bluuebunny/crossref_metadata_2025_split huggingface dataset:
Evaluation of the Degree of Exfoliation in Poly(ε‐caprolactone)/Organoclay Nanocomposites Based on Viscoelastic Relaxation
Authors: Chung Jae Woo , Oh Kwang Sei , Kwak Seung‐Yeop 
Published: May 2007

AbstractPoly(ε‐caprolactone) nanocomposites, PCLOC25A and PCLOC30B, with organoclays (OCs) having nonpolar and polar organic modifiers, respectively, were prepared by the melt mixing method and additional heat treatment. WXRD analysis revealed that both nanocomposites were exfoliated, irrespective of the OC polarity. However, WXRD failed to show the degree of exfoliation of the nanocomposites, because the d001 peaks disappeared. Thus, dynamic mechanical analysis (DMA) was carried out to compare the degree of exfoliation of the PCL nanocomposites. From DMA, PCLOC30B showed higher elasticity, storage moduli, viscosity, and activation energy than PCLOC25A, indicating that PCLOC30B had a more exfoliated structure than PCLOC25A. This is due to the polar interaction in PCLOC30B, as verified by the plots of aT versus temperature. Thus, it was confirmed that DMA provides an alternative approach to evaluating the degree of exfoliation of nanocomposites.magnified image
On CLARKSON's Inequalities and Interpolation
Authors: Maligranda Lech , Persson Lars Erik 
Published: May 2007

AbstractWe consider some elementary proofs of local versions of CLARKSON's inequalities and point out the fact that these inequalities can be generalized to hold for a much wider class of parameters. In particular it is easy to generalize our interpolation proof in various ways to higher dimensions. We point out explicitely some examples of such generalizations and we also prove some corresponding global versions. In this elementary way we obtain both new proofs of some previous results of this kind and also some new complements, unifications and further generalizations of these results.
On a Problem of BABUŠKA (Stable Asymptotics of the Solution to the DIRICHLET Problem for Elliptic Equations of Second Order in Domains with Angular Points)
Authors: Maz'ya Vladimir , Rossmann Jürgen 
Published: May 2007

AbstractWe consider the DIRICHLET problem for linear elliptic differential equations with smooth real coefficients in a two‐dimensional domain with an angle point. We find an asymptotic representation of the solution near this point, which is stable under small variations of the angle.
Long‐Time Behaviour of the Weakly Asymmetric Exclusion Process and the BURGERS Equation without Viscosity
Authors: Dittrich P. 
Published: May 2007

AbstractWe investigate macroscopic properties of the onedimensional weakly asymmetric nearest neighbour exclusion process for long times. We show that the particle system can be approximated by the solution of a discrete version of the viscid BURGERS equation, but with random initial datum. In a larger space scale we show the convergence to a deterministic solution of the BURGERS equation without viscosity.
Global Attractivity and ‘Level‐Crossings’ in a Periodic Logistic Integrodifferential Equation
Authors: Gopalsamy K. , He Xue‐Zhong , Wen Lizhi 
Published: May 2007

AbstractSufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the logistic integrodifferential equation where a, b are continuous positive periodic functions and K is a nonnegative integrable function defined on {0, ∞). We also derive sufficient conditions for all positive solutions to have “level crossings” about the unique positive periodic solution.
Uniqueness Theorems for CR Functions
Authors: Schmalz Gerd 
Published: May 2007

AbstractLet M be a CR manifold embedded in ℭs of arbitrary codimension. M is called generic if the complex hull of the tangent space in all points of M is the whole ℭs. M is minimal (in sense of Tumanov) in p ϵ M if there does not exist any CR submanifold of M passing through p with the same CR dimension as M but of smaller dimension. Let M be generic and minimal in some point p ϵ M and N be a generic submanifold of M passing through p. We prove that a continuous CR function on M vanishes identically in some neigbourhood of p if its restriction to N either vanishes in p faster then some function with non‐integrable logarithm or it vanishes on a subset of N of positive measure.
Compatibility Conditions and the Manifold of Solutions of some Nonlinear Cauchy‐Riemann System in Several Complex Variables
Authors: Hayashi Yasuo 
Published: May 2007

