[16] **viXra:1403.0925 [pdf]**
*replaced on 2015-08-25 09:09:31*

**Authors:** Koji Nagata, Tadao Nakamura

**Comments:** 4 Pages. Open Access Library Journal, Volume 2 (2015), e1803/1--4, http://dx.doi.org/10.4236/oalib.1101803

We study about the metamathematics of Zermelo-Fraenkel set theory
with the axiom of choice.
We use the validity of Addition and Multiplication.
We provide an example that the two operations
Addition and Multiplication do not commute with each other.
All analyses are performed in a finite set of natural numbers.

**Category:** Mathematical Physics

[15] **viXra:1403.0286 [pdf]**
*replaced on 2014-07-02 12:52:37*

**Authors:** Arm Boris Nima

**Comments:** 14 Pages.

Did you ever wondered what is the Taylor formula for an arbitrary chosen basis ? The answer of this question is the Arm theory introduced in this article.

**Category:** Mathematical Physics

[14] **viXra:1403.0285 [pdf]**
*submitted on 2014-03-17 06:10:06*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We introduce the p-Arm theory which give rise to a new mathematical
object that we call the "p-exponential" which is invariant under
p derivation. We calculate its derivate and we use this new
function to solve dierential equations. Next, we
dene its real and imaginary part which are
the p-cosinus and the p-sinus respectively.

**Category:** Mathematical Physics

[13] **viXra:1403.0284 [pdf]**
*submitted on 2014-03-17 06:11:48*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We introduce the Arm prime factors decomposition
which is the equivalent of the Taylor formula
for decomposition of integers on the basis
of prime numbers. We make the link
between this decomposition and
the p-adic norm known in the
p-adic numbers theory.
To see how it works,
we give examples
of these two
formulas.

**Category:** Mathematical Physics

[12] **viXra:1403.0283 [pdf]**
*submitted on 2014-03-17 06:13:24*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We construct the equivalent of the Taylor
formula in the basis of all roots
fx kgK when K is Z iZ,
Q iQ and C.

**Category:** Mathematical Physics

[11] **viXra:1403.0282 [pdf]**
*submitted on 2014-03-17 06:15:09*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We give the developpment of functions in C[z] C[z
1
] with a scalar product which
involves an integral and a residue calculus. Then we give some examples
of those developpments and nd new 'representations' of the
exponential and the logarithm function . We draw those
representations and we see that there are
similar to their original
representations

**Category:** Mathematical Physics

[10] **viXra:1403.0281 [pdf]**
*submitted on 2014-03-17 06:17:47*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We developp the Arm-Lie group theory which is a theory based
onthe exponential of a changing of matrix variable u(X).
We dene a corresponding u-adjoint action, the
corresponding commutation relations in the
Arm-Lie algebra and the u-Jacobi identity.
Throught the exponentiation, Arm-Lie
algebras become Arm-Lie groups.
We give the example of pp
so(2) and
pp
su(2).

**Category:** Mathematical Physics

[9] **viXra:1403.0280 [pdf]**
*submitted on 2014-03-17 06:19:35*

**Authors:** Arm Boris Nima

**Comments:** 6 Pages.

After diagonalizing the Lorentz Matrix,
we nd the frame where the Dirac
equation is one derivation and
we calculate the 'speed' of
the Schwarschild metric

**Category:** Mathematical Physics

[8] **viXra:1403.0279 [pdf]**
*submitted on 2014-03-17 06:20:51*

**Authors:** Arm Boris Nima

**Comments:** 10 Pages.

We calculate the Poisson-Lie sigma model for every 4-dimensional
Manin triples (function of its structure constant) and we
give the 6-dimensional models for the Manin triples
(sl(2; C) sl(2; C)
; sl(2; C); sl(2; C)
),
(sl(2; C) sl(2; C)
; sl(2; C)
); sl(2; C),
(sl(2; C); su(2; C); sb(2; C)) and
(sl(2; C); sb(2; C); su(2; C))

**Category:** Mathematical Physics

[7] **viXra:1403.0278 [pdf]**
*submitted on 2014-03-17 06:22:13*

**Authors:** Arm Boris Nima

**Comments:** 16 Pages.

We calculate the torsion free spin connection on the quantum group Bq[SU2]
at the fourth root of unity. From this we deduce the covariant derivative
and the Riemann curvature. Next we compute the Dirac operator
of this quantum group and we give numerical
approximations of its eigenvalues.

