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Applying functional differentiation to the density field with Newtonian gravity, we obtain the static, nonlinear equation of the three-point correlation function $\zeta$ of galaxies, to the third order density perturbations. We make the…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for…
Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are…
We derive hypergeometric formulas for Euler's constant, gamma. A "by-product" of Thomae's transformation is an infinite product for e^gamma involving the binomial coefficients. Alternate, non-hypergeometric proofs use a double integral for…
We give a brief account of the key properties of elliptic hypergeometric integrals -- a relatively recently discovered top class of transcendental special functions of hypergeometric type. In particular, we describe an elliptic…
We consider supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere. The three-manifold is always equipped with an almost contact structure and an associated Reeb vector field. We show that the…
We provide the general solution of problems concerning AC star circuits by turning them into geometric problems. We show that one problem is strongly related to the Fermat-point of a triangle. We present a solution that is well adapted to…
We describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It brings us to a…
We show that Euler's relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations…
We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric function field Gamma-function are explained…
The elliptic gamma function is a generalization of the Euler gamma function. Its trigonometric and rational degenerations are the Jackson q-gamma function and the Euler gamma function. We prove multiplication formulas for the elliptic gamma…
The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formul\ae\ for Gauss' hypergeometric functions. We define the tau-function of such a system as the…
In this paper, we consider a subclass of starlike functions associated with a vertical strip domain. Several results concerned with integral representations, convolutions, and coefficient inequalities for functions belonging to this class…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
We study the $\Gamma$-convergence of the following functional ($p>2$) $$ F_{\epsilon}(u):=\epsilon^{p-2}\int_{\Omega}|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\epsilon^{\frac{p-2}{p-1}}}\int_{\Omega}W(u) d(x,\partial…
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
The Bombieri-Dwork conjecture predicts that the differential equations satisfied by $G$-functions come from geometry. In this paper, we will look at special $G$-functions whose differential equations have a special singularity with…
Two exact different solutions to the Telegraph equation in three-dimensional space are obtained in terms of Airy functions. As a result, these solutions unveil a distinctive propagation pattern along a coordinate that resembles a…
We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of $\Gamma$-convergence theory, in two steps: firstly, we…