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A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most…
We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.
As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…
We prove some theorems on decomposable continua. In particular, we prove; (i) the property of being a Wilder continuum is not a Whitney reversible property, (ii) inverse limits of D**-continua with surjective monotone upper semi-continuous…
We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.
In this paper, we have investigated the generalized Wiener space of bounded variation with $p$-variable. Various results are obtained such as uniform convexity and reflexivity, there was characterized the set of points of discontinuity of…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…
Extends previous work on block-partitioned mixed generalized inverses from two subsets of system variables with distinct consistency requirements to three subsets. Does not include any notable theoretical contributions.
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…
A generalization of the notion of an $\infty$-category is presented, allowing for ($\infty$-)cat(egorie)s that may have non-invertible higher morphisms.
We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.