Related papers: Aggregation functions as lax morphisms of quantale…
In this paper we show how certain techniques of image processing, having different scopes, can be joined together under a common "algebraic roof".
Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
The generating function of the cumulants in random matrix models, as well as the cumulants themselves, can be expanded as asymptotic (divergent) series indexed by maps. While at fixed genus the sums over maps converge, the sums over genera…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
We consider composite functions in the elementary algebraic framework. Without any use of the Fourier transform, we find almost periodic orbits which suitably characterizes certain composite functions. In particular, we provide special…
Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is…
In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy…
The series of papers is devoted to the study of convergence for pairs of surfaces and smooth functions thereon. We model such pairs with varifolds and multiple-valued functions to capture their limits. In the present paper, we study Young…
We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in…
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…
$n$-Dimensional fuzzy sets are a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] increasingly ordered, called n-dimensional intervals. The set of n-dimensional intervals is denoted by…