Weak uniqueness is established for the martingale problem associated to a family of catalytic branching networks. This martingale problem corresponds to a stochastic differential equation with a degenerate Hölder continuous diffusion matrix. Our approach uses the semigroup perturbation method of Stroock and Varadhan and a modification of a Banach space of weighted Hölder continuous functions in...

A novel noise subspace based method is applied to the minimum localization system using time-of-arrival (TOA) measurements from three base stations (BS). Since the distance measurement between the mobile station (MS) and the BS bears analogy to the multidimensional similarity (MDS) between their coordinates, we express the MS coordinate as the linear combination of the BSs’ coordinates, where t...

In this paper we consider the fundamental question of optimizing finite field multiplications with one fixed element. Surprisingly, this question did not receive much attention previously. We investigate which field representation, that is which choice of basis, allows for an optimal implementation. Here, the efficiency of the multiplication is measured in terms of the number of XOR operations ...

Maximal Distance Separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching 4×4 MDS matrices over GL(4,F2). By this algorithm, we find that all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices can be classified to 3 types, and some necessary and sufficient conditions are presented for them ...

It is known that maximum distance separable and maximum distance profile convolutional codes exist over large enough finite fields of any characteristic for all parameters (n, k, δ). It has been conjectured that the same is true for convolutional codes that are strongly maximum distance separable. Using methods from linear systems theory, we resolve this conjecture by showing that, over a large...

In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For this purpose, we present new boundary correctors which preserve the common convergence rates of the LOD, even if the boundary condition has a rapidly oscillating fine scale structure. We prove a corresponding a prior...

We consider a non degenerate quasilinear parabolic stochastic partial differential equation with a uniformly elliptic diffusion matrix. It is driven by a nonlinear noise. We study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine conditions on coefficients and initial data under which the weak solution is Hölder continuous in time an...

Absrtract. Group classification of systems of two coupled nonlinear reaction-diffusion equation with a general diffusion matrix started in papers [1], [2] is completed in present paper where all non-equivalent equations with triangular diffusion matrix are classified. In addition, symmetries of diffusion systems with nilpotent diffusion matrix and additional first order derivative terms are des...

Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...

The diffusion process on weblogs has attracted great interest since the early days of weblog studies. We propose a ranking technique which extracts topics and innovators by analyzing that process. Our method identifies URLs of topics and the bloggers who trigger topic diffusion. Our assumption is that the strength of propagation of a topic is determined by the influences of topics and bloggers....