Suppose $f$ is a map from a non-empty finite set $X$ to a finite group $G$. Define the map $zeta^f_G: Glongrightarrow mathbb{N}cup {0}$ by $gmapsto |f^{-1}(g)|$. In this article, we show that for a suitable choice of $f$, the map $zeta^f_G$ is a character. We use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin G$) is a character, where $w(t_1,...

In transportation via containers, unbalanced movement of loaded containers forces shipping companies to reposition empty containers. This study addresses the problem of empty container repositioning (ECR) in the distribution network of a European logistics company, where some restrictions impose decision making in an uncertain environment. The problem involves dispatching empty contain...

We study the relationships between weakened forms of the Kinna-Wagner Selection Principle (KW), the Axiom of Choice (AC), and the Axiom of Multiple Choice (MC). Introduction. In this paper we study the relationships between weakened forms of the Kinna-Wagner Selection Principle (KW), the Axiom of Choice (AC), and the Axiom of Multiple Choice (MC). The forms of these statements that we shall use...

We follow the rules: D is a non empty set, f1, f2 are finite sequences of elements of D, and i, n, n1, n2, n3, n4, n5, n6 are natural numbers. We now state two propositions: (1) If n ¬ len f1, then (f1 a f2)⇂n = ((f1)⇂n) a f2. (2) (f1 a f2)↾(len f1 + i) = f1 a (f2↾i). A Gene-Set is a non-empty non empty finite sequence. Let S be a Gene-Set. We introduce GA− SpaceS as a synonym of UnionS. Let f ...

The aim of the paper is to show that the only subcontinua of the Jordan curve are arcs, the whole curve, and singletons of its points. Additionally, it has been shown that the only subcontinua of the unit interval I are closed intervals. [9] provide the notation and terminology for this paper. 1. PRELIMINARIES One can check that every simple closed curve is non trivial. Let T be a non empty top...