This investigation deals with M/M/R/N machine repair problem with R non-reliable service stations which are subjected to unpredictable breakdown. 1here is provision of an additional server to reduce backlog in the case of heavy load of failed machines. 1he permanent service stations repair the failed machines at an identical rate m and switch to faster repair rate when all service stations are ...

This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into a consistent PC matrix which is generated by the geometric means of rows of a given inconsistent PC matrix. The distance-based inconsistency indicator was de...

Using a new formulation of the Bézout matrix, we construct bivariate matrix polynomials expressed in a tensor-product Lagrange basis. We use these matrix polynomials to solve common tasks in computer-aided geometric design. For example, we show that these bivariate polynomials can serve as stable and efficient implicit representations of plane curves for a variety of curve intersection problems.

We discuss in the paper the use of the Riemannian mean given by the differential geometric tools. This geometric mean is used in this paper for computing the class centers in the polarimetric H/α unsupervised classification process. We show that the class centers remain more stable during the iteration process, leading to a different interpretation of the H/α/A classification. This technique ca...

Non-negative matrix factorization (NMF) is a widely used tool for exploratory data analysis in many disciplines. In this paper, we describe an approach to NMF based on random projections and give a geometric analysis of a prototypical algorithm. Our main result shows the proto-algorithm requires κ̄k log k optimizations to find all the extreme columns of the matrix, where k is the number of extre...

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence interv...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

In this paper, we describe our development of GABLE, a Matlab implementation of the Geometric Algebra based on C̀ p,q (where p+ q = 3) and intended for tutorial purposes. Of particular note are the matrix representation of geometric objects, effective algorithms for this geometry (inversion, meet and join), and issues in efficiency and numerics.

This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci of the hypersurface, that are computed with the aid of representation theory of quivers.