in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

Second order regular variation is a reenement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 ? F which possesses second order regular variation, we discuss how this property is inherited by 1 ? F 2 and 1 ? F 2. We also discuss the relationship of central limit be...

We study a linear recursion with random Markov-dependent coefficients. In a “regular variation in, regular variation out” setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.

In this paper we study the distribution of eigenvalues of regular graphs , regular hypergraphs , and biregular bipartite graphs of given girth by considering the polynomials orthogonal with respect to the measures attached to the spectra of such graphs and to the continuous spectra of their ‘universal covers’ . Our estimates are tight for Biggs graphs and generalized polygons . We also give an ...

This paper investigates a discrete-time impatient customer queue with Bernoulli-schedule vacation interruption. The  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. Cost analysi...

One of the approaches to statistical machine translation is based on joint probability distributions over some source and target languages. In this work we propose to model the joint probability distribution by stochastic regular bi-languages. Specifically we introduce the stochastic k-testable in the strict sense bi-languages to represent the joint probability distribution of source and target...