A subtree of a tree is any induced subgraph that again (i.e., connected). The mean order the average number vertices its subtrees. This invariant was first analyzed in 1980s by Jamison. An intriguing open question raised Jamison asks whether maximum order, given tree, always attained some caterpillar. While we do not completely resolve this conjecture, find evidence favor proving different feat...

suppose that  is a finite group. then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . suppose that . then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . in this paper, we prove that if  is a group such that , where , then . here  denotes the family of suzuk...

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

the cracked brazilian disc (cbd) specimen is widely used in order to determine mode-i/ii and mixed-mode fracture toughness of a rock medium. in this study, the stress intensity factor (sif) on the crack-tip in this specimen is calculated for various geometrical crack conditions using the extended-finite element method (x-fem). this method is based upon the finite element method (fem). in this m...

Finite element simulation of stretch flanging process was carried out in order to investigate the effect of process parameters on maximum thinning (%) in stretch flanging process. Influences of initial flange length, punch die clearance, width of sheet metal blank and blank holding force were investigated on maximum thinning (%). Finite element simulation was done using FEM software package ABA...

In this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane. We introduce a general approach for connecting these methods with finite element method analysis. This unified approach is used to prove known convergence results in the H1, L2 norms and new results in the max-norm. For the elliptic ...

This paper studies the application of an inverse methodology for problem solving in fracture mechanics using the finite element analysis. The method was applied to both detection of subsurface cracks and the study of propagating cracks. The procedure for detection of subsurface cracks uses a first order optimization analysis coupled with a penalty function to solve for the unknown geometric par...

Let F be a family of subsets of an n-element set not containing four distinct members such that A∪B ⊆ C∩D. It is proved that the maximum size of F under this condition is equal to the sum of the two largest binomial coefficients of order n. The maximum families are also characterized. A LYM-type inequality for such families is given, too.

We develop a generalized method of moments (GMM) estimator for the distribution of a variable where summary statistics are available only for intervals of the random variable. Without individual data, one cannot calculate the weighting matrix for the GMM estimator. Instead, we propose a simulated weighting matrix based on a first-step consistent estimate. When the functional form of the underly...