We compute the scalar curvature of 7-dimensional G2-manifolds admitting a connection with totally skew-symmetric torsion. We prove the formula for the general solution of the Killing spinor equation and express the Riemannian scalar curvature of the solution in terms of the dilation function and the NS 3-form field. In dimension n = 7 the dilation function involved in the second fermionic strin...

We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with variable, rational coefficients. In an earlier treatment this condition was integrated by first transforming it to a hypergeometric equation. We demonstrate...

1. GENERAL FORM OF FINITE VOLUME METHODS We consider vertex-centered finite volume methods for solving diffusion type elliptic equation (1) −∇ · (K∇u) = f in Ω, with suitable Dirichlet or Neumann boundary conditions. Here Ω ⊂ R is a polyhedral domain (d ≥ 2), the diffusion coefficient K(x) is a d× d symmetric matrix function that is uniformly positive definite on Ω with components in L∞(Ω), and...

Mathematical physics problems are often formulated using differential oprators of vector analysis invariant operators of first order, namely, divergence, gradient and rotor operators. In approximate solution of such problems it is natural to employ similar operator formulations for grid problems, too. The VAGO (Vector Analysis Grid Operators) method is based on such a methodology. In this paper...

We show that the set of all functions is equivalent to the set of all symmetric functions up to deterministic time complexity. In particular, for any function f , there is an equivalent symmetric function fsym such that f can be computed form fsym and vice-versa (modulo an extra deterministic linear time computation). For f over finite fields, fsym is (necessarily) over an extension field. This...

For steady states of cells that have uniform cell membranes, there must be zero net fluxes of each ion. This provides a set of conditions more restrictive than the condition of zero net current flow that is used to derive the Goldman equation. We show that this leads to a set of general relations between the membrane potential, ion activities, ion permeabihties, and pump fluxes and that the Gol...

In this article we study holomorphic isometries of the Poincaré disk into bounded symmetric domains. Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometries up to normalizing constants with respect to the Bergman metric, showing in particular that the graph V0 of any germ of holomorphic isometry of the Poincaré disk ∆ into...

Abstract The aim of this paper is to discuss the theory relativistic charged double polytropes with generalized polytropic equation state. A general framework presented develop Lane-Embden equations for spherically symmetric configuration. stability developed investigated by means Tolman mass. We will also examine structure these under various constraints.

In this paper, we discuss the existence of positive radially symmetric entire solutions p-k-Hessian equation σk1kλDi|Du|p−2Dju=α1k(|x|)f(u), and general system σk1kλDi|Du|p−2Dju=α1k(|x|)f1(v)f2(u), σk1kλDi|Dv|p−2Djv=β1k(|x|)g1(u)g2(v).

In this article we study holomorphic isometries of the Poincaré disk into bounded symmetric domains. Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometries up to normalizing constants with respect to the Bergman metric, showing in particular that the graph V0 of any germ of holomorphic isometry of the Poincaré disk ∆ into...