Related papers: On identity theorem for real functions
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…
In the paper new representations are obtained for duals and dual hulls of the classes of analytic functions. The Ruscheweyh duality principle is shown to hold under somewhat weaker assumptions. For a compact class of functions its subclass…
We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant and the case of…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is…
It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions…
Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…
The definition of similarity is a key prerequisite when analyzing complex data types in data mining, information retrieval, or machine learning. However, the meaningful definition is often hampered by the complexity of data objects and…
We show that a function is real analytic at the origin iff it is arc-analytic, has a subanalytic graph, and its restriction to every monomial curve is analytic. This complements recent results of Kucharz and Kurdyka.
A statistical algorithm for categorizing different types of matches and fraud in image databases is presented. The approach is based on a generative model of a graph representing images and connections between pairs of identities, trained…
One-parameter smooth families of circles in the complex plane with the following property are described: a function is polyanalytic if and only if it has meromorphic extension inside any circle from the family, with the only singularity-a…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane C have uniformly perfect attractor sets. Examples are given to illustrate the main theorem, as well as to indicate…
We report on a verification of the Fundamental Theorem of Algebra in ACL2(r). The proof consists of four parts. First, continuity for both complex-valued and real-valued functions of complex numbers is defined, and it is shown that…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…