bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Newman-type theorems for maps from Riemannian manifolds into manifolds
Authors: Hai-bao Duan
Published: November 2011

Synopsis

Letf: Mm→Nnbe a map from a Riemannianm-manifold(Mm, d)into ann-manifold Nn. The major purpose of this paper is to give a lower bound for the number

by examining the behaviour of the cohomology homomorphisms induced byf. This idea will be used to generalise the classical Newman theorem and present a geometric background for a well-known non-embedding theorem in topology.
A remark on the nodal regions of the solutions of some superlinear elliptic equations
Authors: Benci Vieri , Fortunato Donato
Published: November 2011

Synopsis

We study the problem

where Ω is a bounded domain in ℝn(N≧3), 2 <p ≦2N/N – 2, λ ∈R. We prove the existence of nontrivial solutions of (*) for which we can estimate the number of nodal regions dependent on the eigenvalues of −Δ less than λ.
C*-algebras of Clifford semigroups
Authors: Duncan John , Paterson A.L.T.
Published: November 2011

Synopsis

We investigate algebras associated with a (discrete) Clifford semigroupS =∪{Ge: e ∈ E{. We show that the representation theory forSis determined by an enveloping Clifford semigroupUC(S) =∪{Gx: x ∈ X} whereXis the filter completion of the semilatticeE.We describe the representation theory in terms of both disintegration theory and sheaf theory.
A note on concentration functions
Authors: Dunnage J. E. A.
Published: November 2011

Synopsis

We give an inequality for the concentration function of a sum X1 + … + Xn of independent random variables when Xv has a finite absolute moment of order kv (2 < kv ≦ 3). It is an extension of somewhat similar inequalities found earlier by Offord and by the author in the case of finite third-order absolute moments.
Propagation of classical solutions to the perturbed wave equation in a space of odd dimension
Authors: Menzala Gustavo Perla
Published: November 2011

Synopsis

We prove that classical solutions of the perturbed wave equation in ℝn × ℝ (n = odd ≧ 3) do not satisfy Huygens' principle in the presence of symmetries. The difficulties arising from the singularities of the Riemann function (for large space dimensions) are overcome by considering a class of potentials and initial data which are radial and smooth. Our method is elementary and based on energy estimates.
Torsion theoretic points and spaces
Authors: Simmons Harold
Published: November 2011

Synopsis

For each ring R, we construct a topological space pt (R) which includes as a subspace both the classical spectrum specR and the torsion theoretic spectrum R-sp. For many rings (e.g. rings with Krull dimension), spec R is a retract of pt (R) and the retraction map θ generalizes the Gabriel correspondence for noetherian rings. There is a natural decomposition theory on MOD-R which extends the Goldman theory in the same way that the tertiary theory extends the primary theory. The map θ provides a direct comparison between this new decomposition theory and the tertiary theory. The space pt (R) is closely connected with the lattice of hereditary torsion theories on R, and for fully bounded (not necessarily noetherian) R, this connection is very tight.
Existence theorems for equations in normed spaces and boundary value problems for nonlinear vector ordinary differential equations
Authors: Cañada A. , Ortega R.
Published: November 2011

Synopsis

The existence of solutions to equations in normed spaces is proved when the nonlinear part of the equation satisfies growth and asymptotic conditions, whether the linear part is invertible or not. For this, we use the coincidence degree theory developed by Mawhin. We apply our abstract results to boundary value problems for nonlinear vector ordinary differential equations. In particular, we consider the Picard boundary value problem at the first eigenvalue and the periodic boundary value problem at resonance. In both cases, the nonlinear term can be of superlinear type. Also, necessary and sufficient conditions of Landesman-Lazer type are obtained.
Products of idempotents in finite full transformation semigroups: some improved bounds
Authors: Howie John M.
Published: November 2011

Synopsis

Let E be the set of idempotents in Sn, the semigroup of all singular selfmaps of {1,…, n}. For each α in Sn, there is a unique (κ(α)≧1 such that αψEκ,(α). It is known that κ(α)≦ n + cycl α -fix α, where cyclα is the number of cyclic orbits of a and fix α is the number of fixed points. Equality holds only in the case where a is of rank n – 1. An improved upper bound is obtained for κ(α), applying to elements of arbitrary rank. A lower bound is obtained also.
Explicit invariant solutions for invariant linear differential operators
Authors: Szmydt Zofia , Ziemian Bogdan
Published: November 2011

Synopsis

Let F be a real analytic function on a real analytic manifold X. Let P be a linear differential operator on X such that , where Q is an ordinary differential operator with analytic coefficients whose singular points are all regular. For each (isolated) critical value z of F, we construct locally an F-invariant solution u of the equation Pu - v, v being an arbitrary F-invariant distribution supported in F−1(z). The solution u is constructed explicitly in the form of a series of F-invariant distributions.
A geometric approach to the study of stationary free surface flows for viscous liquids
Authors: Abergel Frédéric
Published: November 2011

