in this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (nd) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and e|x | f | =0 , f = ?(x ,…, x ) for every n>l.

We deal with a variant of the well-known Longest Common Subsequence (LCS) problem for weighted sequences. A (biological) weighted sequence determines the probability for each symbol to occur at a given position of the sequence (such sequences are also called Position Weighted Matrices, PWM). Two possible such versions of the problem were proposed by (Amir et al., 2009 and 2010), they are called...

For a finite positive Borel measure μ on the unit circle, let D(μ) be associated harmonically weighted Dirichlet space. A shift invariant subspace M recognizes strong approximate spectral cosynthesis if there exists sequence of subspaces M_k, with codimension, such that orthogonal projections onto M_k converge in operator topology to projection M. If is sum atoms, then we show admits cosynthesis.

‎In this article‎, ‎we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I times I‎, ‎c)$ by applying measure of noncompactness‎ and Meir-Keeler condensing operators‎. By presenting an example, we have illustrated our results‎. ‎For validity of the results we introduce a modified semi-analytic method in the case of tw...

the paper describes an investigation about the application of the new multiple-impedance discontinuities model for optimizing profile diffuser barriers. the new multiple-impedance discontinuities model is much faster than the numerical method, thus it is used in an optimization process. the a-weighted insertion loss was used for the traffic noise spectrum. the result of optimization, which is d...

We investigate the existence of higher order `-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space X = T [( n;Sn) 1 n=1]: (1) Every block subspace of X contains an `1-S!-spreading model, (2) The Bourgain `-index Ib(Y ) = I(Y ) > ! ! for any block subspace Y of X, (3) limm lim supn m+n= n > 0 an...

We investigate the existence of higher order l-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space X = T [(θn,Sn) ∞ n=1]: (1) Every block subspace of X contains an l-Sω-spreading model, (2) The Bourgain l-index Ib(Y ) = I(Y ) > ω ω for any block subspace Y of X, (3) limm lim supn θm+n/θn > 0 an...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of first occurrence of the respective symbol in the original sequence. Since a pattern is the result of data processing on the original sequence, its entropy c...

Detecting the interleaving relationship between sequences has become important because of its wide applications to genomic and signal comparison. Given a target sequence T and two merging sequences A and B, recently Huang et al. propose algorithms for the merged LCS problem, without or with block constraint, whose aim is to find the longest common subsequence (LCS) with interleaving relationshi...