** Jean-Luc Paillet, Andrew Meulenberg

**Comments:** 12 Pages. Submitted to 12th Intern. Workshop on Anomalies in Hydrogen Loaded Metal.

In previous works, we analyzed and countered arguments against the deep orbits, as discussed in
published solutions. Moreover, we revealed the essential role of Special Relativity as source of electron deep orbits (EDOs). We also showed, from a well-known analytic method of solution of the Dirac equation, that the obtained EDOs have a positive energy. When including the magnetic interactions near the nucleus, we observed a
breakthrough in how to satisfy the Heisenberg Uncertainty Relation (HUR) for electrons confined near the nucleus, in a radial zone of only a few fm. Here we chose a different method, by directly facing the HUR for such confined electrons, from which we deduce the coefficient γ of these highly relativistic electrons. Then we show the effective Coulomb potential due to a relativistic correction, can maintain the electrons in containment. Next we resume and deepen our study of the effects of EM interactions near the nucleus. We first obtain computation
results: though approximate, we can effectively expect high-energy resonances near the nucleus. These results should be confirmed by using QFT-based methods.

**Category:** Mathematical Physics

[642] **viXra:1707.0266 [pdf]**
*submitted on 2017-07-20 05:11:07*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 4 Pages. This paper has not been submitted to a journal. Your comments are welcome

In recent years, there are several proposals of using MHD theory for clean power generators on top of coal plant. But the theory involved appears too complicated, so in this paper we will use a simpler approach using ideal MHD equations which then they can be reduced to a system of coupled quaternionic Riccati equations. Further numerical and experimental investigations are advisable.

**Category:** Mathematical Physics

[641] **viXra:1707.0216 [pdf]**
*submitted on 2017-07-15 19:08:22*

**Authors:** Tracy Klein

**Comments:** 9 Pages.

The following manuscript establishes the role of dialectical forces in our physical universe.
The dialectical relationship links opposing theories of quantum mechanics and bridges the gap
between quantum physics and general relativity.

**Category:** Mathematical Physics

[640] **viXra:1707.0195 [pdf]**
*submitted on 2017-07-14 03:38:22*

**Authors:** Paris Samuel Miles-Brenden

**Comments:** 10 Pages. The laws of physics in their abstraction are blind to the world.

The laws of physics in their abstraction are blind to the world.

**Category:** Mathematical Physics

[639] **viXra:1707.0193 [pdf]**
*submitted on 2017-07-13 13:33:10*

**Authors:** William O. Straub

**Comments:** 3 Pages.

An intriguing connection between some work of Oswald Veblen with that of Hermann Weyl is presented.

**Category:** Mathematical Physics

[638] **viXra:1707.0144 [pdf]**
*submitted on 2017-07-11 03:13:02*

**Authors:** John Peel

**Comments:** 35 Pages. Part 1 of two files regarding information fields

The role of geometry in particle physics

**Category:** Mathematical Physics

[637] **viXra:1707.0129 [pdf]**
*submitted on 2017-07-09 21:31:05*

**Authors:** John Peel

**Comments:** 72 Pages. Perhaps important

This paper hopes to clarify the notion of Information Fields and the role of geometry in particle physics.

**Category:** Mathematical Physics

[636] **viXra:1707.0128 [pdf]**
*submitted on 2017-07-09 22:59:57*

**Authors:** Jack Bidnik

**Comments:** 13 Pages.

Abstract:
This paper explains my derivation of a number of equations to describe gravitational forces from the relativistic relative momentum of Albert Einstein's Special Relativity. One of these equations parallels Issac Newton's Gravitational Equation by replacing the Gravitational Constant, G, with a velocity dependent expression. The resulting equation is applied to the orbital parameters of the planets and a number of their moons, with very close results. The forces derived have applications in other areas of physics, including electromagnetic force, and have some surprising properties hitherto unknown in physics. I derive these results with no external forces assumed to be present, so that the only mechanical force here must be gravity.

**Category:** Mathematical Physics

[635] **viXra:1707.0109 [pdf]**
*submitted on 2017-07-07 10:28:47*

**Authors:** Ehsan Azadi

**Comments:** 28 pages

In this article, we give a general exact mathematical framework that all of the fundamental relations and conservation equations in continuum mechanics can be derived based on it. We consider a general integral equation contains the parameters that act on the volume and the surface of the integral's domain. The idea is to determine how many local relations can be derived from this general integral equation and what these local relations are? Thus, we first derive the general Cauchy lemma and then by a new general exact tetrahedron argument derive two other local relations. So, there are three local relations that can be derived from the general integral equation. Then we show that all of the fundamental laws in continuum mechanics, include the conservation of mass, linear momentum, angular momentum, energy, and the entropy law, can be shown and considered in this general framework. So, we derive the integral form of these fundamental laws in this framework and applying the general three local relations lead to exactly derivation of the mass flow, continuity equation, Cauchy lemma for traction vectors, existence of stress tensor, general equation of motion, symmetry of stress tensor, existence of heat flux vector, differential energy equation, and differential form of the Clausius-Duhem inequality for entropy law.
The general exact tetrahedron argument is an exact proof that removes all of the challenges on the derivation of fundamental relations in continuum mechanics. During this proof, there is no approximating or limiting process and the parameters are exact point-base functions. Also, it gives a new understanding and a deep insight into the origins and the physics and mathematics of the fundamental relations and conservation equations in continuum mechanics. This general mathematical framework can be used in many branches of continuum physics and the other sciences.

**Category:** Mathematical Physics

[634] **viXra:1707.0106 [pdf]**
*submitted on 2017-07-06 13:56:20*

**Authors:** Ehsan Azadi

**Comments:** 34 pages

Cauchy in 1822 presented the idea of traction vector that contains both the normal and tangential components of the internal surface forces per unit area and gave the tetrahedron argument to prove the existence of stress tensor. These great achievements form the main part of the foundation of continuum mechanics. During nearly two centuries, some versions of tetrahedron argument and a few other proofs for the existence of stress tensor are presented in every text in continuum mechanics, fluid mechanics, and the related subjects. In this article, we show the birth, importance, and location of these Cauchy's achievements, then by presenting the formal tetrahedron argument in detail, for the first time we extract some fundamental challenges. These conceptual challenges are related to the result of applying the conservation of linear momentum to any mass element and the order of its surface and volume terms, the definition of traction vectors on the surfaces that pass through the same point, the limiting and approximating processes in the derivation of stress tensor, and some others. In a comprehensive review, we present the different tetrahedron arguments and the proofs for the existence of stress tensor, consider the challenges in each one, and classify them in two general approaches. In the first approach that is followed in most texts, the traction vectors do not define exactly on the surfaces that pass through the same point so, most of the challenges hold. But in the second approach, the traction vectors are defined on the surfaces that pass exactly through the same point, so some of the related challenges are removed. We also represent the improved works of Hamel and Backus, and show that the original work of Backus removes most of the challenges. This article shows that the foundation of continuum mechanics is not a finished subject and there are still some fundamental challenges.

**Category:** Mathematical Physics

[633] **viXra:1707.0022 [pdf]**
*submitted on 2017-07-02 10:02:30*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 10 Pages. This paper has not been submitted to a journal

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.

**Category:** Mathematical Physics

[632] **viXra:1706.0572 [pdf]**
*submitted on 2017-06-30 11:04:20*

**Authors:** Gary D. Simpson

**Comments:** 11 Pages.

This text continues the development of pentuples begun in Part – 2 of these works. Matrix formulations are presented that are easily inverted. The presentation of a pentuple is similar to the form of a quaternion. A functionality is presented in Equation 4.2 that mimics wave-function collapse. Octonion multiplication is shown to be very similar irrespective of whether the complex i commutes normally or anti-commutes.

**Category:** Mathematical Physics

[631] **viXra:1706.0456 [pdf]**
*submitted on 2017-06-23 18:05:12*

**Authors:** Mauro Bernardini

**Comments:** 44 Pages. Comment (Abstract) replacement

This is a brief summary of the Theory of Transcendent Reality (TTR), which describes the main postulates and mathematics used to describe and support the rationality of the Alef's model as unique and absolute being container of all the existences. This first issiue allow to describe the real physical composition of all the parallel universes contained in Alef's body. Universes that are logically and rationally constituted exclusively by Particles of Existence with a mass equal to that of a Proton and which generate an "apparent" existence since they are interpreted as existent only by the under-dimensional beings they generate in each single universe. Highlighting therefore that the Particles of Existence present in every universe are in fact 11 dimensional body slices of the Points of Alef, which, in turn, are the only real components of Alef's body: and, therefore, Particles of Existence that never really born nor died.

**Category:** Mathematical Physics

[630] **viXra:1706.0416 [pdf]**
*submitted on 2017-06-21 09:12:37*

**Authors:** Miroslav Josipović

**Comments:** 1 Page.

There is an erroneous formula in the article Functions of multivectors in 3D Euclidean geometric algebra via spectral decomposition (for physicists and engineers).

**Category:** Mathematical Physics

[629] **viXra:1706.0193 [pdf]**
*submitted on 2017-06-15 01:41:20*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[628] **viXra:1706.0189 [pdf]**
*submitted on 2017-06-15 03:48:11*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 6 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Normalized Similarity Measure considered to Exhaustion [1] (please see the addendum of [1] as well).

**Category:** Mathematical Physics

[627] **viXra:1706.0137 [pdf]**
*submitted on 2017-06-09 16:04:55*

**Authors:** Marcellin Nonti, Fernando Y. J. Kpomahou, Jean Akande, Damien K. K. Adjaï, Lucas H. Koudahoun, Marc D. Monsia

**Comments:** 3 pages

Hamiltonian dynamics and exact Gibbs statistical mechanics of a system of quadratic Liénard type oscillators have been investigated. The work has shown that the canonical ensemble for the harmonic oscillator is a particular case of the Gibbs ensemble theory developed in this paper.

**Category:** Mathematical Physics

[626] **viXra:1706.0123 [pdf]**
*submitted on 2017-06-09 01:36:02*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 8 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Normalized Similarity Measure considered to Exhaustion [1] (please see the addendum of [1] as well).

**Category:** Mathematical Physics

[625] **viXra:1706.0034 [pdf]**
*submitted on 2017-06-05 02:03:41*

**Authors:** Richard L Amoroso, Georges Lemaitre

**Comments:** 13 Pages. Lemaitre's 1948 paper translated from original French, ACTA, Vol. XII, No. 8, pp. 57-80

The author applies the notion of quaternions, as practiced by Klein in the Erlangen program, to determine the fundamental
properties of elliptical space.