Synopsis

We use a direct, geometric approach to study the free surface boundary conditions for stationary flows of viscous liquids. The free surface problem is characterised by a mapping on smooth variations of a given configuration; this mapping has a simple structure, which we determine by computing its differential, and studying it in terms of the space dimension and the surface tension coefficient. Applications are given to problems of existence, uniqueness and regularity in free surface flows.
Rank one property for derivatives of functions with bounded variation
Authors: Alberti Giovanni
Published: November 2011

Synopsis

In this paper we introduce a new tool in geometric measure theory and then we apply it to study the rank properties of the derivatives of vector functions with bounded variation.
Some interior and exterior boundary-value problems for the Helmholtz equation in a quadrant
Authors: Meister E. , Penzel F. , Speck F.-O. , Teixeira F. S.
Published: November 2011

Synopsis

The Dirichlet, Neumann and mixed boundary-value problems for the two-dimensional Helmholtz equation in the interior or exterior of a quadrant are considered in a Sobolev space setting. It is shown that the potential operators arising in the interior problems can be used to derive systems of boundary integral equations to the exterior problems, which can be solved explicitly.
On class numbers of a finite group and of its subgroups
Authors: Vera-López A. , Sangroniz J.
Published: November 2011

Synopsis

In this paper we obtain new results which relate the number of conjugacy classes of л-elements of a finite group and an arbitrary subgroup, which are analogous to some results about normal subgroups. We also prove some new results which show the relationship between class numbers and splitting theorems. Our proofs only involve elementary techniques.
Primitive near-rings do not form an axiomatisable class
Authors: Zayed Maher
Published: November 2011

Synopsis

It is shown that for each v ∊ {0, 1, 2}, the class of v-primitive near-rings is not axiomatisable.
Generalised factorisation for a class of Jones form matrix functions
Authors: Câmara M. C. , Lebre A. B. , Speck F.-O.
Published: November 2011

Synopsis

A systematic approach is proposed for the generalised factorisation of certain non-rational n × n matrix functions. The first main result consists in a transformation of a meromorphic into a generalised factorisation by algebraic means. It closes a gap between the classical Wiener-Hopf procedure and the operator theoretic method of generalised factorisation. Secondly, as examples we consider certain matrix functions of Jones form or of N-part form, which are equivalent to each other, in a sense. The factorisation procedure is complete and explicit, based only on the factorisation of scalar functions, of rational matrix functions and upon linear algebra. Applications in elastodynamic diffraction theory are treated in detail and in a most effective way.
Solution branches of a semilinear elliptic problem at corank-2 bifurcation points with Neumann boundary conditions
Authors: Zhen Mei
Published: November 2011

Synopsis

Solution branches of a semilinear elliptic problem with Neumann boundary conditions are studied at its corank-2 bifurcation points. It is shown that generally there are exactly four different nontrivial solution branches passing through a corank-2 bifurcation point. The bifurcating solution branches are parametrised via a nonsingular enlarged problem. Branch switching at bifurcation points is incorporated with a continuation method.
L∞-continuity of Henkin operators solving in certain weakly pseudoconvex domains of ℂ2
Authors: Verdera Joan
Published: November 2011

Synopsis

Let ψ ∈ C2[0,1] be a positive function on (0, 1]. Under certain assumptions on ψ, the set

is a pseudoconvex domain with C2-boundary, for which it is possible to construct a Henkin-type operator Hψ = Kψ + Bψ solving in Dψ. The operator Bψ, is L∞-continuous because it has a Riesz potential type kernel, while the L∞-continuity of Kψ depends on the flatness of ψ at 0. Our main result states that Kψ is continuous from L∞(∂Dψ) into L∞(Dψ) if and only if
Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
Authors: Lurie K. A. , Cherkaev A. V.
Published: November 2011

Synopsis

This paper is a sequel to [1-4]. We consider the problem of G-closure, i.e. the description of the set GU of effective tensors of conductivity for all possible mixtures assembled from a number of initially given components belonging to some fixed set U. Effective tensors are determined here in a sense of G-convergence relative to the operator ∇· D · ∇, of the elements DeU ∈ [5, 6].

