2008jbl

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2008jbk

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2008jaz

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2008jay

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2008jax

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2008jaw

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Modern higher energy physics
2008jav | K. V. Stepanyantz  // Russia, Moscow State University, physical faculty, department of theoretical physic, sstepan@phys.msu.ru

We briefly review the modern higher energy physics. Description of the strong and electroweak interactions is considered both in the Standard model and in Grand Unification theories. We discuss the origin of the small neutrino mass and the necessity of supersymmetry. We also consider description of the gravity, modern cosmological experimental data, supergravity theories, and a relation of gravity with other interactions. We draw attention to problems, which appear describing the gravity, and possible ways of their solution. In particular, achievements and drawbacks of superstrings theories are discussed.

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2008jau

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2008jat

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Poly-Numbers (Matrions) in Biological and Computer Informatics
2008jas | Sergey Petoukhov, Elena Petoukhova  // Mechanical Engineering Research Institute RAS, Moscow, petoukhov@hotmail.com

The article is devoted to $2^n$-dimensional poly-numbers, which generalize complex and double numbers on the basis of a block-fractal (or Kronecker) algorithm. These poly-numbers were named circular and hyperbolic matrions correspondingly. They were constructed in a course of investigations of genetic code systems from the viewpoint of matrix methods of informatics. Data about algebras of these poly-numbers are presented. A meaning of these poly-numbers for theoretical biology and information science is under discussion.

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2007jbz

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2007jby

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2007jbx

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On the possibility of the OMPR effect in the space with Finsler geometry. Part 1.
2007jbw | Brinzei N., Siparov S. V.  // "Transilvania" University, Brasov, Romania, nico.brinzei@rdslink.ro, & State University of Civil Aviation, Sankt-Petersburg, Russia, sergey@siparov.ru

The effect of the optic-metrical parametric resonance could provide the possibility to obtain the experimental evidence of the gravitational waves existence. The effect might change, if the geometry of the physical space-time is not Riemannian but Finslerian one. The investigation of this situation is undertaken.

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Einstein Equations for the Homogeneous Finsler Prolongation to TM, with Berwald-Moor Metric
2007jbv | Atanasiu Gh., Brinzei N.  // "Transilvania" University, Brasov, Romania, gh_atanasiu@yahoo.com, nico.brinzei@rdslink.ro

Within the geometrical framework provided by (h,v)-metric structures, an important case is that of the homogeneous prolongation (lift) of a Finsler metric to the tangent bundle TM, constructed by R. Miron. In this case, we perform a study of Einstein equations. A special attention is paid to the Berwald-Moor metric, and to metrics conformally related to it.

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An extension of electrodynamics theory to complex Lagrange geometry
2007jbu | Gh. Munteanu  // Transilvania Univ., Faculty of Mathematics and Informatics, Bra\c{s}ov, Romania, gh.munteanu@unitbv.ro

In this note our purpose is to introduce the Maxwell type equations in a complex Lagrange space, particularly in a complex Finsler space. The electromagnetic tensor fields are defined as the sum between the differential of the complex Liouville 1-form and the symplectic 2-form of the space relative to the adapted frame of Chern-Lagrange complex nonlinear connection. Is proved that the (1,1)-type electromagnetic field of a complex Finsler space vanish and the differential of the (2,0)-type electromagnetic field yields the generalized Maxwell equations. The complex electromagnetic currents are also introduced and the conditions when they are conservative are deduced. Finally we apply the results to the electrodynamics Lagrangian considered in [Mu] and to the case of complex Randers spaces.

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2007jbt

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2007jbs

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2007jbr

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2007jbq

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Stumbling blocks for standard cosmology in the light of six-dimensional one
2007jbp | I. A. Urusovskii  // Acoustic institute n.a, acad. N.N. Andreev, Moscow, Russia

An account of an increase of speed of light in the actual three-dimensional Universe and its effect on redshift for distant sources and on theoretical redshift dependencies compared with observed data is given. The investigation is carried out on the basis of the simplest six-dimensional treatment of the expanding Universe in the form a three-dimensional sphere appeared as a result of the intersection of three simplest geometrical objects of finite dimensions in the six-dimensional Euclidean space -- of three uniformly expanding five-dimensional spheres. A scenario in which the speed of light (and the energy of each elementary particle) in the six-dimensional space is constant in time is considered. Some difficulties of standard cosmology are discussed on the base of six-dimensional cosmology.

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2007jbo

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2007jaz

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2007jay

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2007jax

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2007jaw

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2007jav

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2007jau

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2007jat

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2007jas

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2007jar

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Inertial navigation equations and the quaternion space-time theory
2007jaq | V. F. Chub  // Korolev Rocket-Space Corporation ``Energiya'', Russia

The comparative analysis of relativistic and nonrelativistic inertial navigation equations in space free of gravitational field was performed in review. In order to represent the equations, the use is made of the quaternions with real, dual, complex and complex-dual factors. Within the theory based upon the quaternions with complex-dual factors (the quaternion space-time theory) it was demonstrated that the transformations forming in the context of a special relativity theory Poincare group and in the context of classical Newton mechanics Galilei group were open. The inertial navigation equation consistent with the quaternion space-time theory was given and its absurdity was noted.

