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Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis
http://hdl.handle.net/10525/425
Title: Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis<br/><br/>Authors: Rychter, Jan<br/><br/>Abstract: It is shown that a Banach space X admits an equivalent uniformlyGateaux differentiable norm if it has an unconditional basis and X*admits an equivalent norm which is uniformly rotund in every direction.<br/><br/>Description: *Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a partof the author’s MSc thesis written under the supervison of Professor V. Zizler.The Space of Differences of Convex Functions on [0, 1]
http://hdl.handle.net/10525/424
Title: The Space of Differences of Convex Functions on [0, 1]<br/><br/>Authors: Zippin, M.<br/><br/>Abstract: The space K[0, 1] of differences of convex functions on theclosed interval [0, 1] is investigated as a dual Banach space. It is provedthat a continuous function f on [0, 1] belongs to K[0, 1]<br/><br/>Description: ∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University,College Station, Texas, 2000. Research partially supported by the Edmund Landau Centerfor Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation(Germany).Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations
http://hdl.handle.net/10525/423
Title: Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations<br/><br/>Authors: Karandjulov, L.; Stoyanova, Y.<br/><br/>Abstract: A boundary-value problems for almost nonlinear singularlyperturbed systems of ordinary differential equations are considered. An asymptoticsolution is constructed under some assumption and using boundaryfunctions and generalized inverse matrix and projectors.Asplund Functions and Projectional Resolutions of the Identity
http://hdl.handle.net/10525/422
Title: Asplund Functions and Projectional Resolutions of the Identity<br/><br/>Authors: Zemek, Martin<br/><br/>Abstract: We further develop the theory of the so called Asplund functions,recently introduced and studied by W. K. Tang. Let f be an Asplundfunction on a Banach space X. We prove that (i) the subspaceY := sp ∂f(X) has a projectional resolution of the identity, and that (ii) ifX is weakly Lindel¨of determined, then X admits a projectional resolution ofthe identity such that the adjoint projections restricted to Y form a projectionalresolution of the identity on Y , and the dual X* admits an equivalentdual norm such that its restriction to Y is locally uniformly rotund.<br/><br/>Description: *Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by theGrant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets
http://hdl.handle.net/10525/421
Title: A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets<br/><br/>Authors: Ivanov, M.; Zlateva, N.<br/><br/>Abstract: We consider the question whether the assumption of convexityof the set involved in Clarke-Ledyaev inequality can be relaxed. In the casewhen the point is outside the convex hull of the set we show that Clarke-Ledyaevtype inequality holds if and only if there is certain geometrical relation between the point and the set.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.Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral
http://hdl.handle.net/10525/414
Title: Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral<br/><br/>Authors: Petrogradsky, V.<br/><br/>Abstract: Let Uc be the variety of associative algebras generated by thealgebra of all upper triangular matrices, the field being arbitrary. We provethat the upper exponent of any subvariety V ⊂ Uc coincides with the lowerexponent and is an integer.<br/><br/>Description: Partially supported by grant RFFI 98-01-01020.On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem
http://hdl.handle.net/10525/413
Title: On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem<br/><br/>Authors: Iliev, Valentin<br/><br/>Abstract: Pólya’s fundamental enumeration theorem and some resultsfrom Williamson’s generalized setup of it are proved in terms of Schur-Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutationgroup W ≤ Sd and a one-dimensional character χ of W , the polynomialfunctor Fχ corresponding via S-MT to the induced monomial representationUχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ )is the weighted inventory of some set J(χ) of W -orbits in the integer-valuedhypercube [0, ∞)d . The elements of J(χ) can be distinguished among allW -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of bothcharacteristics is a consequence of S-MT, and is equivalent to a result ofWilliamson. Pólya’s theorem can be obtained from the above identity bythe specialization χ = 1W , where 1W is the unit character of W.Asymptotic Behaviour of Colength of Varieties of Lie Algebras
http://hdl.handle.net/10525/412
Title: Asymptotic Behaviour of Colength of Varieties of Lie Algebras<br/><br/>Authors: Mishchenko, S.; Zaicev, M.<br/><br/>Abstract: We study the asymptotic behaviour of numerical characteristicsof polynomial identities of Lie algebras over a field of characteristic 0. Inparticular we investigate the colength for the cocharacters of polynilpotentvarieties of Lie algebras. We prove that there exist polynilpotent Lie varietieswith exponential and overexponential colength growth. We give the exactasymptotics for the colength of a product of two nilpotent varieties.<br/><br/>Description: This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and00-15-96128.Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation
http://hdl.handle.net/10525/411
Title: Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation<br/><br/>Authors: Di Pomponio, Stefania<br/><br/>Abstract: We treat the oscillatory problem for semilinear wave equation.The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x).By using suitable variants of Strichartz estimate we extend the results from[6] on a priori estimates of the approximations of geometric optics.The mainimprovement is the fact that we can obtain a priori estimates for the caseσ = 1, while in [6] we could treat only the case σ > n/2 − 1.<br/><br/>Description: The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodinella Teoria delle Equazioni Iperboliche”.On Minimizing ||S−(AX−XB)||Pp
http://hdl.handle.net/10525/410
Title: On Minimizing ||S−(AX−XB)||Pp<br/><br/>Authors: Mecheri, Salah<br/><br/>Abstract: In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp ,where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such thatAX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.