A word $w$ is called rich if it contains $| w|+1$ palindromic factors, including the empty word. We say that a can be extended in at least two ways there are distinct letters $x,y$ such $wx,wy$ rich. Let $R$ denote set of all words. Given $w\in R$, let $K(w)$ words $u\in K(w)$ then $wu\in R$ and $wu$ ways. $\omega(w)=\min\{| u| \mid u\in K(w)\}$ $\phi(n)=\max\{\omega(w)\mid w\in R\mbox{ }| w|=n...

In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.

Let D be an unbounded domain in R with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x)dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r...

Modeling of crack propagation by a finite element method under mixed mode conditions is of prime importance in the fracture mechanics. This article describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. Crack - growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress c...

modelling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. this paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion,...