A multigraph M with maximum degree (M) is called critical, if the chromatic index 0 (M) > (M) and 0 (M ? e) = 0 (M) ? 1 for each edge e of M. The weak critical graph conjecture 1, 7] claims that there exists a constant c > 0 such that every critical multigraph M with at most c (M) vertices has odd order. We disprove this conjecture by constructing critical multigraphs of order 20 with maximum d...

in the literature of life-testing, general progressive censoring has been studied extensively. but, all the results have been developed under the key assumption that the units undertest are independently distributed. in this paper, we study general progressively type-ii censored order statistics arising from identical units under test which are jointly distributed according to an archimedean co...

‎second derivative general linear methods (sglms) as an extension‎ ‎of general linear methods (glms) have been introduced to improve‎ ‎the stability and accuracy properties of glms‎. ‎the coefficients of‎ ‎sglms are given by six matrices‎, ‎instead of four matrices for‎ ‎glms‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually runge--kutta stability conditions‎. ‎in this p...

in this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. method is tested on problems to ensure the computational eciency. we have compared numerical results with results obtained by other method in literature. we conclude that propose method is computationally ecient and eective.

This dissertation considers a suite of search problems in which agents are trying to find goals in minimum expected time. Unlike search in data structures in which time is measured by a number operations, search in metric spaces measures time by units of distance and has received much less attention. In particular, search strategies that attempt to minimize expected search time are only availab...

By Doob’s theorem, supermartingales indexed by the natural numbers decompose into the difference of a uniformly integrable martingale and an increasing process. The relative ease of working with increasing processes rather than supermartingales explains the prominent role of this result in stochastic analysis and in the theory of stochastic integration. Meyer [19] then proved that, under the us...

Let G be a (molecular) graph with vertex set V 1⁄4 fv1;v2; . . . ;vng. Let dðv iÞ be the degree of the vertex v i 2 V . If the vertices v i1 ;v i2 ; . . . ;v ihþ1 form a path of length h;h P 1, in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif...

Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the RieszThorin interpolation theorem we get the corresponding results in Lp(R+), 1 ≤ p ≤ 2 for the Kontorovich-Lebedev, Mehler-Fock and Olevskii index transforms. An inversion theorem is proved for general index transformat...

Many results involving expected utility theory call upon the notions of absolute risk aversion, prudence and/or temperance. The present paper exploits a representation of the FriedmanSavage utility premium to give a general foundation for such coefficients and for their higherorder extensions.

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...