bluuebunny/crossref_metadata_2025 huggingface dataset:
Acoustic radiation of long wavelength
Authors: Jones D. S.
Published: November 2011

Synopsis

Formulae are derived for the first two approximations to the radiation pattern of a penetrable body in the long wavelength limit. They are expressed in terms of a solution of Laplace's equation satisfying certain boundary conditions. Various inequalities and principles which help fix this solution are given.
Energy stability for the flow between rotating, coaxial disks
Authors: Elcrat Alan R.
Published: November 2011

Synopsis

A stability condition is derived for solutions of the Von Kárman-Batchelor equations for the flow of a viscous, incompressible fluid between rotating, coaxial (infinite) disks. The rigid motion solution which arises when the angular velocities of the disks are equal is stable with respect to perturbations which go to zero sufficiently rapidly at infinity, for all values of the Reynolds number. If the angular velocities are sufficiently close the stability condition derived applies to perturbations whose “deformation energy” is sufficiently confined to a “core” region.
The isomorphism semigroup of a periodic abelian group
Authors: Kirkwood Ian
Published: November 2011

Synopsis

The isomorphism semigroup S(G) of a group G is the semigroup of isomorphic mappings between subgroups of G, with composition its operation. This paper will show that a periodic abelian group is uniquely determined by its isomorphism semigroup.
On convergence and error estimates for the horizontal line method applied to Maxwell's initial boundary problem in anisotropic, inhomogeneous media
Authors: Picard Rainer
Published: November 2011

Synopsis

In the following paper, the horizontal line method (the Rothe method) is applied to Maxwell's initial boundary value problem. By means of results from abstract perturbation theory, convergence results and error estimates are established.
The existence of eigenvalues of infinite multiplicity for the Schrödinger operator
Authors: Thurlow Christine R. , Eastham Michael S.P.
Published: November 2011

Synopsis

It is shown that eigenvalues of infinite multiplicity can exist for the Schrödinger equation holding in the whole N-dimensional space RN(N ≧ 2). In the example which is constructed, the potential is separable and bounded in RN, and the method is an application of inverse spectral theory.
On the separation property of symmetric ordinary fourth-order differential expressions
Authors: Das Jyoti , Sett Jayasri
Published: November 2011

Synopsis

Conditions are given on the coefficients p, q and r of the fourth-order, symmetric differentia expression

where y ∈ L2(0, ∞) and L[y] ∈ L2(0, ∞), such that some or all of the individual terms in L[y] are also in L2(0, ∞).
Wiener processes on manifolds of maps
Authors: Baxendale Peter
Published: November 2011

Synopsis

The solutions of stochastic differential equations are used to construct Markov processes on the Banach manifold C(S, M) of continuous maps from a compact metric space S into a smooth complete finite dimensional Riemannian manifold M. In the special case where S is a single point the construction gives a large class of diffusion processes on the manifold M, including (under certain curvature conditions) the Brownian motion process.
An example of “secondary bifurcation” in a non-autonomous two-point boundary value problem
Authors: Clément Ph. , vanKan J.
Published: November 2011

Synopsis

We consider the continuation of positive solutions of -u" = λs(x)f(u), with appropriate boundary conditions and with positive s and f. We show by an example that bifurcation may occur from the curve of these positive solutions.
Generation of p-groups by elements of bounded breadth
Authors: Vaughan-Lee M. R. , Wiegold James
Published: November 2011

Synopsis

The following conjecture of I. D. Macdonald is confirmed in this paper. If G is a finite ρ-group generated by elements of breadth at most n, then the nilpotency class of G is bounded in terms of nonly.
Point transfer matrices for the Schrödinger equation: the algebraic theory
Authors: Gordon N. A. , Pearson D. B.
Published: November 2011

This paper deals with the theory of point interactions for the one-dimensional Schrödinger equation. The familiar example of the δ-potential V(x) = gδ(x−x0), for which the transfer matrix across the singularity (point transfer matrix) is given by

is extended to cover cases in which the transfer matrix M(z) is dependent on the (complex) spectral parameter z, and which can be obtained as limits of transfer matrices across finite intervals for sequences of approximating potentials Vn.

The case of point transfer matrices polynomially dependent on z is treated in detail, with a complete characterization of such matrices and a proof of their factorization as products of point transfer matrices linearly dependent on z.

The theory presented here has applications to the study of point interactions in quantum mechanics, and provides new classes of point interactions which can be obtained as limiting cases of regular potentials.
Spectral properties of compact multiparameter operators
Authors: Binding Paul , Browne Patrick J. , Turyn Lawrence
Published: November 2011

Synopsis

Let

be, for each λ∈ℝk, a compact symmetric operator on a complex Hilbert space. Let the“fundamental” eigenset Z be denned by the relation λ∈Z if and only if W(λ) has maximal eigenvalue one. Conditions are given for Z to be the boundary of an open convex set P. A detailed investigation is given of the structure of P, including its recession cone and its representations as intersections of half-spaces.
A stable method for an inverse problem in acoustic scattering by an obstacle with an impedance boundary condition
Authors: Smith Robert T.
Published: November 2011

