In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...

In this note I give a proof of the existence of a Smith normal form for matrices with integer entries. The existence of a good basis for a lattice with a finite index sublattice is a consequence of the Smith normal form. I conclude with an easy application to toric varieties. Theorem 1. Let A be a matrix with integer entries. Then there exist integer-values invertible matrices C and B such that...

This paper formulates a stochastic inventory model for a single-period seasonal or fashion product inventory system consisting of multiple stocking echelons in series and retailers. By transforming model, an equivalent two-stage stochastic linear program model is developed to solve this stochastic inventory problem, which makes the inventory problem easier to analyze. The optimal placement poli...

where Mk,n is the set of all k-by-n matrices with coefficients in {0, 1} and the variables y l are interpreted as follows: y i l = 1 if and only if z i = l. The matrix (y j) can be seen as a {0, 1} assignment matrix where each column contains exactly one coefficient equal to 1 while h denotes the index of the lowest row that is not identically equal to the zero row (cf. Fig. 1). Another variant...

A new necessary and sufficient condition for the row W-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the extended vertical linear complementarity problem under the row W-property, which extend the error bounds given in [2, 10] for the P-matrix linear complementarity problem, respectively. We show that one of the new error ...

In this project, we had to implement a parallel solver for linear equation systems, using a technique known as Gaussian elimination (GE). As with many other algorithms for solving linear equation systems, GE is performed on the matrix representation of the system, Ax = b, where A is the coefficient matrix and b is the vector of known values. GE works by applying a set of elementary row operatio...

* Receive the edge-weight matrix */ if (rcv(MATRIX_TYPE) < 0) { pvm_perror("rcv"); exit(1); } if (getndfloat(matrix, SQR(nodes))) { pvm_perror("getndfloat"); exit(1); } /* Compute the appropriate row of the new matrix */ comp_short_paths(matrix, nodes, inum, newrow); /* Send the new row back to the master */ initsend(); if (putndfloat(newrow, nodes)) { pvm_perror("putndfloat"); exit(1); } if (s...

* Receive the edge-weight matrix */ if (rcv(MATRIX_TYPE) < 0) { pvm_perror("rcv"); exit(1); } if (getndfloat(matrix, SQR(nodes))) { pvm_perror("getndfloat"); exit(1); } /* Compute the appropriate row of the new matrix */ comp_short_paths(matrix, nodes, inum, newrow); /* Send the new row back to the master */ initsend(); if (putndfloat(newrow, nodes)) { pvm_perror("putndfloat"); exit(1); } if (s...

We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence assumptions on the matrix row space that are necessary for passive sampling procedures. For exact recovery of a low-rank matrix, our algorithm judiciously selects a fe...

This paper presents direct, explicit algebraic constructions of concatenation and Kleene star on deterministic finite automata (DFA), using the Boolean-matrix method of Zhang [5] and ideas of Kozen [2]. The consequence is trifold: (1) it provides an alternative proof of the classical Kleene’s Theorem on the equivalence of regular expressions and DFAs without using nondeterministic finite automa...