The G-closure problem for an arbitrary initial set U in the two-dimensional case has already been solved [3, 4]. It remained, however, unclear how to construct, in the most economic way, a composite with some prescribed effective conductivity, or, equivalently, how to describe the set GmU of composites which may be assembled from given components taken in some prescribed proportion. This problem is solved in what follows for a set U consisting of two isotropic materials possessing conductivities D+ = u+E and D− = u−E where 0<u−<u+<∞ and E ( = ii+jj) is a unit tensor.
On regular semigroup rings
Authors: Okniński Jan
Published: November 2011

Synopsis

It is shown that if A is an algebra over a field, then the regularity of the semigroup algebra A[G] implies that the semigroup G is periodic. This enables us to characterize regular semigroup algebras of semigroups with d.c.c. on principal ideals. Also, regular self-injective semigroup algebras are described.
Multiparameter Sturm theory
Authors: Binding Paul , Browne Patrick J.
Published: November 2011

Synopsis

Let Sturm–Liouville problems

with continuous coefficients and appropriate boundary conditions, be coupled by the eigenvalue λ = (λ1, … λk). When k = 1, there are various oscillation, perturbation and comparison theorems concerning existence and continuous or monotonic dependence of eigenvalues, eigenfunctions and their zeros (i.e. focal points).

We attempt a unified theory for such results, valid for general fc, under conditions known as "left" and “right” definiteness. A representative result may be stated loosely as follows: if LD holds then (elementwise) monotonic dependence of p, q and the matrix [ars] forces monotonic dependence of λ. LD is a generalisation of the “polar” case for k = 1, and was originally conceived for a quite different purpose, viz. completeness of eigenfunctions via elliptic partial differential equation theory.
Linear and convex combinations of projections in simple C* -algebras
Authors: Robertson A. Guyan
Published: November 2011

Synopsis

Motivated by results of G. K. Pedersen, showing how a simple C*-algebra must contain an abundance of projections whenever it contains a single nontrivial projection, we provide generalisations and new proofs using more algebraic methods.
A note on the paper “Existence conditions for eigenvalue problems generated by compact multiparameter operators” by P. Binding, P. J. Browne and L. Turyn
Authors: Schäfke R. , Volkmer H.
Published: November 2011

Synopsis

We give a direct and simple proof of a central result of the above paper.
A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions
Authors: Harris B. J.
Published: November 2011

Synopsis

In an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equation

has the asymptotic expansion

as |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.

We show that if the real valued function q admits the expansion

in a neighbourhood of 0, then
A system of order 2 in which small sub-harmonics and large sub-harmonics coexist
Authors: Obi Chike
Published: November 2011

Synopsis

This paper establishes the coexistence of small and large subharmonics in a special case of the ordinary non-linear differential equation

of order 2, where κ, ε are small parameters, λ>0 is a parameter independent of κ, ε, h(t) has the least period 2π and

It is divided into three sections. In Section 1 a general analysis of the periodic solutions of (.), classified into small, medium or large, is given. In Section 2 the general theory of Section 1 is applied to the special form of (.) where k = vε1+s, v>0, s>0 constants, to obtain results from which we extract in Section 2 a theorem (Section 3) on the coexistence of a small periodic solution of order 1, several small sub-harmonics and several large sub-harmonics of the special case

of (.), where Q≧1 is an integer.
Convergence criteria for Aronszajn's method and for the Bazley-Fox method
Authors: Brown R. D.
Published: November 2011

Synopsis

Convergence criteria are derived for Aronszajn's method and for the Bazley-Fox C*C method applied to self-adjoint eigenvalue problems of the form Bx = λx. These criteria generalise previously used criteria and are seen to be, in a certain restricted sense, the best possible. The framework used is general enough to allow approximations where the intermediate problems are not finite dimensional perturbations of the base problem.
The nilpotency index of the radicals of group algebras of finite groups whose Sylow 3-subgroups are extra-special of order 27 of exponent 3
Authors: Koshitani Shigeo
Published: November 2011

Synopsis

Let J(FG) be the Jacobson radical of the group algebra FG of a finite groupG with a Sylow 3-subgroup which is extra-special of order 27 of exponent 3 over a field F of characteristic 3, and let t(G) be the least positive integer t with J(FG)t = 0. In this paper, we prove that t(G) = 9 if G has a normal subgroup H such that (|G:H|, 3) = 1 and if H is either 3-solvable, SL(3,3) or the Tits simple group 2F4(2)'.
A distributional approach to Namias' fractional Fourier transforms
Authors: Kerr Fiona H.
Published: November 2011

Synopsis

A fractionalisation of the Fourier transform was developed formally by Namias. By workingin ℐ, we found that this theory could be made mathematically rigorous. Here we extend our previous results to the space ℐ′ to consider fractional powers of the distributional Fourier transform. The paper concludes with an application to an ordinary differential equation which shows how a distributional approach can sometimes be more useful than a classical approach.
Decomposition matrices for spin characters of symmetric groups
Authors: Morris A. O. , Yaseen A. K.
Published: November 2011

