bluuebunny/crossref_metadata_2025_split huggingface dataset:
The accelerated convergence of heat transfer series in high frequency oscillating boundary layer flows of compressible fluids
Authors: Gribben R. J. 
Published: November 2011

SynopsisSeries, previously derived, for the heat transfer at the surface of a cylinder fixed in a compressible gas which flows with a high frequency oscillation about a steady mean velocity, are considered in the range of frequencies for which the convergence is slow. Different methods of accelerated convergence, suitable for Fourier and power series, are applied over different parts of the cycle and graphs of the heat transfer over a period of the oscillation are obtained.
Remark on Hilbert's boundary value problem for Beltrami systems
Authors: Begehr Heinrich 
Published: November 2011

SynopsisThe Schauder continuation method for nonlinear problems is based on appropriate a priori estimates for related linear equations. Recently, in a paper by the present author and G. C. Hsiao, the Hilbert boundary value problem with positive index for nonlinear elliptic systems in the plane was solved by this method but the constructive derivation of the a priori estimate necessarily required a restriction on the ellipticity condition. This is because the norm of the generalized Hilbert transform in the case of positive index is too big. Here, as in a forthcoming paper by G.C. Wen, an indirect and therefore non-constructive proof of the a priori estimate is given which does not require any further restrictions and allows the Hilbert boundary value problem to be solved for nonlinear elliptic systems in general.
Quasispectral subspaces of quasinilpotent operators
Authors: Omladič Matjaž 
Published: November 2011

SynopsisWe give a definition of “quasispectral maximalč subspaces for a quasinilpotent, but not nilpotent, bounded Banach space operator. The definition applies to a class of operators, close to the Volterra operator.
Relaxation for some dynamical problems
Authors: Dacorogna B. 
Published: November 2011

SynopsisIn this article, we study the functionalWhere Ω ⊂ ĝnis a bounded open set andu: Ω ×(0,T)→ ĝmand whenF: Rnm→R fails to be quasiconvex. We show that with respect to strong convergence of ∂u/∂tand weak convergence of ∇×u, the above functional behaves aswhereQFis the lower quasiconvex envelope ofF.
On a nonlinear eigenvalue problem occurring in population genetics
Authors: Clément Ph. , Peletier L. A. 
Published: November 2011

SynopsisWe discuss the nonlinear eigenvalue problemwithr(–×) = –r(×) and r'≧0.For ε =h=0, the solution to Problem P is wellknown, and every solution, exceptu= 0 andu=1, is unstable with respect to the corresponding parabolic problem.
Convergence theorems for intermediate problems
Authors: Beattie Christopher A. , Greenlee W. M. 
Published: November 2011

SynopsisGeneral convergence theorems are established for the lower part of the intermediate operator spectra arising in lower bound methods of Aronszajn type.Convergence of the T*T method is considered in detail, as are constructions that allow perturbations that are nonclosable in the underlying Hilbert space. Problems with essential spectra are admitted, as is the use of infinite rank projections capable of displacing essential spectra. These last features are necessary for a theory applicable to Schrodinger operators corresponding to atomic systems.
Lattices of congruences on free finitely generated commutative semigroups and direct products of cyclic monoids
Authors: Trueman D. C. 
Published: November 2011

SynopsisLet S11× V1 be a direct product of a cyclic monoid S11with S1 not a group, and a semigroup V1 with an adjoined identity. We prove thatboth the lattice of congruences on (S11 × V1)/{(1,1)} and the lattice of congruences on (S11 × V1) are neither lower semimodular nor uppersemimodular. We then prove that the lattice of congruences on a free finitely generated commutative semigroup with more than one generator is neither lower semimodular nor upper semimodular.
Effects of commensurable delays in the stability of difference equations
Authors: Ferreira José M. 
Published: November 2011

SynopsisThis paper studies how, in a difference equation, uniform asymptotic stability for commensurable delays implies uniform asymptotic stability globally in the delays. A result is also given on renorming the space C= C([ – ∥r∥, 0]; ℂn so that a difference operator has norm less than one if it is uniformly asymptotically stable globally in the delays.
The arithmetic of certain quartic curves
Authors: Cassels J. W. S. 
Published: November 2011

