Irreducibility criteria for pairs of polynomials whose resultant is a prime number

We use some classical estimates for polynomial roots to provide several irreducibility criteria for pairs of polynomials with integer coefficients whose resultant is a prime number, and for some of their linear combinations. Similar results are then obtained for multivariate polynomials over an arbitrary field, in a non-Archimedean setting.Comment: 20 page

ON D(-1)- Quadruples

Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any two of them is one more than a perfect square are studied. Improved lower and upper bounds for the entries b and c are established. As an application of these results, a bound for the number of such quadruples is obtained

New Stationary Methods for Studying the Kinetics of Redox Reactions Occurring at Inert Semiconductor/Redox Electrolyte Electrodes. I. The »L ∩ P« Method

In this first paper, a new method has been theoretically grounded, for studying the kinetics of redox reactions occurring simultaneously at multielectrodes of the type inert semiconductor / redox electrolyte, representing Schottky barriers. The method is based on the simultaneously changing of both the intensity of the illumination (L), and the polarization (P), of the multielectrode; for this reason, the method has been called an »intersection method«, and symbolized by »L ∩ P«. A kinetic model has been developed to account for the effects of these dL and dP variations, in open and closed circuit conditions, and on its basis, the equations of the potentiostatic and galvanostatic »L ∩ P« methods have been obtained. Further, an expression of the specific admittance has resulted, and some particular cases are given, including that of an inert metal/redox electrolyte multielectrode

New Stationary Methods for Studying the Kinetics of Redox Reactions Occurring at Inert Semiconductor/Redox Electrolyte Electrodes. II. The »a ∩ P« Method

In this second paper an other »intersection« method is theoretically grounded. The method is symbolized »a ∩ P«, and it is based on the simultaneously changing of both the activity (activities) of one (or more) electrochemical active species (a), and the polarization (P), of the multielectrode: inert semiconductor / redox electrolyte. Equations for the potentiostatic, respective galvanostatic »a ∩ P« methods have been deduced, and some important kinetic and electroanalytic applications, especially those referring to the inert metallredox electrolyte unielectrodes are given. These methods permit not only to determine the kinetic parameters, but also to separate the total current density j(U) into the two partial current densities j+(U), j-(U), irrespective of the electrode potential U. Finally, the expression resulted for the specific admittance is equivalent to that obtained in the first paper by using the theory of the »L ∩ P« method; this demonstrates the correctness of both »L ∩ P«, and »a ∩ P« theories

New Stationary Methods for Studying the Kinetics of Redox Reactions Occurring at Inert Semiconductor/Redox Electrolyte Electrodes. I. The »L ∩ P« Method

In this first paper, a new method has been theoretically grounded, for studying the kinetics of redox reactions occurring simultaneously at multielectrodes of the type inert semiconductor / redox electrolyte, representing Schottky barriers. The method is based on the simultaneously changing of both the intensity of the illumination (L), and the polarization (P), of the multielectrode; for this reason, the method has been called an »intersection method«, and symbolized by »L ∩ P«. A kinetic model has been developed to account for the effects of these dL and dP variations, in open and closed circuit conditions, and on its basis, the equations of the potentiostatic and galvanostatic »L ∩ P« methods have been obtained. Further, an expression of the specific admittance has resulted, and some particular cases are given, including that of an inert metal/redox electrolyte multielectrode

Some elementary zero-free regions for Dirichlet series and power series

Adapting some elementary methods used by a number of authors to investigate the location of roots of polynomials with complex coefficients, we present some results which provide zero-free regions for Dirichlet series and power series

ON D(-1)- Quadruples

Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any two of them is one more than a perfect square are studied. Improved lower and upper bounds for the entries b and c are established. As an application of these results, a bound for the number of such quadruples is obtained