Department of Mathematics
Recent Submissions

A survey of results on primes in short intervals
(CRC Press, 1998) 
Preface
(CRC Press, 1998) 
Fibre products, character sums and geometric Goppa codes
(CRC Press, 1998)The purpose of this paper is to construct some new families of smooth projective curves over a finite field Fq with extremely many Fqrational points. The genus in every such family is considerably less than the number ... 
Hessian Tensor and standard static spacetimes
(2008)In this brief survey, we will remark the interaction among the Hessian tensor on a semiRiemannian manifold and some of the several questions in Lorentzian (and also in semiRiemannian) geometry where this 2covariant ... 
The development of the principal genus theorem
(Springer, 2007)Genus theory today belongs to algebraic number theory and deals with a certain part of the ideal class group of a number field that is more easily accessible than the rest. Historically, the importance of genus theory stems ... 
Polarization of free electromagnetic field and electromagnetic radiation in quantum domain
(Institute of Physics Publishing, 19980706)Il is shown that conventional disreg;ird.of lo.ngitudinal component, which always e~ists iil radiation ofa localized source, can lead to some. qualitative errors in the description 9f polarization within the quantum domain. ... 
Persistent perfect entanglement in atomic systems
(Institute of Physics Publishing, 2004)It is show that the system of an even number of threelevel atoms in the A configuration in a cavity can evolve into a persistent maximum entangled state. The time of formation or such an entangled state is estimated. 
Maximum entanglement
(Institute of Physics Publishing, 200308)We discuss a novel variational principle in quantummechanics defining maximum entangled states in terms of quantum fluctuations of observables specifying these stales. 
Steadystate bipartite entanglement supported by a squeezed environment
(Institute of Physics Publishing, 200505)We examine the entanglement of two atoms induced by an external quantum system. Both twolevel atoms are coupled to a third twolevel system by dipole interaction, and the third system is under the influence of a certain ... 
The problem of localizing photons
(Institute of Physics Publishing, 200101)It is shown that the boundary conditions, specifying the plane waves of photons, are incapable of description of the photon localization at detection and emission. It is also shown that deflection from the plane waves ... 
Nonoscillating Paleywiener functions
(SpringerVerlag, 2004)A nonoscillating PaleyWiener function is a real entire functionf of exponential type belonging toL 2(R) and such that each derivativef (n),n=0, 1, 2,…, has only a finite number of real zeros. It is established that the ... 
Classical Zariski pairs
(Worldwide Center of Mathematics, 2010)We compute the fundamental groups of the complements of all irreducible plane sextics constituting classical Zariski pairs. 
Semicommutativity of amalgamated rings
(Journal of Mathematical Research with Applications, 2018)In this paper, we study some cases when an amalgamated construction A ◃▹f I of a ring A along an ideal I of a ring B with respect to a ring homomorphism f from A to B, is prime, semiprime, semicommutative, nilsemicommutative ... 
WaringGoldbach problem with PiatetskiShapiro primes
(Institut de Mathematique de Bordeaux, 2018)In this paper, we exhibit an asymptotic formula for the number of representations of a large integer as a sum of a fixed power of PiatetskiShapiro primes, thereby establishing a variant of WaringGoldbach problem with ... 
Interpolation for completely positive maps: Numerical solutions
(Societatea de Stiinte Matematice din Romania, 2018)We present a few techniques to find completely positive maps between full matrix algebras taking prescribed values on given data, based on semidefinite programming, convex minimization supported by a numerical example, as ... 
A nil approach to symmetricity of rings
(Allahabad Mathematical Society, 2018)We introduce a weakly symmetric ring which is a generalization of a symmetric ring and a strengthening of both a GWS ring and a weakly reversible ring, and investigate properties of the class of this kind of rings. A ring ... 
The spectral theorem for locally normal operators
(AGH University of Science and Technology, 2018)We prove the spectral theorem for locally normal operators in terms of a locally spectral measure. In order to do this, we first obtain some characterisations of local projections and we single out and investigate the ... 
Dimension functions for spherical fibrations
(Mathematical Sciences Publishers, 2018)Given a spherical fibration ξ over the classifying space BG of a finite group G we define a dimension function for the mfold fiber join of ξ, where m is some large positive integer. We show that the dimension functions ... 
Bases in some spaces of Whitney functions
(Duke University Press, 20170629)We construct topological bases in spaces of Whitney functions on Cantor sets, which were introduced by the first author. By means of suitable individual extensions of basis elements, we construct a linear continuous exten ...