in this paper, we extend and generalize some recent results on the strong laws of large numbers (slln) for pairwise independent random variables [3]. no assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). also chandra’s result on cesàro uniformly integrable r.v.’s is extended.

We prove that on a punctured oriented surface with Euler characteristic χ < 0, the maximal cardinality of a set of essential simple arcs that are pairwise nonhomotopic and intersecting at most once is 2|χ|(|χ|+1). This gives a cubic estimate in |χ| for a set of curves pairwise intersecting at most once on a closed surface. We also give polynomial estimates in |χ| for sets of arcs and curves pai...

A pseudocircle is a simple closed curve on the sphere or in the plane. The study of arrangements of pseudocircles was initiated by Grünbaum, who defined them as collections of simple closed curves that pairwise intersect in exactly two crossings. Grünbaum conjectured that the number of triangular cells p3 in digon-free arrangements of n pairwise intersecting pseudocircles is at least 2n−4. We p...

In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβopen sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the charact...

In this paper, the use of weighted pairwise likelihood instead of the full likelihood in estimating the parameters of the multivariate AR(1) is investigated. A closed formula for typical elements of the Godambe information (sandwich information) is presented. Some efficiency calculations are also given to discuss the feasibility and computational advantages of the weighted pairwise likelihood a...

A long standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least (1− o(1))n. We confirm the above conjecture in several important cases, including the case (1) when all curves are convex, and (2) when the f...

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.

In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.