The aim of this paper is to present a proof of the hyperbolicity of the family $f_c(x)=c(x-frac{x^3}{3}), |c|>3$, on an its invariant subset of $mathbb{R}$.

In the transformation semigroup (X, S) we introduce the height of a closed nonempty invariant subset of X, define the transformed dimension of nonempty subset S of X and obtain some results and relations.

All yield criteria that determine the onset of plastic deformation in crystalline materials must be invariant under inversion symmetry associated with a simultaneous change sign slip direction and plane normal. We demonstrate consequences this on functional form effective stress, where only lowest order terms obey are retained. A particular criterion is obtained for do not Schmid law, hereafter...

Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

x-100 steel is one of the most recently developed materials for production of gas transportation pipelines. this material is severely anisotropic. smooth and notched round bars with different notch radius and flat notched specimens with different notch radius and notch depth in tension are tested to characterize the failure of this material under quasi-static loading condition. triaxiality fact...

Let X1 and X2 be two independent random variables from gamma populations Pi1,P2 with means alphaθ1 and alphaθ2 respectively, where alpha(> 0) is the common known shape parameter and θ1 and θ2 are scale parameters. Let X(1) ≤ X(2) denote the order statistics ofX1 and X2. Suppose that the population corresponding to the largest X(2) (or the smallest X(1)) observation is selected. The problem ofin...

In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invari...

In this paper we give some characterizations of topological extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative topological left invariant mean then T is topological left lumpy if and only if there is a multiplicative topological left invariant mean M on M(S)* ...

Evidence suggests that slip in earthquakes and the resultant stress changes are spatially heterogeneous. If crustal stress from past earthquakes is spatially heterogeneous, then earthquake focal mechanisms should also be spatially variable. We describe the statistical attributes of simulated earthquake catalogs, including hypocenters and focal mechanisms, for a spatially 3D, time-varying model ...