SynopsisLet F(X, Y, Z) be a non-singular quadratic form with rational coefficients. The curve EF(x2, y2, z2) = 0 is of genus 3. A procedure is described for deciding whether there is an effective divisor on E of degree 3 defined over the rationals. There is such a divisor if and only if there is a point on E defined over some algebraic number field of odd degree. An example is constructed for which there is no such divisor although (i) there are points on E defined over all p-adic fields and over the reals and (ii) there are infinitely many rational points on each of the three curves F(X, y2, z2) = 0, F(x2, Y, z2) = 0 and F(x2, y2, Z) = 0.
On Opial type inequalities in two independent variables
Authors: Pachpatte B. G. 
Published: November 2011

SynopsisThe aim of the present paper is to establish some new integral inequalities of Opial type in two independent variables. Our results are the two independent variable generalizations of some of the inequalities recently established by the present author and in special cases yield the two independent variable analogue of the Opial inequality and its generalization given by G. S. Yang.
Existence and continuity of a weak solution to the problem of a free boundary in a concentrated capacity
Authors: Shillor M. 
Published: November 2011

SynopsisA weak (enthalpy) formulation of the problem of a free boundary moving in the thermal concentrated capacity is given. The problem is to solve the heat equation in a given domain, while on a part of the boundary of this domain the solution (or rather its trace) solves a Stefan problem with forced convection. The existence of a global weak solution is proved by the method of finite differences. Some regularity is obtained from this proof, and the continuity of the temperature is proved. The uniqueness, which is related to the existence of mushy regions, is discussed. A classical enthalpy formulation is conjectured.
An Ω-estimate for the lattice rest of a convex planar domain
Authors: Nowak Werner Georg 
Published: November 2011

SynopsisLet D be a compact convex planar domain containing the origin, the boundary of which is of class C∞ and has finite non-vanishing curvature throughout. For the number A(i) of lattice points in the “blown up” domain √tD, the estimateis established. This is a generalization of Hardy's classical result for the circle problem. The proof is based on asymptotic formulae for certain exponential integrals due to E. Hlawka.
Existence conditions for higher order eigensets of multiparameter operators
Authors: Binding Paul , Browne Patrick J. , Turyn Lawrence 
Published: November 2011

SynopsisWe consider classes of self-adjoint operators for which the nonpositive part of the spectrum consists of eigenvalues ρ0(λ)≦ ρ1(») ≦ … repeated according to multiplicity. The sets of λ where ρi(λ) is negative and zero are labelled Ni and Zi respectively, and Pi = ℝk\(Ni ∪ Zi). We study conditions on the Vj sufficient to ensure nonemptiness of at least one of Ni, Zi and Pi for all T or for all positive definite T, as well as conditions which are necessary in the sense that failure permits emptiness for at least one T.As an example of our results, we show in the Sturm–Liouville casewith L∞ coefficients and separated end conditions, that nonemptiness of Zi for all T (i.e. for all p > 0, all q and all boundary data) is equivalent to the i-independent condition that the ftj do not vanish simultaneously on a set of positive measure.
The extension problem and the mod 2 cohomology of the space of loops on Spin (N)
Authors: Kuribayashi Katsuhiko 
Published: November 2011

SynopsisLet {Er, dr} be a spectral sequence converging to a Hopf algebra H*. We give a method of reconstructing H* from E∞**. By using our method, we determine the mod 2 cohomology of the space of loops on a simply-connected space whose mod 2 cohomology is isomorphic to that of Spin(N) as an algebra over the Steenrod algebra.
Function spaces related to gauge groups
Authors: Sutherland W. A. 
Published: November 2011

SynopsisComponents in the function space of maps from a space X to the classifying space BG of a topological group G can sometimes be distinguished up to homotopy type by a Samelson product method. When X is a closed Riemann surface and G is a unitary group, this method is nearly sufficient to classify the components up to homotopy type.
Regularity and large time behaviour of solutions of a conservation law without convexity
Authors: Dafermos C. M. 
Published: November 2011