Synopsis

We examine the case of plane, time-harmonic acoustic waves in two dimensions, scattered by an obstacle on the surface of which an impedance boundary condition is imposed. A stable method is developed for solving the inverse problem ofdetermining both the shape of the scatterer and the surface impedance from measurements of the asymptotic behaviour of the scattered waves at low frequencies. We accomplish this by minimizing an appropriate functional over a compact set of admissible boundary curves and admissible impedances.
Amalgamation properties in the class of MS-algebras
Authors: Blyth T. S. , Varlet J. C.
Published: November 2011

Synopsis

We determine which subvarieties of the class of MS-algebras enjoy the amalgamation property, the embedding property, the strong amalgamation property, or the special amalgamation property.
Counting common representatives and symmetric chain decompositions
Authors: Anderson I.
Published: November 2011

Synopsis

We obtain lower bounds for the number of common systems of distinct representatives of two families of sets and the number of symmetric chain decompositions of certain ranked partially ordered sets.
Singular perturbation of a nonlinear problem with multiple solutions
Authors: Lefevere Anne-Marie
Published: November 2011

Synopsis

A nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().
On Sobolev type integral inequalities
Authors: Pachpatte B. G.
Published: November 2011

Synopsis

The aim of this paper is to establish some new integral inequalities of the Sobolev type involving functions of several independent variables. The analysis used in the proofs is elementary and the results established provide new estimates for this type of inequality.
Is elasticity the proper asymptotic theory for materials with small viscosity and capillarity?
Authors: Boldrini Jose L.
Published: November 2011

Synopsis

We consider the equations for the isothermal motion of a one-dimensional unbounded body composed of a material with viscosity and capillarity. Using a technique derived from the theory of compensated compactness, we find conditions which guarantee that, as viscosity and capillarity approach zero, the solutions to these equations converge to a solution to the corresponding equations in elasticity.
Semidirect products of semigroups
Authors: Preston G. B.
Published: November 2011

Synopsis

Two alternative characterizations of semidirect products of semigroups are given. Characterizations are provided of such products that are groups, regular semigroups, and inverse semigroups, respectively.
The Palais–Smale conditions for the Yang–Mills functional
Authors: Wilkins D. R.
Published: November 2011

Synopsis

We consider the Yang–Mills functional denned on connections on a principal bundle over a compact Riemannian manifold of dimension 2 or 3. It is shown that if we consider the Yang–Mills functional as being defined on an appropriate Hilbert manifold of orbits of connections under the action of the group of principal bundle automorphisms, then the functional satisfies the Palais–Smale condition.
Abel–Gontscharoff interpolation error bounds for derivatives
Authors: Wong Patricia J. Y. , Agarwal Ravi P.
Published: November 2011

Synopsis

We obtain best possible uniform error bounds for the derivatives of the Abel–Gontscharoff polynomial interpolation of a function on the interval [a, b].
Lower semicontinuity of surface energies
Authors: Fonseca Irene
Published: November 2011

Synopsis

Using the theory of indicator measures, a lower semicontinuity result for quasiconvex functions in W1,1 and assuming only L1 convergence is obtained.
On the semigroups of order-decreasing finite full transformations
Authors: Umar Abdullahi
Published: November 2011

Synopsis

Let Singn be the subsemigroup of singular elements of the full transformation semigroup on a totally ordered finite set with n elements. Let be the subsemigroup of all decreasing maps of Singn. In this paper it is shown that is a non-regular abundant semigroup with n − 1 -classes and . Moreover, is idempotent-generated and it is generated by the n(n − 1)/2 idempotents in J*n−1. Let

and

Some recurrence relations satisfied by J*(n, r) and sh (n, r) are obtained. Further, it is shown that sh (n, r) is the complementary signless (or absolute) Stirling number of the first kind.
Linear initial value problems with a singular perturbation of hyperbolic type
Authors: Geel R.
Published: November 2011

Synopsis

This paper deals with initial value problems in ℝ2 which are governed by a hyperbolic differential equation containing a small positive factor ε in front of the second order part of the differential operator. Pointwise a priori estimates for the solution are established by means of an energy integral method. With the help of these estimates it is shown that the solution admits an asymptotic expansion into powers of ε which is uniformly valid in compact subsets of ℝ2. All results are obtained under the assumption that the characteristics of the first order part of the differential operator satisfy a so-called “timelike” condition. A discussion of the concepts “timelike” and “spacelike” is given.
Dual solutions in mixed convection
Authors: Wilks G. , Bramley J. S.
Published: November 2011

Synopsis

Dual similarity solutions in the context of mixed convection are presented. In contrast to the Falkner–Skan solutions the bifurcation point is found to be distinct from the point of vanishing skin friction. The eigenvalue problem arising out of a stability analysis of these solutions is examined numerically. The numerical evidence would seem to indicate that the margin of stability is associated with the onset of reverse flow as opposed to the bifurcation point, as conjectured by Banks and Drazin in 1973.
A limit-point criterion for 2n-th order symmetric differential expressions
Authors: Schultze Bernd
Published: November 2011