AbstractThe system of differential equationsmagnified imageIs studied. On the assumption that the system admits certain class of solutions, necessary conditions of compatibility are deduced, and by introducing some changes of variables the system is reduced to a single differential equation, then conversely by solving it, the formula giving all local solutions of the system is infered. The validity of the factorization theorem and the identity theorem for solutions in the class is also treated.
An Operation Connected to a Young‐Type Inequality
Authors: Strömberg Thomas 
Published: May 2007

AbstractGiven two φ‐functions F and G we consider the largest φ‐function H = F ⊕ G such that the Young‐type inequality H(xy) ⩽ F(x) + G(y) holds for all x, y > 0. We prove an equivalence theorem for F ⊕ G with the best constants and, for the special case when F and G are log‐convex and satisfy a certain growth condition, a representation formula for F G. Moreover, further properties and examples are presented and the relations to similar results are discussed.
Complemented Copies of l1 in Orlicz Spaces
Authors: Chen Shutao , Hudzik Henryk , Sun Huying 
Published: May 2007

AbstractCriteria for Orlicz spaces containing an isomorphic as well as an almost isometric complemented copy of l1 are given. The same is made for copies of l∞ and c0 in Orlicz spaces and in the subspace of order continuous elements in Orlicz space, respectively. The Hahn‐Banach theorem is not used in the constructions of the projections.
The Laplace Transformation on Certain Spaces of Generalized Functions
Authors: Baier A. , Glaeske H.‐J. 
Published: May 2007

AbstractIn this paper the Laplace transformation in spaces of generalized functions introduced by McBride in the seventieth is investigated. As an application products of operators of fractional calculus as Riemann Liouville‐operator and Weyl‐operator with the Laplace transform are evaluated.
Approximated Solution of a Nonlinear Singular Equation of Prandtl's Type
Authors: Oestreich D. 
Published: May 2007

AbstractA nonlinear strongly singular integral equation, which can be reduced to a nonlinear singular integro‐differential equation of Prandtl's type, is considered. A collocation method for solution is treated and the convergence of the approximated solution to the unique solution of the nonlinear integral equation is proved.
Eigenvalues and Pole Functions of Hamiltonian Systems with Eigenvalue Depending Boundary Conditions
Authors: Dijksma Aad , Langer Heinz , de Snoo Henk 
Published: May 2007

AbstractThis paper consists of two chapters. The first chapter concerns matrix functions belonging to the generalized Nevanlinna class Nkm × m. We present results about the operator representation of such functions. These representations are then used to obtain information about the (generalized) poles of generalized Nevanlinna functions. The second chapter may be viewed as a continuation of our paper [DLS3] and treats Hamiltonian systems of differential equations with boundary conditions depending on the eigenvalue parameter. In particular we study the eigenvalues, both isolated and embedded eigenvalues.
Asymptotics of Solutions of Difference Equations with Variable Coefficients
Authors: Maz'ya Vladimir , Sulimov Michail 
Published: May 2007

AbstractLinear difference equations in a Hilbert space with coefficients depending on the number n of the equation are considered. It is assumed that the coefficients differ from constant ones by a finite sum of exponentially vanishing terms as n → ∞. An asymptotic formula for solutions as n → ∞ is obtained. The coefficients in the asymptotic expansion are expressed as linear functionals on the space of sequences in the terms on the right‐hand side.
Entire Functions of Bounded Type on Fréchet Spaces
Authors: Galindo Pablo , García Domingo , Maestre Manuel 
Published: May 2007

AbstractWe show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.
On Identification of Memory Kernels in Linear Viscoelasticity
Authors: Wolfersdorf L. V. 
Published: May 2007

AbstractThe inverse problem of identification of the memory kernel in the linear constitutive stress‐strain‐relation of Boltzmann type is reduced to an optimal control problem for an initial‐boundary‐value problem of the related wave equation for the displacement.For the control problem the existence of an optimal control is proved, where both classical and generalized solutions of the equation are dealt with. Further the existence and an expression for the gradient of the cost functional are derived.
On Mordell‐Weil Lattices of Type D5
Authors: Usui Hisashi 
Published: May 2007

AbstractWe establish the analogue for D5 of the theory of algebraic equation of type Er (T. SHIODA: Construction of elliptic curves with high rank via the invariants of the Weyl groups, J. Math. Soc. Japan 43, 1991, No. 4, 673‐719), which is one of the results of the theory of Mordell‐Weil lattices. As an application, we give a method of constructing an elliptic curve over Q(t) with rank 5, together with explicit generators of the Mordell‐Weil group.
A Unified Approach to Shifts Induced by Right Invertible Operators
Authors: Binderman Zbigniew 
Published: May 2007

