Revista Matemática Complutense
type: channel
description: Revista Matemática Complutense (ISSN 1139-1138, ISSN-e 1988-2807), currently published three times a year, it includes original or literature reviews that are carefully selected from all areas of Mathematics including the “Conferenciante Santaló” article, written by a designated prestigious mathematician. Since January 2010, Springer has been responsible for its publication
publisher: Springer
language: en
publication name: Revista Matemática Complutense
issn: 1139-1138
copyright: LICENCE OF USE: The full text articles included on the Scientific Journals of the Complutense website are open access and the property of their authors and/or publishers. Therefore, any reproduction, distribution, public communication and/or total or partial transformation requires their express and written consent. Links to the full text of the articles on the Scientific Journals of the Complutense website should be to the official URL of the Complutense University of Madrid.
items: Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation
items: Coincidence of some classes of universal functions
items: Monodromy zeta-functions of deformations and Newton diagrams
items: Asymptotic uniform moduli and Kottman constant of Orlicz sequence spaces
items: Weighted composition operators between spaces of Dirichlet type
items: The SL(2,C)-character varieties of torus knots
items: Symmetrization and sharp Sobolev inequalities in metric spaces
items: Erratum to “Fundamental groups of some special quadric arrangements”
items: Uniqueness of Entropy Solutions of Nonlinear Elliptic-Parabolic-Hyperbolic Problems in One Dimension Space
items: Renormalized Solutions for Nonlinear Degenerate Elliptic Problems with L1 Data
items: Semistability of Certain Bundles on a Quintic Calabi-Yau Threefold
items: Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula
items: A Discrete Hardy-Laptev-Weidl-Type Inequality and Associated Schrödinger-Type Operators
items: Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces
items: On Dilation Operators in Besov Spaces
items: Newton Binomial Formulas in Schubert Calculus
items: Extremal Vector Valued Inequalities for Hankel Transforms
items: Boundary Sentinels with Given Sensitivity
items: A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with Non-Smooth Negative Definite Symbols
items: About the Banach Envelope of l1,∞
items: 2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability
items: Besov and Triebel-Lizorkin Spaces Related to Singular Integrals with Flag Kernels
items: Erratum to “Feller Semigroups Obtained by Variable Order Subordination" (Rev. Mat. Complut. 20 (2007), no. 2, 293-307)
items: Divergent Cesàro Means of Jacobi-Sobolev Expansions
items: Strongly Invertible Knots, Rational-Fold Branched Coverings, and Hyperbolic Spatial Graphs
items: A General Hilbert Space Approach to Framelets
items: Weighted Composition Operators between Weighted Bergman Spaces and Weighted Banach Spaces of Holomorphic Functions
items: On the Distribution of the Power Generator over a Residue Ring for Parts of the Period
items: Note on Coupled Linear Systems Related to Two Soliton Collision for the Quartic gKdV Equation
items: Rigorous Numerics for the Cahn-Hilliard Equation on the Unit Square

Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation
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description: This paper is an overview of known and new results about the coupling of Navier-Stokes and Darcy equations to model the filtration of incompressible fluids through porous media. We discuss coupling conditions and we analyze the global coupled model in order to prove its well-posedness and to characterize effective algorithms to compute the solution of its numerical approximation.
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creator: Marco Discacciati
creator: Alfio Quarteroni
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 315
ending page: 426
doi: 10.5209/rev_REMA.2009.v22.n2.16263

Coincidence of some classes of universal functions
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description: Let Ω a domain in the complex plane such that Ω satisfies appropriate geometrical and topological properties. We prove that if f is a holomorphic function in Ω, then its Taylor series, with center at any ξ Є Ω , is universal with respect to overconvergence if and only if its Cesáro (C, k)-means are universal for any real k > −1. This is an extension of the same result, proved recently by F. Bayart, for any integer k ≥ 0. As a consequence, several classes of universal functions introduced in the related literature are shown to coincide.
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creator: Emmanuel S. Katsoprinakis
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 427
ending page: 445
doi: 10.5209/rev_REMA.2009.v22.n2.16279

Monodromy zeta-functions of deformations and Newton diagrams
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description: For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.
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creator: Gleb Gusev
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 447
ending page: 454
doi: 10.5209/rev_REMA.2009.v22.n2.16282

Asymptotic uniform moduli and Kottman constant of Orlicz sequence spaces
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description: We give lower and upper bounds, involving moduli of asymptotic uniform convexity and smoothness, for the Kottman separation constant of Orlicz sequence spaces equipped with the Luxemburg norm.
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creator: Sylvain Delpech
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date: 2009-07-27
publication date: 2009-07-27
starting page: 455
ending page: 467
doi: 10.5209/rev_REMA.2009.v22.n2.16285

