In the summer of 2004, I participated in an REU program at East Tennessee State University. Many of the investigations I worked on were successful, leading to 4-6 papers, some of which have been submitted, and others are still in the writing process. There are many unanswered questions left in the investigations that I was conducting, and some of the work already done is not complete. Given tha...

We introduce the notion of a matron M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrons and its inverse, the universal enveloping functor. We define the free matron H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...

In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solutio...

The purpose of this paper is to introduce the concept of fuzzy variational-like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy variational-like inequalities in Hilbert spaces. By using the general auxiliary principle technique, Ky Fan’s KKM theorem, Nadler’s fixed point theorem, and some new analytic techniques, so...

We introduce the notion of a matron M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrons and its inverse, the universal enveloping functor. We define the free matron H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...