Alexander O. Gelfond

Gelfond-Zhang Aggregates as Propositional Formulas

We show that any ASP aggregate interpreted under Gelfond and Zhang’s (GZ) semantics can be replaced (under strong equivalence) by a propositional formula. Restricted to the original GZ syntax, the resulting formula is reducible to a disjunction of conjunctions of literals but the formulation is still applicable even when the syntax is extended to allow for arbitrary formulas (including nested a...

The Gelfond-schnirelman Method in Prime Number Theory

Abstract. The original Gelfond-Schnirelman method, proposed in 1936, uses polynomials with integer coefficients and small norms on [0, 1] to give a Chebyshevtype lower bound in prime number theory. We study a generalization of this method for polynomials in many variables. Our main result is a lower bound for the integral of Chebyshev’s ψ-function, expressed in terms of the weighted capacity. T...

Alexander Ogilvy

Alexander M

As a former student of Professor Ostrowski—one of his last— I am delighted to recall here the life and work of one of the great mathematicians of the 20th century. Needless to say that, in view of Ostrowski’s immense and vastly diverse mathematical legacy, this can be done only in a most summary fashion. Further literature on Ostrowski can be found in some of the references at the end of this a...

Alexander Sturn

Cluster Analysis for Large Scale Gene Expression Studies High throughput gene expression analysis is becoming more and more important in many areas of biomedical research. cDNA microarray technology is one very promising approach for high throughput analysis and provides the opportunity to study gene expression patterns on a genomic scale. Thousands or even tens of thousands of genes can be spo...