Related papers: Applications of a duality between generalized trig…
We prove that, under certain assumptions, generalized Hilbert-Kunz multiplicities can be expressed as linear combinations of classical Hilbert-Kunz multiplicities.
We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and…
A study of sigma models whose target space is a group G that admits a compatible Poisson structure is presented. The natural action of O(D,D;Z) on the generalised tangent bundle TG+T*G and a generalisation of the Courant bracket that…
In this paper, usual Sturm-Liouville problems are extended for symmetric functions so that the corresponding solutions preserve the orthogonality property. Two basic examples, which are special cases of a generalized Sturm-Liouville…
In this work, we generalize the D'Aurizio-S\'andor inequalities (\cite{D'Aurizio,Sandor}) using an elementary approach. In particular, our approach provides an alternative proof of the D'Aurizio-S\'andor inequalities. Moreover, as an…
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's…
This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
This paper is devoted for the study of a new generalization of Struve function type. In this paper , We establish four new integral formulas involving the Galue type Struve function, which are express in term of the generalized (Wright)…
We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are…
In our previous paper, Real Polynomials with a Complex Twist [see http://archives.math.utk.edu/ICTCM/VOL28/A040/paper.pdf], we used advancements in computer graphics that allow us to easily illustrate more complete graphs of polynomial…
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…
Let $\alpha\in(1,\infty)$ and $\mu$ be a regular finite Borel measure on a locally compact abelian group. The paper deals with a general trigonometric approximation problem in $L^\alpha(\mu)$, which arises in prediction theory of…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.
Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…
The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings P1-to-P1. This…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…