**Category:** Mathematical Physics

[624] **viXra:1705.0470 [pdf]**
*submitted on 2017-05-31 08:41:13*

**Authors:** Renzun Lian

**Comments:** 20 Pages.

In the Part I of Line-Surface formulation of the ElectroMagnetic-Power-based Characteristic Mode Theory for Metal-Material combined objects (LS-MM-EMP-CMT), the relevant fundamental principle had been established, and some very valuable complements and improvements are done in this Part II.
In this Part II, the traditional surface equivalent principle for a homogeneous material body whose boundary is only constructed by a closed surface is generalized to the line-surface equivalent principle of a homogeneous material body whose boundary can include some lines and open surfaces besides a closed surface; a new line-surface formulation of the input/output power operator for metal-material combined objects is given, and the new formulation is more advantageous than the formulation given in Part I; some more detailed formulations for establishing LS-MM-EMP-CMT are explicitly provided here, such as the formulations corresponding to the decompositions for currents and their domains and the formulations corresponding to variable unification.
In addition, a new concept intrinsic resonance is introduced in this paper, and then a new Characteristic Mode (CM) set, intrinsic resonant CM set, is introduced into the EMP-CMT family.

**Category:** Mathematical Physics

[623] **viXra:1705.0374 [pdf]**
*submitted on 2017-05-25 20:55:10*

**Authors:** Zihao Song

**Comments:** 5 Pages. If one physical quantity can't find where it is originated, it's not a good physical quantity.

Physicists are proposing different mechanics to describe the nature, physical body is measured by intrinsic properties like electric charge, and extrinsic properties being related to space like generalized coordinates or velocities etc., with these properties we can predict what event will happen. We can naturally define the fact of the event and the cause of the event as information, the information grasped by physicist must be originated from something objective, information must have its object container. Intrinsic property information is contained by object itself, but container of extrinsic property information like position is ambiguous, position is a relation based on multiple objects, it's hard to define which one is the information container. With such ambiguity, no mechanics is a complete theory, errors hidden in assumptions are hard to find. Here we show a new theoretical framework with strict information container restriction, on which we can build complete determinism theories to approach grand unification.

**Category:** Mathematical Physics

[622] **viXra:1705.0358 [pdf]**
*submitted on 2017-05-24 13:09:34*

**Authors:** Paul B. Slater

**Comments:** 35 pages, 26 figures

We investigate relationships between two forms of Hilbert-Schmidt two-re[al]bit and two-qubit "separability functions''--those recently advanced by Lovas and Andai (arXiv:1610.01410), and those earlier presented by Slater ({\it J. Phys. A} {\bf{40}} [2007] 14279). In the Lovas-Andai framework, the independent variable $\varepsilon \in [0,1]$ is the ratio $\sigma(V)$ of the singular values of the $2 \times 2$ matrix $V=D_2^{1/2} D_1^{-1/2}$ formed from the two $2 \times 2$ diagonal blocks ($D_1, D_2$) of a
randomly generated $4 \times 4$ density matrix $D$. In the Slater setting, the independent variable $\mu$ is the diagonal-entry ratio $\sqrt{\frac{d_ {11} d_ {44}}{d_ {22} d_ {33}}}$--with, importantly, $\mu=\varepsilon$ or $\mu=\frac{1}{\varepsilon}$ when both $D_1$ and $D_2$ are themselves diagonal. Lovas and Andai established that their two-rebit function $\tilde{\chi}_1 (\varepsilon )$ ($\approx \varepsilon$) yields the
previously conjectured Hilbert-Schmidt separability probability of $\frac{29}{64}$. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we similarly obtain its new (much simpler) two-qubit counterpart, $\tilde{\chi}_2(\varepsilon) =\frac{1}{3} \varepsilon ^2 \left(4-\varepsilon ^2\right)$. Verification of the companion conjecture of a Hilbert-Schmidt separability probability of $\frac{8}{33}$ immediately follows in the Lovas-Andai framework. We obtain the formulas for $\tilde{\chi}_1(\varepsilon)$ and $\tilde{\chi}_2(\varepsilon)$ by taking $D_1$ and $D_2$ to be diagonal, allowing us to proceed in lower (7 and 11), rather than the full (9 and 15) dimensions occupied by the convex sets of two-rebit and two-qubit states. The CAD's themselves involve 4 and 8 variables, in addition to $\mu=\varepsilon$. We also investigate extensions of these analyses to rebit-retrit and qubit-qutrit ($6 \times 6$) settings.

**Category:** Mathematical Physics

[621] **viXra:1705.0357 [pdf]**
*submitted on 2017-05-24 16:04:15*

**Authors:** Victor Christianto

**Comments:** 5 Pages. this paper has been submitted to MDPI - Mathematics

The problem of the formal connection between electrodynamics and wave mechanics has attracted the attention of a number of authors, especially there are some existing proofs on Maxwell-Dirac isomorphism. Here the author will review two derivations of Maxwell-Dirac isomorphism i.e. by Hans Sallhofer and Volodimir Simulik. A few plausible extensions will be discussed too.

**Category:** Mathematical Physics

[620] **viXra:1705.0347 [pdf]**
*submitted on 2017-05-24 01:33:15*

**Authors:** Preobrazhenskiy Andrey

**Comments:** 10 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.

**Category:** Mathematical Physics

[619] **viXra:1705.0330 [pdf]**
*submitted on 2017-05-22 05:15:16*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 11 Pages.

This article explores the nonlinear aspects underlying music , particularly focusing on melody. By using the concept of scale as the basis, the article explores ways to formulate and study the features and 'feature richness' of a given melody or Raga, and to do this, the Raga scale is represented as a 1-Dimensional array. The Signature graph of a Raga plotted as Interval as a function of Note position, established a graphic visualization of the Raga. The progression and trend of intervals was computed using the Second Level Interval Array. This trend graph reveals the complexity in a Raga structure, through looping, crowded and intricate curves in the graph. Next, the concept of chaos in the context of melody is explored, fundamentally by performing a sensitivity test, which analyzes that given a Raga, and a particular evolution path, how starting at two nearby Swaras results in two entirely different ending Swaras, when sampled after a certain period in time. As a measure of the complexity in a Raga, the entropy, a measure of uncertainty is proposed, and computed using the interval arrays as bases for an occurrence array yielding empirical probabilities. The entropy is seen as a measure of richness, a measure of variety of inter-Swara intervals that a given Raga possesses. One notes that Ragas with high entropy, on account of their interval richness, usually fall under the category of pleasant, appealing and melodious Ragas. These are also the Ragas one finds being employed in film music, clearly owing to their pleasant feel.

**Category:** Mathematical Physics

[618] **viXra:1705.0300 [pdf]**
*submitted on 2017-05-20 09:41:01*

**Authors:** Miroslav Josipović

**Comments:** 79 Pages.

This is translation of the article "Multiplication of Vectors and Structure of 3D Euclidean Space" to Croatian.

**Category:** Mathematical Physics

[617] **viXra:1705.0274 [pdf]**
*submitted on 2017-05-18 09:56:01*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 46 Pages.

Using the cogito ergo sum as a starting point, I introduce a methodology which allows non-trivial knowledge to be obtained without the formal introduction of axioms. Using this methodology which I formalize, I then obtain a theory of everything (ToE) in physics. This method allows me to avoid the self-referential problem of a ToE which I argue is the core difficulty of any ToE built upon formal axioms. The theory obtained has enough generality to recover both general relativity and quantum field theory. Some of the new physics derived herein include a hard arrow time, an explanation of the quantum mechanical measurement, and a thermodynamic proof that the speed of light is maximal.

**Category:** Mathematical Physics

[616] **viXra:1705.0262 [pdf]**
*submitted on 2017-05-18 03:29:30*

**Authors:** D. K. K. Adjaï, L. H. Koudahoun, J. Akande, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 11 Pages. 1-11

This paper slightly extends the theory of exact trigonometric periodic solutions to quadratic
Liénard type equations introduced earlier by the authors of the present contribution. The
extended theory is used to determine the general periodic solutions to the Duﬃng equation and to some Painlevé-Gambier equations as illustrative examples. Finally the mathematical equivalence between the Duﬃng equation and the Painlevé-Gambier XIX equation has been highlighted by means of the proposed extended theory.

**Category:** Mathematical Physics

[615] **viXra:1705.0261 [pdf]**
*submitted on 2017-05-18 03:29:03*

**Authors:** Zhi Cheng

**Comments:** 14 Pages. Include Chinese version

In this paper, we propose a concept of vector complex function to prove that the whole world can be reduced to a very simple function f(Z) = F + iG by introducing the knowledge of complex function theories. We can also derive Maxwell equations through the differential and integral analysis of the vector complex function.

**Category:** Mathematical Physics

[614] **viXra:1705.0251 [pdf]**
*submitted on 2017-05-16 19:11:11*

**Authors:** Victor Christianto

**Comments:** 39 Pages. This paper has not been submitted to a journal

The present book consists of 6 papers that I and some colleagues developed throughout the last 3-4 years. The subjects discussed cover wireless energy transmission, soliton model of DNA, cosmology, and also solutions of Navier-Stokes equations both in 2D and 3D.
Some additional graphical plots for solution of 3D Navier-Stokes equations are also given. Hopefully the readers will find these papers at least interesting to ponder.

**Category:** Mathematical Physics

[613] **viXra:1705.0212 [pdf]**
*submitted on 2017-05-14 02:26:57*

**Authors:** Sjaak Uitterdijk

**Comments:** 3 Pages.

Showing that the Special Theory of Relativity is an untenable theory, many times leads to the reaction that the GPS is so accurate thanks to the STR corrections. This article shows that the supposed relativity errors are by far negligible relative to the errors caused by atmospheric circumstances.

**Category:** Mathematical Physics

[612] **viXra:1705.0203 [pdf]**
*submitted on 2017-05-12 22:53:16*

**Authors:** ShengYu.Shu

**Comments:** 62 Pages.

I have mainly analyzed the mathematical meaning of non-classical mathematical theory for three fundamental physics equations - Maxwell’s equations, Dirac’s equations, Einstein’s equations from the quantized core theory of ancient China’s Taoism, and found they have some structures described in the core of the theory of ancient China’s Taoism, especially they all obviously own the yin-yang induction structure. This reveals the relations between the ancient China’s Taoism and modern mathematics and physics in a way, which may help us to understand some problems of the fundamental theory of physics.

**Category:** Mathematical Physics

[611] **viXra:1705.0133 [pdf]**
*submitted on 2017-05-08 07:55:21*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 2 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Similarity Measure considered to Exhaustion [1].

**Category:** Mathematical Physics

[610] **viXra:1705.0104 [pdf]**
*submitted on 2017-05-04 12:18:15*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 4 Pages.

In this research investigation, the author has presented a Recursive Past Equation based on the Ananda-Damyanthi Similarity Measure [1]. Also, in this research investigation, the author has presented a Recursive Future Equation based on the Ananda-Damyanthi Similarity Measure [1].

