[7] **viXra:1308.0125 [pdf]**
*replaced on 2016-11-16 11:11:38*

**Authors:** Robert A. Herrmann

**Comments:** 34 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 refinement 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.

**Category:** Mathematical Physics

[6] **viXra:1308.0118 [pdf]**
*replaced on 2017-07-02 02:49:19*

**Authors:** Malcolm Macleod

**Comments:** 7 Pages.

The fundamental physical constants are regarded as immutable and as non-derivable from more fundamental principles. They can be categorized between dimensionless and dimensionful constants, i.e.: those constants that describe a physical quantity but whose numerical value depends on the system of units used. In the “Trialogue on the number of fundamental physical constants” was debated the number, from 0 to 3, of dimensionful units required. Described here is a model based on a black-hole electron that uses 2 mathematical constants (the fine structure constant alpha and a proposed Omega) and 1 dimensionful unit $u$ to define the SI units $kg, m, s, A, K$ as interlocking geometrical forms. From these, the SI numerical value for the ampere can be used as a scalar to derive the SI values for the physical constants $G, h, c, e, m_e, k_B$. Units for MLTA (mass, length, time, ampere) are proposed as overlapping and canceling in these ratios; $(AL)^3/T = M^9 T^{11}/L^{15}$, units = 1. These ratios are embedded in a dimensionless electron function $f_e$ whereby the electron is seen as periodically oscillating between 2 states; a magnetic-monopole $(AL)^3$ and time T 'electric-state' and a 'mass-state'. The geometries of mass M=1, time T=$2\pi$, velocity V=$2\pi\Omega^2$, length L=$2\pi^2\Omega^2$ suggest angular motion may be the means by which dimensionality is conferred to mathematical forms. The $u^n$ relationships suggest that dimensionful units are mathematical rather than physical constructs, if so then 0 dimensionful units are required, a key condition for a virtual or a mathematical universe hypothesis. The sqrt of Planck momentum is used to link charge constants with mass constants, this permits us to define and solve the least accurate dimensionful constants $G, h, e, m_e, k_B...$ using the fine structure constant and the 3 most accurate dimensionful constants; $c$, $\mu_0$ (exact values), and the Rydberg constant (12-13 digits precision).

**Category:** Mathematical Physics

[5] **viXra:1308.0107 [pdf]**
*replaced on 2014-06-05 23:50:12*

**Authors:** Temur Z. Kalanov

**Comments:** 22 Pages.

Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.

**Category:** Mathematical Physics

[4] **viXra:1308.0091 [pdf]**
*replaced on 2017-02-25 13:07:05*

**Authors:** Peter Waaben

**Comments:** 3 Pages.

An infinitesimal approach

**Category:** Mathematical Physics

[3] **viXra:1308.0069 [pdf]**
*replaced on 2014-04-19 05:51:03*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 9 Pages.

ABSTRACT: We Study the use of Abel summation applied to the evaluation of infinite
series and infinite (divergent) integrals , we give several examples of how we can
obtain a regularization for the case of divergent sums and integrals.
Keywords: = Abel sum formula,Abel-Plana formula, poles , infinities, renormalization,
regularization, multiple integrals, Casimir effect.

**Category:** Mathematical Physics

[2] **viXra:1308.0034 [pdf]**
*submitted on 2013-08-06 07:04:55*

**Authors:** Dan Visser

**Comments:** 20 Pages. A copy has been send to the Clay Mathematics Institute.

The Double Torus Hypothesis is a newly proposed cosmological model. It reaches further than quantum-dynamics. It are ‘sub-quantum dynamics’ in the Double Torus, which show how new insights lead to the solution of the Riemann hypothesis. The secret is the existence of the continuous recalculation by two additional time-clocks from below the Planck-scale. Several of my papers describe this additional time in a new dark energy-force formula. This formula shows that a quantum-Newton-force and a sub-quantum dark matter-space-force perform extreme small accelerations that function as the exponent of the number ‘e’, where it enables sub-quantum-vacuum to expand or contract. The clue to the solution of the Riemann hypothesis is, that these physics sub-quantum-accelerations connect with ’π’ for surfaces below the elementary quantum-surface. I show how the famous Euler-formula e^iπ +1=0 is related to that process and I also show this Euler-formula can be related to the Riemann hypothesis by expressing the prime-numbers in the inverse Riemann hypothesis. I relate that configuration to the divided structure of an elementary quantum-surface. This leads to a configuration that solves the Riemann hypothesis. So, now is the moment to announce how I did that. I realize this might be experienced as shocking, because I am an outsider: I’m an independent cosmologist. Hopefully my solution awards me with the 1 million USD-price by the Clay Mathematics Institute (this dated pdf-file has been send to the Clay Mathematics Institute).

**Category:** Mathematical Physics

[1] **viXra:1308.0018 [pdf]**
*submitted on 2013-08-04 10:05:46*

**Authors:** John Frederick Sweeney

**Comments:** 76 Pages.

The G2 Root system is the only root system in which the angle of pi / 6
appears between two roots. This is made necessary in nature by the
demand for circular objects which can be divided by six or twelve,
according to Vedic literature concerning the 28 Nakshastra or
astrological houses. In addition, G2 provides the key linkage between
the Sedenions, which curiously contain properties related to the
number 29 and the Octonions. G2 is key to the transformation from
Binary to Trinary,Fano Plane to Tetrahedron and the Sedenions, mixing
the 8 x 8 to 9 x 9 aspects of matter, or the Satwa and Raja aspects.
Finally, from the Sedenions this paper develops toward the Hopf
Fibration and the Boerdijk-Coxeter Helix, which is composed of
Sedenions in the form of tetrahedra. Along the way we travel all the
way back to the Osiris Temple of Abydos, Egypt, where G2 appears.

**Category:** Mathematical Physics