We consider bivariate real valued polynomials orthogonal with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between polynomials of different degrees. These formulas link the orthogonal polynomials constructed using the lexicographical ordering with those constructed using the re...

We consider first-order specifications together with the restriction to accept only programmable algebras as models. We provide a criterion which links this approach with the “generation principle”: all programmable models of any specification SP that meets this criterion are reachable. We also show an example of a specification which does not satisfy the criterion and admits a programmable yet...

Currently there exist many full featured data models and specific data modelling techniques which are based on different basic principles. For examples, some models are based on first order logic and predicate calculus. Other models are based on set theory. The third class of models proceeds from the separation between entities and relationships and the fourth direction for data modelling empha...

This thesis considers issues related to the multivariate analysis and calibration of chemical data collected in a vector format (one–way data). The work is designed to facilitate the task of the analytical chemist, focusing on methods of maximizing the amount of information that can be obtained by multivariate modeling from full sets of data generated by instruments or experiments. It is shown ...

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized sim...

We propose a simple but powerful approach to the verification of parameterised systems. The approach is based on modelling the reachability between parameterized states as deducibility between suitable encodings of states by formulae of first-order predicate logic. To establish a safety property, that is non-reachability of unsafe states, the finite model finder is used to find a finite counter...

Traditional databases do not explicitly represent the portions over their schemas for which they are sound and complete. This paper proposes a method by which very fine grained meta-data descriptions may be attached to relational data sources to describe, among other things, the portions of various tables for which the database has complete data. Because of the formal properties of the meta-dat...