Related papers: Arithmetic BF theory and the Cassels-Tate pairing
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a…
Moving from the mirror theory Bethe-Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe Ansatz equations which should control the spectrum of the planar $\text{AdS}_5/\text{CFT}_4$ correspondence. The…
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral…
We consider the pairing Hamiltonian and systematically construct its density functional in the strong-coupling limit and in the limit of large particle number. In the former limit, the functional is an expansion into central moments of…
This paper describes an axiomatic theory BT for constructive mathematics. BT has a predicative comprehension axiom for a countable number of set types and usual combinatorial operations. BT has intuitionistic logic, is consistent with…
In the first part of this paper we prove a conjecture of Hikami on the values of the radial limits of a family of $q$-hypergeometric false theta functions. Hikami conjectured that the radial limits are obtained by evaluating a truncated…
In this work we generalize the MacDowell-Mansouri theory of gravity using strict 2-groups. To achieve this, we construct the categorical generalization of the ISO(4,1) group, which we call the de Sitter 2-group. We then proceed to…
An extensive table of pairs of functions linked by the Legendre transformation is presented. Many special functions and formulas that are used in the sciences are included in the pairs. Formulations are provided for finding the Legendre…
In this article, we study the distribution of the irrational factor function of order $k$, introduced first by Atanassov for $k=2$ and later it was generalized by Dong et al. for all $k\geq 2$. We introduce the irrational factor function in…
The nature of the BA function and its adjoint for KP-Toda is traced through the averaging method in generating the Whitham equations, differentials, and symplectic forms, with connections to EM duality.
We present a worldline description of topological non-abelian BF theory in arbitrary space-time dimensions. It is shown that starting with a trivial classical action defined on the worldline, the BRST cohomology has a natural representation…
We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and…
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.
We prove, for an arbitrary finite root system, the periodicity conjecture of Al.B.Zamolodchikov concerning Y-systems, a particular class of functional relations arising in the theory of thermodynamic Bethe ansatz. Algebraically, Y-systems…
In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we…
Disanto, Ferrari, Pinzani and Rinaldi have introduced the concept of 'Catalan pair', which is a pair of partial orders (S,R) satisfying certain axioms. They have shown that Catalan pairs provide a natural description of objects belonging to…