Related papers: Calculus of linear extensions and Newton interpola…
We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first…
An analog of the Gelfand--Shilov estimate of the matrix exponential is proved for Green's function of the problem of bounded solutions of the ordinary differential equation $x'(t)-Ax(t)=f(t)$.
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
The 1/N expansion can be successfully used to calculate the Green functions of the two-dimensional O(2N) Gross - Neveu model. In parallel, the methods of analytic perturbation theory are also applied. Comparing the results of these two…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
Linear and nonlinear optical effect has been widely discussed in large quantity of materials using theoretical or experimental methods. Except linear optical conductivity, higher-order nonlinear responses are not studied fully. Starting…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
In this paper we construct a generating polynomial over the rationals for the generic Newton polygon for the L function of exponential sums of the family of f = x^d+ a x^s parameterized by a, and prove some of its key properties. The…
A conjecture of Graham (repeated by Erd\H{o}s) asserts that for any set $A \subseteq \mathbb{F}_p \setminus \{0\}$, there is an ordering $a_1, \ldots, a_{|A|}$ of the elements of $A$ such that the partial sums $a_1, a_1+a_2, \ldots,…
Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation…
For each member $\mathcal{A}$ of a family of linear cycle sets whose underlying abelian group is cyclic of order a power of a prime number, we compute all the central extensions of $\mathcal{A}$ by an arbitrary abelian group.
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain…
We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial…