# Mathematical Physics

## 1403 Submissions

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

### Do the Two Operations Addition and Multiplication Commute with Each Other?

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

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

### The Arm Theory

Authors: Arm Boris Nima

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

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

### The p-Arm Theory

Authors: Arm Boris Nima

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

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

### The Arm Prime Factor Decomposition

Authors: Arm Boris Nima

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

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

### The Arm Factorization

Authors: Arm Boris Nima

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

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

### The Arm Fourier Theory

Authors: Arm Boris Nima

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

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

### The Arm Lie Group Theory

Authors: Arm Boris Nima

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

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

### Remarks Around Lorentz Transformation

Authors: Arm Boris Nima

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

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

### Some Poisson Lie sigma Models

Authors: Arm Boris Nima

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

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

### Noncommutative_ricci_curvature_and_dirac_operator_on_b_qsu_2_at_the_fourth_root_of_unity

Authors: Arm Boris Nima

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

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

### Noncommutative_geometry_on_d6.

Authors: Arm Boris Nima

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

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

### Non_commutative_geometry_on_usb2

Authors: Arm Boris Nima

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

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

### The Triangular Properties of Associated Legendre Functions Using the Vectorial Addition Theorem for Spherical Harmonics

Authors: Rami Mehrem

Triangular properties of associated Legendre functions are derived using the Vectorial Addition Theorem of spherical harmonics
Category: Mathematical Physics

 viXra:1403.0059 [pdf] replaced on 2018-04-28 15:30:19

### Navier-Stokes Equations. on the Existence and the Search Method for Global Solutions. \\ Уравнения Навье-Стокса. Существование и метод поиска глобального решения.

Authors: Solomon I. Khmelnik

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

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

### Matrices and Quaternions

Authors: Gary D. Simpson