AbstractIn this paper, shifts for a right invertible operator D induced by an analytic function acting in a linear complete metric space are considered. The case when these shifts coincide with the operator ‐ valued function on a set which contains the set of all D‐polynomials and the set of all exponentials is studied. It is shown that in this case these shifts are R‐shifts and D‐shifts (cf. [1], [10]).
Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces
Authors: Galbis Antonio , Peris Alfredo 
Published: May 2007

AbstractIn this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)‐spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Fréchet spaces. We give an example of a Fréchet‐Schwartz space which is not the projective limit of a sequence of superreflexive Banach spaces.
A Note on the Convergence of Integral Functionals of Diffusion Processes. An Application to Strong Convergence
Authors: Liese F. , Schmidt W. 
Published: May 2007

AbstractFor a diffusion type process dXt = dWi + a(t, X)dt and a sequence (fn) of nonnegative functions necessary and sufficient conditions to the fn are established which guarantee the a.s. convergence of fn(Xt)dt to zero. This result is applied to derive simple necessary and sufficient conditions for the strong convergence of distributions of diffusion processes formulated in terms of the corresponding drift functions.
D‐Algebras with Logarithms
Authors: Przeworska‐Rolewicz D. 
Published: May 2007

AbstractA new definition of logarithms and antilogarithms in algebras with right invertible operators is proposed. It will be shown that in the considered class of such algebras all investigations can be reduced to three cases: either right invertible operators are multiplicative or satisfy the classical Leibniz condition for products or logarithms and antilogarithms do not exist. An analogue of power functions is defined by means of the introduced logarithmic and antilogarithmic mappings.
Non‐classical Eigenvalue Asymptotic for Elliptic Operators of Second Order in Unbounded Trumpet‐shaped Domains with Neumann Boundary Conditions
Authors: Berger Günter 
Published: May 2007

AbstractThe paper deals with spectral properties of elliptic operators of second order in irregular unbounded domains with cusps. The eigenvalue asymptotic of the operator with Neumann boundary conditions is proved. The eigenvalue asymptotic in these domains is different from that with Dirichlet boundary conditions.
Differenzenschemata und Darstellungspolynome für Restklassenabbildungen modulo m
Authors: Burde Klaus 
Published: May 2007

AbstractIn 1. werden Differenzenschemata ganzzahliger Folgen mit der Periode m modulo m betrachtet, wobei die maximale unter den auftretenden endlichen Längen solcher Schemata interessiert. Aus den Ergebnissen von 1. werden in 2. Aussagen über Existenz und Grad von Darstellungspolynomen zu Abbildungen des Restklassenrings modulo m in sich hergeleitet.
Infinite Dimensional Parametric Optimal Control Problems
Authors: Aizicovici Sergiu , Papageorgiou Nikolaos S. 
Published: May 2007

AbstractIn this paper we study parametric optimal control problems monitored by nonlinear evolution equations. The parameter appears in all the data, including the nonlinear operator. First we show that for every value of the parameter, the optimal control problem has a solution. Then we study how these solutions as well as the value of the problem respond to changes in the parameter. Finally, we work out in detail two examples of nonlinear parabolic optimal control systems.
Approximation of Functions on [−1,1] and Their Derivatives by Polynomial Projection Operators
Authors: Balázs K. , Kilgore T. 
Published: May 2007

AbstractPointwise estimates are obtained for the simultaneous approximation of a function f ϵCq[‐1,1] and its derivatives f(1), …, f(q) by means of an arbitrary sequence of bounded linear projection operators Ln which map C[‐1,1] into the polynomials of degree at most n, augmented by the interpolation of f at some points near ± 1.
Approximation by Spherical Functions
Authors: König Hermann 
Published: May 2007

AbstractResults on the degree of approximation of continuous or Lipschitz‐continuous functions f:Sn−1 → ℝ on the sphere in ℝn by spherical functions of degree k are given in terms of k and n, strengthening results of Newman and Shapiro. An example of (restriction of) a norm shows the result to be the best possible in k and n. Further, results for smoother functions are discussed.
Two Projection Theorems and Symbol Calculus for Operators with Massive Local Spectra
Authors: Finck T. , Roch S. , Silbermann B. 
Published: May 2007