**Category:** Mathematical Physics

[609] **viXra:1705.0095 [pdf]**
*submitted on 2017-05-03 22:01:08*

**Authors:** John Peel

**Comments:** 6 Pages. The sets at the end are important

Calculating certain aspects of geometry has been difficult. They have defied analytics. Here I propose a
method of analysing shape and space in terms of two variables (n,m).

**Category:** Mathematical Physics

[608] **viXra:1705.0091 [pdf]**
*submitted on 2017-05-04 06:15:57*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 2 Pages.

The author has presented a Recursive Future Equation

**Category:** Mathematical Physics

[607] **viXra:1705.0012 [pdf]**
*submitted on 2017-05-01 22:52:24*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 3 Pages.

In this research manuscript, the author has presented a Recursive Equation Connecting Future And Past

**Category:** Mathematical Physics

[606] **viXra:1705.0011 [pdf]**
*submitted on 2017-05-01 23:45:14*

**Authors:** Richard L. Amoroso

**Comments:** 14 Pages. Version to be published in 10th proceedings honoring mathematical physicist Jean-Pierre Vigier by World Scientific

Ontological-Phase Topological Field Theory (OPTFT) under seminal development to formally describe 3rd regime Unified Field Mechanics (UFM) (classical-Quantum-UFM) is extended to relate the duality of Newton-Einstein gravitation theory by added degrees of freedom in a semi-quantum limit enabling insight into topological Dirac-Majorana doublet fusion supervening the uncertainty principle.

**Category:** Mathematical Physics

[605] **viXra:1704.0396 [pdf]**
*submitted on 2017-04-30 05:48:03*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 1 Page.

In this research manuscript, the author has presented a Recursive Future Equation.

**Category:** Mathematical Physics

[604] **viXra:1704.0320 [pdf]**
*submitted on 2017-04-24 08:43:53*

**Authors:** Yakov A. Iosilevskii

**Comments:** 72 pages

This exposition has the following main objects in view. (1) All main depth-integrated time-dependent and time-averaged characteristics, – as the velocity potential, velocity, pressure, momentum flux density tensor, volumetric kinetic, potential, and total energies, Poynting (energy flux density) vector, radiation (wave) stress tensor, etc, – of the ideal (inviscid, incompressible, and irrotational) fluid flow in an imaginary wave-perturbed infinite water layer with an arbitrary shaped bed and with a free upper boundary surface, and also the pertinent depth-integrated time-dependent and time-averaged differential continuity equations, – as those of the mass density, energy density, and momentum flux density (Euler’s and Bernoulli’s equations), etc, – are rigorously deduced from the respective basic local (bulk and surface) characteristics and from the respective bulk continuity equations, with allowance for the corresponding exact kinematic boundary conditions at the upper (free) and bottom surfaces and also with allowance for the corresponding exact dynamic boundary condition at the free surface, which follows from the basic Bernoulli equation. (2) The recursive asymptotic perturbation method with respect to powers of ka that has been developed recently by the present author for the local characteristics and bulk continuity equations of the ideal fluid flow in the presence of a priming (seeding) progressive, or standing, monochromatic gravity water wave (PPPMGWW or PSPMGWW) of a wave number k>0 and of wave amplitude a>0 in an imaginary infinite water layer of a uniform depth d>0 is extended to flow’s momentary and time-averaged (TA), depth-integrated (DI) characteristics and to their continuity equations, particularly to the 3x3 radiation, or wave, stress tensor (RST). (3) The extended recursive method is applied to PPPMGWW’s and PSPMGWW’s with the purpose to obtain their main TADI characteristics in terms of elementary functions. (4) The first non-vanishing asymptotic approximation of a characteristic, particularly that of the 3x3-TADIRST, of a PPPMGWW or PSPMGWW is generalized to a priming progressive, or standing, quasi-pane (PPQP or PSQP) MGWW. (5) The longshore wave–induced sediment transport rate, expressed by the so-called CERC (Coastal Engineering Research Council) formula, is briefly discussed in its relation to the (x,y)-component of the 3x3-TADIRST of the pertinent PPQPMGWW. (6) The presently common 2x2-TADIRST’s of progressive and standing water waves, which have been deduced by various writers from intuitive considerations and have been canonized about 55 years ago, are revised in accordance with the 3x3 ones of the recursive asymptotic theory.

**Category:** Mathematical Physics

[603] **viXra:1704.0264 [pdf]**
*submitted on 2017-04-20 18:59:25*

**Authors:** Paul J. Werbos

**Comments:** 15 pages, 36 equations, 34 references

Today’s standard model of physics treats the physical masses of elementary particles as given, and assumes that they have a bare radius of zero, as in the older classical physics of Lorentz. Many physicists have studied the properties of the Yang-Mills-Higgs model of continuous fields in hopes that it might help to explain where elementary particles (and their masses) come from in the first place. This paper reviews some of the important prior work on Yang-Mills-Higgs and solitons in general, but it also shows that stable particles in that model cannot have intrinsic angular momentum (spin). It specifies four extensions of Yang-Mills Higgs, the Lagrangians L1 through L4, which are closer to the standard model of physics, and shows that one of the four (L3) does predict/explain spin from a purely neoclassical theory. The paper begins by summarizing the larger framework which has inspired this work, and ends by discussing two possibilities for further refinement.

**Category:** Mathematical Physics

[602] **viXra:1704.0199 [pdf]**
*submitted on 2017-04-15 08:20:18*

**Authors:** J. Akande, D.K.K. Adjaï, L.H. Koudahoun, Y.J.F. Kpomahou, M.D. Monsia

**Comments:** 16 Pages. 1-16

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the inverted Painlevé-Gambier XVIII equation and other quadratic Liénard type equations may exhibit trigonometric functions as exact periodic solutions but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[601] **viXra:1704.0157 [pdf]**
*submitted on 2017-04-12 08:50:23*

**Authors:** Valery B. Smolensky

**Comments:** 3 Pages.

The article, according to the author, sheds new light on the nature of PI. The original output of PI as a function of States of nature.

**Category:** Mathematical Physics

[600] **viXra:1704.0135 [pdf]**
*submitted on 2017-04-11 08:21:43*

**Authors:** Yakov A. Iosilevskii

**Comments:** 137 pages

It is shown with complete logical and mathematical rigor that under the appropriate hypotheses of analytical extension and of asymptotic matching, which are stated in the article, the nonlinear problem of irrotational and incompressible gravity waves on an infinite water layer of a constant depth d reduces to an infinite recursive sequence of linear two-plane boundary value problems for a harmonic velocity potential with respect to powers of a dimensionless real-valued scaling parameter ‘ka’, where k>0 is the wave number and a>0 the amplitude of a priming (seeding) progressive, or standing, plane monochromatic gravity water wave (briefly PPPMGWW or PSPMGWW respectively). The method, by which the given nonlinear water wave problem is treated in the exposition from scratch, can be regarded as a peculiar instance of the general perturbation method, which is known as the Liouville-Green (LG) method in mathematics and as the Wentzel-Kramers-Brillouin (WKB) method in physics. In the framework of the recursive theory developed, the velocity potential and any bulk or surface measurable characteristic of the wave motion is represented by an infinite asymptotic power series with respect to ‘ka’, whose all coefficients are expressed in quadratures in accordance with a well-established an algorithm for their successive calculation. The theory developed applies particularly in the case where the depth d is taken to infinity. Besides the priming velocity potential of the first, linear asymptotic approximation in ka, the partial velocity potential and all relevant characteristics of wave motion of the second order with respect to ka are calculated in terms of elementary functions both in the case of a PPPMGWW and in the case of a PSPMGWW. Accordingly, the recursive theory incorporates the conventional Airy (linear) theory of water waves linear as its first non-vanishing approximation with the following proviso. In the Airy theory, the boundary condition at the perturbed free (upper) surface of a water layer is paradoxically stated at the equilibrium plane z=0, in spite of the fact that at any instant of time some part of the plane is necessarily located in air or in vacuum, and not in water. This and also a similar paradox arising in computing the time averages of bulk characteristics at spatial points close to the perturbed free surface are solved in the article.

**Category:** Mathematical Physics

[599] **viXra:1704.0108 [pdf]**
*submitted on 2017-04-08 14:03:01*

**Authors:** Frederick Ira Moxley III

**Comments:** 9 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture.

**Category:** Mathematical Physics

[550] **viXra:1802.0355 [pdf]**
*replaced on 2018-02-25 07:26:12*

**Authors:** Robert A. Herrmann

**Comments:** 32 Pages.

The methods of nonstandard analysis are applied to general language logic-systems. This allows the
operators for the only known mathematical cosmogony, the General Grand Unification Model (GGUmodel), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and
processes are predicted from certain observable entities, which are physical processes and mental
procedures that we use to construct physical objects. It is shown that, for each of the four types of
instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is
applied to it an ultra-logic-system is *-deduced. Another application of an hyper-algorithm yields a
hyperfinite instruction paradigm that is hyper-deduced in the in the required sequential order. It is
shown that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the
Patten and Wheeler participator universe requirements. In this version, the participator process portion
of the GGU-model is significantly altered from the original process presented and a correction is
made to an equation and its applications. A specific data-set is generalized and the set of all ultrapropertons is obtained and its properties examined. This set is shown to be sufficient for universe
construction. GGU-model schemes are presented in diagram form. A process is introduced that leads,
when applied, to the individual developmental of each universe-wide frozen-frame. An operator is
shown to exist, which, via a substratum medium and processes, changes hyper-instruction information
into substratum info-fields. From these info-fields, all physical-systems are produced. In this
refinement, the page 11 statement, in the original version of this paper on quantum theory, is
completely modified and the previous statement is now essentially incorrect.

**Category:** Mathematical Physics

[549] **viXra:1802.0109 [pdf]**
*replaced on 2018-02-23 10:57:19*

**Authors:** Antoine Balan

**Comments:** 3 pages, written in french

The KdV equations are defined over manifolds. The system is integrable and we show that it is reduced to usual KdV equations.

