We consider a sequence of independent and identicaly distributed (iid) random variables with absolutely continuous distribution function F(x) and probability density function (pdf) f(x). Let Rnl be the largest observation after observing nth record and R(ns) be the smallest observation after observing the nth record. Then we say Wnr = Rnl− R(ns), n > 1, as the nth record range. We will c...

The cohomology of operator algebras introduced by B. E. Johnson, R. V. Kadison, and J. R. Ringrose in a series of three papers is a useful tool for obtaining new invariants for operator algebras or to prove stability results by the vanishing of their cohomology groups (see [14]). If X is a von Neumann algebra and a Banach bimodule over M, and if « is a positive integer, then the nth cohomology ...

Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the nth roots of unity. Based on these data, how can we approximately evaluate f(z) or f (m)(z) at a point z in the disk? How can we calculate the zeros or poles of f in the disk? These questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integ...

In this paper‎, ‎we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $mathcal{S}^{*}(alpha),$ $mathcal{K}(alpha),$ $mathcal{M}(beta),$ $mathcal{N}(beta)$ and $mathcal{KD}(mu,beta).$‎

introduction: this study compared apical dye penetration using lateral condensation technique (lc) and lc technique with a reciprocal handpiece (mechanical lateral condensation or mlc) as a new method. materials and methods: forty-eight human extracted straight canine teeth were used. after crown amputation, the teeth were randomly divided into four experimental groups of 10 teeth each and two ...

We explicitly compute all the slopes of the Hecke operator U2 acting on overconvergent 2-adic level 1 cusp forms of weight 0: the nth slope is 1 + 2v((3n)!/n!), where v denotes the 2-adic valuation. We formulate an explicit conjecture about what these slopes should be for weight k forms.