This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate lter banks and their applications to signal processing and especially compression. By their inherent structure, multiwavelets are t for processing multi-channel signals. First, we will recall some general results on multiwavelets and the convergence of the iterated matrix product. Then,...

The distance vector routing protocol satisfies the following property. If this protocol is used to route a sequence of data messages from a source to a destination, then these data messages will follow the same shortest-distance path from the source to the destination. In this paper, we show how to modify this protocol, without adding new messages, in order to satisfy the following load balanci...

Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than π/6 and strictly smaller than π/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (aff...

Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1 + o(1)) lnn/ ln lnn balls in it. Suppose instead that for each ball we choose two boxes at random and place the ball into the one which is less full at the time of placement. We show that with high probabili...

"Dipartimento di Matematica Pura ed Applicata, Universiti di Padova, Via Belzoni 7, 35131 Padova, Italy. tCarnegie Mellon University, Schenley Park, Pittsburgh, PA 15213. ICarnegie Mellon University, Schenley Park, Pittsburgh, PA 15213. §Indian Institute of Management, Bannerghatta rd. 560076 Bangalore, India. 1 Carnegie Mellon University, Schenley Park, Pittsburgh, PA 15213. This work was supp...

An additive cellular automaton is a linear map on the set of infinite multidimensional arrays of elements in a finite cyclic group Z/mZ. In this paper, we consider simplices appearing in the orbits generated from arithmetic arrays by additive cellular automata. We prove that they constitute a source of balanced simplices, that are simplices containing all the elements of Z/mZ with the same mult...

We develop a heuristic for a problem motivated by the loading of aircraft or trucks: pack blocks into a bin so that their center-of-gravity is as close as possible to a target point. Our heuristic either produces good solutions or else signals that none is possible. It also works when loading non-homogeneous blocks into a bin of non-zero and possibly non-

A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. We begin by establishing a less well-known companion result, which states that both of these quantities are equal to the number of partitions of n into even parts along with exactly one triangular part. We then introduce the characteristic of a partition, which is...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.