Colimit theorems for coarse coherence with applications

Colimit Theorems for Relative Homotopy Groups

The first paper [10] (whose results were announced in [8]) developed the necessary ‘algebra of cubes’. Categories G of ω-groupoids and C of crossed complexes were defined, and the principal result of [10] was an equivalence of categories γ : G → C. Also established were a version of the homotopy addition lemma, and properties of ‘thin’ elements, in an ω-groupoid. In particular it was proved tha...

Coarse Function Value Theorems

Coarse functions are functions whose graphs appear to be continuous at a distance, but in fact may not be continuous. In this paper we explore examples and properties of coarse functions. We then generalize several basic theorems of continuous functions which apply to coarse functions.

Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

Coarse-grain Coherence Tracking

Extension theorems for plate elements with applications

Extension theorems for plate elements are established. Their applications to the analysis of nonoverlapping domain decomposition methods for solving the plate bending problems are presented. Numerical results support our theory.