DSpace Collection: Volume 29 Number 1
http://hdl.handle.net/10525/1689
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On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation
http://hdl.handle.net/10525/1696
Title: On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation<br/><br/>Authors: Khristov, E.<br/><br/>Abstract: By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator. As an illustration of this approach, the Bäcklund transformations for the KdV equation are constructed.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53Wed, 01 Jan 2003 00:00:00 GMTOn Arrangements of Real Roots of a Real Polynomial and Its Derivatives
http://hdl.handle.net/10525/1695
Title: On Arrangements of Real Roots of a Real Polynomial and Its Derivatives<br/><br/>Authors: Kostov, Vladimir<br/><br/>Abstract: We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realized by real polynomials.<br/><br/>Description: 2000 Mathematics Subject Classification: 12D10.Wed, 01 Jan 2003 00:00:00 GMTAdequate Compacta which are Gul’ko or Talagrand
http://hdl.handle.net/10525/1694
Title: Adequate Compacta which are Gul’ko or Talagrand<br/><br/>Authors: Čížek, Petr; Fabian, Marián<br/><br/>Abstract: We answer positively a question raised by S. Argyros: Givenany coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko and not Talagrand. Further, given any Borel, non Fσ subset Σ′ of the irrationals, we construct, in c1(Σ′), an adequate compact which is Talagrand and not Eberlein.<br/><br/>Description: 2000 Mathematics Subject Classification: 54H05, 03E15, 46B26Wed, 01 Jan 2003 00:00:00 GMTAcceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
http://hdl.handle.net/10525/1693
Title: Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions<br/><br/>Authors: Geoffroy, M.; Hilout, S.; Pietrus, A.<br/><br/>Abstract: In this paper we investigate the existence of a sequence (xk )satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.<br/><br/>Description: 2000 Mathematics Subject Classification: 47H04, 65K10.Wed, 01 Jan 2003 00:00:00 GMTSylow P-Subgroups of Abelian Group Rings
http://hdl.handle.net/10525/1692
Title: Sylow P-Subgroups of Abelian Group Rings<br/><br/>Authors: Danchev, P.<br/><br/>Abstract: Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the present work, the p-primary components Up(KA) and S(KA) of the group of units U(KA) and V(KA) in the semisimple abelian group ring KA are studied when they belong to some central classes of abelian groups. The established criteria extend results obtained by us in Compt. rend. Acad. bulg. Sci. (1993). Moreover, the question for the isomorphic type of the basic subgroup of S(KA) is also settled. As a final result, it is proved that if A is a direct sum of cyclics, the group of all normed p-units S(KA) modulo A, that is, S(KA)/A, is a direct sum of cyclics too. Thus A is a direct factor of S(KA) with a direct sum of cyclics complementary factor provided sp(K) ⊇ N. This generalizes a result due to T. Mollov in Pliska Stud. Math. Bulgar. (1986).<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary16U60, 16S34.Wed, 01 Jan 2003 00:00:00 GMTA PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function
http://hdl.handle.net/10525/1691
Title: A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function<br/><br/>Authors: Pang, Li-Ping; Xia, Zun-Quan<br/><br/>Abstract: A general framework of the (parallel variable transformation)PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization.As a particular scheme of this framework an ε-scheme is also presented. Theglobal convergence of this algorithm is given under the assumptions of strongconvexity of the objective function and an ε-descent condition determinedby an ε-forced function. An appendix stating the proximal point algorithmis recalled in the last section.<br/><br/>Description: 2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.Wed, 01 Jan 2003 00:00:00 GMTCharacterizations of the Solution Sets of Generalized Convex Minimization Problems
http://hdl.handle.net/10525/1690
Title: Characterizations of the Solution Sets of Generalized Convex Minimization Problems<br/><br/>Authors: Ivanov, Vsevolod<br/><br/>Abstract: In this paper we obtain some simple characterizations of thesolution sets of a pseudoconvex program and a variational inequality. Similarcharacterizations of the solution set of a quasiconvex quadratic program arederived. Applications of these characterizations are given.<br/><br/>Description: 2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.Wed, 01 Jan 2003 00:00:00 GMT