We propose a matrix approach to the computation of BattleLemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m . The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m . We approximate this bi-infinite ma...

In this paper we analyze the bi-conjugate gradient algorithm in finite precision arithmetic, and suggest reasons for its often observed robustness. By using a tridiagonal structure, which is preserved by the finite precision bi-conjugate gradient iteration, we are able to bound its residual norm by a minimum polynomial of a perturbed matrix (i.e. the residual norm of the exact GMRES applied to ...

Total clan games are characterized using monotonicity, veto power of the clan members, and a concavity condition re°ecting the decreasing marginal contribution of non-clan members to growing coalitions. This decreasing marginal contribution is incorporated in the notion of a bi-monotonic allocation scheme, where the value of each coalition is divided over its members in such a way that the clan...

The quadratic assignment problem (QAP) was first proposed by Koopmans and Beckman [5] in the context of the plant location problem. Given n facilities, represented by the set F f1 fn , and n locations represented by the set L l1 ln , one must determine to which location each facility must be assigned. Let An n ai j be a matrix where ai j represents the flow between facilities fi and f j. Let Bn...

The three active light neutrinos are used to explain the neutrino oscillations. The inherently bi-large mixing neutrino mass matrix and the Fritzsch type, bi-small mixing charged lepton mass matrix are assumed. By requiring the maximal νμ − ντ mixing for the atmospheric neutrino problem and the masssquared difference approperiate for the almost maximal mixing solution to the solar neutrino prob...

where the transformation or supercell matrix M is nonsingular with integer components, which implies that the SC is commensurate to the pc. The determinant of M is the multiplicity N of the SC, i.e. the ratio of the respective volumes VSC/vpc. The hexagonal pc and orthorhombic SC of the two-dimensional honeycomb net is depicted in figure A.1a. In reciprocal space, there are consequently two dis...

A bi-component nanostructured system composed by a Co dot array embedded in a Ni80Fe20 antidot matrix has been prepared by means of the self-assembling polystyrene nanospheres lithography technique. Reference samples constituted by the sole Co dots or Ni80Fe20 antidots have also been prepared, in order to compare their properties with those of the bi-component material. The coupling between the...

I present parallel algorithms for finding the bridgeand bi-connected components of an undirected graph G = (V, E) with n vertices and e edges on an n 112 x n 112 mesh of processing elements. The algorithms find the bridge-co~nected components in o (n ) time for input both in the form of an adjacency matrix and in the form of edges. For bi-connectivity, I show how to achieve 0 (n 3/2) time when ...

The biclustering, co-clustering, or subspace clustering problem involves simultaneously grouping the rows and columns of a data matrix to uncover biclusters or sub-matrices of the data matrix that optimize a desired objective function. In coherent biclustering, the objective function contains a coherence measure of the biclusters. We introduce a novel formulation of the coherent biclustering pr...

Acknowledgement First and foremost I would like give my best appreciation to my supervisor, Lexing Xie who offers a lot of support during the project development and composing this report. In the development process, she provides us a clear guidance of project direction and makes lots of useful suggestions towards problems encountered. Secondly, I would like show my thankfulness to my teammate ...