‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

We present a simplified randomized incremental construction (RIC) for the Hausdorff Voronoi diagram of non-crossing point-clusters. Our algorithm comes in two variants: using a conflict graph and a history graph, respectively. Both variants have O(n log n + k log n log k) expected time complexity and require expected O(n) space, where k is the number of clusters and n is the total number of poi...

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices that are not themselves rank-deficient, but have off-diagonal blocks that are; specifically, the class of so called Hierarchically Semi-Separable (HSS) matric...

recently, offshore and ocean engineering have been dealing with novel materials that play a significant role in reducing the weight of structures used in the ship construction industry. 5xxx series of aluminum alloys are of the novel alloys are suitable for construction of ship hulls and the topside structures of offshore platforms. within different 5xxx aluminum alloys, aa5083 is of great impo...

Christopher J.C. Burges Advanced Technologies, Bell Laboratories, Lucent Technologies Holmdel, New Jersey [email protected] We show that the recently proposed variant of the Support Vector machine (SVM) algorithm, known as v-SVM, can be interpreted as a maximal separation between subsets of the convex hulls of the data, which we call soft convex hulls. The soft convex hulls are controlled by ch...

Most of the earlier work on clustering has mainly been focused on numerical data whose inherent geometric properties can be exploited to naturally define distance functions between data points. Working only on numeric values prohibits it from being used to cluster real world data containing categorical values. Recently, the problem of clustering categorical data has started drawing interest. Th...

In the polynomial approach to systems control, the static output feedback problem can be formulated as follows: given two polynomial matrices D(s) and N(s), nd a constant matrix K such that polynomial matrix D(s) + KN(s) is stable. In this paper, we show that solving this problem amounts to solving a linear matrix inequality with a non-convex rank constraint. Several numerical experiments illus...

We fully characterize quasiconvex hulls for three arbitrary solenoidal (divergence free) wells in dimension three. With this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic twodimensional planes and convex in (up to three) rank-2 directions within the planes. Within the framework of the theory of compensated compactness, the latter represe...

This paper is concerned with the eigenvalue decay of the solution to operator Lya-punov equations with right-hand sides of finite rank. We show that the kth eigenvalue decays exponentially in √ k, provided that the involved operator A generates an exponentially stable continuous semigroup, and A is either self-adjoint or diagonalizable. Numerical experiments with discretizations of 1D and 2D PD...