**Category:** Mathematical Physics

[548] **viXra:1801.0110 [pdf]**
*replaced on 2018-02-11 05:07:04*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 307 Pages. This book will be published by Pons Publisher, Brussels. Your comments are welcome

This book is a compilation of some rather old papers and some new papers, by myself and also Prof. Florentin Smarandache. In some papers, we also join working with other colleagues, e.g. Dr. Volodymyr Krasnoholovets from IOP Ukraine, and Dr. Yunita Umniyati. This compilation is inspired from a series of prophetic seminars by Rev. Jan Friso from Kingdom Impact , and also a discussion with Minister Dr. Robby Chandra. All in all, we are also grateful to a number of colleagues, including Prof. Thee Houw Liong, Prof. Liek Wilardjo, Prof. Atmonobudi Soebagyo, Dr. David Widihandojo, Sujarwo Silas & Linda, Dr. Wonsuk Ma, Minister Gatut Budiyono, Minister Gani Wiyono, Dr. Yonky Karman, Dr. Joas Adiprasetya, Dr. Paskalis Edwin Nyoman Paska, Minister Yulia Oeniyati, Prof. Akira Kanda, Dr. Carmen Wrede, Mrs. Hiroko Morioka, Prof. Jose Carlos Tiago Oliveira and Prof. Gusto Gadama, and many others, who often encouraged and reminded us to keep on being faithful Christians in this darkness time. As a last note, we also thank to Holy Spirit who always guide us in our way, especially whenever we were lost of our path to find the truth. That is why this book with title: Let The Wind blows is dedicated to Holy Spirit. Let us pray that the Holy Spirit will be poured once again in our time, as prophesied by Joel, one of OT prophets.

**Category:** Mathematical Physics

[547] **viXra:1801.0066 [pdf]**
*replaced on 2018-01-06 13:41:52*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages. minor correction - as always..

This paper is an appendix to the article "From Bernoulli to Laplace and Beyond"
(refenced below), and discusses different aspects of it: electromagnetism, field tensors,
general relativity, and probability.

**Category:** Mathematical Physics

[546] **viXra:1801.0025 [pdf]**
*replaced on 2018-02-25 06:22:41*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Left out background information, tried to increase focus on gravity itself. Corrected misprints.

Reviewing Laplace's equation of gravitation from the perspective of D. Bernoulli, known as Poisson-equation, it will be shown that Laplace's equation tacitly assumes the temperature T of the mass system to be approximately 0 degrees of Kelvin. For temperatures greater zero, the gravitational field will have to be given an additive correctional field. Now, temperature is intimately related to the heat, and heat is known to be radiated as an electromagnetic field. It is shown to take two things in order to get at the gravitational field in the low temperature limit: the total square energy density of the source in space-time and a (massless) field, which expresses the equivalence of inert and gravitational mass/energy in a quadratic, Lorentz-invariant form. This field not only necessarily must include electromagnetic interaction, it also will be seen to behave like it.

**Category:** Mathematical Physics

[545] **viXra:1801.0025 [pdf]**
*replaced on 2018-02-24 05:17:35*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Left out background information, tried to increase focus on gravity itself.

Reviewing Laplace's equation of gravitation from the perspective of D. Bernoulli, known as Poisson-equation, it will be shown that Laplace's equation tacitly assumes the temperature T of the mass system to be approximately 0 degrees of Kelvin. For temperatures greater zero, the gravitational field will have to be given an additive correctional field. Now, temperature is intimately related to the heat, and heat is known to be radiated as an electromagnetic field. It is shown to take two things in order to get at the gravitational field in the low temperature limit: the total square energy density of the source in space-time and a (massless) field, which expresses the equivalence of inert and gravitational mass/energy in a quadratic, Lorentz-invariant form. This field not only necessarily must include electromagnetic interaction, it also will be seen to behave like it.

**Category:** Mathematical Physics

[544] **viXra:1712.0399 [pdf]**
*replaced on 2017-12-19 15:09:52*

**Authors:** D. K. K. Adjaï, J. Akande, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 4 pages

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear two-point boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared with the sinh-Poisson and Poisson-Boltzmann equations to be special cases of a more general equation. As a result, various initial and boundary value problems for these equations may be solved explicitly and exactly.

**Category:** Mathematical Physics

[543] **viXra:1711.0446 [pdf]**
*replaced on 2017-11-29 23:58:35*

**Authors:** Vu B Ho

**Comments:** 15 Pages.

In this work, we will investigate possible spacetime structures of massless particles by formulating Dirac equation in a six-dimensional spatial-temporal continuum in both pseudo-Euclidean and Euclidean metrics. We show that the state of a massless particle flows as an irrotational and incompressible fluid in steady fluid dynamics in the sense that all spatial and temporal components of the wavefunction of a massless particle can be described by Laplace equation. Furthermore, we also show that the six components of the wavefunction are coupled in pairs to form two-dimensional subspaces and this result may suggest why quantum particles possess an intrinsic spin angular momentum that takes half-integral values.

**Category:** Mathematical Physics

[542] **viXra:1711.0435 [pdf]**
*replaced on 2017-12-10 17:42:53*

**Authors:** Dan Visser

**Comments:** 26 Pages.

This article breaks with the inviolability of the quantum-unit. It ‘crumbles’ (or cuts up, or refines) the quantum-vacuum. That also crumbles the constant vacuum-energy-density, or dark energy. It offers a new definition for dark energy. New dark energy does no longer belong to the Big Bang-universe: New dark energy is part of a rotating-hologram universe. Such a universe has the shape of a Double Torus, which has an inner-torus that rotates while an outer-torus represents the ‘crumble of the vacuum’ with time below the Planck-scale. The ‘vacuum-crumbling’ implies a ‘new ‘building-stone’ for vacuum: Tdan. This is a new (rotating) energy-tensor, which has two states , one for above and one for below the Planck-scale. The ‘beauty’ is the dimension of the tensor remains unchanged in those two states! Hence, the quantum-Planck-unit is transparent for migration. That makes the Big Bang-universe no longer a fundamental universe. The Big Bang-universe is emerged (or induced) by rotation of the hologram-universe. This means the Big Bang-universe will exist in every place of the rotating hologram-universe implying: parallel universes ‘outside’ a Big Bang-universe are a nonissue. Parallel universes exist embedded in the rotating hologram-universe. Thereby the origin of the ‘old Big Bang-universe’ is no longer relevant. A new definition of age of the universe lies in the cycle-duration of one cycle, although rotation goes on eternally. Continuously the origin is recalculated. Seemingly the Big Bang-universe is materialized above the Planck-scale and dé-materializes below the Planck-scale, however, such a perspective is reciprocal facing the transparent frontier. Against all expectations my formulas show that one can migrate from one to the other parallel-universe. Locally that is interpreted as ‘change’, but on larger scales it is called traveling through time without space. Because there is extra time (or refined time in the crumble of vacuum), which affects relativistic time that can make traveling faster than traveling through space with the speed of light. There is no horizon between the physics of the ‘soul’ and the physics of ‘materialization’ including the other way around. At last two physics-problems are solved: firstly a more fundamental cause for the origin of hurricanes wherein the building stone of vacuum is involved and secondly the hierarchy problem, the explanation why there is a large emptiness between the Planck-scale and the scale-existence of the smallest particles.

**Category:** Mathematical Physics

[541] **viXra:1711.0435 [pdf]**
*replaced on 2017-12-06 09:10:16*

**Authors:** Dan Visser

**Comments:** 23 Pages.

This article breaks with the inviolability of the quantum-unit. It ‘crumbles’ (or cuts up, or refines) the quantum-vacuum. That also crumbles the constant vacuum-energy-density, or dark energy. It offers a new definition for dark energy. New dark energy does no longer belong to the Big Bang-universe: New dark energy is part of a rotating-hologram universe. Such a universe has the shape of a Double Torus, which has an inner-torus that rotates while an outer-torus represents the ‘crumble of the vacuum’ with time below the Planck-scale. The ‘vacuum-crumbling’ implies a ‘new ‘building-stone’ for vacuum: Tdan. This is a new (rotating) energy-tensor, which has two states, one for above and one for below the Planck-scale. The ‘beauty’ is the dimension of the tensor remains unchanged in those two states! Hence, the quantum-Planck-unit is transparent for migration. That makes the Big Bang-universe no longer a fundamental universe. The Big Bang-universe is emerged (or induced) by rotation of the hologram-universe. This means the Big Bang-universe will exist in every place of the rotating hologram-universe implying: parallel universes ‘outside’ a Big Bang-universe are a nonissue. Parallel universes exist embedded in the rotating hologram-universe. Thereby the origin of the ‘old Big Bang-universe’ is no longer relevant. A new definition of age of the universe lies in the cycle-duration of one cycle, although rotation goes on eternally. Continuously the origin is recalculated. Seemingly the Big Bang-universe is materialized above the Planck-scale and dé-materializes below the Planck-scale, however, such a perspective is reciprocal facing the transparent frontier. Against all expectations my formulas show that one can migrate from one to the other parallel-universe. Locally that is interpreted as ‘change’, but on larger scales it is called traveling through time without space. Because there is extra time (or refined time in the crumble of vacuum), which affects relativistic time that can make traveling faster than traveling through space with the speed of light. There is no horizon between the physics of the ‘soul’ and the physics of ‘materialization’ including the other way around.

**Category:** Mathematical Physics

[540] **viXra:1711.0395 [pdf]**
*replaced on 2017-11-29 07:41:26*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Making an intuitive assumption, and using the completeness of the position and momentum eigenstates, along with the postulates of quantum mechanics, we provide a geometric presentation of the position and momentum representations in quantum mechanics, in the hope of offering a perspective complementary to those given in standard textbooks.

**Category:** Mathematical Physics

[539] **viXra:1711.0365 [pdf]**
*replaced on 2017-12-05 14:08:19*

**Authors:** Giuliano Bettini

**Comments:** 24 Pages. In English. Updated. Some minor corrections.

Starting from the 32 crystal classes, we find a complete classification scheme of the same with only 5 bits, and at least in part the meaning of the various bits.
There is no inverse demonstration, ie only 5 bits must generate all 32 crystalline classes in nature.
However, the proposed classification seems to invoke a logical process of formation of the various classes, doing this way:
the matter first aggregates without any symmetry, then it adopts various rotation symmetries (no symmetry, binary, ternary, etc., simple or composite) and then adds to each symmetry of rotation the additional symmetries c (center), m (planes) or c + m together

**Category:** Mathematical Physics

[538] **viXra:1711.0365 [pdf]**
*replaced on 2017-11-30 10:23:23*

**Authors:** Giuliano Bettini

**Comments:** 20 Pages. In Italian. This is the update to the Italian version v1.

Starting from the 32 crystal classes, we find a complete classification scheme of the same with only 5 bits, and at least in part the meaning of the various bits.
There is no inverse demonstration, ie only 5 bits must generate all 32 crystalline classes in nature.
However, the proposed classification seems to invoke a logical process of formation of the various classes, doing this way:
the matter first aggregates without any symmetry, then it adopts various rotation symmetries (no symmetry, binary, ternary, etc., simple or composite) and then adds to each symmetry of rotation the additional symmetries c (center), m (planes) or c + m together

**Category:** Mathematical Physics

[537] **viXra:1710.0219 [pdf]**
*replaced on 2017-10-19 20:09:02*

**Authors:** Huai-Yi Xie

**Comments:** 115 Pages.

In this paper, we have derived planar multilayer dyadic Green’s functions by Fourier expansion method and have checked its correctness by comparing results for reflected electric fields from dipole emissions near such structures available in previous literature. Furthermore, we show how these dyadic Green’s functions can be applied to calculate reflected fields from a dipole source with arbitrary orientations. We believe our formulation will be powerful in the modeling of molecular fluorescence near these structures.

