in the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. let be a double sequence of pairwise negatively dependent random variables. if for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). in addition, it also converges to 0 in . the res...

let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.

In spectral clustering and spectral image segmentation, the data is partioned starting from a given matrix of pairwise similarities S. the matrix S is constructed by hand, or learned on a separate training set. In this paper we show how to achieve spectral clustering in unsupervised mode. Our algorithm starts with a set of observed pairwise features, which are possible components of an unknown,...

We prove the following isoperimetric inequality in R, conjectured by Glazyrin and Morić. Given a convex body S and k pairwise disjoint convex bodies C1, . . . , Ck that are contained in S, then ∑k i=1 Per(Ci) ≤ Per(S) + 2(k − 1)Diam(S). Here Per(·) denotes the perimeter of a set and Diam(·) is the diameter of a set.

The concept of  somewhat pairwise fuzzy $alpha$-irresolute continuous mappings and somewhat pairwise fuzzy irresolute $alpha$-open mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.

An important problem in multiresolution analysis of signals and images consists in restoring continuous hidden random variables x = {xs}s∈S from observed ones y = {ys}s∈S . This is done classically in the context of Hidden Markov Trees (HMT). HMT have been generalized recently to Pairwise Markov Trees (PMT). In this paper we propose a smoothing restoration algorithm for Gaussian PMT.

Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...