Synopsis

A perturbation theorem for symmetric differential expressions is given and applied to even-order expressions. We assume the coefficients p0(t), pn(t) to be eventually positive and to have real powers of t as dominating terms. Then we are able to admit for the absolute values of the other coefficients a rate of growth depending on the growth of both of the coefficients p0, pn in order to obtain minimal deficiency indices.
On uniform boundedness properties in exhausting additive set function spaces
Authors: Moltó Aníbal
Published: November 2011

Synopsis

Valdivia (1978) introduced the class of suprabarrelled spaces, and (1979) deduced some uniform boundedness properties for scalar valued exhausting additive set functions on a σ-algebra from the suprabarrelledness of certain spaces. In this paper, it is shown that those uniform boundedness properties hold for G-valued exhausting additive set functions, G being a commutative topological group, on a larger class of Boolean algebras. Such properties are proved in Valdivia (1979) by means of duality theory arguments and ‘sliding hump’ methods, whereas here they are derived from the Baire category theorem. This generalization enables us to find a wide class of compact topological spaces K such that the subspaces of C(K) which satisfy a mild property are suprabarrelled.
The simplicity of near-rings of mappings
Authors: Meldrum J. D. P. , Zeller Mike
Published: November 2011

Synopsis

Let G be a group and S a group of automorphisms of G. The simplicity of the near-ring, MS(G), of zero preserving functions on G which commute with the elements of S, is investigated. The relationship between simplicity, 2-primitivity and containment relations among the stabilizers of elements of G is explored.
Non-linear mixed boundary value problems for elliptic partial differential equations
Authors: Bailet-Intissar Joëlle
Published: November 2011

Synopsis

A sufficient condition on the angles of a bounded open subset of ℝn is given, ensuring the best regularity of solutions of a class of elliptic problems with non-linear mixed boundary conditions.
Perturbation of two-point boundary value problems with eigenvalue parameter in the boundary conditions
Authors: Turyn Lawrence
Published: November 2011

Synopsis

We discuss smooth changes of eigenvalues under perturbation of the boundary value problems given in the title. The simple eigenvalue criterion is developed in the setting of Banach spaces, so very general perturbations of both the differential equation and the boundary conditions are allowed. Further, we need no assumptions about self-adjointness of the original or perturbed problems. The discussion is concluded with the application of the simple eigenvalue criterion to two examples.
The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space
Authors: Dawlings R. J. H.
Published: November 2011

Let H be a separable Hilbert space and let CL(H) be the semigroup of continuous, linear maps from H to H. Let E+ be the idempotents of CL(H). Let Ker ɑ and Im ɑ be the null-space and range, respectively, of an element ɑ of CL(H) and let St ɑ be the subspace {x∊H: xɑ = x} of H. It is shown that 〈E+〉 = I∪F∪{i}, where

and ι is the identity map. From the proof it is clear that I and F both form subsemigroups of 〈E+〉 and that the depth of I is 3. It is also shown that the depths of F and 〈E+〉 are infinite.
A complex polytope as generalized quadrangle
Authors: Hoggar S. G.
Published: November 2011

Synopsis

We show that the classical generalized quadrangle W(3) is modelled by a complex polytope, and give an explicit embedding in PG(3, 3)
Periodic solutions of time-dependent, semilinear evolution equations of compact type
Authors: Sager Herbert C.
Published: November 2011

Synopsis

We establish the existence of solutions in a weak sense of

where t Є J = [0, T] and′ = d/dt. It is supposed that the unbounded, linear operators A(t) generate analytic and compact semigroups on a Hilbert space H and that B(t, x) are bounded linear operators. The function f(t, x) with values in H may have asymptotically sublinear growth.

We prove the existence of a periodic solution with the help of Schauder’s fixed point theorem.

Accordingly, we first verify that the corresponding linearized version of (0.1),

has a unique solution for each square integrable ψ(t), provided that the homogeneous problem has only the zero solution.
Discrete and shift Kolmogorov type inequalities
Authors: Ditzian Z.
Published: November 2011

Synopsis

The operators Δhf ≡ f(x) on function spaces and Δxn ≡ xn+1–xn on sequence spaces replace derivatives to yield analogues of the Kolmogorov inequality. Estimates for best constants are given for many spaces and for a few the best constants are actually given.
Singularities of solutions for first order quasilinear hyperbolic systems
Authors: Da-tsin(Li Ta-tsien) Lee , Jia-hong Shi
Published: November 2011

Synopsis

In this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.
Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces
Authors: Webb G. F.
Published: November 2011

Synopsis

The following theorem is proved: Let S(t), t≧0 be a dynamical system in an infinite dimensional Banach space X such that S(t) = S1(t)+S2(t) for t≧0, where (1) uniformly in bounded sets of x in X, and (2) S2(t) is compact for t sufficiently large. Then, if the orbit {S(t)x: t ≧0} of x ∈ X is bounded in X, it is precompact in X. Applications are made to an age dependent population model, a non-linear functional differential equation on an infinite interval, and a non-linear Volterra integrodifferential equation.
The inverse scattering problem for a cylinder
Authors: Colton David
Published: November 2011

Synopsis

Let D be a bounded simply connected domain in the plane and Ω the unit disk. Let F(Θ;k) be the far field pattern arising from the scattering of an incoming plane wave by the obstacle D and let an(k) denote the nth Fourier coefficient of F. Then if f conformally maps ℝ2\D onto ℝ2\Ω, a “moment” problem is derived which expresses an(k) in terms of f−1 for small values of the wave number k. The solution of this moment problem then gives the Laurent coefficients of f−1 and hence ∂D.
Bands with distributive congruence lattice
Authors: Fountain J. B. , Lockley P.
Published: November 2011