Weighted composition operators between spaces of Dirichlet type
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description: In this work we characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures. We also find essential norm estimates for these operators.
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creator: Sanjay Kumar
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 469
ending page: 488
doi: 10.5209/rev_REMA.2009.v22.n2.16288

The SL(2,C)-character varieties of torus knots
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description: Let G be the fundamental group of the complement of the torus knot of type (m, n). This has a presentation G = ‹x, y | xm= yⁿ›. We find the geometric description of the character variety X(G) of characters of representations of G into SL(2,C).
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creator: Vicente Muñoz
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 489
ending page: 497
doi: 10.5209/rev_REMA.2009.v22.n2.16290

Symmetrization and sharp Sobolev inequalities in metric spaces
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description: We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and Faber-Krahn estimates for H¨ormander vector fields.
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creator: Mario Milman
creator: Jan Kališ
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 499
ending page: 515
doi: 10.5209/rev_REMA.2009.v22.n2.16292

Erratum to “Fundamental groups of some special quadric arrangements”
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description: This erratum relates to our work “Fundamental groups of some special quadric arrangements”. The original Theorems 2.2, 2.5, 2.8 and Propositions 2.3(ii)(iii), 2.6(ii)(iii), 2.9(ii)(iii) have wrong results. They need to be rephrased. Corollaries 2.4 and 2.7 are incomplete, and they are extended. We add a new Corollary 2.10, which does not appear in the original paper. Proposition 3.1 has a wrong result and it is rephrased and reproved. In Proposition 4.1 and its Corollary 4.2 a slight error has occurred: as the correct proofs in the paper show, the monodromy is a quadruple fulltwist.
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creator: Meirav Amram
creator: Mina Teicher
rights: Copyright (c)
date: 2009-07-27
publication date: 2009-07-27
starting page: 517
ending page: 550
doi: 10.5209/rev_REMA.2009.v22.n2.16299

Uniqueness of Entropy Solutions of Nonlinear Elliptic-Parabolic-Hyperbolic Problems in One Dimension Space
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description: We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form b(u)t — a(u, φ(ux)x= f with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an L1-contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data.
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creator: Stanislas Ouaro
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 7
ending page: 36
doi: 10.5209/rev_REMA.2009.v22.n1.16303

Renormalized Solutions for Nonlinear Degenerate Elliptic Problems with L1 Data
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description: We are interested in a class of nonlinear degenerate diffusion problems with a diffusion function a(x, u, Vu) which is not controlled with respect to u and which is not uniformly coercive on the weighted Sobolev spaces W1,p0 (Ω, w). Existence of a renormalized solution is proved in the L1-setting.
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creator: Kaouther Ammar
creator: Hicham Redwane
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 37
ending page: 52
doi: 10.5209/rev_REMA.2009.v22.n1.16308

Semistability of Certain Bundles on a Quintic Calabi-Yau Threefold
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description: In a recent paper Douglas and Zhou aim for explicit examples of string theory compactifications that have a different number of generations and can be connected. For this purpose, they provide a list of bundles on a quintic Calabi-Yau threefold. They need to show that (at least some of) these bundles are semistable and leave this as an open question. In this paper we prove the semistability of most of the bundles in the list, thus completing the result of Douglas and Zhou.
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creator: Maria Chiara Brambilla
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 53
ending page: 61
doi: 10.5209/rev_REMA.2009.v22.n1.16310

Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula
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description: This paper deals with variational inclusions of the form: 0 ε f(x)+F(x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ε f(xk)+∑M i=1 aiΛf(xk+βi(xk+1-xk))(xk+1-xk)+F(xk+1) where the single-valued function involved in this relation is an approximation of the function f based on a multipoint iteration formula and we show that this method is locally cubically convergent.
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creator: Catherine Cabuzel
creator: Alain Pietrus
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 63
ending page: 74
doi: 10.5209/rev_REMA.2009.v22.n1.16314

A Discrete Hardy-Laptev-Weidl-Type Inequality and Associated Schrödinger-Type Operators
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description: Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality.
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creator: W. Desmond Evans
creator: Karl Michael Schmidt
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 75
ending page: 90
doi: 10.5209/rev_REMA.2009.v22.n1.16316

Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces
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description: In this paper, we study the problem:—div a(x, u, ∆u) — div Φ(u) + g(x; u) = f in the framework of Orlicz spaces. The main contribution of our work is to prove the existence of a renormalized solution without any restriction on the N-function of the Orlicz space.
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creator: Lahsen Aharouch
creator: Jaouad Bennouna
creator: Abdelfettah Touzani
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 91
ending page: 110
doi: 10.5209/rev_REMA.2009.v22.n1.16319

On Dilation Operators in Besov Spaces
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description: We consider dilation operators Tk : f → f(2k.) in the framework of Besov spaces Bsp,q (Rn) when 0 < p≤ 1. If s > n(1/p — 1) Tk is a bounded linear operator from Bsp,q (Rn) into itself and there are optimal bounds for its norm. We study the situation on the line s = n(1/p — 1), an open problem mentioned in [5, 2.3.1, 2.3.2]. It turns out that the results shed new light upon the diversity of different approaches to Besov spaces on this line, associated to definitions by differences, Fourier-analytical methods, and subatomic decompositions.
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creator: Cornelia Schneider
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 111
ending page: 128
doi: 10.5209/rev_REMA.2009.v22.n1.16324

Newton Binomial Formulas in Schubert Calculus
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description: We prove Newton’s binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
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creator: Jorge Cordovez
creator: Letterio Gatto
creator: Taíse Santiago
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 129
ending page: 152
doi: 10.5209/rev_REMA.2009.v22.n1.16330

Extremal Vector Valued Inequalities for Hankel Transforms
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description: Sin resumen
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creator: Elena Romera
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 153
ending page: 163
doi: 10.5209/rev_REMA.2009.v22.n1.16337

Boundary Sentinels with Given Sensitivity
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description: The notion of sentinels with given sensitivity was introduced by J.-L. Lions in [10] in order to identify parameters in a problem of pollution ruled by a semilinear parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. Reconsidering this notion of sentinels in a more general framework, we prove the existence of the new sentinels by solving a boundary null-controllability problem with constraint on the control. Our results use a Carleman inequality which is adapted to the constraint.
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creator: Gisèle Massengo Mophou
creator: Jean-pierre Puel
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 165
ending page: 185
doi: 10.5209/rev_REMA.2009.v22.n1.16342

A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with Non-Smooth Negative Definite Symbols
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description: We consider pseudodifferential operators that have non-smooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of non-smooth symbols that are asymptotically constant in the co-variable we succeed infunding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential operators with non-smooth negative definite symbols are pregenerators of Feller semigroups.
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creator: Alexander Potrykus
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date: 2009-03-11
publication date: 2009-03-11
starting page: 187
ending page: 207
doi: 10.5209/rev_REMA.2009.v22.n1.16347

About the Banach Envelope of l1,∞
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description: We study the Banach envelope of the quasi-Banach space l1,∞ consisting of all sequences x=(ξ k) with sn(x)=O(1/n), where (sn (x)) denotes the non-increasing rearrangement of x=(ξ k) The situation turns out to be much more complicated than that in the well-known case of the separable subspace lo1,∞, whose members are characterized by sn(x) =o(1/n).
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creator: Albrecht Pietsch
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 209
ending page: 226
doi: 10.5209/rev_REMA.2009.v22.n1.16350

2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability
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description: We introduce 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability and give a characterization by local means. These spaces cover spaces of variable exponent, spaces of variable smoothness and weighted spaces that have been studied in recent years.
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creator: Henning Kempka
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 227
ending page: 251
doi: 10.5209/rev_REMA.2009.v22.n1.16353

Besov and Triebel-Lizorkin Spaces Related to Singular Integrals with Flag Kernels
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description: Let s1, s2 Є (—1, 1) and s = (s1, s2). In this paper, the author introduces the Besov space Bspqq(R2) with p, q Є [1, ∞] and the Triebel-Lizorkin space Fspqq(R2) with p Є (1, ∞) and q Є (1, ∞] associated to singular integrals with flag kernels. Some basic properties, including their dual spaces, some equivalent norm characterizations via Littlewood-Paley functions, lifting properties and some embedding theorems, on these spaces are given. Moreover, the au thor obtains the boundedness of flag singular integrals and fractional integrals on these spaces.
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creator: Dachun Yang
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 253
ending page: 302
doi: 10.5209/rev_REMA.2009.v22.n1.16358

Erratum to “Feller Semigroups Obtained by Variable Order Subordination" (Rev. Mat. Complut. 20 (2007), no. 2, 293-307)
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description: Sin resumen
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creator: Kristian P. Evans
creator: Niels Jacob
rights: Copyright (c)
date: 2009-03-11
publication date: 2009-03-11
starting page: 303
ending page: 304
doi: 10.5209/rev_REMA.2009.v22.n1.16368

