The three dimensional theory of gravitation based on a temporal scalar field in Riemanian geometry

A new approach to the model of the universe based on work by Rippl, Romero, Tavakol is presented. We have used the scheme for relating the vacuum (D + 1) dimensional theories to D dimensional theories for setting up a correspondence between vacuum 4-dimensional Einstein theory with 3-dimensional gravity theory with temporal scalar field. These ideas we continued by using the 3-dimensional analog of Jordan, Brans-Dicke theory with temporal scalar field. As the result space and time are treated in completely different ways. For the case of a static spherically symmetric field new vacuum static solutions are found.Comment: 9 pages, Based on talks given at Santa Clara 2004. International Workshop on Gravitation and Cosmology, Central University of Las Villas, 31 may-3 June, 2004, Cub

Static spherically symmetric constant density relativistic and Newtonian stars in the Lobachevskyan geometry

The present paper has the purpose to illustrate the importance of the ideas and constructions of the Non-Euclidean (Lobachevsky) Geometry, which can be applied even today for solving some conceptually important problems. We study the static and spherically symmetric solutions to the Einstein field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. A new exact solution of a perfect fluid sphere of constant (homogeneous) energy-density which agrees with interior Lobachevsky geometry for 3D and 4D spaces are found. We discuss the property of temporal scalar field arise in lower-dimensional theories as the reduction of extra dimension.Comment: 10 page

On the Stability of Spherically Symmetric Configurations in Newtonian Limit of Jordan, Brans-Dicke Theory

We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it emerges that the more compact a model is, the more stable it is. Moreover, linear stability analysis shows the existence of stable configurations for any polytropic index.Comment: 11 page

Composite spherically symmetric configurations in Jordan-Brans-Dicke theory

In this article, a study of the scalar field shells in relativistic spherically symmetric configurations has been performed. We construct the composite solution of Jordan-Brans-Dicke field equation by matching the conformal Brans solutions at each junction surfaces. This approach allows us to associate rigorously with all solutions as a single glued "space", which is a unique differentiable manifold M^4.Comment: 6 page

Biology is a constructive physics

Yuri Manin's approach to Zipf's law (Kolmogorov complexity as energy) is applied to investigation of biological evolution. Model of constructive statistical mechanics where complexity is a contribution to energy is proposed to model genomics. Scaling laws in genomics are discussed in relation to Zipf's law. This gives a model of Eugene Koonin's Third Evolutionary Synthesis (physical model which should describe scaling in genomics).Comment: 9 pages, commentaries adde

Dynamical systems where time is a quantum group and quantum ergodicity

We define dynamical systems where time is a quantum group. We give the definition of quantum ergodicity for the introduced dynamical system with noncommutative (or quantum) time, and discuss the examples.Comment: 4 pages, LaTe

Classification by Ensembles of Neural Networks

We introduce a new procedure for training of artificial neural networks by using the approximation of an objective function by arithmetic mean of an ensemble of selected randomly generated neural networks, and apply this procedure to the classification (or pattern recognition) problem. This approach differs from the standard one based on the optimization theory. In particular, any neural network from the mentioned ensemble may not be an approximation of the objective function.Comment: 8 pages, LaTe

The Heckmann's wormholes in Jordan-Brans-Dicke gravity

A simple Heckmann's vacuum wormhole solution of Jordan-Brans-Dicke gravitation is presented and analysed. It is shown that in contrast with class I Brans solution where the throat radius becomes real when $\omega < -4/3$ here it becomes positive when $\omega < -1$.Comment: 4 page

New static spheroidal solution in Jordan-Brands-Dicke theory

The static spheroidal solutions of Jordan-Brands-Dicke theory (JBD) are studied. We consider the effect of the anisotropic stresses of scalar field on the shape of JBD self-graviting objects. It is shown that scalar fields can have significant effect on the structure and properties of self-graviting objects. In contrast with general relativity in JBD theory there are nonflat static spheroidal solutions.Comment: 5 page

The noncommutative replica procedure

The alternative to the replica procedure, which we call the noncommutative replica procedure, is discussed. The detailed comparison with the standard replica procedure is performed.Comment: 12 pages, LaTeX, Commentaries adde