Synopsis

This paper investigates the effect on the structure of a band of imposing conditions on the congruence or right congruence lattice of the band. Bands whose congruence lattices are distributive or Boolean are characterized, as are bands whose right congruence lattices are Boolean.
On a class of interpolation series
Authors: Hille Einar
Published: November 2011

Synopsis

This paper deals with a class of interpolation series of the form

called R-series. It is equiconvergent with the Dirichlet series

If the nth Legendre polynomial for the interval (0,1) is denoted by (−1)nLn(t), then the bilinear formula

serves as generating function for the Rn(z). It also leads in easy steps to R-series expansions for rational functions.

Lagrange [7] has shown that a function holomorphic and of finite rate of growth in a right half-plane can be expanded in an R-series whose abscissa of convergence is limited by the rate of growth of f(z). The converse problem is attacked in Theorem 2 below where it is shown that
The periodic quasigeostrophic equations: existence and uniqueness of strong solutions
Authors: Bennett A. F. , Kloeden P. E.
Published: November 2011

Synopsis

The periodic quasigeostrophic equations are a coupled system of a second order elliptic equation for a streamfunction and first order hyperbolic equations for the relative potential vorticity and surface potential temperatures, on a three-dimensional domain which is periodic in both horizontal spatial co-ordinates. Such equations are used in both numerical and theoretical studies in meteorology and oceanography. In this paper Schauder estimates and a Schauder fixed point theorem are used to prove the existence and uniqueness of strong, that is classical, solutions of the periodic quasigeostrophic equations for a finite interval of time, which is inversely proportional to the sum of the norms of the initial vorticity and surface temperatures.
Dissipative operators with finite dimensional damping
Authors: Röh Harald
Published: November 2011

Synopsis

LetG: ε(G)⊂ℋ → ℋ be a maximal dissipative operator with compact resolvent on a complex separable Hilbert space ℋ andT(t) be theCosemigroup generated byG. A spectral mapping theorem σ(T(t))\{0} = exp (tσ(G))/{0} together with a condition for 0 ε σ(T(t)) are proved if the set {xε ⅅ(G) | Re (Gx, x) = 0} has finite codimension in ε(G) and if some eigenvalue conditions forGare satisfied. Proofs are given in terms of the Cayley transformationT= (G+I)(G−I)−1ofG. The results are applied to the damped wave equationutt+ γutx+uxxxx+ ßuxx= 0, 0 ≦t< ∞ 0 <x< 1, β, γ ≧ 0, with boundary conditionsu(0,t) =ux(0,t) =uxx(1,t) =uxxx(1,t) = 0.
A note on the exact solutions for non-conservative three-wave resonance
Authors: Craik A. D. D.
Published: November 2011

Synopsis

Exact solutions recently discovered for non-conservative three-wave resonance are here related to the ‘one-lump’ solutions obtained by Backlund transformation in conservative cases.
Comparison principles for strongly coupled reaction-diffusion equations
Authors: Sleeman B. D. , Tuma E.
Published: November 2011

Synopsis

Comparison principles for systems of reaction-diffusion equations coupled via both the reaction and diffusion terms are considered. Applications to the FitzHugh–Nagumo equations and models of coupled nerve fibres are included.
The approximation of exterior Neumann problems in a halfspace by means of problems with compact boundary
Authors: Becker Ronald I. , New Ronald
Published: November 2011

Synopsis

This paper describes a proof that the solutions of Neumann problems for the exterior of spheres {x ∊ ℝ3∣ converge to the solutions of the exterior problem for the halfspace {x ∊ ℝ3 } x1 ≧ 0} as b → ∞ provided that the boundary data converge in a certain sense. The method requires that there be some dissipation which can be arbitrarily small. Fredholm integral equations are set up for the boundary data, and these are solved by means of Neumann series for large b. Estimates on the terms of the series (which involve singular integrals), in terms of b, allow the convergence proof to be carried through.

The procedure of expressing problems with infinite boundaries in terms of problems with finite boundaries allows the implementation of an effective numerical procedure for determining, for example, the entire near-field of a baffled piston, a problem whose solution has proved elusive for many years.
The mod 2 homology of the space of loops on the exceptional Lie group
Authors: Kono Akira , Kozima Kazumuto
Published: November 2011

Synopsis

The Hopf algebra structure of H*(ΩG, F2) and the action of the dual Steenrod algebra are completely and explicitly determined when G isone of the connected, simply connected, exceptional, simple Lie groups. The approach is homological, using connected coverings and spectral sequences.
On the geometric properties of Vandermonde's mapping and on the problem of moments
Authors: Kostov V. P.
Published: November 2011

