We prove an O(nk 1=3) upper bound for planar k-sets. This is the rst considerable improvement on this bound after its early solutions approximately twenty seven years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k-levels in arrangements of line segments, k convex polygons in the union of n lines, parametric minimum spanning trees and p...

and Applied Analysis 3 Here are some useful examples of regularized quasi-semigroups. Example 2.2. Let {Tt}t≥0 be an exponentially bounded strongly continuous C-semigroup on Banach space X, with the generator A. Then K s, t : Tt, s, t ≥ 0, 2.5 defines a C-quasi-semigroup with the generator A s A, s ≥ 0, and so D D A . Example 2.3. Let X BUC R , the space of all bounded uniformly continuous func...

Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They specified by correlation matrix and map g, called density generator. While latter can easily be estimated from pseudo-samples observations, generator is harder estimate, especially when it does not belong parametric family. We give sufficient conditions non-parametrically identify this...

We prove that for any positive integers n and k such that n≥ k≥ 1, there exists an [n, k] generalized Reed-Solomon (GRS) code that has a sparsest and balanced generator matrix (SBGM) over any finite field of size q ≥ n+ ⌈ k(k−1) n ⌉, where sparsest means that each row of the generator matrix has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two c...

Extended Abstract. Let Xi1 ,..., Xini   ,i=1,2,3,....,k  be independent random samples from distribution $F^{alpha_i}$،  i=1,...,k, where F is an absolutely continuous distribution function and $alpha_i>0$ Also, suppose that these samples are independent. Let Mi,ni and  M'i,ni  respectively, denote the maximum and minimum of the ith sa...

It is known that extremal doubly-even self-dual codes of length n ≡ 8 or 0 (mod 24) yield 3or 5-designs respectively. In this paper, by using the generator matrices of bordered double circulant doubly-even self-dual codes, we give 3-(n, k; m)-SEEDs with (n, k, m) ∈ {(32, 8, 5), (56, 12, 9), (56, 16, 9), (56, 24, 9), (80, 16, 52)}. With the aid of computer, we obtain 22 generator matrices of bor...

This paper presents a random generator of discrete event systems that are by construction kdiagnosable. The aim of this generator is to provide an almost infinite set of diagnosable systems for creating benchmarks. The goal of such benchmarks is to provide a solid set of examples to test and compare algorithms that solve many problems around diagnosable discrete event systems.