**Category:** Mathematical Physics

[536] **viXra:1710.0074 [pdf]**
*replaced on 2018-02-04 05:58:23*

**Authors:** L. H. Koudahoun, J. Akande, D. K. K. Adjaï, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 14 pages

Authors introduce a generalized singular differential equation of quadratic Liénard
type for study of exact classical and quantum mechanical solutions. The equation
is shown to exhibit periodic solutions and to include the linear harmonic
oscillator equation and the Painlevé-Gambier XVII equation as special cases.
It is also shown that the equation may exhibit discrete eigenstates as quantum
behavior under Nikiforov-Uvarov approach after several point transformations.

**Category:** Mathematical Physics

[535] **viXra:1710.0014 [pdf]**
*replaced on 2017-12-28 11:39:44*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages.

We describe a fluid motion in three dimensions with rectangular, cylindrical and spherical coordinates.

**Category:** Mathematical Physics

[534] **viXra:1710.0011 [pdf]**
*replaced on 2017-10-30 08:47:52*

**Authors:** Spiros Konstantogiannis

**Comments:** 28 Pages.

The quasi-exact solvability of symmetrized quartic anharmonic oscillators has been studied first by Znojil [2] and then by Quesne [3]. In this work, we examine the solvability of these models using, as basic parameter, the energy-dependent, constant (i.e. position-independent) term of a quotient polynomial. We examine the cases n=0 and n=1, and we show that our results are in agreement with those of Quesne. For n=2, following a different path from that of Znojil, we derive the cubic equation that our parameter satisfies and for the case it has a root at zero, we follow the zero root to obtain an even-parity, ground-state wave function and an odd-parity, third-excited-state wave function. As in the case of the sextic anharmonic oscillator [6], the straightforwardness and transparency of the analysis demonstrates the eligibility of the quotient polynomial as a solvability tool of polynomial oscillators.

**Category:** Mathematical Physics

[533] **viXra:1709.0332 [pdf]**
*replaced on 2017-11-15 02:12:05*

**Authors:** Christopher Andreadis

**Comments:** 15 Pages.

Pondering existence is a journey of the mind that has no boundaries. In contrast to this lofty mesa, however, we must also accept the fact that our own existence is, regrettably, quite finite. This concern invariably encompasses the desire to foresee events that may adversely affect our lives. Thus, fundamental to our existence is the innate ability to understand how the choices we make today shape all our future tomorrows (τι μέλλει γενέσθαι;) as inexorably driven by cause and effect. Yet there may be undiscovered phenomena not strictly bound by causal reality that can never be completely observed or understood, and that may in some way forge our destinies. It is suggested that such phenomena are rooted in nonlinear time, specifically, they may not consistently flow from past to future, or from cause to effect.
Section [13] of this paper states the core hypothesis of how a prognostic system, based on a network of identical NRCL devices (section [1]), may be affected by unusual or extraordinary phenomena. Additionally, section [10] describes the basic configuration of such a network. If the core hypothesis is true, and each NRCL device can be optimally adjusted to collectively forecast events yet to come, then we may discover that our existence is not completely founded on causal reality, but may also be influenced by processes of “cause preceded by effect” that propagate at the macroscopic scale. Section [2] states proposals A through E of how existence may be more than what any casual observer can discern.

**Category:** Mathematical Physics

[532] **viXra:1709.0332 [pdf]**
*replaced on 2017-10-24 14:20:29*

**Authors:** Chris L. Andreadis

**Comments:** 15 Pages.

Pondering existence is a journey of the mind that has no boundaries. In contrast to this lofty mesa, however, we must also accept the fact that our own existence is, regrettably, quite finite. This concern invariably encompasses the desire to foresee events that may adversely affect our lives. Thus, fundamental to our existence is the innate ability to understand how the choices we make today shape all our future tomorrows (τι μέλλει γενέσθαι;) as inexorably driven by cause and effect. Yet there may be undiscovered phenomena not strictly bound by causal reality that can never be completely observed or understood, and that may in some way forge
our destinies. It is suggested that such phenomena are rooted in nonlinear time, specifically, they may not consistently flow from past to future, or from cause to effect.

**Category:** Mathematical Physics

[531] **viXra:1709.0332 [pdf]**
*replaced on 2017-10-19 08:48:27*

**Authors:** Chris L. Andreadis

**Comments:** 15 Pages.

The updated NRCL Low Entropy Calibration procedure radically alters the function of the NRCL prototype from an enhanced true random number generator (TRNG) to a network component that may have significant ramifications with respect to forecasting schemes.

**Category:** Mathematical Physics

[530] **viXra:1709.0332 [pdf]**
*replaced on 2017-10-05 14:12:26*

**Authors:** Christopher L. Andreadis

**Comments:** 16 Pages.

Exploring the mutability of "cause and effect" at the macroscopic scale.

**Category:** Mathematical Physics

[529] **viXra:1709.0330 [pdf]**
*replaced on 2017-09-24 09:06:33*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. misspelling corrected.

Usually, physics students don't like thermodynamics: it is incomprehensible. They commonly get told to get used to it. Later on, as an expert, they'll find that the thermodynamic calculations come with surprises: sometimes evil, sometimes good. That can mean only one thing: The theory is inconsistent. In here, it will be shown where that is.

**Category:** Mathematical Physics

[528] **viXra:1709.0029 [pdf]**
*replaced on 2017-09-05 06:02:43*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Among the one-dimensional, smooth and real polynomial potentials, the sextic anharmonic oscillator is the only one that can be quasi-exactly solved [6, 7], in the sense that it is expressed in terms of a non-negative integer n and for every value of n, we can find n+1 energies and the respective eigenfunctions in closed form. In this work, we use, as basic parameter, the constant term of a quotient polynomial [3], to quasi-exactly solve the sextic anharmonic oscillator and demonstrate that the new parameter is a preferential one to study the system, as it makes the analysis straightforward and transparent.

**Category:** Mathematical Physics

[527] **viXra:1708.0445 [pdf]**
*replaced on 2018-01-29 09:35:59*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 15 Pages. This paper has been submitted to JOURNAL OF PURE AND APPLIED MATHEMATICS. Your comments are welcome

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate our propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modelling.

**Category:** Mathematical Physics

[526] **viXra:1708.0328 [pdf]**
*replaced on 2017-10-29 11:13:19*

**Authors:** Spiros Konstantogiannis

**Comments:** 17 Pages.

Making use of the Bethe ansatz, we introduce a quotient polynomial and we show that the presence of intermediate terms in it, i.e. terms other than the constant and the leading one, constitutes a non-solvability condition of the respective potential. In this context, both the exact solvability of the quantum harmonic oscillator and the quasi-exact solvability of the sextic anharmonic oscillator stem naturally from the quotient polynomial, as in the first case, it is an energy-dependent constant, while in the second case, it is a second-degree binomial with no linear term. In all other cases, the quotient polynomial has at least one intermediate term, the presence of which makes the respective potential non-solvable.

**Category:** Mathematical Physics

[525] **viXra:1708.0254 [pdf]**
*replaced on 2017-12-21 07:37:10*

**Authors:** Robert B. Easter

**Comments:** 26 pages. Extended paper, extending the 10-page conference paper Double Conformal Space-Time Algebra (ICNPAA 2016; DOI:10.1063/1.4972658).

The G(4,8) Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra that extends the concepts introduced with the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the G(1,3) Space-Time Algebra (STA). Two G(2,4) Conformal Space-Time subalgebras (CSTA) provide spacetime entities for points, hypercones, hyperplanes, hyperpseudospheres (and their intersections) and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion. G(4,8) DCSTA is a doubling product of two orthogonal G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new 2-vector entities for general (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime surface entities that use the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in hyperpseudospheres. An operation for the directed non-uniform scaling (anisotropic dilation) of the 2-vector general quadric entities is defined using the boost operator and a spatial projection. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the Thomas-Wigner rotation and length contraction of special relativity. DCSTA is an algebra for computing with general quadrics and their inversive geometry in spacetime. For applications or testing, G(4,8) DCSTA can be computed using various software packages, such as the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[524] **viXra:1708.0254 [pdf]**
*replaced on 2017-12-03 03:13:32*

**Authors:** Robert B. Easter

**Comments:** 25 pages. Extended paper, extending the 10-page conference paper Double Conformal Geometric Algebra (ICNPAA 2016).

The G(4,8) Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra that extends the concepts introduced with the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the G(1,3) Space-Time Algebra (STA). Two G(2,4) Conformal Space-Time subalgebras (CSTA) provide spacetime entities for points, hypercones, hyperplanes, hyperpseudospheres (and their intersections) and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion. G(4,8) DCSTA is a doubling product of two orthogonal G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new 2-vector entities for general (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime surface entities that use the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in hyperpseudospheres. An operation for the directed non-uniform scaling (anisotropic dilation) of the 2-vector general quadric entities is defined using the boost operator and a spatial projection. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the Thomas-Wigner rotation and length contraction of special relativity. DCSTA is an algebra for computing with general quadrics and their inversive geometry in spacetime. For applications or testing, G(4,8) DCSTA can be computed using various software packages, such as the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[523] **viXra:1708.0184 [pdf]**
*replaced on 2017-09-18 07:37:47*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 11 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[522] **viXra:1708.0184 [pdf]**
*replaced on 2017-09-07 09:50:53*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 11 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[521] **viXra:1708.0149 [pdf]**
*replaced on 2017-09-09 17:23:30*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 39 Pages.

According to the second law of thermodynamics, a physical system will tend to increase its entropy over time. In this paper, I investigate a universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if, over the course of the computation, the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Ω, the system will follow the laws of physics. Specifically, I show that the computation will obey algorithmic information theory (AIT) analogues to general relativity, entropic dark energy, the Schrödinger equation, a maximum computation speed analogous to the speed of light, the Lorentz's transformation, light cone, the Dirac equation for relativistic quantum mechanics, spins, polarization, etc. As the universe follows the second law of thermodynamics, these results would seem to suggest an affinity between an "entropic UTM" and the laws of physics.