Synopsis

In this paper we prove that the domain of hyperbolicity of the polynomial xn + λ2nn−2+λ3xn−3+ … + λn,λiϵR intersected by the half-space λ2 ≧ – 1, has the property of Whitney, i.e., every two points of this set can be connected by a piecewise-smooth curve belonging to it, whose length is ≦C times greater than the euclidian distance between the points, where the constant C does not depend on the choice of the points. Parallel with this, we show that the values x1≦x2≦…≦xn of a random variable are uniquely determined by the corresponding probabilities and by thefirst n moments.
Fractional powers of operators and Riesz fractional integrals
Authors: Schiavone S. E.
Published: November 2011

Synopsis

In this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.
M(λ)-computation for singular differential systems
Authors: Kaper Hans G. , Krall Allan M.
Published: November 2011

Synopsis

Depending upon the initial data associated with the fundamental matrix, the function M(λ), used to generate L2-solutions of homogeneous linear differential systems, may vary. We show that there is a matrix bilinear transformation between such functions M(λ) with different initial data and illustrate how the result can be used to simplify the calculation of a specific M(λ)-function for a scalar second-order problem.
Erratum: Multiparameter definiteness conditions II [Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 47-61]
Authors: Binding Paul
Published: November 2011

Page 58: Lemma 7.1 is incorrect. It is claimed that Ao =cocl for c =k−l when in fact the result is proved for c = (dim H)−1. Thus while Corollaries 7.4 and 7.6 still stand (as does Corollary 7.3 by alternative arguments) the remaining results in Section 7 must be withdrawn.
Global blow-up of a nonlinear heat equation
Authors: Lacey A. A.
Published: November 2011

Synopsis

Solutions to semilinear parabolic equations of the form ut = Δu + f(u), x in Ω, which blow up at some finite time t* are investigated for “slowly growing” functions f. For nonlinearities such as f(s) = (2 +s)(ln(2 +s))1+b with 0 < b < l,u becomes infinite throughout Ω as t→t* −. It is alsofound that for marginally more quickly growing functions, e.g. f(s) = (2 + s)(ln(2 +s))2, u is unbounded on some subset of Ω which has positive measure, and is unbounded throughout Ω if Ω is a small enough region.
Corrigendum: Convergence theorems for intermediate problems
Authors: Beattie Christopher A. , Greenlee W. M.
Published: November 2011

Professor R. D. Brown has brought to our attention an error in our Theorem 4.2. This would, in turn, invalidate Theorem 3.6 which depends on Theorem 4.2. The basic flaw is that the alignment hypothesis of Proposition 4.1 is not satisfied by the product space projections, Qn. Interestingly, such product space constructions are a common computational device in applications of the T*T method, but apparently seldom satisfy the alignment hypothesis of Proposition 4.1. We wish here to correct these theorems, and comment on the resulting implications for Example 6.1. In independent and as yet unpublished work, Professor Brown has obtained further new results on convergence of the method of intermediate problems.
Intersection properties of ball sequences and uniqueness of Hahn–Banach extensions
Authors: Oja E. , Põldvere M.
Published: November 2011

LetXbe a Banach space andYa closed subspace. We introduce an intrinsic geometric property ofY—thek-ball sequence property—which is a weakening of the famousk-ball property due to Alfsen & Effros. We prove thatYsatisfies the 2-ball sequence property if and only ifYhas the Phelps uniqueness property U (i.e. every continuous linear functionalg ∈Y*has a unique norm-preserving extensionf ∈X*). We prove thatYis an ideal having property U if and only ifYsatisfies the 3-ball sequence property, and in this case,Ysatisfies thek-ball sequence property for allk.
Counting completely 0-simple and completely simple semigroups
Authors: Houghton C. H.
Published: November 2011

Synopsis

Formulae are derived for the numbers of completely 0-simple and completely simple semigroups with m ℒ-classes, n ℜ-classes and underlying finite group G.
A Liapunov functional for a scalar differential difference equation
Authors: Infante E. F. , Walker J. A.
Published: November 2011

Synopsis

Given the scalar, retarded differential difference equation x'(t)=ax(t) +bx(t−τ), a quadratic functional in explicit form is obtained that yields necessary and sufficient conditions for the asymptotic stability of this equation. This functional a Liapunov functional, is obtained through the study of the Liapunov functions associated with a difference equation approximation of the difference differential equation. The functional then obtained not only yields necessary and sufficient conditions for asymptotic stability, but provides estimates for rates of decay of the solutions as well as conditions, for asymptotic stability independent of the magnitude of the delay τ.
Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function
Authors: Payne L. E.
Published: November 2011

Synopsis

In this paper maximum principles are employed to relate solutions of certain classes of nonlinear elliptic problems to solutions of the associated torsion problem. By this method a number of new isoperimetric inequalities are derived. In special cases solutions of the nonlinear problems are also related to solutions of the clamped membrane problem.
V-regular semigroups
Authors: Nambooripad K. S. S. , Pastijn F.
Published: November 2011

Synopsis

A regular semigroup S is called V-regular if for any elements a, b ∈ S and any inverse (ab)′ of ab, there exists an inverse a′ of a and an inverse b′ of b such that (ab)′ = b′a′. A characterization of a V-regular semigroup is given in terms of its partial band of idempotents. The strongly V-regular semigroups form a subclass of the class of V-regular semigroups which may be characterized in terms of their biordered set of idempotents. It is shown that the class of strongly V-regular semigroups comprises the elementary rectangular bands of inverse semigroups (including the completely simple semigroups), a special class of orthodox semigroups (including the inverse semigroups), the strongly regular Baer semigroups (including the semigroups that are the multiplicative semigroup of a von Neumann regular ring), the full transformation semigroup on a set, and the semigroup of all partial transformations on a set.
Solution periodique d'une équation d'évolution
Authors: Coron J. M.
Published: November 2011

