In this paper we study a system consisting of c parallel servers with possibly different service rates. Jobs arrive according to a Poisson stream and generate an exponentially distributed workload. An arriving job joins the shortest queue, where in case of multiple shortest queues, one of these queues is selected according to some arbitrary probability distribution. If the maximum difference be...

Padberg [2] introduced a geometric notion of ranks for (mixed) integer rational polyhedrons and conjectured that the geometric rank of the matching polytope is one. In this work, we prove that this conjecture is true. 1 Preliminaries Padberg [2] defined the notion of geometric ranks for the facets of the polytopes. All definitions provided in this section could be found in [2]. Let the followin...

Simple geometric proofs are given for the total positivity of the B-spline collocation matrix and the variation diminishing property of the B-spline representation of a spline.

In this study, the mechanical and thermal behavior of the nano-reinforced polymer composite reinforced by Montmorillonite (MMT) nanoparticles is investigated. Due to low cost of computations, the 3D representative volume elements (RVE) method is utilized using ABAQUS finite element commercial software. Low density poly ethylene (LDPE) and MMT are used as matrix and nanoparticle material, respec...

We consider a bulk service G I / M / l queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, I\) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We des...

The singular value decomposition SVD is a powerful technique in many matrix computa tions and analyses Using the SVD of a matrix in computations rather than the original matrix has the advantage of being more robust to numerical error Additionally the SVD exposes the geometric structure of a matrix an important aspect of many matrix calcula tions A matrix can be described as a tranformation fro...

We have developed a hit-and-miss Monte Carlo geometric ray-tracing program to compute the scattering phase matrix for concentrically stratified spheres. Using typical refractive indices for water and aerosols in the calculations, numerous rainbow features appear in the phase matrix that deviate from the results calculated from homogeneous spheres. In the context of geometric ray tracing, rainbo...

Spectra and pseudospectra of matrix polynomials are of interest in geometric intersection problems, vibration problems, and analysis of dynamical systems. In this note we consider the effect of the choice of polynomial basis on the pseudospectrum and on the conditioning of the spectrum of regular matrix polynomials. In particular, we consider the direct use of the Lagrange basis on distinct int...

Various geometric and algebraic computations (e.g., of the convex hulls, Voronoi diagrams, and scalar, univariate and multivariate resultants) boil down to computing the sign or the value of the determinant of a matrix. For these tasks numerical factorizations of the input matrix is the most attractive approach under the present day computer environment provided the rounding errors are controll...

In recent years, structured matrix recovery problems have gained considerable attention for its real world applications, such as recommender systems and computer vision. Much of the existing work has focused on matrices with low-rank structure, and limited progress has been made on matrices with other types of structure. In this paper we present non-asymptotic analysis for estimation of general...