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We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are…
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Understanding issues involved in expertise in physics problem solving is important for helping students become good problem solvers. In part 1 of this article, we summarize the research on problem-solving relevant for physics education…
In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak…
In this paper I present a brief survey of the active area of Special Functions associated with Root Systems. The article is intended for a general mathematical audience. It will not suppose prerequisites on either special functions or root…
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the S-spectrum has applications, for example, in the formulation…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…