On montre que l'existence d'une solution de période T pour l'équation

n'implique pas que

appartient à l'enveloppe convexe de l'image de ∂ϕ.
Bénard convection and the Cattaneo law of heat conduction
Authors: Straughan B. , Franchi F.
Published: November 2011

Synopsis

Critical Rayleigh numbers are obtained for the onset of convection when the Maxwell–Cattaneo heat flux law is employed. It is found that convection is possible in both heated above and below cases.
Diffusion processes with non-smooth diffusion coefficients and their density functions
Authors: Lyons T. J. , Zheng W. A.
Published: November 2011

Synopsis

Denote by Xt an n-dimensional symmetric Markov process associated with an elliptic operator

where (aij) is a bounded measurable uniformly positive definite matrix-valued function of x. Let f(x, t) be a measurable function defined on Rn × [0, 1]. In this paper, we prove that f(Xt, t) is a regular Dirichlet process if and only if the following two conditions are satisfied:

(i) For almost every and

(ii) Let be a sequence of subdivisions of [0,1] so that

Then

As an application of the above result, we prove the following fact: Let p(y, t) be the probability density of the diffusion process Yt, associated with the elliptic operator

where (bi) are bounded measurable functions of x and we suppose that . Then, p(Yt, t) is a regular Dirichlet process and therefore p(.,.) satisfies (i) and (ii).
Transformation and canonical forms of functional-differential equations
Authors: Neuman František
Published: November 2011

Synopsis

Functional-differential equations, especially linear ones, are considered with respect to global pointwise transformations. Two types of canonical forms for certain classes of these equations are introduced. These transformations and the corresponding canonical forms preserve oscillatory or non-oscillatory behaviour of solutions. They are also suitable for studying both-side solutions of equivalent functional-differential equations.
Travelling-wave solutions to the Korteweg-de Vries-Burgers equation
Authors: Bona J. L. , Schonbek M. E.
Published: November 2011

Synopsis

The existence and certain qualitative properties of travelling-wave solutions to the Korteweg-de Vries-Burgers equation,

are established. The limiting behaviour of these waves, when ε tends to zero and when δ tends to zero is examined together with a singular limit wherein both ε and δ tend to zero.
General edge asymptotics of solutions of second-order elliptic boundary value problems I
Authors: Costabel Martin , Dauge Monique
Published: November 2011

Synopsis

This is the first of two papers in which we study the singularities of solutions of second-order linear elliptic boundary value problems at the edges of piecewise analytic domains in ℝ3. When the opening angle at the edge is variable, there appears the phenomenon of “crossing” of the exponents of singularities. For this case, we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted Sobolev spaces for the regular part of the solution and for the coefficients of the singularities. These combinations appear in a natural way as sections of an analytic bundle above the edge. Their behaviour is described with the help of divided differences of powers of the distance to the edge. The class of operators considered includes second-order elliptic operators with analytic complex-valued coefficients with mixed Dirichlet, Neumann or oblique derivative conditions. With our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works. In this first part, we prove the basic facts in a simplified framework. Nevertheless the tools we use are essentially the same in the general situation.
General edge asymptotics of solutions of second-order elliptic boundary value problems II
Authors: Costabel Martin , Dauge Monique
Published: November 2011

Synopsis

This is the second of two papers in which we study the singularities of solutions of second-order linear elliptic boundary value problems at the edges of piecewise analytic domains in ℝ3. When the opening angle at the edge is variable, there appears trie phenomenon of “crossing” of the exponents of singularities. In Part I, we introduced for the Dirichlet problem appropriate combinations of the simple tensor product singularities.

In this second part, we extend the results of Part I to general non-homogeneous boundary conditions. Moreover, we show how these combinations of singularities appear in a natural way as sections of an analytic vector bundle above the edge. In the case when the interior operator is the Laplacian, we give a simpler expression of the combined singular functions, involving divided differences of powers of a complex variable describing the coordinates in the normal plane to the edge.
On compactness results for multi-scale convergence
Authors: Balder Erik J.
Published: November 2011

Two relative compactness results for two-scale convergence in homogenization, due to G. Nguetseng, were recently extended to the multi-scale case by G. Allaire and M. Briane. Whereas their extension of Nguetseng's first result, which is in L2, is straightforward, their extension of his second result, which takes place in the Sobolev space H1, is quite complicated, even though it follows Nguetseng by using the fact that the image of H1 under the gradient mapping is the orthogonal complement of the set of divergence-free functions. Here a much simpler proof is provided by deriving the H1-type result from combining the first extension result with the fact that the above-mentioned image space is also the space of all rotation-free fields. Moreover, this approach reveals that the two results can be seen as corollaries of a fundamental relative compactness result for Young measures.
Some geometric properties of the set of generalized Young functionals
Authors: Kružík Martin , Roubíček Tomáš
Published: November 2011