SynopsisUsing the method of generalized characteristics, we discuss the regularity and large time behaviour of admissible weak solutions of a single conservation law, in one space variable, with one inflection point.We show that when the initial data are C∞ then, generically, the solution is C∞ except: (a) on a finite set of C∞ arcs across which it experiences jump discontinuities (genuine shocks or left contact discontinuities); (b) on a finite set of straight line characteristic segments across which its derivatives of order m, m = 1, 2,…, experience jump discontinuities (weak waves of order m); and (c) on the finite set of points of interaction of shocks and weak waves. Weak waves of order 1 are triggered by rays grazing upon contact discontinuities. Weak waves of order m, m ≥ 2, are generated by the collision of a weak wave of order m − 1 with a left contact discontinuity.We establish sharp decay rates for solutions with initial data of the following types: (a) with bounded primitive; (b) with primitive having sublinear growth; (c) in L1; (d) of compact support; and (e) periodic.
Travelling waves in radially symmetric parabolic systems
Authors: Bates Peter W. 
Published: November 2011

SynopsisIt is shown that all travelling or standing plane-wave solutions to certain radially symmetric parabolic systems may be found by solving a related scalar ordinary differential equation (ODE). The radially symmetric systems considered here are those whose reaction term is radially directed and points inward near infinity. The stability of these waves is also discussed. Many systems arising in the physical sciences are included in the class studied and so the classification and stability of the travelling waves has physical significance.
Certain 3-decompositions of complete graphs, with an application to finite fields
Authors: Rowlinson Peter 
Published: November 2011

SynopsisA necessary condition is obtained for a complete graph to have a decomposition as the line-disjoint union of three isomorphic strongly regular subgraphs. The condition is used to determine the number of non-trivial solutions of the equation x3+y3 = z3 in a finite field of characteristic p ≡ 2 mod 3.
A transmission problem for the plate equation
Authors: Leis R. , Roach G. F. 
Published: November 2011

SynopsisA scattering theory is developed for transmission problems associated with the plate equation. Asymptotic methods of solution for large time are examined as are questions concerning regularity of solution, nature of the associated spectrum and existence of appropriate wave operators. It is shown that in contrast to solutions of the wave equation, signals can propagate with an infinite dispersion velocity.
Homoclinic solutions for coupled systems of differential equations
Authors: Grindrod P. , Sleeman B. D. 
Published: November 2011

SynopsisTopological ideas based on the notion of flows and Wazewski sets are used to establish the existence of homoclinic orbits to a class of Hamiltonian systems. The results, as indicated, are applicable to a variety of reaction diffusion equations including models of bundles of unmyelinated nerve axons.
Corrigenda: Resolution of a semilinear equation in L1
Authors: Gallouët Thierry , Morel Jean-Michel 
Published: November 2011

Page 277, line 14: Read “measure” instead of “distribution”.Page 287, line 1: Read “(Ω)” instead of “′(Ω)”,line 13: Read “explanation” instead of “generalization”,line 23: Read “In fact, Corollary 1” instead of “In fact, Corollary 2”.We thank Professor L. Véron for directing our attention to these mistakes.
A note on a resonance problem
Authors: Lupo Daniela , Solimini Sergio 
Published: November 2011

SynopsisIn this paper, we prove the existence of at least one solution to the problemwhere ∆k is an eigenvalue of the linear part, h is orthogonal to the eigenspace corresponding to ∆R and g is a nonlinear perturbation which can be, for instance, a continuous periodic real function with mean value zero. We employ the techniques used by the second author in a previous paper in which the same result was obtained in the case in which ∆R is assumed to be simple. The final result is obtained by using variational methods and in particular a suitable version of the saddle point theorem of P. Rabinowitz.
Critical behaviour of nonlinear elliptic boundary value problems suggested by exothermic reactions
Authors: Wiebers Henning 
Published: November 2011

SynopsisWe consider a class of semilinear elliptic boundary value problems depending on a parameter, which arise in the theory of combustion. Based on the results in another paper by the same author, a rigorous quantitative connection is shown between the solution set of the boundary value problem and that of a simple scalar equation (the Semenov approximation).
Rees matrix semigroups over inverse semigroups
Authors: Pastijn F. J. , Petrich Mario 
Published: November 2011

SynopsisA Rees matrix semigroup over an inverse semigroup contains a greatest regular subsemigroup. The regular semigroups obtained in this manner are abstractly characterized here. The greatest completely simple homomorphic image and the idempotent generated part of such semigroups are investigated. Rectangular bands of semilattices of groups and some special cases are characterized in several ways.
Generalizations of the Landau–Hadamard inequality and inequalities for quadratic polynomials of operators
Authors: Boyadzhiev Khr. N. 
Published: November 2011