**Category:** Mathematical Physics

[520] **viXra:1708.0147 [pdf]**
*replaced on 2017-08-28 07:33:28*

**Authors:** Harry Watson

**Comments:** 2 Pages.

Consider the product (4pi)(4pi-1/pi)(4pi-2/pi)(4pi-2/pi)(4pi-4/pi). The product of the first three terms is 1836.15. The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15. We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13. harry.watson@att.net

**Category:** Mathematical Physics

[519] **viXra:1708.0147 [pdf]**
*replaced on 2017-08-19 12:51:05*

**Authors:** Harry Watson

**Comments:** 2 Pages.

Consider the product (4pi)(4pi-1/pi)(4pi-2/pi)(4pi-2/pi)(4pi-4/pi). The product of the first three terms is 1836.15. The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15. We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13. harry.watson@att.net

**Category:** Mathematical Physics

[518] **viXra:1708.0031 [pdf]**
*replaced on 2017-09-17 22:28:49*

**Authors:** Hideki Mutoh

**Comments:** 6 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[517] **viXra:1708.0031 [pdf]**
*replaced on 2017-08-04 07:06:47*

**Authors:** Hideki Mutoh

**Comments:** 5 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[516] **viXra:1708.0011 [pdf]**
*replaced on 2017-10-03 00:04:34*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more general case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics

[515] **viXra:1708.0011 [pdf]**
*replaced on 2017-09-04 08:14:07*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more universal case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics

[514] **viXra:1707.0356 [pdf]**
*replaced on 2017-10-15 08:44:39*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 29 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if over the course of the computation the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibbs ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically that special relativity, general relativity and an arrow of time can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Mathematical Physics

[513] **viXra:1707.0356 [pdf]**
*replaced on 2017-09-30 10:14:47*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 29 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if over the course of the computation the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibbs ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically that special relativity, general relativity and an arrow of time can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Mathematical Physics

[512] **viXra:1707.0356 [pdf]**
*replaced on 2017-09-26 07:57:49*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 28 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if over the course of the computation the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibbs ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically that special relativity, general relativity and an arrow of time can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Mathematical Physics

[511] **viXra:1707.0356 [pdf]**
*replaced on 2017-09-25 12:32:41*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 29 Pages.

**Category:** Mathematical Physics

[510] **viXra:1707.0356 [pdf]**
*replaced on 2017-09-04 15:24:50*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 27 Pages.

**Category:** Mathematical Physics

[509] **viXra:1707.0356 [pdf]**
*replaced on 2017-09-03 06:52:27*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 27 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if, over the course of the computation, the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibb's ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically, that special relativity and general relativity can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Mathematical Physics

[508] **viXra:1707.0356 [pdf]**
*replaced on 2017-09-01 12:51:31*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 26 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if, over the course of the computation, the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibb's ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically, that special relativity and general relativity can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Mathematical Physics

[507] **viXra:1707.0356 [pdf]**
*replaced on 2017-08-31 17:26:38*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 26 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if, over the course of the computation, the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibb's ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically, that special relativity and general relativity can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Mathematical Physics

[506] **viXra:1707.0356 [pdf]**
*replaced on 2017-08-29 16:51:53*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 25 Pages.

**Category:** Mathematical Physics

[505] **viXra:1707.0266 [pdf]**
*replaced on 2017-09-12 11:36:00*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 6 Pages. This paper has been submitted to a conference administered for IEEE (BCWSP 2017)

In recent years, there are several proposals of using MHD theory for clean power generators on top of coal plant. But the theory involved appears too complicated, so in this paper we will use a simpler approach using ideal MHD equations which then they can be reduced to a system of coupled quaternionic Riccati equations. Further numerical and experimental investigations are advisable.

**Category:** Mathematical Physics

[504] **viXra:1707.0109 [pdf]**
*replaced on 2017-10-24 08:37:37*

**Authors:** Ehsan Azadi

**Comments:** 28 pages

In this article, we give a general exact mathematical framework that all the fundamental relations and conservation equations of continuum mechanics can be derived based on it. We consider a general integral equation contains the parameters that act on the volume and the surface of the integral's domain. The idea is to determine how many local relations can be derived from this general integral equation and what these local relations are. After obtaining the general Cauchy lemma, we derive two other local relations by a new general exact tetrahedron argument. So, there are three local relations that can be derived from the general integral equation. Then we show that all the fundamental laws of continuum mechanics, including the conservation of mass, linear momentum, angular momentum, energy, and the entropy law, can be considered in this general framework. Applying the general three local relations to the integral form of the fundamental laws of continuum mechanics in this new framework leads to exact derivation of the mass flow, continuity equation, Cauchy lemma for traction vectors, existence of stress tensor, general equation of motion, symmetry of stress tensor, existence of heat flux vector, differential energy equation, and differential form of the Clausius-Duhem inequality for entropy law.
The general exact tetrahedron argument is an exact proof that removes all the challenges on derivation of the fundamental relations of continuum mechanics. In this proof, there is no approximate or limited process and all the parameters are exact point-based functions. Also, it gives a new understanding and a deep insight into the origins and the physics and mathematics of the fundamental relations and conservation equations of continuum mechanics. This general mathematical framework can be used in many branches of continuum physics and the other sciences.

**Category:** Mathematical Physics

[503] **viXra:1707.0106 [pdf]**
*replaced on 2017-10-22 06:26:44*

**Authors:** Ehsan Azadi

**Comments:** 34 pages

In 1822, Cauchy presented the idea of traction vector that contains both the normal and tangential components of the internal surface forces per unit area and gave the tetrahedron argument to prove the existence of stress tensor. These great achievements form the main part of the foundation of continuum mechanics. For about two centuries, some versions of tetrahedron argument and a few other proofs of the existence of stress tensor are presented in every text on continuum mechanics, fluid mechanics, and the relevant subjects. In this article, we show the birth, importance, and location of these Cauchy's achievements, then by presenting the formal tetrahedron argument in detail, for the first time, we extract some fundamental challenges. These conceptual challenges are related to the result of applying the conservation of linear momentum to any mass element, the order of magnitude of the surface and volume terms, the definition of traction vectors on the surfaces that pass through the same point, the approximate processes in the derivation of stress tensor, and some others. In a comprehensive review, we present the different tetrahedron arguments and the proofs of the existence of stress tensor, discuss the challenges in each one, and classify them in two general approaches. In the first approach that is followed in most texts, the traction vectors do not exactly define on the surfaces that pass through the same point, so most of the challenges hold. But in the second approach, the traction vectors are defined on the surfaces that pass exactly through the same point, therefore some of the relevant challenges are removed. We also study the improved works of Hamel and Backus, and indicate that the original work of Backus removes most of the challenges. This article shows that the foundation of continuum mechanics is not a finished subject and there are still some fundamental challenges.

**Category:** Mathematical Physics

[502] **viXra:1707.0056 [pdf]**
*replaced on 2017-10-23 06:28:26*

**Authors:** Ehsan Azadi

**Comments:** 20 pages

The birth of modern continuum mechanics is the Cauchy's idea for traction vectors and his achievements of the existence of stress tensor and derivation of the general equation of motion. He gave a proof of the existence of stress tensor that is called Cauchy tetrahedron argument. But there are some challenges on the different versions of tetrahedron argument and the proofs of the existence of stress tensor. We give a new proof of the existence of stress tensor and derivation of the general equation of motion. The exact tetrahedron argument gives us, for the first time, a clear and deep insight into the origins and the nature of these fundamental concepts and equations of continuum mechanics. This new approach leads to the exact definition and derivation of these fundamental parameters and relations of continuum mechanics. By the exact tetrahedron argument we derived the relation for the existence of stress tensor and the general equation of motion, simultaneously. In this new proof, there is no limited, average, or approximate process and all of the effective parameters are exact values. Also in this proof, we show that all the challenges on the previous tetrahedron arguments and the proofs of the existence of stress tensor are removed.

**Category:** Mathematical Physics

[501] **viXra:1707.0056 [pdf]**
*replaced on 2017-07-05 15:43:42*

**Authors:** Ehsan Azadi

**Comments:** 19 pages

The birth of modern continuum mechanics was the Cauchy's idea for traction vectors and his achievements of the existence of stress tensor and derivation of the general equation of motion. He gave a proof for the existence of stress tensor that is called Cauchy tetrahedron argument. But there are some challenges on the different versions of tetrahedron argument and the proofs for the existence of stress tensor. We give a new proof for the existence of stress tensor and derivation of the general equation of motion. The exact tetrahedron argument for the first time gives us a clear and deep insight into the origins and the nature of these fundamental concepts and equations in continuum mechanics. This new approach leads to the exact point-base definition and derivation of these fundamental parameters and relations in continuum mechanics. By the exact tetrahedron argument we derived the relation for the existence of stress tensor and the general equation of motion, simultaneously. In this new proof, there is no approximating or limiting process and all of the effective parameters are exact values not average values. Also, we show that in this proof, all the challenges on the previous tetrahedron arguments and the proofs for the existence of stress tensor are removed.

**Category:** Mathematical Physics

[500] **viXra:1707.0022 [pdf]**
*replaced on 2017-07-03 00:54:24*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 8 Pages. This paper has not been submitted to a journal. Your comments are welcome

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.

**Category:** Mathematical Physics

[499] **viXra:1706.0456 [pdf]**
*replaced on 2017-10-28 10:38:15*

**Authors:** Mauro Bernardini

**Comments:** 45 Pages. this version corrects some accidental writing errors of the previous loaded version.

This is a brief summary of the Theory of Transcendent Reality (TTR), which describes the main postulates and mathematics used to describe and support the rationality of the Alef's model as unique and absolute being container of all the existences. This first issiue allow to describe the real physical composition of all the parallel universes contained in Alef's body. Universes that are logically and rationally constituted exclusively by Particles of Existence with a mass equal to that of a Proton and which generate an "apparent" existence since they are interpreted as existent only by the under-dimensional beings they generate in each single universe. Highlighting therefore that the Particles of Existence present in every universe are in fact 11 dimensional body slices of the Points of Alef, which, in turn, are the only real components of Alef's body: and, therefore, Particles of Existence that never really born nor died.

**Category:** Mathematical Physics

[498] **viXra:1706.0193 [pdf]**
*replaced on 2017-07-15 21:47:18*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Also, another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[497] **viXra:1706.0193 [pdf]**
*replaced on 2017-07-03 01:18:21*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Also, another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[496] **viXra:1706.0137 [pdf]**
*replaced on 2017-06-14 12:16:22*

**Authors:** Marcellin Nonti, Fernando Y. J. Kpomahou, Jean Akande, Damien K. K. Adjaï, Lucas H. Koudahoun, Marc D. Monsia

**Comments:** 4 pages

Hamiltonian dynamics and exact Gibbs statistical mechanics of a system of quadratic Liénard type oscillators have been investigated. The work has shown that the canonical ensemble for the harmonic oscillator is a particular case of the Gibbs ensemble theory developed in this paper.

