A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schrödinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothin...

We give a parallel algorithm for computing all row minima in a totally monotone n = n matrix which is simpler and more work efficient than previous polylog-time Ž . Ž . algorithms. It runs in O lg n lg lg n time doing O n lg n work on a CRCW ' 2 Ž Ž . . Ž . PRAM, in O lg n lg lg n time doing O n lg n work on a CREW PRAM, and in ' Ž . Ž . O lg n lg n lg lg n time doing O n lg n lg lg n work on a...

How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles. With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, Ch...

This paper presents a hierarchically designed polymer nanocomposite approach in which nanofillers at ultralow volume loading generate large dielectric enhancement blends of high temperature polymers with tailored nanostructures. We blend poly(1,4-phenylenen ether sulfone) (PES) polymers, such as polyetherimide (PEI), that possess more coiled chain conformations to tailor nano-morphologies. Maki...

We study noncompact and static membrane solutions in Matrix theory. Demanding axial symmetry on a membrane embedded in three spatial dimensions, we obtain a wormhole solution whose shape is the same with the catenoidal solution of Born-Infeld theory. We also discuss another interesting class of solutions, membranes embedded holomorphically in four spatial dimensions, which are 1/4 BPS. Matrix t...

Martin Ohlson, M. Rauf Ahmad and Dietrich von Rosen, More on the Kronecker Structured Covariance Matrix, 2012, Communications in Statistics Theory and Methods, (41), 13-14, 2512-2523. Communications in Statistics Theory and Methods is available online at informaworld TM : http://dx.doi.org/10.1080/03610926.2011.615971 Copyright: Taylor & Francis: STM, Behavioural Science and Public Health Title...

This paper discusses random linear network coding with and without the use of a Vandermonde matrix to obtain the coding coefficients. Performance comparisons of such random linear network coded networks with networks employing traditional store and forward technique are also provided. It is shown that random linear network coding using a Vandermonde matrix can improve the network utilization fa...