SynopsisWe give generalizations of the Landau–Hadamard inequality ‖u′‖2 ≦ K ‖u‖ ‖u″‖ replacing u” by the second-order differential expression u″ − (α + β)u′ + αβu (α, β ∈ ℂ). The new functional inequalities are then used to obtain similar inequalities for dissipative and skew-Hermitian operators.
A non-linear Goursat problem for a high order polyvibrating equation
Authors: Borzymowski Andrzej 
Published: November 2011

SynopsisThis paper proves the existence of a solution of a non-linear Goursat problem for a partial differential equation of order 2p (p ≧ 2) with the boundary conditions given on 2p curves emanating from a common point. The problem is reduced to a system of integro-differential-functional equations and then Schauder's fixed point theorem is applied.
A repeated transformation in the asymptotic solution of linear differential systems
Authors: Eastham M. S. P. 
Published: November 2011

SynopsisA sequence of transformations of the type Y = (I + o(1))Z is developed for the system Y′(x) = {Λ(x) + R(x)}Y(x), where Λ is diagonal. The transformations bring in the derivatives of R in succession until the Levinson form is obtained when a given derivative is reached. This theory covers rapidly varying coefficients and it extends results which are known for constant Λ.
Minors of the Wronskian of the differential equation Lny + p(x)y = 0. II. Dominance of solutions
Authors: Elias Uri 
Published: November 2011

SynopsisThe equation studied here is Lny + p(x)y = 0, where Ln is a disconjugate differential operator and p(x) is of a fixed sign. We define a basis of the solution space and order its elements according to their relative magnitudes near infinity. Our method is independent of the possible oscillation or nonoscillation of the solutions and it is achieved by utilising the fact that some minors of the Wronskian never vanish.
Non-negative solutions for a class of non-positone problems
Authors: Castro Alfonso , Shivaji R. 
Published: November 2011

SynopsisIn the recent past many results have been established on non-negative solutions to boundary value problems of the formwhere λ>0, f(0)>0 (positone problems). In this paper we consider the impact on the non-negative solutions when f(0)<0. We find that we need f(u) to be convex to guarantee uniqueness of positive solutions, and f(u) to be appropriately concave for multiple positive solutions. This is in contrast to the case of positone problems, where the roles of convexity and concavity were interchanged to obtain similar results. We further establish the existence of non-negative solutions with interior zeros, which did not exist in positone problems.
Positive solutions of elliptic systems with bounded nonlinearities
Authors: Noussair Ezzat S. , Swanson Charles A. 
Published: November 2011

SynopsisSemilinear elliptic partial differential systems of second order with weak coupling are considered in exterior domains Ω ⊆ ℝN, N≧3. Conditions on the nonlinearities are given which guarantee the existence of solutions u with positive components in Ω such that u|∂Ω = 0 and u(x)→0 uniformly as |x|→∞. Asymptotic decay estimates for the solutions are established, including an exponential decay law under extra hypotheses.
Oscillation criteria and the discreteness of the spectrum of self-adjoint, even order, differential operators
Authors: Došlý Ondřej 
Published: November 2011

SynopsisThis paper deals with the oscillation properties of self-adjoint differential equationsThe oscillation criteria are derived, which allows a unified approach to the investigation of (*) near a finite or infinite singularity. These criteria are used to study spectral properties of singular differential operators associated with (*).
Maximisation and minimisation on classes of rearrangements
Authors: Burton G. R. , McLeod J. B. 
Published: November 2011

SynopsisMaximisation and minimisation of the Dirichlet integral of a function vanishing on the boundary of a bounded domain are studied, subject to the constraint that the Laplacean be a rearrangement of a given function. When the Laplacean is two-signed, non-existence of minimisers is proved, and some information on the limits of minimising sequences obtained; this contrasts with the known existence of minimisers in the one-signed case. When the domain is a ball and the Laplacean is one-signed, maximisers and minimisers are shown to be radial and monotone. Existence of maximisers is proved subject additionally to a finite number of linear constraints, with particular reference to ideal fluid flows of prescribed angular momentum in a disc.
Homogenisation of a class of fourth order equations with application to incompressible elasticity
Authors: Francfort G. A. 
Published: November 2011

