Related papers: Refined Holonomic Summation Algorithms in Particle…
In this thesis, a new class of algorithms based on Sums of Squares Programming is developed. These allow to reduce a degree-$d$ homogeneous polynomial $T = \sum_{i = 1}^m \langle a_i, X \rangle^d $ to a quadratic form being close to a…
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…
In this work, simple exact results are presented for summations in two-particle potential with long-range interactions. Polygamma function is used to evaluate summations. Results are found when a periodic media is consider. Periodic…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…
Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The recursion formulas for these sums are derived, which are easily…
A new simulation package, GSEIM, for solving a set of ordinary differential equations is presented. The organisation of the program is illustrated with the help of a block diagram. Various features of GSEIM are discussed. Two ways of…
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptability but lacking spectral constraints, and spectral-based…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
This paper introduces ReflectSumm, a novel summarization dataset specifically designed for summarizing students' reflective writing. The goal of ReflectSumm is to facilitate developing and evaluating novel summarization techniques tailored…
The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version (Nikitin, et al. JQSRT, 2003, pp. 239--249) was especially designed for separate or…
Molecular simulation is a scientific tool dealing with challenges in material science and biology. This is reflected in a permanent development and enhancement of algorithms within scientific simulation packages. Here, we present…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
This article describes the REDUCE package ZEILBERG implemented by Gregor St\"olting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of…
Cosmic-ray acceleration processes in astrophysical plasmas are often investigated with fully-kinetic or hybrid kinetic numerical simulations, which enable us to describe a detailed microphysics of particle energization mechanisms. Tracing…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…