Unique builders for classes of matrices

On Some Special Classes of Sonnenschein Matrices

‎In this paper we consider the special classes of Sonnenschein matrices‎, ‎namely the Karamata matrices $K[alpha,beta]=left(a_{n,k}right)$ with the entries‎ ‎[{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l}‎ ‎n\‎ ‎v‎ ‎end{array} right){{left( {1‎ - ‎alpha‎ - ‎beta } right)}^v}{alpha ^{n‎ - ‎v}}left( begin{array}{l}‎ ‎n‎ + ‎k‎ - ‎v‎ - ‎1\‎ ‎,,,,,,,,,,k...

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

Classes of Elliptic Matrices

Classes of chromatically unique graphs

Borowiecki, M. and E. Drgas-Burchardt, Classes of chromatically unique graphs, Discrete Mathematics Ill (1993) 71-75. We prove that graphs obtained from complete equibipartite graphs by deleting some independent sets of edges are chromatically unique. 1. Preliminary definitions and results In this paper we consider finite, undirected, simple and loopless graphs. Two graphs G and H are said to b...

Paxos for System Builders

This paper presents a complete specification of the Paxos replication protocol such that system builders can understand it and implement it. We evaluate the performance of a prototype implementation and detail the safety and liveness properties guaranteed by our specification of Paxos.