SynopsisUpon formalising an analogy between two-dimensional Stokes flow and two-dimensional isotropic conductivity, we exhibit a class of fourth order equations which behave “isomorphically” like isotropic conductivity from the standpoint of homogenisation and from that of corresponding bounding methods on possible effective behaviours. In particular, Lipton's result on the G-closure problem for mixtures of two incompressible elastic materials is recovered in the two-dimensional case.
Initial conditions for integrable-square solutions to singular differential equations
Authors: Walker Philip W. 
Published: November 2011

SynopsisThis paper deals with determining in a constructive manner those members of a linear space of functions which are of integrable-square. The space considered is the set of solutions to an ordinary differential equation, and the solutions of integrable-square are delineated by way of initial conditions. Numerical procedures for implementing the construction are discussed, and application is made to the deficiency index problem. Results from some specific computations are given.
On periodic solutions for singular perturbation problems
Authors: Korman Philip 
Published: November 2011

SynopsisWe apply a version of the Nash–Moser method to prove existence of periodic solutions for nonlinear elliptic equations and systems, involving singular perturbations. We allow nonlinearities depending on derivatives of order two more than that of the linear part, thus extending the previous results. Our result is new even in the case of one equation in one spatial dimension.
Classification of regularly solvable first-order differential operators
Authors: Benammar M. 
Published: November 2011

SynopsisIn this article the expression τφ: = pφ + qφ with complex-valued coefficients is considered. We are particularly concerned with this expression when it is not formally symmetric, i.e., τ ≠ τ+, where τ+ is the formal adjoint of τ, and especially with the operators which are regularly solvable with respect to the minimal operators generated by τ and τ+ in the sense of W. D. Evans in [3]. This article is divided into five sections: Section 1 is an introduction, Section 2 is a brief study of the regular problem, in Section 3, some preliminary results in the singular case are displayed in Section 4, the joint field of regularity in the singular case is investigated and in Section 5, we discuss the case when .
Rank-one convexity does not imply quasiconvexity
Authors: Šverák Vladimír 
Published: November 2011

We consider variational integralsdefined for (sufficiently regular) functionsu: Ω→Rm. Here Ω is a bounded open subset ofRn,Du(x) denotes the gradient matrix ofuatxandfis a continuous function on the space of all realm×nmatrices Mm×n. One of the important problems in the calculus of variations is to characterise the functionsffor which the integralIis lower semicontinuous. In this connection, the following notions were introduced (see [3], [9], [10]).
On the minimization of singular quadratic functional
Authors: Bradley John S. , Hinton Don B. , Kauffman Robert M. 
Published: November 2011

SynopsisA quadratic functional Q is considered which is defined by an integral on a subset of functions in a weighted Hilbert space. The functional Q is minimized subject to the Dirichlet index of the associated differential operator being minimal. The infimum of Q is shown to be the least point in the spectrum of a certain self-adjoint operator which arises as a Friedrichs extension.
On the Lax-Phillips scattering theory
Authors: Amrein W. O. , Wollenberg M. 
Published: November 2011

SynopsisWe give a simple description of the wave operators appearing in the Lax-Phillips scattering theory. This is used to derive a relation between the scattering matrix and a kind of time delay operator and to characterize all scattering systems having the same scattering operator.
Concerning the “panneaux” of M. Sova
Authors: Donegan H. A. , McMaster T. B. M. 
Published: November 2011

SynopsisFor the investigation of certain kinds of reflexivity in topological vector spaces, Sova has shown that the ideas of panneaux and of espaces pannelés are as crucial as are those of barrels and of barrelled spaces. The objectives of this note are: (i) to establish the existence of (concentrated) barrels which are not panneaux, and (ii) to observe the equivalence of the conditions “pannelé” and “barrelled” for metrizable spaces, and the failure of this equivalence for general spaces.
Smoothing effect and asymptotic behaviour for the solutions of a nonlinear time dependent system
Authors: Dias João-Paulo , Haraux Alain 
Published: November 2011

SynopsisIn this paper we obtain some new results on a nonlinear parabolic system related to the equations of the nematic liquid crystals and introduced in earlier papers by J. P. Dias.These results mainly concern the existence and uniqueness of generalized solutions for discontinuous data and also their asymptotic behaviour in various cases.