Related papers: Real Functions and its Differentiation in Alternat…
The concept of monogenic functions over real alternative $\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and…
This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
We consider thermal $n$-point Green functions in the framework of quantum field theory at finite temperature. We show how analytic continuations from imaginary to real energies relate these functions originally defined in the imaginary-time…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…
Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example,…
We established order-preserving versions of the basic principles of functional analysis such as Hahn-Banach, Banach-Steinhaus, open mapping and Banach-Alaoglu theorems.
Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…
We continue the analysis in [3] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [5]. We amend and improve some…
Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
While automata theory often concerns itself with regular predicates, relations corresponding to acceptance by a finite state automaton, in this article we study the regular functions, such relations which are also functions in the…
Methods of construction of the composition function, left- and right-invariant vector fields and differential 1-forms of a Lie group from the structure constants of the associated Lie algebra are proposed. It is shown that in the second…
In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous,…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…
We study higher rank Jacobi partial and false theta functions (generalizations of the classical partial and false theta functions) associated to positive definite rational lattices. In particular, we focus our attention on certain Kostant's…
The paper starts out from pseudomeasures (in the sense of Serre) which hold the arithmetic properties of the abelian $l$-adic Artin $L$-functions over totally real number fields. In order to generalize to non-abelian $l$-adic $L$-functions,…
A process of extending sets which can be used as foundation for an alternative organization for Differential and Integral Calculus is presented.