**Category:** Mathematical Physics

[495] **viXra:1706.0122 [pdf]**
*replaced on 2017-09-13 15:07:37*

**Authors:** Louai Hassan Elzein Bashier

**Comments:** 21 Pages.

This paper is prepared to show the synthesis of the Newtonian mechanical
force and its counter part the inertial force. It is shows that the Newtonian
mechanical force splits into two counter forces when it is act upon a rigid
body. The paper is also shows the derivation of the momentum and the
kinetic energy that occur due to the presence of the inertial force.

**Category:** Mathematical Physics

[494] **viXra:1706.0122 [pdf]**
*replaced on 2017-07-25 08:07:41*

**Authors:** Louai Hassan Elzein Bashier

**Comments:** 21 Pages.

This paper is prepared to show the synthesis of the Newtonian mechanical
force and its counter part the inertial force. It is shows that the Newtonian
mechanical force splits into two counter forces when it is act upon a rigid
body. The paper is also shows the derivation of the momentum and the
kinetic energy that occur due to the presence of the inertial force.

**Category:** Mathematical Physics

[493] **viXra:1705.0374 [pdf]**
*replaced on 2017-06-12 02:09:24*

**Authors:** Zihao Song

**Comments:** 6 Pages. If one physical quantity can't find where it is originated, it's not a good physical quantity.

Physicists are proposing different mechanics to describe the nature, physical body is measured by intrinsic properties like electric charge, and extrinsic properties being related to space like generalized coordinates or velocities etc., with these properties we can predict what event will happen. We can naturally define the fact of the event and the cause of the event as information, the information grasped by physicist must be originated from something objective, information must have its object container. Intrinsic property information is contained by object itself, but container of extrinsic property information like position is ambiguous, position is a relation based on multiple objects, it's hard to define which one is the information container. With such ambiguity, no mechanics is a complete theory, errors hidden in assumptions are hard to find. Here we show a new theoretical framework with strict information container restriction, on which we can build complete determinism theories to approach grand unification.

**Category:** Mathematical Physics

[492] **viXra:1705.0347 [pdf]**
*replaced on 2017-06-19 04:02:19*

**Authors:** Preobrazhenskiy Andrey

**Comments:** 13 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.

**Category:** Mathematical Physics

[491] **viXra:1705.0347 [pdf]**
*replaced on 2017-05-27 09:01:13*

**Authors:** Preobrazhenskiy Andrey

**Comments:** 11 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.

**Category:** Mathematical Physics

[490] **viXra:1705.0300 [pdf]**
*replaced on 2017-05-23 08:56:56*

**Authors:** Miroslav Josipović

**Comments:** 80 Pages. geometric algebra

This is the translation of the article "Multiplication of Vectors and Structure of 3D Euclidean Space" to Croatian.

**Category:** Mathematical Physics

[489] **viXra:1705.0274 [pdf]**
*replaced on 2017-10-27 14:06:00*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 66 Pages.

In this work, I present a minimalist approach to first-order logic and show how it implies an irrefutable equation which connects to our major theories of physics.
The minimalist approach is, in many ways, similar to the constructivist project in mathematics but taken to the extreme. The approach starts from first-order logic with no axioms and further removes all rules of inference with the exception of the proof by construction. Although this severely cripples first-order logic it nonetheless gives it the following advantage.
From an argument originally made by Plato, I argue that any axioms or rules of inference that are removed increases the "epistemological irrefutability" of the theory. Taken to the extreme, once all axioms and all rules of inference are removed, the theory becomes entirely irrefutable and specifically in the case of this approach, as the first-order logic system is minimal, the epistemological irrefutability of its theorems is maximal.
Using this approach, I construct a universal language defined by a small list of first-order sentences. Each of the sentences claims the existence of an object of language which is provable by construction, the only rule of inference allowed by the minimalist system. As a result of being a theorem of a minimal system, the existence of the constructed universal language is therefore maximally irrefutable. This proof closely resembles René Descartes' derivation of the 'cogito ergo sum'. Like Descartes' method, this method also produces a statement that cannot be denied. But, unlike Descartes, as the proof is written in the language of first order logic, the irrefutable statement obtained is an actual equation.
Part I is the minimalist derivation of the irrefutable equation. The equation obtained is formulated as a Gibbs ensemble and relates the algorithmic notions of provable-sentences to that of entropy.
Part II is the derivation of the physical laws. I recover, from the irrefutable equation, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR) and the holographic principle. These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws obtained are shown to be emergent from informational entropy.
Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive that the irrefutable equation should be promoted to a tentative Theory of Everything (ToE)-candidate. This result motivates the ToE claim made in this paper.

**Category:** Mathematical Physics

[488] **viXra:1705.0274 [pdf]**
*replaced on 2017-09-26 08:01:33*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 66 Pages.

In this work, I present a minimalist approach to first-order logic and show how it implies an equation which necessarily bounds any possible Theory of Everything (ToE). The bound is of sufficient strength to recover actual laws of physics including general relativity and the Dirac equation. The minimalist approach is, in many ways, similar to the constructivist project in mathematics but taken to the extreme. The approach starts from first-order logic with no axioms and further removes all rules of inference with the exception of the proof by construction. Although this severely cripples first-order logic it nonetheless gives it the following advantage. From an argument originally made by Plato, I argue that any axioms or rules of inference that are removed increases the "epistemological irrefutability" of the theory. Taken to the extreme, once all axioms and all rules of inference are removed, the theory becomes entirely irrefutable and specifically in the case of this approach, as the first-order logic system is minimal, the epistemological irrefutability of its theorems is maximal. Using this approach, I construct a universal language defined by a small list of first-order sentences. Each of the sentences claims the existence of an object of language which is provable by construction, the only rule of inference allowed by the minimalist system. As a result of being a theorem of a minimal system, the existence of the constructed universal language is therefore maximally irrefutable. On the grounds that any ToE must at the very least recover all maximally irrefutable knowledge, I recover a strong restriction applicable to any possible ToE candidate. Part I is the minimalist derivation of the ToE restriction. From this derivation I obtain a master equation formulated as a Gibbs ensemble and relating the algorithmic notions of provable-sentences to that of entropy. PartII is the derivation of the physical laws. I recover, from the master equation, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR) and the holographic principle. These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws obtained are shown to be emergent from informational entropy. Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive that the ToE-restriction should be promoted to a ToE-candidate. This result motivates the ToE claim made in this paper.

**Category:** Mathematical Physics

[487] **viXra:1705.0274 [pdf]**
*replaced on 2017-09-25 12:31:29*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 65 Pages.

In this work, I present a minimalist approach to first-order logic and show how it implies an equation which necessarily bounds any possible Theory of Everything (ToE). The bound is of sufficient strength to recover actual laws of physics including general relativity and the Dirac equation.
The minimalist approach is, in many ways, similar to the constructivist project in mathematics but taken to the extreme. The approach starts from first-order logic with no axioms and further removes all rules of inference with the exception of the proof by construction. Although this severely cripples first-order logic it nonetheless gives it the following advantage.
From an argument originally made by Plato, I argue that any axioms or rules of inference that are removed increases the "epistemological irrefutability" of the theory. Taken to the extreme, once all axioms and all rules of inference are removed, the theory becomes entirely irrefutable and specifically in the case of this approach, as the first-order logic system is minimal, the epistemological irrefutability of its theorems is maximal.
Using this approach, I construct a universal language defined by a small list of first-order sentences. Each of the sentences claims the existence of an object of language which is provable by construction, the only rule of inference allowed by the minimalist system. As a result of being a theorem of a minimal system, the existence of the constructed universal language is therefore maximally irrefutable. On the grounds that any ToE must at the very least recover all maximally irrefutable knowledge, I recover a strong restriction applicable to any possible ToE candidate.
Part I is the minimalist derivation of the ToE restriction. From this derivation I obtain a master equation formulated as a Gibbs ensemble and relating the algorithmic notions of provable-sentences to that of entropy.
PartII is the derivation of the physical laws. I recover, from the master equation, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR) and the holographic principle. These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws obtained are shown to be emergent from informational entropy.
Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive that the ToE-restriction should be promoted to a ToE-candidate. This result motivates the ToE claim made in this paper.

**Category:** Mathematical Physics

[486] **viXra:1705.0274 [pdf]**
*replaced on 2017-09-17 15:07:54*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 64 Pages.

In this work, I present a minimalist approach to first-order logic and show how it implies a restriction on any possible Theory of Everything in physics (ToE) of sufficient strength to recover actual laws of physics. The minimalist approach is, in many ways, similar to the constructivist project in mathematics but taken to the extreme. The approach starts from first-order logic with no axioms and further removes all rules of inference with the exception of the proof by construction. Although this severely cripples first-order logic it nonetheless impairs it with the following advantage.
From an argument originally made by Plato, I argue that each axioms or rules of inference that are removed increases the "epistemological irrefutability" of the theory. Taken to the extreme, once all axioms and all rules of inference are removed, the theory becomes entirely irrefutable and specifically in the case of this approach, as the first-order logic system is minimal, the epistemological irrefutability of its theorems is maximal.
Using this approach, I construct a universal language defined by a small list of first-order sentences. Each of these sentences claims the existence of an object of language which is provable by construction, the only rule of inference allowed by the minimalist system. As a result of being a theorem of a minimal system, the existence of the constructed universal language is therefore maximally irrefutable. On the grounds that any ToE must at the very least recover all maximally irrefutable knowledge, I recover a strong restriction applicable to any possible ToE candidate.
Part I is the minimalist derivation of the ToE restriction. From this derivation I obtain a master equation formulated as a Gibbs ensemble and relating the algorithmic notions of provable-sentences to that of entropy.
Part II is the derivation of the physical laws. I recover, from the master equation, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR) and the holographic principle. These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws obtained are shown to be emergent from informational entropy.
Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive that the ToE-restriction should be promoted to a ToE-candidate. This result motivates the ToE claim made in this paper.

**Category:** Mathematical Physics

[485] **viXra:1705.0274 [pdf]**
*replaced on 2017-09-12 09:43:06*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 71 Pages.

In this work, I present a formal construction of the axiomless position as originally argued by Plato. This construction ultimately leads to a theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to establish the soundness of the methodology.
Part I is the axiomless derivation of the ToE. From this derivation I obtain a master equation formulated as a Gibbs ensemble and relating the algorithmic notions of program-observables to that of physical entropy.
Part II is the derivation of the physical laws. I recover, in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws are emergent.
Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive of a ToE candidate. This result motivates the ToE claim made in this paper.

**Category:** Mathematical Physics

[484] **viXra:1705.0274 [pdf]**
*replaced on 2017-09-11 12:00:42*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 70 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to convince the skeptical reader of the validity of the methodology. Part I is the axiomless derivation of the ToE. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy. Part III is the derivation of physical laws so as to provide evidence that it is the ToE. I recover, in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR as necessary consequences and limiting cases of this equation is suggestive of unification.