AbstractIn this paper we construct a symbol calculus for Banach algebras generated by two idempotents and a coefficient algebra. This, combined with local principles for „embedding algebras”︁, leads to a symbol calculus for singular integral operators on spaces with Muckenhoupt weight and for singular integral operators with measurable coefficients.
Orthogonal Systems of Eigenvectors and Associated Vectors for Symmetric Holomorphic Operator Functions
Authors: Möller Manfred 
Published: May 2007

AbstractIn Banach spaces the principal parts of the inverse of a holomorphic Fredholm valued operator function can be written as sums of tensor products of biorthogonal canoncial systems of eigenvectors and associated vectors of the operator function and its adjoint. If we impose a symmetry condition on the operator function, then for real eigenvalues the eigenvectors and associated vectors of the operator function and its adjoint coincide at this point. We shall show that we can always choose a suitable canonical system of eigenvectors and associated vectors which is orthogonal, i.e., biorthogonal to itself. An application to elliptic differential operators is given.
A Generalization of the Arnold‐Wendland Lemma to a Modified Collocation Method for Boundary Integral Equations in ℝ3
Authors: Hsiao George C. , Prössdorf Siegfried 
Published: May 2007

AbstractWe prove quasioptimal and optimal order estimates in various Sobolev norms for the approximation of linear strongly elliptic periodic pseudodifferential equations in two independent variables by a modified method of nodal collocation by odd degree polynomial splines. In the one‐dimensional case, our method coincides with the method of nodal collocation when odd degree polynomial splines are employed for the trial functions. The convergence analysis is based on an equivalence which we establish between our method and a nonstandard Galerkin method for an operator closely related to the given operator. This equivalence is realized through a crucial intermediate result (which we now term the Arnold‐Wendland lemma) to connect the solution of central finite difference equations and that of certain nonstandard Galerkin equations. The results of this paper are genuine two‐dimensional generalizations of the results obtained by ARNOLD and WENDLAND in [2] for the one‐dimensional equations.
On the MacNeille Completion of the Category of Partially Ordered Topological Spaces
Authors: Schauerte A. 
Published: May 2007

AbstractPreordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the T0(T1, T2) preordered spaces and the (completely regular) partially ordered spaces. We also show that a functor due to L. NACHBIN from the quasi‐uniform spaces to the preordered spaces preserves initial sources.
On the Titchmarsh‐Weyl Coefficients for Singular S‐Hermitian Systems I
Authors: Hinton D. B. , Schneider A. 
Published: May 2007

AbstractSingular S‐Hermitian systems are studied with the goal of defining a Titchmarsh‐Weyl M(λ)‐coefficient directly in terms of separated, selfadjoint boundary conditions. A general deficiency index is allowed. The resolvent operator is constructed and a self‐adjoint operator A is constructed in the Hilbert space which gives an equivalent description of the singular S‐Hermitian boundary value problem.
Inserting L‐fuzzy Real‐valued Functions
Authors: Kotzé Wesley , Kubiak Tomasz 
Published: May 2007

AbstractA new proof of the Katêtov‐Tong Insertion Theorem for L‐fuzzy topological spaces is given. All the proofs are performed in such a way that the presented results hold true in the more general case in which L‐fuzzy topologies are replaced by σ‐additive rings of L‐fuzzy subsets.
Necessary and Sufficient Conditions for a Fourth Order Functional Differential Equation to be Oscillatory
Authors: Gopalsamy K. , Wen Lizhi , Chen Yong‐Shao , He Xue‐Zhong 
Published: May 2007

AbstractNecessary and sufficient conditions for a fourth order functional differential equation of the form(1) [r(t)y″(t)]″+f(t,y(h1(t)), y(h2(t)), …, y(hn(t)))=0to be oscillatory are given when f is strongly superlinear or strongly sublinear.
The Inequality 8pg < μ for Hypersurface Two‐dimensional Isolated Double Points
Authors: Tomari Masataka 
Published: May 2007

