Two-weight and three-weight linear codes based on Weil sums

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their weight distributions are determined using Weil sums. Some of the linear codes obtained are optimal or almost optimal with respect to the Griesmer bound.     

关于连续Domain权的进一步结果

在连续格理论的基础上探索连续Domain的权与相应Scott拓扑空间的权之间的关系，并进一步讨论其与相应的Lawson拓扑空间的权之间的关系，最后给出在连续Domain中W（P）＝W（∑P）=W（AP）的结论。     

Multiobjective design of survivable IP networks

Modern communication networks often use Internet Protocol routing and the intra-domain protocol OSPF (Open Shortest Path First). The routers in such a network calculate the shortest path to each destination and send the traffic on these paths, using load balancing. The issue of survivability, i.e. the question of how much traffic the network will be able to accommodate if components fail, is increasingly important. We consider the problem of designing a survivable IP network, which also requires determining the routing of the traffic. This is done by choosing the weights used for the shortest path calculations.     

A WEIGHTED ESTIMATE OF THE HORMANDER MULTIPLIER ON THE HEISENBERG GROUP

In this article, the authors prove the weighted boundedness of Hormander-type multiplier on the Heisenberg group.     

Core blocks of Ariki–Koike algebras

We examine blocks of the Ariki–Koike algebra, in an attempt to generalise the combinatorial representation theory of the Iwahori–Hecke algebra of type A. We identify a particular type of combinatorial block, which we call a core block, which may be viewed as an analogue of a simple block of the Iwahori–Hecke algebra. We give equivalent characterisations of core blocks and examine their basic combinatorics.     

Special linear combinations of orthogonal polynomials

The paper lists a number of problems that motivate consideration of special linear combinations of polynomials, orthogonal with the weight p(x) on the interval (a,b). We study properties of the polynomials, as well as the necessary and sufficient conditions for their orthogonality. The special linear combinations of Chebyshev orthogonal polynomials of four kinds with absolutely constant coefficients hold a distinguished place in the class of such linear combinations.     

A version of Wiener’s and Lévy’s theorems

We obtain weighted algebra analogues of the classical theorems of N. Weiner and P. Lévy on absolutely convergent Fourier series      

On a reverse Hardy-Littlewood-Polya's inequality

By the use of the weight coefficients, the idea of introduced parameters and Euler-Maclaurin summation formula, a reverse Hardy-Littlewood-Polya''s inequality with parameters as well as the equivalent forms are provided. The equivalent statements of the best possible constant factor related to a few parameters and some particular cases are given.     

Promoting symmetric weight selection in data envelopment analysis: A penalty function approach

Traditionally, data envelopment analysis models assume total flexibility in weight selection, though this assumption can lead to several variables being ignored in determining the efficiency score. Existing methods constrain weight selection to a predefined range, thus removing possible feasible solutions. As such, in this paper we propose the symmetric weight assignment technique (SWAT) that does not affect feasibility and rewards decision making units (DMUs) that make a symmetric selection of weights. This allows for a method of weight restrictions that does not require preference constraints on the variables. Moreover, we show that the SWAT method may be used to differentiate among efficient DMUs.