**Category:** Mathematical Physics

[483] **viXra:1705.0274 [pdf]**
*replaced on 2017-08-16 20:21:03*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 71 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to convince the skeptical reader of the validity of the methodology. Part I is the axiomless derivation of the ToE. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy. Part III is the derivation of physical laws so as to provide evidence that it is the ToE. I recover, in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR as necessary consequences and limiting cases of this equation is suggestive of unification.

**Category:** Mathematical Physics

[482] **viXra:1705.0274 [pdf]**
*replaced on 2017-08-14 10:34:44*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 71 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to convince the skeptical reader of the validity of the methodology. Part I is the axiomless derivation of the ToE. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy. Part III is the derivation of physical laws so as to provide evidence that it is the ToE. I recover, in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR as necessary consequences and limiting cases of this equation is suggestive of unification.

**Category:** Mathematical Physics

[481] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-26 08:04:32*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 74 Pages.

**Category:** Mathematical Physics

[480] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-26 07:05:11*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 74 Pages.

**Category:** Mathematical Physics

[479] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-25 19:07:22*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 75 Pages.

**Category:** Mathematical Physics

[478] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-25 12:50:01*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 75 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to convince the skeptical reader of the validity of the methodology.
Part I is the axiomless derivation of the ToE. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the derivation of physical laws so as to provide evidence that it is the ToE. I recover, in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR as necessary consequences and limiting cases of this equation is suggestive of unification.
These are some suggestive results that may indicate that this idea, while not yet fully completed*, could be a promising area of future research.
*As of the last revision date of this paper, a derivation of the elementary particles from this theory as per the standard model has not yet been investigated by the author.

**Category:** Mathematical Physics

[477] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-24 06:58:20*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 73 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to convince the skeptical reader of the validity of the methodology.
Part I is the axiomless derivation of the ToE. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the derivation of physical laws so as to provide evidence that it is the ToE. I recover, in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR as necessary consequences and limiting cases of this equation is suggestive of unification.
These are some suggestive results that may indicate that this idea, while not yet fully completed*, could be a promising area of future research.
*As of the last revision date of this paper, a derivation of the elementary particles from this theory as per the standard model has not yet been investigated by the author.

**Category:** Mathematical Physics

[476] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-23 13:00:22*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 74 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE). The purpose of this paper is to first derive the ToE from the axiomless position, then to derive sufficient physics from it so as to convince the skeptical reader of the validity of the methodology.
Part I is the axiomless derivation of the ToE. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is to convince the skeptical reader that this master equation is indeed the ToE. To show evidence of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR as necessary consequences and limiting cases of this equation is suggestive of unification.
These are some suggestive results that may indicate that this idea, while incomplete*, could be a promising area of future research.
*As of the last revision date of this paper, a derivation of the elementary particles from this theory as per the standard model has not yet been investigated by the author.

**Category:** Mathematical Physics

[475] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-22 05:29:56*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 72 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to a candidate for the theory of everything in physics (ToE). Part I is the axiomless derivation of the ToE-candidate. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy. Part III is the thesis that this master equation is indeed a credible ToE-candiate. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR from this equation is considered strong evidence that they are unified in it. Using this unification, we also propose a quantum mechanical description of black holes, and derive laws specific to it.

**Category:** Mathematical Physics

[474] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-21 13:53:03*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 71 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to a candidate for the theory of everything in physics (ToE).
Part I is the axiomless derivation of the ToE-candidate. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the thesis that this master equation is indeed a credible ToE-candiate. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GM). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GM from this equation is considered strong evidence that they are unified in it. Using this unification, we also propose a quantum mechanical description of black holes, and derive laws specific to it.

**Category:** Mathematical Physics

[473] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-12 07:20:57*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 66 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE).
Part I is the axiomless derivation of the ToE. From this derivation I obtain a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the thesis that this master equation is indeed the ToE. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are derived entirely from pure reason with no appeal to physical observations.
\end{abstract}

**Category:** Mathematical Physics

[472] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-11 20:36:09*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 66 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE).
Part I is the axiomless derivation of the ToE. From this derivation I obtain a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the thesis that this master equation is indeed the ToE. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are derived entirely from pure reason with no appeal to physical observations.

**Category:** Mathematical Physics

[471] **viXra:1705.0274 [pdf]**
*replaced on 2017-05-26 07:05:40*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 48 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE).
Part I of this work is the axiomless derivation of the ToE. From this derivation I obtain a master equation relating the notions of truth, knowledge and information to that of entropy.
Part II is the thesis that this master equation is indeed the ToE. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are derived entirely from pure reason with no appeal to physical observations.
The work here can also be interpreted as a constructive proof of René Descartes' cogito ergo sum. Where-as he proved the existence of the thinking self by contradiction, it is here proven by construction.

**Category:** Mathematical Physics

[470] **viXra:1705.0274 [pdf]**
*replaced on 2017-05-23 14:09:54*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 48 Pages.

Plato recognized that most of the disagreement in philosophy is ultimately linked to the choice of axioms made by the parties involved. He believed that by grinding away at the assumptions made for any argument, one could recover a kind universal truth. He believed that this universal truth, comprised of whatever survives the grinding process, could ultimately be used to build a logical framework in a manner that is entirely irrefutable. This is the axiomless position.
In this work, I present such a derivation.
Part I of this work is the axiomless derivation of the theory of everything in physics. From this derivation I obtain a master equation relating the notions of truth, knowledge and information to that of entropy.
Part II is the thesis that this master equation is indeed the theory of everything in physics. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are entirely derived from pure reason with no appeal to physical observations.
The work here can also be interpreted as a constructive proof of René Descartes' cogito ergo sum. Where-as he proved the existence of the thinking self by contradiction, it is here proven by construction.

**Category:** Mathematical Physics

[469] **viXra:1705.0274 [pdf]**
*replaced on 2017-05-18 12:57:31*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 46 Pages.

Using the cogito ergo sum as a starting point, I introduce a methodology which allows non-trivial knowledge to be obtained without the formal introduction of axioms. Using this methodology which I formalize, I then obtain a theory of everything (ToE) in physics. This method allows me to avoid the self-referential problem of a ToE which I argue is the core difficulty of any ToE built upon formal axioms. The theory obtained has enough generality to recover both general relativity and quantum field theory. Some of the new physics derived herein include a hard arrow time, an explanation of the quantum mechanical measurement, and a thermodynamic proof that the speed of light is maximal.

**Category:** Mathematical Physics

[468] **viXra:1705.0262 [pdf]**
*replaced on 2017-10-24 07:14:41*

**Authors:** D.K.K. Adjaï, L. H. Koudahoun, J. Akande, Y.J.F. Kpomahou, M. D. Monsia

**Comments:** 12 pages

This paper shows that explicit and exact general periodic solutions for various types of Lienard
equations can be computed by applying the generalized Sundman transformation. As an il-
lustration of the efficiency of the proposed theory, the cubic Duffing equation and Painleve-
Gambier equations were considered. As a major result, it has been found, for the first time, that equation XII of the Painleve-Gambier classication can exhibit, according to an appropriate parametric choice, trigonometric solutions, but with a shift factor.

**Category:** Mathematical Physics

[467] **viXra:1705.0262 [pdf]**
*replaced on 2017-08-24 03:38:22*

**Authors:** D.K.K. Adjaï, L. H. Koudahoun, J. Akande, Y.J.F. Kpomahou, M. D. Monsia

**Comments:** 10 pages

This paper exhibits a generalization of the theory of linearizing quadratic Lienard type equa-
tions introduced earlier by the authors of the current work and its application to determine the
general periodic solutions for the cubic Dung equation and for some equations of Painleve-
Gambier classication as illustrative examples. The mathematical equivalence between the
cubic Dung equation and the Painleve-Gambier XIX equation has been also highlighted us-
ing the present generalized theory.

**Category:** Mathematical Physics

[466] **viXra:1704.0264 [pdf]**
*replaced on 2017-06-06 07:20:18*

**Authors:** Paul Werbos

**Comments:** 15 Pages. 15p, 36 eq. typos corrected -- eq 7, refs to eqs 26 and 27.

Today’s standard model of physics treats the physical masses of elementary particles as given, and assumes that they have a bare radius of zero, as in the older classical physics of Lorentz. Many physicists have studied the properties of the Yang-Mills-Higgs model of continuous fields in hopes that it might help to explain where elementary particles (and their masses) come from in the first place. This paper reviews some of the important prior work on Yang-Mills-Higgs and solitons in general, but it also shows that stable particles in that model cannot have intrinsic angular momentum (spin). It specifies four extensions of Yang-Mills Higgs, the Lagrangians L1 through L4, which are closer to the standard model of physics, and shows that one of the four (L3) does predict/explain spin from a purely neoclassical theory. The paper begins by summarizing the larger framework which has inspired this work, and ends by discussing two possibilities for further refinement.

**Category:** Mathematical Physics

[465] **viXra:1704.0199 [pdf]**
*replaced on 2017-04-28 10:55:41*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 16 pages

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the Painlevé-Gambier XVIII equation and its inverted version may exhibit exact trigonometric periodic solutions as well as other quadratic Liénard type equations but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are also shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[464] **viXra:1704.0199 [pdf]**
*replaced on 2017-04-17 09:28:29*

**Authors:** J. Akande, D.K.K. Adjaï, L.H. Koudahoun, Y.J.F. Kpomahou, M.D. Monsia

**Comments:** 16 pages

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the Painlevé-Gambier XVIII equation and its inverted version may exhibit exact trigonometric periodic solutions as well as other quadratic Liénard type equations but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are also shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[463] **viXra:1704.0108 [pdf]**
*replaced on 2017-05-06 15:26:07*

**Authors:** Frederick Moxley

**Comments:** 14 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained. Finally, it is shown that all of the nontrivial zeros are located at $\Re(z)=1/2$.

**Category:** Mathematical Physics

[462] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-25 23:28:28*

**Authors:** Frederick Moxley

**Comments:** 15 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained. Finally, it is shown that all of the nontrivial zeros are located at $\Re(z)=1/2$.

**Category:** Mathematical Physics

[461] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-12 02:44:54*

**Authors:** Frederick Moxley

**Comments:** 12 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained.

**Category:** Mathematical Physics

[460] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-11 09:55:38*

**Authors:** Frederick Moxley

**Comments:** 12 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained.

**Category:** Mathematical Physics

[459] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-10 10:53:56*

**Authors:** Frederick Moxley

**Comments:** 11 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained.

**Category:** Mathematical Physics

[458] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-10 02:23:55*

**Authors:** Frederick Moxley

**Comments:** 11 Pages.

**Category:** Mathematical Physics

[457] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-09 09:26:07*

**Authors:** Frederick I Moxley

**Comments:** 11 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture.

**Category:** Mathematical Physics