Z-scan studies on porphyrin derivative

Received: 10 January 1996 / Revised version: 15 June 1996     

System-theoretic and algebraic aspects of the rings of stable and proper stable rational functions

A new approach in transfer-function methods for solving a variety of control-theoretic problems is to work with fractional representations over the ring of stable or proper stable rational functions of various transfer matrices. The rings of stable and proper stable rational functions are well known to be Euclidean domains. These rings differ critically from the polynomial ring by the nonuniqueness of the remainders obtained. This major difficulty in extending the idea of polynomial models of Fuhrmann to the rings of stable and causal stable rational functions is circumvented by choosing a remainder in a special form. A natural realization theory is thus developed for matrix fraction representations of transfer-function matrices over these rings. As an application of the new theory developed, linear matrix equations (QX+RY=T and QX+YR=T) over the rings of stable and causal stable rational functions are reduced to finite sets of linear equations over the base field.     

A Primal Simplex Based Solution Procedure for the Rectilinear Distance Multifacility Location Problem

In this paper a primal simplex based solution procedure is developed for a multiproduct, multi-facility location problem using rectilinear distance measures. By overcoming the combinatorial nature of the problem which arises in the presence of degeneracy, this procedure is capable of handling large size problems. Computational results are also provided.     

A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts

A finite algorithm is presented in this study for solving Bilinear programs. This is accomplished by developing a suitable cutting plane which deletes at least a face of a polyhedral set. At an extreme point, a polar cut using negative edge extensions is used. At other points, disjunctive cuts are adopted. Computational experience on test problems in the literature is provided.This paper is based upon work supported by the National Science Foundation under Grant No. ENG-77-23683.     

Skew-prime polynomial matrices: The polynomial-model approach

We examine the concept of skew-primeness of polynomial matrices in terms of the associated polynomial model. It is shown that skew-primeness can be characterized in terms of the property of decomposition of a vector space relative to an endomorphism. This basic result is then applied to the special case of nonsingular polynomial matrices. We investigate the nonuniqueness of skew-complements of a skew-prime pair. It is shown that the space of equivalence classes of skew-complements is in bijective correspondence with a finite-dimensional linear space. Finally, the equivalence of the solutions to the problem of output regulation with internal stability obtained via geometric methods and via polynomial matrix techniques is shown explicitly.     

A finitely convergent procedure for facial disjunctive programs

This paper addresses an important class of disjunctive programs called facial disjunctive programs, examples of which include the zero-one linear integer programming problem and the linear complementarity problem. Balas has characterized some fundamental properties of such problems, one of which has been used by Jeroslow to obtain a finitely convergent procedure. This paper exploits another basic property of facial disjunctive programs in order to develop an alternative finitely convergent algorithm.