Divergent Cesàro Means of Jacobi-Sobolev Expansions
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description: Let µ be the Jacobi measure supported on the interval [­1; 1]. Let introduce the Sobolev-type inner product …. In this paper we prove that, for certain indices δ, there are functions whose Ces_aro means of order δ in the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product are divergent almost everywhere on [-1; 1].
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creator: Bujar Xh. Fejzullahu
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 427
ending page: 433
doi: 10.5209/rev_REMA.2008.v21.n2.16394

Strongly Invertible Knots, Rational-Fold Branched Coverings, and Hyperbolic Spatial Graphs
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description: A construction of a spatial graph from a strongly invertible knot was developed by the second author, and a necessary and sufficient condition for the given spatial graph to be hyperbolic was provided as well. The condition is improved in this paper. This enable us to show that certain classes of knots can yield hyperbolic spatial graphs via the construction.
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creator: Kazuhiro Ichihara
creator: Akira Ushijima
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 435
ending page: 451
doi: 10.5209/rev_REMA.2008.v21.n2.16395

A General Hilbert Space Approach to Framelets
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description: In arbitrary separable Hilbert spaces it is possible to deffine multiscale methods of constructive approximation based on product kernels, restricting their choice in certain ways. These wavelet techniques have already filtering and localization properties and they are applicable in many areas due to their generalized deffinition. But they lack detailed information about their stability and redundancy, which are frame properties. So in this work frame conditions are introduced for approximation methods based on product kernels. In order to provide stability and redundancy the choice of product kernel ansatz function has to be restricted. Taking into account the kernel conditions for multiscale and for frame approximations one is able to deffine wavelet frames (= framelets), inheriting the approximation properties of both techniques and providing a more precise tool for multiscale analysis than the normal wavelets.
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creator: Dominik Michel
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 453
ending page: 473
doi: 10.5209/rev_REMA.2008.v21.n2.16399

Weighted Composition Operators between Weighted Bergman Spaces and Weighted Banach Spaces of Holomorphic Functions
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description: We characterize boundedness and compactness of weighted composition operators acting between weighted Bergman spaces Aw;p and weighted Banach spaces H1v of holomorphic functions.
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creator: Elke Wolf
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 475
ending page: 480
doi: 10.5209/rev_REMA.2008.v21.n2.16402

On the Distribution of the Power Generator over a Residue Ring for Parts of the Period
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description: This paper studies the distribution of the power generator of pseudorandom numbers over a residue ring for parts of the period. These results compliment some recently obtained distribution bounds of the power generator modulo an arbitrary number for the entire period. Also, the arbitrary modulus case may have some cryptography related applications and could be of interest in other settings which require quality pseudorandom numbers.
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creator: Edwin D. El-mahassni
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 319
ending page: 325
doi: 10.5209/rev_REMA.2008.v21.n2.16374

Note on Coupled Linear Systems Related to Two Soliton Collision for the Quartic gKdV Equation
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description: We consider linear systems related to the description of the collision of two solitons for the gKdV equation with quartic nonlinearity. The computations presented in this note are applied in Martel and Merle [10] to prove a result concerning inelastic (but almost elastic) collision for a nonintegrable equation.
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creator: Yvan Martel
creator: Frank Merle
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 327
ending page: 350
doi: 10.5209/rev_REMA.2008.v21.n2.16378

Rigorous Numerics for the Cahn-Hilliard Equation on the Unit Square
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description: While the structure of the set of stationary solutions of the Cahn-Hilliard equation on one-dimensional domains is completely understood, only partial results are available for two-dimensional base domains. In this paper, we demonstrate how rigorous computational techniques can be employed to establish computerassisted existence proofs for equilibria of the Cahn-Hilliard equation on the unit square. Our method is based on results by Mischaikow and Zgliczy´nski [22], and combines rigorous computations with Conley index techniques. We are able to establish branches of equilibria and, under more restrictive conditions, even the local uniqueness of specific equilibrium solutions. Sample computations for several branches are presented, which illustrate the resulting patterns.
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creator: Stanislaus Maier-paape
creator: Ulrich Miller
creator: Konstantin Mischaikow
creator: Thomas Wanner
rights: Copyright (c)
date: 2008-07-15
publication date: 2008-07-15
starting page: 351
ending page: 426
doi: 10.5209/rev_REMA.2008.v21.n2.16380