Physical Sciences and Mathematics Commons^™

Poincaré Types Solutions Of Systems Of Difference Equations, Raghib Abu-Saris, Saber Elaydi, Sophia Jang

Mathematics Faculty Research

No abstract provided.

An Extension Of The Fundamental Theorem Of Linear Programming, A Brown, A Gedlaman, Allen G. Holder, S Martinez

Mathematics Faculty Research

In 1947 George Dantzig developed the Simplex Algorithm for linear programming, and in doing so became known as The Father of Linear Programming. The invention of the Simplex Algorithm has been called "one of the most important discoveries of the 20th century," and linear programming techniques have proven useful in numerous fields of study. As such, topics in linear optimization are taught in a variety of disciplines. The finite convergence of the simplex algorithm hinges on a result stating that every linear program with an optimal solution has a basic optimal solution; a result known as the Fundamental Theorem of …

On The Number Of Factorizations Of An Element In An Atomic Monoid, Scott T. Chapman, Juan Ignacio García-García, Pedro A. García Sánchez, José Carlos Rosales

Mathematics Faculty Research

Let S be a reduced commutative cancellative atomic monoid. If s is a nonzero element of S, then we explore problems related to the computation of η(s), which represents the number of distinct irreducible factorizations of s∈S. In particular, if S is a saturated submonoid of N^d, then we provide an algorithm for computing the positive integer r(s) for which

0 < limn→∞η(sⁿ)n^r(s)-1∞.

We further show that r(s) is constant on the Archimedean components of S. We apply the algorithm to show how to …

Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu

Mathematics Faculty Research

In this article, we prove that in connected metric spaces k - cycles are not globally attracting (where k>2). We apply this result to a two species discrete-time Lotka-Volterra competion model with stocking. In particular, we show that an k-cycle cannot be the ultimate life-history of evolution of all population sizes. This solves Yakubu's conjecture but the question on the structure of the boundary of the basins of attraction of the locally stable n-cycles is still open.