Related papers: Is the function 1/x continuous at 0?
Uninorms with continuous underlying t-norm and t-conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown. This set is proved to be a subset of the graph of a special symmetric, surjective,…
A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both the drift and volatility of the driving process. At a technical level, the analysis requires a…
If a vertex in a graph can be deleted without affecting distances among the other vertices, we shall say it is distance-redundant. Graphs with all, some or no such vertices are discussed. (The latter class was termed distance-critical by…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
In this article, we study finite dynamical systems defined over graphs, where the functions are applied asynchronously. Our goal is to quantify and understand stability of the dynamics with respect to the update sequence, and to relate this…
One of the ways that connectedness has been studied through the history of topology is by using chains, the so called chain connectedness. Here we combine this notion together with continuity up to a covering to provide the inheritance of…
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…
We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal…
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
We survey known results related to nowhere-zero flows and related topics, such as circuit covers and the structure of circuits of signed graphs. We include an overview of several different definitions of signed graph colouring.
The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are…
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has been extended and generalized in various…
We define the indefinite logarithm [log x] of a real number x>0 to be a mathematical object representing the abstract concept of the logarithm of x with an indeterminate base (i.e., not specifically e, 10, 2, or any fixed number). The…
Let $X$ and $Y$ be topological spaces, let $Z$ be a metric space, and let $f: X\times Y\to Z$ be a mapping. It is shown that when $Y$ has a countable base $\mathcal B$, then under a rather general condition on the set-valued mappings $X\ni…
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
In this work, topological spaces are enriched by additional structures in order to give a more realistic representation of real life phenomena and computational processes and at the same time, to provide for utilization of the powerful…
For topological spaces $X$ and $Y$, a (not necessarily continuous) function $f:X \rightarrow Y$ naturally induces a functor from the category of closed subsets of $X$ (with morphisms given by inclusions) to the category of closed subsets of…