Related papers: Darmon's Program: A survey
In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.
We derive a system of difference equations satisfied by the three-term recurrence coefficients of some families of discrete orthogonal polynomials.
Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn-Sham density functional theory…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
We formulate an exponential Diophantine equation, which is is some sense one order higher that Fermat's Last Theorem. We also give three examples of solutions to this exponential Diophantine equation and formulate a conjecture.
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…
In this paper, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on (Barkatou, 1997). A first step was set in…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the…
We provide a generalization of a problem first considered by Saffari and fully solved by Saffari, Erd\H{o}s and Vaughan on direct factor pairs, to arbitrary finite families of direct factors, and solve it using a method of Daboussi. We end…
We develop an arithmetic analogue of elliptic partial differential equations. The role of the space coordinates is played by a family of primes, and that of the space derivatives along the various primes are played by corresponding Fermat…
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
We present a generic technique, automated by computer-algebra systems and available as open-source software \cite{scuff-em}, for efficient numerical evaluation of a large family of singular and nonsingular 4-dimensional integrals over…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the…