AbstractThe Milnor number μ and the geometric genus pg of normal 2‐dimensional double points are studied by using Zariski's canonical resolution. By using formulas due to E. HORIKAWA and H. LAUFER, we represent μ − 8pg in terms of the number of blowing‐ups along ℙ1 and the number l of „even”︁ components in the resolution process. A key point of our arguments is the fact that if l is small then the resolution process is restricted very much. For rational double points and double points with pa = 1, each classes are characterized by numerical invariants appearing in this resolution process. For the case pa = 1, we can make our inequality sharper and can prove 12 · pg − 3 ≤ μ. This is an another proof of Xu‐Yau's inequality for the singularity with pa = 1 in our situation.
Conditional Local States and Decomposition of Locally Normal States
Authors: Liebscher Volkmar 
Published: May 2007

AbstractFor infinite boson systems in the framework of [5, 9] it is proven that all locally normal states possess conditional local states. This result is used to find a tail‐field‐measurable decomposition of these states and to characterize their position distributions in completion to [6] as ‐Point processes. As an example mixed coherent states are investigated.
Continuous Linear Extension of Ultradifferentiable Functions of Beurling Type
Authors: Franken Uwe 
Published: May 2007

AbstractFor a weight function ω and a closed set A ⊂ ℝN let ℰ(ω)(A) denote the space of all ω‐Whitney jets of Beurling type on A. It is shown that for each closed set A ⊂ ℝN there exists an ω‐extension operator EA: ℰ(ω)(A) → ℰ(ω)(ℝN) if and only if ω is a (DN)‐function (see MEISE and TAYLOR [18], 3.3). Moreover for a fixed compact set K ⊂ ℝN there exists an ω‐extension operator EK: ℰ(ω)(K) → ℰ(ω)(ℝN) if and only if the Fréchet space ℰ(ω)(K) satisfies the property (DN) (see Vogt [29], 1.1.).
An Uncertainty Principle for Commutative Hypergroups and Gelfand Pairs
Authors: Voit Michael 
Published: May 2007

AbstractWe extend sharp forms of the classical uncertainty principle to the context of commutative hypergroups. This hypergroup setting includes Gelfand pairs, Riemannian symmetric spaces, and locally compact abelain groups. For some Gelfand pairs our inequalities will be sharper than those in a recent paper by J. A. WOLF.
Oscillations and Convergence in a Diffusive Delay Logistic Equation
Authors: Gopalsamy K. , He Xue‐Zhong , Sun Da‐Qing 
Published: May 2007

AbstractSufficient conditions are obtained for all positive solutions of the diffusive delay‐logistic system magnified image to be oscillatory about the positive equilibrium K. A comparison result is established with which the global asymptotic stability of the positive equilibrium is investigated.
Equilibrium States and Hausdorff Measures for Interval Maps
Authors: Hofbauer Franz , Keller Gerhard 
Published: May 2007

AbstractFor a class of piecewise monotone interval maps T (including unimodal maps with negative Schwarzian derivative) and real valued functions f of bounded variation we compare equilibrium states μ of f with Hausdorff measures v and give an integral test for the dichotomy μ ≪ v or μ ⊥ v. For certain classes of rational maps such a result was proved in [15] and [3].
Leray‐Schauder Degree Method in Functional Boundary Value Problems Depending on the Parameter
Authors: Stanêk Svatoslav 
Published: May 2007

AbstractUsing the Leray‐Schauder degree method sufficient conditions for the one‐parameter boundary value problem x″ = f(t, x, x′, λ), α(x) = A, x(0) − x(1) = B, x′(0) − x′(1) = C, are stated. The application is given for a class of functional boundary value problems for nonlinear third‐order functional differential equations depending on the parameter.
An Omega Theorem for a Class of Arithmetic Functions
Authors: Kühleitner Manfred , Nowak Werner Georg 
Published: May 2007

AbstractThis paper deals with the average order of arithmetic functions a(n) with a generating function of the shape (1.1) where fk and gj possess certain characteristic properties of the zera‐function. Under fairly general conditions, a lower bound for the error term in the asymptotic formula for the corresponding Dirichlet summatory function is established. Finally, several specific applications to functions from elementary number theory and to arithmetic problems in number fields are discussed.
On Singular Integral Operators with Bounded Measurable Coefficients
Authors: Andrew Paul 
Published: May 2007

AbstractNecessary and sufficient analytical conditions are determined for a singular integral operator of the form aP + bQ with bounded measurable coefficients to be a ϕ‐operator on Lp(Γ) for all 1 < p < ∞. where Γ is a closed Lyapunov curve.