Diameter 2 properties and convexity

Structural properties of graphs of diameter 2 and defect 2 ∗

Using eigenvalue analysis, it was shown by Erdös et al. that with the exception of C4, there are no graphs of diameter 2, maximum degree d and d vertices. In this paper, we prove a number of structural properties of regular graphs of diameter 2, maximum degree d and order d − 1.

Multimodularity, Convexity, and Optimization Properties

We investigate in this paper the properties of multimodular functions. In doing so we give alternative proofs for properties already established by Hajek, and we extend his results. In particular, we show the relation between convexity and multimodularity, which allows us to restrict the study of multimodular functions to convex subsets of Z m. We then obtain general optimization results for av...

Convexity Properties of Graamannians

Convexity Properties of Special Functions

Convexity properties are often useful in characterizing and nding bounds for special function and their zeros, as well as in questions concerning the existence and uniqueness of zeros in certain intervals. In this survey paper, we describe some work related to the gamma function, the q-gamma function, Bessel and cylinder functions and the Hermite function.

Some Properties of B-convexity

In this paper, we give a characteristic of B-convexity structures of finite dimensional B-spaces: if a finite dimensional B-space has the weak selection property then its B-convexity structure satisfies H-condition. We also get some relationships among B-convexity structures, selection property and fixed point property. We show that in a compact convex subset of a finite dimensional B-space sat...