Related papers: Multivalued Functions in Digital Topology

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.

In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

Clustering is one of the most common tasks of Machine Learning. In this paper we examine how ideas from topology can be used to improve clustering techniques.

We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous for the Euclidean topology. We further study this type of functions which…

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.

This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common…

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…

We characterize the valuations on the space of quasi-concave functions defined on the $N$-dimensional Euclidean space, that are rigid motion invariant and continuous with respect to a suitable topology. Among them we also provide a specific…

We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…

Let A be a closed polar subset of a domain D in the complex plane C. We give a complete description of the pluripolar hull in D X C of the graph of a holomorphic function defined on D A. To achieve this, we prove for pluriharmonic measure…

Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…

We make an estimation of the support of a multivariable scaling function for an arbitrary dilation matrix. We give a method of calculating the values of the scaling function on a tight set using the knowledge of the size of the support.

In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.

We explore a new form of DFT, which we call the Polynomial Transform. It functions over finite fields, and a size $n$ transform takes $O(n)$ operations. In the multitape Turing machine model, it allows us to multiply two $n$ bit numbers in…

In the space of bounded real-valued functions on the interval $(0,1)$, we study the convergent sequences of $q$-analogues of multiple zeta values which do not converge to $0$. And we obtain the derived sets of the set of some $q$-analogue…

We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…

We study the space of vector-valued (twisted) conjugate invariant functions on a connected reductive group.

Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…