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We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $\Gamma$-convergence, providing an integral…
We define an absolutely convergent series for the upper incomplete Gamma function $\Gamma(s,z)$ for $z\geq 1$ and $s\in \mathbb{C}$. We express this series using certain polynomials which we define using the Stirling numbers of the first…
We construct static and spherically symmetric black hole solutions in the Einstein-Euler-Heisenberg (EEH) system which is considered as an effective action of a superstring theory. We considered electrically charged, magnetically charged…
In this paper we study black hole interior solutions and cosmologies in different dimensions using tools from canonical gravity and nonsupersymmetric string quantum cosmology. We find that the quantum wave functions associated with these…
By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…
The gravitational properties of the {\em only} static plane-symmetric vacuum solution of Einstein's field equations without cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field…
The Euler equations of ideal gas dynamics posess a remarkable nonlinear involutional symmetry which allows one to factor out an arbitrary uniform expansion or contraction of the system. The nature of this symmetry (called by cosmologists…
We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show that many properties which $\Ga(z)$ enjoys extend in a…
We present $\gamma $-ray spectra for a set of Type Ia supernovae models. Our study is based on a detailed Monte Carlo transport scheme for both spherical and full 3-D geometries. Classical and new challenges of the $\gamma $ ray astronomy…
From the algebraic solution of $x^{n}-x+t=0$ for $n=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these…
We verify a method which allows to obtain the $\beta$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general…
We study the Emden-Fowler equation $-\Delta u=|u|^{p-1}u$ on the hyperbolic space ${\mathbb H}^n$. We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for…
We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers,…
The triangle anomalies in conformal field theory, which can be used to determine the central charge a, correspond to the Chern-Simons couplings of gauge fields in AdS under the gauge/gravity correspondence. We present a simple geometrical…
Neutron stars are natural laboratories for testing gravity in the strong field regime. That is why the full spectrum of neutron star solutions in different modified theories should be thoroughly studied. Among the most natural modifications…
An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific $q$-hypergeometric integrals whose key building block is the…
A new representation of solutions to the equation $-y"+q(x)y=\omega^2 y$ is obtained. For every $x$ the solution is represented as a Neumann series of Bessel functions depending on the spectral parameter $\omega$. Due to the fact that the…
We study 3d theories determined by three-manifolds. Previously, we found that some basic 3d dualities relate to the surgeries of three-manifolds and defined gauge circles and matter circles. In this note, we discuss some operations…
We propose a relatively new notion of two-valued elements, which arises naturally in constructing the star exponential functions of the quad-ratics in the Weyl algebra over the complex number field. This notion enables us to describe the…
The continuous point symmetry algebra of the hyperbolic Ernst equation is presented. In a second step the corresponding group transformations are considered. Accordingly, the solutions of the hyperbolic Ernst equation that are invariant…