Related papers: Analytic Expressions and Bounds for Special Functi…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators…
Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed…
We provide the two fundamental sets of functional relations which describe the strong coupling limit of scattering amplitudes in $\mathcal{N} = 4$ SYM dual to Wilson loops in $AdS_3$: the basic $QQ$-system and the derived $TQ$-system. We…
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in…
We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may…
In this paper, we develop some basic techniques towards the Riemann hypothesis for higher rank non-abelian zeta functions of an integral regular projective curve of genus $g$ over a finite field $\mathbb F_q$. As an application of the…
The evaluation of integral transforms of special functions is required in different research and practical areas. Analyzing the $\kappa$-$\mu$ fading distribution also khown as the generalized Rician distribution, we find out that the…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis…
Existing works on the expressive power of neural networks typically assume real parameters and exact operations. In this work, we study the expressive power of quantized networks under discrete fixed-point parameters and inexact fixed-point…
Let $(-A,B,C)$ be a linear system in continuous time $t>0$ with input and output space ${\bf C}$ and state space $H$. The function $\phi_{(x)}(t)=Ce^{-(t+2x)A}B$ determines a Hankel integral operator $\Gamma_{\phi_{(x)}}$ on $L^2((0, \infty…
We use the Aubry-Perret bound for singular curves, a generalization of the Hasse-Weil bound, to prove the following curious result about rational functions over finite fields: Let $f(X),g(X)\in\Bbb F_q(X)\setminus\{0\}$ be such that $q$ is…
The optimized effective potential (OEP) approach has so far mainly been used in benchmark studies and for the evaluation of band gaps. In this work, we extend the application of the OEP by determining the analytical ionic forces within the…
We generalize some widely used mother wavelets by means of the q-exponential function $e_q^x \equiv [1+(1-q)x]^{1/(1-q)}$ ($q \in {\mathbb R}$, $e_1^x=e^x$) that emerges from nonextensive statistical mechanics. Particularly, we define…
The recently introduced independent fluctuating two-ray (IFTR) fading model, consisting of two specular components fluctuating independently plus a diffuse component, has proven to provide an excellent fit to different wireless…
We consider transmission over a wireless multiple antenna communication system operating in a Rayleigh flat fading environment with no channel state information at the receiver and the transmitter with coherence time T=1. We show that,…
This paper investigates the performance of terahertz~(THz) wireless systems over the $\alpha$-$\mathcal{F}$ fading channels with beam misalignment and mobility. New expressions are derived for the probability density, cumulative…
In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…