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A mathematical description of the fermionic state
2007jap | Rowlands P.  // Department of Physics, University of Liverpool, Oliver Lodge Laboratory, Liverpool, UK, p.rowlands@liverpool.ac.uk

The fermionic state is the foundation for the whole of physics. Physics is entirely concerned with fermions and their interactions, and nothing else. It is possible to derive a mathematical expression for the fermionic state, which is an operator only, not an equation, or wavefunction. This operator appears to contain within it all the information needed to construct fermion interactions and particle states. Extensions to particle representations using Finsler geometry could find this formalism a particularly accessible link.

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2007jao

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2007jan

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2006jbz

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2006jby

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2006jbx

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2006jbw

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2006jbv

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2006jbu

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Finsler spaces with polynomial metric
2006jbt | L. Tamassy

In this paper we want to show that Finsler spaces with polynomial metric allow metrical tensorial connections (linear for a given type of tensors). Many of them induce, in a natural way, metrical non-linear connections in $\tau_M$.

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Pairs of metrical Finsler structures and Finsler connections compatible to them
2006jbs | Atanasiu Gh.

We consider a pair of metrical Finsler structure $g_{ij}\left( x,y\right),s_{ij}\left( x,y\right) , \left( x,y\right) \in TM,\;i,j=\overline{1,n},\dim M=n$ and we investigate the cases in which is possible to find Finsler connections compatible to them:$\;rank\left\| g_{ij}\left( x,y\right) \right\| =n,$ $rank\left\| s_{ij}\left( x,y\right) \right\| =n-k,\;k\in\left\{ 0,1,...,n-1\right\} ,\forall \left( x,y\right) \in TM\setminus \left\{ 0\right\} .$

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The horizontal and vertical semisymmetric metrical $d$-connections in the Relativity Theory
2006jbr | Atanasiu Gh., Stoica E.

Let $E$ be the $(m+n)$-dimensional total space of a vector bundle $(E,p,M)$, $dim\;M=n$, a given fixed nonlinear connection $N$ on $E$ and a given $(h,v)$-metrical structure $G\in \mathcal{T}_{2}^{0}\left( E\right) $. In the paper, we determine the Einstein equations of an $h$- and $v$-semisymmetric metrical distinguished connection on $E=TM$, if $n=4$, for a Riemann -- local Minkowski model.

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CMC and minimal surfaces in Berwald-Moor spaces
2006jbq | Balan V.

For Randers and Kropina Finsler spaces are described the extended equations of minimal and CMC hypersurfaces. For the Berwald-Moor type Finsler metric are then considered different types of symmetric polynomials generating the fundamental function and classes of CMC surfaces are evidentiated. Maple 9.5 representations of indicatrices point out structural differences among Berwald-Moor fundamental functions of different order, leading to different CMC approaches.

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Geodesics, connections and Jacobi fields for Berwald-Moor quartic metrics
2006jbp | Balan V., Brinzei N., Lebedev S.

For Finsler spaces $(M,F)$ with quartic metrics $F=\sqrt[4]{G_{ijkl}(x,y) y^{i}y^{j}y^{k}y^{l}},$ we determine the equations of geodesics and the corresponding arising geometrical objects-canonical spray, nonlinear Cartan connection, Berwald linear connection -- in terms of the non-homogenized flag Lagrange metric $h_{ij}=G_{ij00}.$ Further, are studied the geodesics and Jacobi fields of the tangent space $TM$ for $hv$-metric models.

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The Lagrangian-Hamiltonian formalism in gauge complex field theories
2006jbo | Munteanu Gh.

An introduction in the study of gauge field theory in terms of complex Finsler geometry on the total space of a $G$-complex vector bundle $E$ was made by us in \cite{Mu2}. Here we briefly recal the obtained results and similar notions are investigated on the dual bundle $E^{*}$ by complex Legendre transformation (the $\mathcal{L}$-dual process).
The complex field equations are determined with respect to a gauge complex vertical connections. The complex Hamilton equations are write for the general $\mathcal{L}$-dual Hamiltonian obtained as a sum of particle Hamiltonian, Yang-Mills and Hilbert-Einstein Hamiltonians.

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Some geometrical aspects of harmonic curves in a complex Finsler space
2006jbn | Munteanu Gh.

In this note we make a short study of the geometry of curves in a complex Finsler space. For harmonic curves we obtain an equivalent characterization to that from \cite{Ni}. A special discussion concerns the holomorphic curves.

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Fundamental equations for a second order generalized Lagrange space endowed with a Berwald-Moor type metric in invariant frames
2006jbm | Paun M.

The purpose of this paper is to study Vranceanu identities and Maxwell equations of a generalized Lagrange space of order 2 endowed with a Berwald Moor type metric in invariant frames end to emphasize their equivalence.

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Theory of the zero-order effect to investigate the space-time geometrical structure
2006jbl | S. V. Siparov

The applicability of Einstein's Relativity Theory on the galactic scale and the role of geometry in the problems of astrophysical observations are discussed. The theory of the zero-order effect to study experimentally the geometrical properties of space-time is suggested

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