Related papers: Functional identities and their applications
In this short article we present some properties regarding the order and the type of an entire function.
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
The paper discusses issues related to the use of faceted classifications in an online environment. The author argues that knowledge organization systems can be fully utilized in information retrieval only if they are exposed and made…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…
Name-passing calculi are foundational models for mobile computing. Research into these models has produced a wealth of results ranging from relative expressiveness to programming pragmatics. The diversity of these results call for…
In recent years, the concepts of ``diversity'' and ``inclusion'' have attracted considerable attention across a range of fields, encompassing both social and biological disciplines. To fully understand these concepts, it is critical to not…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
Fraud (swindling money, property, or authority by fictionizing, counterfeiting, forging, or imitating things, or by feigning other persons privately) forms its threats against public security and network security. Anti-fraud is essentially…
We consider functional ellipsoids in the sense defined by Ivanov and Nasz\'odi and we study the problem of constructing a decomposition of the identity similar to the one given by Fritz John in his fundamental theorem.
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…
Background: Understanding the distinction between function and role is vexing and difficult. While it appears to be useful, in practice this distinction is hard to apply, particularly within biology. Results: I take an evolutionary…
We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it…
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…