we study the exponential decay of global solution for an n-dimensional thermo-elasticity systemin a bounded domain of ℜn . by using the multiplier technique and constructing an energy functional welladapted to the system, the exponential decay is proved.

The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a ds 2 e+1 blog2(Ds+1)c+1 -approximation algorithm for MVRST where Ds is the minimum diameter of spanning trees of G.

Given a matrix M (not necessarily nonnegative) and a factorization rank r, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix U with r columns and a nonnegative matrix V with r rows such that UV is the best possible approximation of M according to some metric. In this paper, we study the properties of semi-NMF from which we develop exact and heuristic algorithms. Our contributi...

There has been continued interest in seeking a theorem describing optimal low-rank approximations to tensors of order 3 or higher, that parallels the Eckart–Young theorem for matrices. In this paper, we argue that the naive approach to this problem is doomed to failure because, unlike matrices, tensors of order 3 or higher can fail to have best rank-r approximations. The phenomenon is much more...

We develop a fast algorithm for computing the “SVD-truncated” regularized solution to the leastsquares problem: minx ‖Ax − b‖2. Let Ak of rank k be the best rank k matrix computed via the SVD of A. Then, the SVD-truncated regularized solution is: xk = A † k b. If A is m × n, then, it takes O(mnmin{m,n}) time to compute xk using the SVD of A. We give an approximation algorithm for xk which const...

Numerical methods in higher dimensions using tensor factorizations I this talk I will collect recent advances in the solution of high-dimensional problems in different application areas: chemistry, biology, mathematics. The language of low-rank factorization gives a unified view on different algorithms for the solution of seemingly diverse and unconnected problems. Typical applications include ...

By a finite-rank (linear functional) system, we mean a system of linear differential, shift and q-shift operators or, any mixture thereof, whose solution space is finite-dimensional. This poster attempts to develop an algorithm for factoring finite-rank systems into “subsystems” whose solution spaces are of lower dimension. This work consists of three parts: 1. using module-theoretic language t...

Deterministic models for radiation transport describe the density of particles moving through a background material. In therapy applications, phase space this is composed energy, spatial position and direction flight. The resulting six-dimensional prohibits fine numerical discretizations, which are essential construction accurate reliable treatment plans. work, we tackle high dimensional dynami...