Multidimensional gravity,flux and black brane solutions governed by polynomials

Two families of composite black brane solutions are overviewed, fluxbrane and black brane ones, in a model with scalar fields and fields of forms. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions \(\mathcal{H}_s \) (for fluxbranes) and H _s (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for \(\mathcal{H}_s \) and H _s are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions H _s and \(\mathcal{H}_s \) , as was conjectured and confirmed (at least partly) earlier, should be polynomials in proper variables if A is a Cartan matrix of some semisimple finite-dimensional Lie algebra. The fluxbrane polynomials \(\mathcal{H}_s \) were shown to be used for the construction of black brane polynomials H _s . This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A ₂, C ₂, and G ₂.     

Possible black universes in a brane world

A black universe is a nonsingular black hole where, beyond the horizon, there is an expanding, asymptotically isotropic universe. Such spherically symmetric configurations have been recently found as solutions to the Einstein equations with phantom scalar fields (with negative kinetic energy) as sources of gravity. They have a Schwarzschild–like causal structure but a de Sitter infinity instead of a singularity. It is attempted to obtain similar configurations without phantoms, in the framework of an RS2 type brane world scenario, considering the modified Einstein equations that describe gravity on the brane. By building an explicit example, it is shown that black–universe solutions can be obtained there in the presence of a scalar field with positive kinetic energy and a nonzero potential.     

Black brane solutions related to non-singular Kac-Moody algebras

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M ₀ × M ₁ × … × M _n , where M _i are Einstein spaces (i ≥ 1). The sigma-model approach and exact solutions with intersecting composite branes (e.g., solutions with harmonic functions and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g., hyperbolic ones) are considered. Some examples of black brane solutions are presented, e.g., those corresponding to hyperbolic KM algebras: H ₂(q, q) (q > 2), HA ₂⁽¹⁾ = A ₂⁺⁺ and to the Lorentzian KM algebra P ₁₀.     

On maximum periodic solutions of integrodifferential equations of volterra type and their stability

Consideration was given to the question of asymptotic (exponential) stability of the maximum periodic solutions of the integrodifferential equations which have an asymptotically stable linear part and small periodic (exponential maximum periodic) perturbation. Under the unlimitedly increasing time, these solutions tend to the periodic modes. The sufficient conditions for asymptotic stability were indicated. In the resonance case where the linearized equation has a pair of purely imaginary roots with the corresponding oscillation frequency coinciding with the oscillation frequency of the periodic part of small perturbation (time function) and the coefficients of the power series expansion of the nonlinear terms, consideration was given to the problem of existence for the maximum periodic solutions of the integrodifferential equation. Conditions were established for existence of such solutions representable by the power series in the fractional degrees of the small parameter characterizing the value of small perturbation in the equation.     

Field equations and vector order parameter in brane world applications

Phase transitions with spontaneous symmetry breaking and a vector order parameter are considered in multidimensional general relativity. Field equations describing the gravitational properties of topological defects, are derived. The topological defects are classified according to the symmetry of the covariant derivative of the vector field. The abilities of the derived equations are demonstrated in application to the brane world concept. New solutions of the Einstein equations with a transverse vector order parameter are presented. In the vicinity of the phase transition the solutions are found analytically. A comparison with the commonly used scalar multiplet approach demonstrates advantages of the vector order parameter.     

Homology models of the mutated EGFR and their response towards quinazoline analogues

One of the most intensely studied tyrosine kinases is the epidermal growth factor receptor (EGFR). The tyrosine kinase receptors are known to be over expressed in some solid tumors and non-small cell lung cancers, causing differential susceptibility to the quinazoline inhibitors. In this study we have taken SYK tyrosine kinase coordinates from PDB database to model two new EGFR receptors with these mutations G695S and L834R and conducted all the docking studies of the inhibitors, also evaluated these two models for quality of structure using PROCHECK. Seven quinazoline analogues (gefitinib, erlotinib, CI-1033, and EKB-569 and other analogues) were selected for comparisons among the two new models. This study determined the receptor/inhibitor interactions, at that active domain binding sites consisting of 15 amino acids. We were able to calculate the energy data for each of the seven inhibitors. This data has been important in interpreting the affinity between the inhibitors evaluated against the three models of EGFR (wild-type and two mutated types). "Affinity"-based studies have indicated the order of response based on docking energy levels (Van der Waals and electrostatic interactions). The active ATP binding sites consisting of 15 amino acid residues were identified and the total energy (E(total)) which showed the affinity between the inhibitor molecules and the receptor (Van der Waals and electrostatic interactions). The selection of the quinazoline analogues was purely on their emergence as possible candidates in the drug discovery areas. This study describes the successful application of these models that we constructed for molecular docking studies to rationally design compounds predicted to bind favorably to the modeled EGFR catalytic sites.     

