Necessary conditions for near-edge stick of complete contacts

Sufficient conditions for maximally edge-connected and super-edge-connected

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

Complete wetting near an edge of a rectangular-shaped substrate.

We consider fluid adsorption near a rectangular edge of a solid substrate that interacts with the fluid atoms via long range (dispersion) forces. The curved geometry of the liquid-vapour interface dictates that the local height of the interface above the edge ℓ(E) must remain finite at any subcritical temperature, even when a macroscopically thick film is formed far from the edge. Using an inte...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

New Necessary Conditions for

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of ρ-Mixing Random Variables

In many stochastic models, the assumption that random variables are independent is not plausible. So it is of interest to extend the concept of independence to dependence cases. One of these dependence structures is ρ∗-mixing. Let {Xn, n ≥ 1} be a sequence of random variables defined on a probability space Ω,F, P , and let Fm n denote the σ-algebra generated by the random variables Xn,Xn 1, . ....