This paper studies geometric properties, in particular extreme points and rays, of various generalizations of Young measures. Applications of the knowledge of extreme points are illustrated on existence results for optimal control problems and on various convergence results for Young measures by using the Choquet theory.
Existence of the solutions for the Ginzburg–Landau equations of superconductivity in three spatial dimensions
Authors: Wang Bixiang , Su Ning
Published: November 2011

The time-dependent Ginzburg-Landau equations of superconductivity in three spatial dimensions are investigated in this paper. We establish the existence of global weak solutions for this model with any Lp (p ≧ 3) initial data. This work generalizes the results of Wang and Zhan.
The finite basis problem for the semigroups of order-preserving mappings
Authors: Vernitskii A. S.
Published: November 2011

Developing an approach of Repnitskii and Volkov, we focus on properties of semigroups of order-preserving mappings on finite chains; in particular, we show that the class of all these semigroups has no finite quasi-identity basis (although it has an infinite one).
Periodic solutions to second order Hamiltonian systems in an unbounded potential well
Authors: Greco C.
Published: November 2011

Synopsis

In this paper we give some results on the existence of periodic solutions to the second order Hamiltonian system:

where and Ω is an open set of ℝn with non-empty bounded complement ℝn\Ω; we suppose V(t, x) is periodic in t, V(t, x)→ + ∞ as x → ∂Ω and V is super (or sub)-quadratic as |x| → + ∞.
A deletion-contraction algorithm for the characteristic polynomial of a multigraph
Authors: Rowlinson Peter
Published: November 2011

Synopsis

The characteristic polynomial of a finite multigraph G is expressed in terms of characteristic polynomials oflocal modifications of G. The resulting formula is used to investigate the largest eigenvalues of certain theta graphs.
Unstable planes for rank 2 reflexive sheaves
Authors: Miró-Roig Rosa M.
Published: November 2011

Synopsis

The purpose of this paper is to give a sharp bound for the order of instability of an unstable hyperplane of a rank 2 stable reflexive sheaf E on ℙn, in terras of the Chern classes of E; and a sharp boundfor the order of instability of an unstable hyperplane of a rank 2 nonstable reflexive sheaf E on ℙn, in terms of the Chern classes of E and the order of nonstability of E.
A lower closure theorem for autonomous orientor fields
Authors: Ambrosio Luigi
Published: November 2011

Synopsis

Given a set valued mapping ∑: ℝ → ∑n, we prove a closure property with respect to -convergence for the differential inclusion

under very mild assumptions on ∑.
Abstract initial boundary value problems
Authors: Palencia C. , Mallo I. Alonso
Published: November 2011

We consider abstract initial boundary value problems in a spirit similar to that of the classical theory of linear semigroups. We assume that the solution u at time t is given by u(t) = S(t) ξ + V(t)g, where ξ and g are respectively the initial and boundary data and S(t) and V(t) are linear operators. We take as a departing point the functional equations satisfied by the propagators S and V. We discuss conditions under which a pair (S, V) describes the solution of an abstract differential initial boundary value problem. Several examples are provided of parabolic and hyperbolic problems that can be accommodated within the abstract theory. We study the backward Euler's method for the time integration of the problems considered.
High-energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponents
Authors: Wang Zhi-Qiang
Published: November 2011

We establish the existence of positive solutions with two peaks being located on the boundary of the domain for the problem−Δu + λu = upin antipodal invariant domains including ball domains with Neumann boundary conditions. Herepis the critical Sobolev exponent (N+ 2)/(N− 2). The shape of the solutions and the location of the peaks are also studied.
On semigroups defined by Coxeter-type presentations
Authors: Campbell C. M. , Robertson E. F. , Ruškuc N. , Thomas R. M.
Published: November 2011

Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.
Open mappings and solvability of nonlinear equations in Banach space
Authors: Welsh Stewart C.
Published: November 2011

We give sufficient conditions under which a funclion f: X → Y is an open mapping, where X and y are Banach spaces. This function is not necessarily continuous, but is assumed to have closed graph. We prove our results without requiring that f be Gateaux differentiable; instead, f is assumed to possess a weak type of Gateaux inverse derivative.
The Penrose–Fife-type equations: counting the one-dimensional stationary solutions
Authors: Novick-Cohen A. , Zheng Songmu
Published: November 2011

A method for counting the solutions for Penrose–Fife-type phase field equations is derived. The method used is similar to that developed recently for obtaining a precise count for the number of solutions for the Cahn–Hilliard equation [9], and is based on the derivation of an extended system of Picard–Fuchs equations as well as on estimates obtained in [11]. The Penrose–Fife-type phase field equations represent a thermodynamically consistent model for phase separation of a conserved order parameter (typically concentration) in binary systems in which latent heat effects are important in the phase separation process.
A systematic study of heteroclinic cycles in dynamical systems with broken symmetries
Authors: Lauterbach Reiner , Maier-Paape Stanislaus , Reissner Ernst
Published: November 2011

