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We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation…
Given an entire transcendental function f with a non-completely invariant Baker domain, we define a Baker lamination on geodesics to study the divergence and convergence of a pinching process of curves in U. If the boundary of some curve in…
We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above…
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne,…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a survey on fundamental operations for various kinds of discrete…
Convexity plays a prominent role in a number of problems, but practical considerations frequently give rise to non-convex functions. We suggest a method for determining convex regions, and also for assessing the lack of convexity in the…
For any given Cuntz semigroup, we introduce a function associated to it, called the ``Rank Ratio Function". This function ensures global control over the oscillation of the rank of any pair of elements in the Cuntz semigroup and, also,…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
We examine the effect of numerical integration on the convergence of high order pyramidal finite element methods. Rational functions are indispensable to the construction of pyramidal interpolants so the conventional treatment of numerical…
A "Bochner-type" integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
In this note we study numerically the combinatorics of curves and geodesics on the torus with one boundary component. A potential computational difficulty is avoided by counting inside specific orbits of the mapping class group up to a…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
In numerical integration, cubature methods are effective, especially when the integrands can be well-approximated by known test functions, such as polynomials. However, the construction of cubature formulas has not generally been known, and…