Related papers: A canonical form for some piecewise defined functi…
A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.
In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.
In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in…
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
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 propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
We give a canonical form of m-by-2-by-2 matrices for equivalence over any field of characteristic not two.
The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regular functions represent a generalization of the classical…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…
Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…
We give a canonical form for a complex matrix, whose square is normal, under transformations of unitary similarity as well as a canonical form for a real matrix, whose square is normal, under transformations of orthogonal similarity.
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
It is shown how piecewise differentiable functions $F: \mathbb R^n \mapsto \mathbb R^m $ that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points $\check x$ and $\hat…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…