DSpace Collection: Volume 26 Number 3
http://hdl.handle.net/10525/400
Serdica Mathematical Journal Volume 26, Number 3, 2000The Collection's search engineSearch the Channelsearch
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Some Examples of Rigid Representations
http://hdl.handle.net/10525/420
Title: Some Examples of Rigid Representations<br/><br/>Authors: Kostov, Vladimir<br/><br/>Abstract: Consider the Deligne-Simpson problem: give necessary andsufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C)(resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matricesMj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp.A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromyoperators and as matrices-residua of fuchsian systems on Riemann’s sphere.We give new examples of existence of such (p+1)-tuples of matrices Mj(resp. Aj ) which are rigid, i.e. unique up to conjugacy once the classes Cj(resp. cj) are fixed. For rigid representations the sum of the dimensions ofthe classes Cj (resp. cj) equals 2n^2 − 2.<br/><br/>Description: *Research partially supported by INTAS grant 97-1644.A Characterization of Varieties of Associative Algebras of Exponent two
http://hdl.handle.net/10525/419
Title: A Characterization of Varieties of Associative Algebras of Exponent two<br/><br/>Authors: Giambruno, A.; Zaicev, M.<br/><br/>Abstract: It was recently proved that any variety of associative algebrasover a field of characteristic zero has an integral exponential growth. It isknown that a variety V has polynomial growth if and only if V does notcontain the Grassmann algebra and the algebra of 2 × 2 upper triangularmatrices. It follows that any variety with overpolynomial growth has exponentat least 2. In this note we characterize varieties of exponent 2 byexhibiting a finite list of algebras playing a role similar to the one played bythe two algebras above.<br/><br/>Description: ∗The first author was partially supported by MURST of Italy; the second author was par-tially supported by RFFI grant 99-01-00233.Differential Equations in Abstract Cones
http://hdl.handle.net/10525/418
Title: Differential Equations in Abstract Cones<br/><br/>Authors: Jankowski, Tadeusz<br/><br/>Abstract: We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, correspondingmonotone iterations converge to the unique solution of our problem and thisconvergence is superlinear or semi–superlinearComplete Systems of Hermite Associated Functions
http://hdl.handle.net/10525/417
Title: Complete Systems of Hermite Associated Functions<br/><br/>Authors: Rusev, Peter<br/><br/>Abstract: It is proved that if the increasing sequence {kn} n=0..∞n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simplyconnected subregion of C\R then the system of Hermite associated functionsGkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.A Recession Notion for a Class of Monotone Bivariate Functions
http://hdl.handle.net/10525/416
Title: A Recession Notion for a Class of Monotone Bivariate Functions<br/><br/>Authors: Moudafi, A.<br/><br/>Abstract: Using monotone bifunctions, we introduce a recession conceptfor general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions onvariational problems. In the process we generalize some results by H. Brezisand H. Attouch relative to the convergence of the resolvents associated withmaximal monotone operators.Perturbed Proximal Point Algorithm with Nonquadratic Kernel
http://hdl.handle.net/10525/415
Title: Perturbed Proximal Point Algorithm with Nonquadratic Kernel<br/><br/>Authors: Brohe, M.; Tossings, P.<br/><br/>Abstract: Let H be a real Hilbert space and T be a maximal monotoneoperator on H.A well-known algorithm, developed by R. T. Rockafellar [16], for solvingthe problem(P) ”To find x ∈ H such that 0 ∈ T x”is the proximal point algorithm.Several generalizations have been considered by several authors: introductionof a perturbation, introduction of a variable metric in the perturbedalgorithm, introduction of a pseudo-metric in place of the classical regularization,. . .We summarize some of these extensions by taking simultaneously intoaccount a pseudo-metric as regularization and a perturbation in an inexactversion of the algorithm.