Interpolation theory suggests a generalization of the usual Vandermonde determinant to numbers with multiplicities. We prove a discriminant formula for this generalized Vandermonde determinant and give an application to the Hermite interpolation problem.

In process semantics of Petri Net, a non-sequential process is a concurrent run of the system represented in a partial order-like structure. For transition systems it is possible to define a similar notion of concurrent run by utilising the idea of confluence. Basically a confluent process is an acyclic confluent transition system that is a partial unfolding of the original system. Given a non-...

In this paper, we consider the monodromy and, in particular, isomonodromy sets of accessory parameters for Heun class equations. We show that equations can be obtained as limits linear systems associated with Painlevé when transcendents go to one actual singular points systems. The are described by Taylor or Laurent coefficients corresponding functions, tau at positions critical values. As an a...

Due to their remarkable application in many branches of applied mathematics such as combinatorics, coding theory, and cryptography, Vandermonde matrices have received a great amount of attention. Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. Lacan and Fimes introduc...

Multipoint polynomial evaluation and interpolation are fundamental for modern algebraic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grew to quadratic for numerical solution. We fix this discrepancy: our new numerical algorithms run in nearly linear arithmetic time. At first we restate our goals as t...

This paper discusses random linear network coding with and without the use of a Vandermonde matrix to obtain the coding coefficients. Performance comparisons of such random linear network coded networks with networks employing traditional store and forward technique are also provided. It is shown that random linear network coding using a Vandermonde matrix can improve the network utilization fa...

Madlener, K., P. Narendran, F. Otto and L. Zhang, On weakly confluent monadic string-rewriting systems, Theoretical Computer Science 113 (1993) 119-165. It is investigated as to how far the various decidability results for finite, monadic, and confluent string-rewriting systems can be carried over to the class of finite monadic string-rewriting systems that are only weakly confluent. Here a mon...