DSpace Collection: Volume 28 Number 2
http://hdl.handle.net/10525/463
Serdica Mathematical Journal Volume 28, Number 2, 2002The Collection's search engineSearch the Channelsearch
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Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0
http://hdl.handle.net/10525/496
Title: Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0<br/><br/>Authors: Mollin, R.<br/><br/>Abstract: This article provides necessary and sufficient conditions forboth of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfectsquare. This is given in terms of the ideal theory of the underlying realquadratic order Z[√D].A Product Twistor Space
http://hdl.handle.net/10525/495
Title: A Product Twistor Space<br/><br/>Authors: Blair, David<br/><br/>Abstract: In previous work a hyperbolic twistor space over a paraquaternionic Kähler manifold was defined, the fibre being the hyperboloid modelof the hyperbolic plane with constant curvature −1. Two almost complexstructures were defined on this twistor space and their properties studied. In the present paper we consider a twistor space over a paraquaternionic Kählermanifold with fibre given by the hyperboloid of 1-sheet, the anti-de-Sitterplane with constant curvature −1. This twistor space admits two naturalalmost product structures, more precisely almost para-Hermitian structures,which form the objects of our study.<br/><br/>Description: ∗Research supported in part by NSF grant INT-9903302.Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups
http://hdl.handle.net/10525/494
Title: Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups<br/><br/>Authors: Artemovych, O.<br/><br/>Abstract: We characterize the groups which do not have non-trivial perfectsections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5
http://hdl.handle.net/10525/493
Title: Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5<br/><br/>Authors: Kostov, Vladimir<br/><br/>Abstract: A real polynomial of one real variable is hyperbolic (resp.strictly hyperbolic) if it has only real roots (resp. if its roots are real anddistinct). We prove that there are 116 possible non-degenerate configurations between the roots of a degree 5 strictly hyperbolic polynomial andof its derivatives (i.e. configurations without equalities between roots).The standard Rolle theorem allows 286 such configurations. To obtainthe result we study the hyperbolicity domain of the family P (x; a, b, c) =x^5 − x^3 + ax^2 + bx + c (i.e. the set of values of a, b, c ∈ R for which thepolynomial is hyperbolic) and its stratification defined by the discriminantsets Res(P^(i) , P^(j) ) = 0, 0 ≤ i < j ≤ 4.<br/><br/>Description: ∗ Research partially supported by INTAS grant 97-1644Partial Quasi-Bilateral Generating Function Involving some Special Functions
http://hdl.handle.net/10525/492
Title: Partial Quasi-Bilateral Generating Function Involving some Special Functions<br/><br/>Authors: Sarkar, Asit<br/><br/>Abstract: A group-theoretic method of obtaining more general class ofgenerating functions from a given class of partial quasi-bilateral generatingfunctions involving Hermite, Laguerre and Gegenbaur polynomials arediscussed.Cerami (C) Condition and Mountain Pass Theorem for Multivalued Mappings
http://hdl.handle.net/10525/491
Title: Cerami (C) Condition and Mountain Pass Theorem for Multivalued Mappings<br/><br/>Authors: Kristály, A.; Varga, Cs.<br/><br/>Abstract: We prove a general minimax result for multivalued mapping.As application, we give existence results of critical point of this mappingwhich satisfies the Cerami (C) condition.<br/><br/>Description: Partially supported by Sapientia Foundation.