Department of Mathematics
Recent Submissions

The Alexander module of a trigonal curve
(Eurpean Mathematical Society, 2014)We describe the Alexander modules and Alexander polynomials (both over ℚ and over finite fields Fp) of generalized trigonal curves. The rational case is completely resolved; in the case of characteristic p > 0, a few points ... 
Correlations between the ranks of submatrices and weights of random codes
(Elsevier, 200908)The results of our study are twofold. From the random matrix theory point of view we obtain results on the rank distribution of column submatrices. We give the moments and the covariances between the ranks (q rank) of ... 
Triplets of Closely Embedded Dirichlet type spaces on the Unit Polydisc
(Springer Basel, 2013)We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted L2 spaces yield this kind of generalized triplets of Hilbert spaces for ... 
On a particular type of product manifolds and shearfree cosmological models
(Institute of Physics Publishing Ltd., 2011)Shearfree flows or observer fields are important objects of study in general relativity; stationary or rigid observers are important examples of shearfree reference frames. In this paper, we introduce a geometric structure ... 
On a problem of H.Shapiro
(Elsevier, 200402)Let μ be a real measure on the line such that its Poisson integral M(z) converges and satisfies M(x+ iy) ≤ Aecyα, y → + ∞, for some constants A, c > 0 and 0 < α ≤ 1. We show that for 1/2 < α ≤ 1 the measure μ must have ... 
Modified Kortewegde Vries surfaces
(American Institute of Physics, 2007)In this work, we consider 2surfaces in R3 arising from the modified Kortewegde Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV ... 
On the sign changes of tempered distributions having a spectral gap at the origin
(Elsevier, 20030215)It is known that if a real finite Borel measure has a spectral gap at the origin then either it must have many sign changes or it is zero identically. Assume the Fourier transform of a real temperate distribution agrees ... 
Interplay of gouge, fluid pressure and porosity in fault zones
(Elsevier, 200305)The objective of this study is to demonstrate how fault dynamics may naturally be placed in the context of incremental stress theory, rock textural evolution modeling and standard conservation laws. Casting the fault ... 
Sums with convolutions of Dirichlet Characters to CubeFree Modulus
(American Mathematical Society, 2011)We find estimates for short sums of the form Σnm≤X x1 (n)x 2 (m), where x1 and x2 are nonprincipal Dirichlet characters to modulus q, a cubefree integer, and X can be taken as small as q 1/2+j{cyrillic, ukrainian}. © 2011 ... 
A note on the Hilbert ideals of a cyclic group of prime order
(Elsevier, 20071201)The Hilbert ideal is the ideal generated by positive degree invariant polynomials of a finite group. For a cyclic group of prime order p, we show that the image of the transfer lie in the ideal generated by invariants of ... 
Quantum and classical integrable sineGordon model with defect
(Elsevier, 20080601)Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sineGordon field model with a defect (DSG), at the classical ... 
Homotopy representations over the orbit category
(International Press, 20141124)Let G be a finite group. The unit sphere in a finitedimensional orthogonal Grepresentation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue and establish its basic ... 
Lines generate the Picard groups of certain Fermat surfaces
(Elsevier, 201502)We answer a question of T. Shioda and show that, for any positive integer m prime to 6, the Picard group of the Fermat surface Φm is generated by the classes of lines contained in Φm. A few other classes of surfaces are ... 
Kortewegde Vries surfaces
(Elsevier, 201401)We consider 2surfaces arising from the Kortewegde Vries (KdV) hierarchy and the KdV equation. The surfaces corresponding to the KdV equation are in a threedimensional Minkowski (M3) space. They contain a family of ... 
On RogersRamanujan functions, binary quadratic froms and etaquotients
(American Mathematical Society, 2014)In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the RogersRamanujan functions. We observe that the function that appears in Ramanujan's identities can be ... 
Separating invariants for arbitrary linear actions of the additive group
(Springer Verlag, 2014)We consider an arbitrary representation of the additive group Ga over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants. © 2013 SpringerVerlag ... 
On the top degree of coinvariants
(Oxford University Press, 2014)For a finite group G acting faithfully on a finitedimensional Fvector space V, we show that in the modular case, the top degree of the vector coinvariants grows unboundedly: lim(m >infinity) topdeg F[Vm](G) = infinity. ... 
Dual piRickart Modules
(, 2012)Let R be an arbitrary ring with identity and M a right Rmodule with S = EndR(M). In this paper we introduce dual Rickart modules as a generalization of regular rings as well as that of dual Rickart modules. The module ... 
Two remarks on monomial Gotzmann sets
(Elsevier, 201204)A homogeneous set of monomials in a quotient of the polynomial ring S:=F[x 1,..,x n] is called Gotzmann if the size of this set grows minimally when multiplied with the variables. We note that Gotzmann sets in the quotient ... 
On the ArtalCarmonaCogolludo construction
(, 2014)We derive explicit defining equations for a number of irreducible maximizing plane sextics with double singular points only. For most real curves, we also compute the fundamental group of the complement; all groups found ...