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

∗ Research partially supported by INTAS grant 97-1644

Formalization of Structural Constraints of Relationships in Model „Entity-Relationship”

The basic conceptions of the model „entity-relationship” as entities, relationships, structural constraints of the relationships (index cardinality, participation degree, and structural constraints of kind (min, max)) are considered and formalized in terms of relations theory. For the binary relations two operators (min and max) are introduced; structural constraints are determined in terms of the operators; the main theorem about compatibility of these operators’ values on the source relation and inversion to it is given here.

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.

Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces

2000 Mathematics Subject Classification: 47H10, 54E15.

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

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.