Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

The Matrix Method of Determining the Fault Tolerance Degree of a Computer Network Topology

This work presents a theoretical-graph method of determining the fault tolerance degree of the computer network interconnections and nodes. Experimental results received from simulations of this method over a distributed computing network environment are also presented.

Sequences of Maximal Degree Vertices in Graphs

2000 Mathematics Subject Classification: 05C35.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

2000 Mathematics Subject Classification: 12D10.