相关论文: WDVV and DZM
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
In this paper we develop the analytic theory of a multiple zeta function in d independent complex variables defined over a global function field. This is the function field analog of the Euler-Zagier multiple zeta function of depth d.
In this paper, we study specific families of multiple zeta values which closely relate to the linear part of Kawashima's relation. We obtain an explicit basis of these families, and investigate their interpolations to complex functions. As…
This short note presents some variant schemes of boundary variation diminishing (BVD) algorithm in one dimension with the results of numerical tests for linear advection equation to facilitate practical use. In spite of being presented in…
The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper…
We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including…
Proper inclusion of van der Waals (vdW) interactions in theoretical simulations based on standard density functional theory (DFT) is crucial to describe the physics and chemistry of systems such as organic and layered materials. Many…
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We prove that, for any $d$ linearly independent functions from some set into a $d$-dimensional vector space over any field, the family of zero sets of all non-trivial linear combination of these functions has VC-dimension and Littlestone…
Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
It is revealed that there exist duality families of the KdV type equation. A duality family consists of an infinite number of generalized KdV (GKdV) equations. A duality transformation relates the GKdV equations in a duality family. Once a…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We have proved that the solution of the KZ system is rational when k is equal to two and n is equal to three (see…
This note is a survey of results on the function $F_{\mathbf{k}}(z)$ introduced by G. Kawashima, and its applications to the study of multiple zeta values. We stress the viewpoint that the Kawashima function is a generalization of the…
We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
We associate ergodic properties to some subsets of the natural numbers. For any given family of subsets of the natural numbers one may study the question of occurrence of certain "algebraic patterns" in every subset in the family. By…
A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…