Related papers: Functional identities and their applications
This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…
Foster's network theorems and their extensions to higher orders involve resistance values and conductances. We establish identities concerning voltage values and conductances. Our identities are analogous to the extended Foster's…
Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval $[0,1]$. While existing literature often focuses on a limited number of families, in the…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
The article describes interesting nonlinear differential identities satisfied by standard exponential and trigonometric functions, which appeared as byproducts of medical imaging research. They look like some kind of non-commutative…
Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
Subject of present paper is the review of results of authors on foliation theory and applications of foliation theory in control systems. The paper consists of two parts. In the first part the results of authors on foliation theory are…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
After defining in detail the Lambert $W$-function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geometrically convergent series for all the branches. In doing so,…
We introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations…
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
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…
This paper presents the basic ideas and properties of elliptic functions and elliptic integrals as an expository essay. It explores some of their numerous consequences and includes applications to some problems such as the simple pendulum,…
We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…
In this paper two identities involving a function defined by the complete elliptic integrals of the first and second kinds are proved. Some functional inequalities and elementary estimates for this function are also derived from the…
This book concentrates on functional analysis. The text is written so that it can be followed on the basis of high school mathematics. The book introduces the set theoretical foundations of mathematics, the basic theories of linear algebra…