**Category:** Mathematical Physics

[6] **viXra:1403.0277 [pdf]**
*submitted on 2014-03-17 06:24:03*

**Authors:** Arm Boris Nima

**Comments:** 22 Pages.

We study the noncommutative geometry of the dihedral group D6
using the tools of quantum group theory. We explicit the
torsion free regular spin connection and the
corresponding 'Levi-Civita' connection.
Next, we nd the Riemann curvature
and its Ricci tensor. The main
result is the Dirac operator
of a representation of the
group which we nd the
eigenvalues and the
eigenmodes

**Category:** Mathematical Physics

[5] **viXra:1403.0276 [pdf]**
*submitted on 2014-03-17 06:25:21*

**Authors:** Arm Boris Nima

**Comments:** 16 Pages.

We study the Borel algebra dene by [xa; xb] = 2a;1xb
as a noncommutative manifold R
3
. We calculate its
noncommutative dierential form relations. We deduce
its partial derivative relations and the derivative
of a plane wave. After calculating its de Rham
cohomology, we deduce the wave operator and
its corresponding magnetic solution

**Category:** Mathematical Physics

[4] **viXra:1403.0271 [pdf]**
*replaced on 2014-12-09 12:37:03*

**Authors:** Rami Mehrem

**Comments:** 7 Pages.

Triangular properties of associated Legendre
functions are derived using the Vectorial Addition Theorem of spherical harmonics

**Category:** Mathematical Physics

[3] **viXra:1403.0059 [pdf]**
*submitted on 2014-03-09 10:41:32*

**Authors:** Solomon I. Khmelnik

**Comments:** Pages.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence. Then we consider the so-called closed systems. We prove that for them the necessary and sufficient conditions of global extremum for the named functional always exist. Accordingly, the search for global extremum is always successful, and so the unique solution of Naviet-Stokes is found. We contend that the systems described by Navier-Stokes equations with determined boundary solutions (pressure or speed) on all the boundaries, are closed systems. We show that such type of systems include systems bounded by impermeable walls, by free space under a known pressure, by movable walls under known pressure, by the so-called generating surfaces, through which the fluid flow passes with a known speed. The book is supplemented by open code programs in the MATLAB system – functions realizing the calculation method and test programs. Links on test programs are given in the text of the book when the examples are described. // Формулируется и доказывается вариационный принцип экстремума для вязкой несжимаемой и сжимаемой жидкости, из которого следует, что уравнения Навье-Стокса являются условиями экстремума некоторого функционала. Описывается метод поиска решения этих уравнений, который состоит в движении по градиенту к экстремуму этого функционала. Формулируются условия достижения этого экстремума, которые являются одновременно необходимыми и достаточными условиями существования глобального экстремума этого функционала. Книга дополняется открытыми кодами программам в системе MATLAB – функциями, реализующими расчетный метод, и тестовыми программами.

**Category:** Mathematical Physics

[2] **viXra:1403.0004 [pdf]**
*submitted on 2014-03-01 09:50:38*

**Authors:** Gary D. Simpson

**Comments:** 11 Pages.

A possibly novel mathematical structure is presented. The structure is a matrix whose elements are quaternions. The structure is distinct from a tensor.

**Category:** Mathematical Physics

[1] **viXra:1403.0002 [pdf]**
*submitted on 2014-03-01 01:01:17*

**Authors:** Vyacheslav Telnin

**Comments:** 7 Pages.

viXra.org 1402.0167 gives general description of raising vector space W in the power M/L. The
result is the new vector space V. In this paper we take W - the 8 – dimensional generalization of
our 4 – dimensional vector space. Then we raise W in the power 1/3. The result is the 2 –
dimensional vector space V. The metric and algebraic tensors for V are the same as in viXra.org
1402.0176.
After that we take some vector from V and use it for construction of Lagrangian. And for
simplicity we restrict us by only first 4 dimensions of W. Then, from the principle of minimal
action, we get the equations for our vector. And we derive that vector from these equations.
Then we define the tensor and vector of energy – momentum for this Lagrangian. And also we
find the density of spin tensor and (with the help of the algebraic tensor) the density of spin
vector. The numerical cofactor in them is 1/3. So we consider that spin of this vector is 1/3. It
coincides with the power of W for V (vector space we took our vector from).

**Category:** Mathematical Physics