Let X be a Banach space or a manifold and G a compact Lie group acting on X. We study G-equivariant (semi)flows on X in the context of forced symmetry breaking. After applying small symmetry breaking perturbations, certain generic invariant manifolds of the above flows persist slightly changed. We obtain necessary and sufficient conditions for the existence of heteroclinic cycles on the perturbed manifolds. Applications are given for the case G = SO(3).
Affine length and affine dimension of a 1-set of ℝ2
Authors: Dibos Françoise
Published: November 2011

We propose here a way to extend to all the 1-set of ℝ2 the well-known affine length which was just defined for a C2 curve. Moreover, this leads us to define the affine dimension of a 1-set which can be used for discriminate rectifiable 1-sets from unrectifiable 1-sets of ℝ2.
H-measures applied to symmetric systems
Authors: Antonić Nenad
Published: November 2011

H-measures were recently introduced by Luc Tartar as a tool which might provide better understanding of propagating oscillations. Independently, Patrick Gerard introduced the same objects under the name of microlocal defect measures. Partial differential equations of mathematical physics can often be written in the form of a symmetric system:

where Ak and B are matrix functions, while u is an unknown vector function, and f a known vector function. In this work we prove a general propagation theorem for H-measures associated to symmetric systems. This result, combined with the localisation property, is then used to obtain more precise results on the behaviour of H-measures associated to the wave equation, Maxwell's and Dirac's systems, and second-order equations in two variables.
The finite Hilbert transform in weighted spaces
Authors: Astala Kari , Päivärinta Lassi , Saksman Eero
Published: November 2011

The mapping properties of the finite Hilbert-transform (respectively the Hilbert transform on the half axis) are studied. Invertibility, surjectivity, injectivity and bounded ness from below of the transform are characterised in general weighted spaces. The results are applied to the restriction of the operator with logarithmic kernel.
Large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas
Authors: Hsiao L. , Luo T.
Published: November 2011

We investigate the large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas. A conclusive answer to the problem of asymptotic behaviour is given in Theorem 1.2.
Unit regular monoids
Authors: Hickey J. B. , Lawson M. V.
Published: November 2011

We derive necessary and sufficient conditions for a unit regular monoid to have a uniquely unit regular, idempotent separating cover.
On the inhomogeneous system of isentropic gas dynamics by the viscosity method
Authors: Fang Weifu , Ito Kazufumi
Published: November 2011

The existence of global weak solutions is shown for the equations of isentropic gas dynamics with inhomogeneous terms by the viscosity method. A generalised version of the method of invariant regions is developed to obtain the uniform L∞ bounds of the viscosity solutions, and the method of compensated compactness is applied to show the existence of weak solutions as limits of the viscosity solutions. The lower positive bound for the density function is also obtained. As an example, a hydrodynamic model for semiconductors is analysed
On the zeros of the second derivative
Authors: Langley J. K.
Published: November 2011

Suppose that f is meromorphic of finite order in the plane, and that f″ has only finitely many zeros. We prove a strong estimate for the frequency of distinct poles of f. In particular, if the poles of f have bounded multiplicities, then f has only finitely many poles.
Regional blow-up of solutions to the initial boundary value problem forut=uδ(Δu +u)
Authors: Tsutsumi Masayoshi , Ishiwata Tetsuya
Published: November 2011

Non-negative solutions of the initial boundary value problem for a degenerate parabolic equation are investigated. It is shown that solutions blow up regionally in finite tine. The size of blow-up sets is determined for radially symmetric cases.
Poincaré series for the occurrence of certain modular representations of GL(n,p) in the symmetric algebra
Authors: Carlisle David P. , Walker Grant
Published: November 2011

Synopsis

The number of occurrences of the Steinberg representation St of GL(n, p) as a composition factor in the symmetric algebra Fp[x1, … xn] has been determined by several authors. We extend this result to the representations of GL(n, p) which are the closest neighbours of St in the SL(n, p) weight diagram. The method is to play off duality for GL(n, p)-modules against connectivity for M(n, p)-modules. The result is equivalent to determining the cohomology groups of the corresponding indecomposable stable summands of the localisation of an n-fold product of complex projective spaces at the prime p.
Asymptotic behaviour of solutions of hyperbolic conservation laws ut + (um)x = 0 as m → ∞ with inconsistent initial values
Authors: Xu Xiangsheng
Published: November 2011

Synopsis

We study the behaviour of solutions u = um of ut, + (um)x = 0 for t > 0, x ∊ R, u(x, 0) = u0(x), u0 ≧0, u0 ∊ L1(R) as m → ∞. This is a singular perturbation problem about m = ∞ if u0 > 1 on a set of positive measure. It is shown that the limit exists and satisfies the stationary equation
Symmetry breaking for Δu + 2δe−u = 0 on a disk with general boundary conditions
Authors: Lin Song-Sun
Published: November 2011

Synopsis

We discuss the radially, symmetric solutions and the symmetry breaking of the equation Δu + 2δe −u = 0 in D and u + b(∂u/∂n) = 0 on ∂D, where D is the unit disk in ℝ2, δ >0 and b is a constant. We prove that for any b < 0, there exists > 0 such that there are exactly two radially symmetric solutions for δ ∊ (0, ), one for δ = and none for δ > δ*b. For , where m is a positive integer, there are (b), k = 1, …, m, such that the equation has symmetry breaking at δ*k (b) on the lower branch of radially symmetric solutions.