On particle collisions near rotating black holes

Scattering of particles with different masses and energy in the gravitational field of rotating black holes is considered both outside and inside the black hole. Expressions for scattering energy of particles in the center-of-mass reference frame are obtained. It is shown that the scattering energy of particles in this frame can acquire very large values not only for extremal black holes but also for nonextremal ones if one takes into account multiple scattering. Numerical estimates for the time needed for a particle to get ultrarelativistic energy are given.     

浅谈校园网安全问题及解决办法

校园网络作为信息化建设的主要载体,校园网络安全已经成为当前各高校网络建设中不可忽视的首要问题。本文基于当前高校网络安全的现状及特点,提出校园网的安全问题及解决办法。     

Mathematical modeling of nonlinearly viscous fluid motion: Strong solutions

This paper studies mathematical modeling of motion of a nonlinearly viscous fluid in the case of strong solutions.     

浅谈电子文档安全的解决方案

信息安全的主要目标就是保证数据安全、系统可用和交易可信,其中保护文档和数据的安全,特别是保护电子文档的安全,是任何组织进行信息安全建设和管理的重中之重.本文以本人在实际项目咨询中策划和构架的电子文档保护方案为基础,介绍如何保护组织的电子文档安全.     

On the computation of analytical solutions of an unsteady magnetohydrodynamics flow of a third grade fluid with Hall effects

In this article, a combination of Lie symmetry and homotopy analysis methods (HAM) are used to obtain solutions for the unsteady magnetohydrodynamics flow of an incompressible, electrically conducting third grade fluid, bounded by an infinite porous plate in the presence of Hall current. In particular, similarity reductions are performed on the governing equations in its complex scalar and corresponding vector system forms. Also, nontrivial conservation laws, using the multiplier approach, are constructed for the complex scalar equation. Furthermore, a comparison of the results with numerical results already existing in the literature is done. The analytical solutions are presented through graphs by choosing a range of the relevant physical parameters. The underlying calculations were obtained via a combination of software packages in Mathematica and Maple, in particular, for the Lie symmetry generators, Euler Lagrange operators and homotopy operators; the latter being towards the construction of the conserved flows.     

Fractional variable order discrete-time systems,their solutions and properties

In this paper, fractional variable order discrete state-space systems based on different definitions of fractional variable order difference are investigated.The general solution of these systems is derived. Moreover, necessary and sufficient conditions for reachability and observability are given and proven. The sufficient conditions for controllability are proposed too.     

On copulas and their diagonals

We formulate the necessary and sufficient conditions for a function δ:[0,1]→[0,1] to be the diagonal section of a multivariate absolutely continuous copula. Moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics.     

Stability of solutions of delay functional integro-differential equations and their discretizations

In this paper we study asymptotic stability and contractivity properties of solutions of a class of delay functional integro-differential equations. These results form the basis for obtaining insight into the analogous properties of numerical solutions generated by continuous Runge-Kutta or collocation methods, where these methods are applied to a suitable reformulation of the given initial-value problem.     

On nonunique solutions in topology optimization

This paper deals with the problem of non-unique solutions in topology optimization. Depending on the optimization path, the solutions, in other words the topologies of a structure, are different. The nonuniqueness problem in topology optimization is presented in connection with the testing of different lower material mass value bounding functions and the use of different material properties updating functions and different threshold functions. The structure strain energy minimum criterion is applied to find the optimum topology. A comparison of the topologies obtained from the energy criterion point of view is made.