Synopsis

Methods are developed for determining the decomposition matrices for the spin characters of the symmetric groups Snfor an odd primep. Some general results are obtained which are non-trivial modifications of the corresponding results for ordinary characters. The methods are used to determine the decomposition matrices for 3 ≦ n ≦ ll, andp= 3 but with an interesting ambiguity in the casen= 9. The second author will deal separately with the casesp= 5, 7, 11.
A shooting argument with oscillation for semilinear elliptic radially symmetric equations
Authors: Jones C. K. R. T. , Küpper T. , Plakties H.
Published: November 2011

Synopsis

A new method is developed for finding radially symmetric solutions of semilinear elliptic problems by phase space methods. The basic idea is to formulate a shooting argument from initial conditions at r = 0 which involves encoding the oscillation information about the trajectories under consideration. The main theorem is applied to a particular nonlinearity and produces a cascade of solutions wherein the multiplicity increases with the number of zeros.
Non-immersibility of a space form as a totally umbilical hypersurface
Authors: Okumura Masafumi , Takahashi Hiroshi
Published: November 2011

Synopsis

Suppose that a space form is immersed into another Riemannian manifold as a totally umbilical hypersurface with constant mean curvature. Then, in the ambient manifold, the lengthof the curvature tensor, that of the Ricci tensor and the scalar curvature must satisfy an inequality. In this paper the authors proved the inequality. As applications of the inequality, some immersibility problems are investigated. For example, it is proved that if a space form is immersed in an Einstein manifold as a totally umbilical hypersurface, then the Einstein manifold has constant sectional curvature along the hypersurface. Moreover, it is proved that a space form cannot be immersed into some Kaehlerian manifolds as a totally umbilical hypersurface with constant mean curvature.
Existence and uniqueness of heteroclinic orbits for the equation λu‴ + u′ = f(u)
Authors: Toland J. F.
Published: November 2011

Synopsis

Iffis a continuous even function which is decreasing on (0,∞) and such that±α are its only zeros and are simple, then in three-dimensional phase spacethe unstable manifold of the equilibrium u = −α and the stable manifold of u = α are both two dimensional. If λ<0 it is shown that there is a unique bounded orbit of the equation λu‴ + u′ = f(u), and that this is a heteroclinic orbit joining these two equilibria. Other results on the existence and uniqueness of heteroclinic orbits are also established when f is not even and when f is not monotone on (0, ∞).
Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire
Authors: Tahraoui R.
Published: November 2011

Synopsis

In this paper, we study problems of the form:

We obtain some existence and regularity results when Ω is either a ball or an annulus, without convexity hypothesis on g. We then apply these results to some shear problems in nonlinear elasticity.
Regularity of plate equations with control concentrated in interior curves
Authors: Jaffard Stéphane , Tucsnak Marius
Published: November 2011

Synopsis

We consider initial and boundary-value problems modelling the vibration of a plate with piezoelectric actuator. The usual models lead to the Bernoulli–Euler and Kirchhoff plate equations with right-hand side given by a distribution concentrated in an interior curve. We obtain regularity results which are stronger than those obtained by simply using the Sobolev regularity of the right-hand side. By duality, we obtain new trace regularity properties for the solutions of plate equations. Our results provide appropriate function spaces for the control of plates provided with piezoelectric actuators.
Influence of mixed boundary conditions in some reaction–diffusion systems
Authors: Martin Robert H. , Pierre Michel
Published: November 2011

Synopsis

We analyse global existence of solutions to a system of two reaction–diffusion equations for whicha ‘balance’ law holds. The main aim is to make clear the influence of different combinations ofboundary conditions on global existence under the assumption that the nonlinearities satisfy polynomial growth estimates.
Oscillation theory for indefinite Sturm-Liouville problems with eigenparameter-dependent boundary conditions
Authors: Binding P. A. , Browne Patrick J.
Published: November 2011

In previous papers we have studied oscillation properties of Sturm–Liouville problems (−Py′)′ + qy = λry, with λ-dependent boundary conditions, under various ‘definiteness’ conditions. Here we present a new, unified, approach which also covers cases previously untreated, e.g. of semidefinite weight, and also the fully indefinite problem.
Robustness and convergence of suboptimal controls in distributed parameter systems
Authors: Fattorini H. O.
Published: November 2011

A fundamental prerequisite for the numerical computation of optimal controls is to show that sequences of suboptimal (that is, close-to-optimal) controls converge. We show this in a version that applies to hyperbolic and parabolic distributed parameter systems, the latter including the Navier–Stokes equations. The optimal problems include control and state constraints; in the parabolic case, the constraints may be pointwise on the solution and the gradient.
Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems
Authors: Iliev Iliya D.
Published: November 2011

We study the bifurcation of limit cycles in general quadratic perturbations of the particular quadratic systemwhich represents one of two codimension-five components in the intersection of two strata in the centre manifold,andQ4. The study of limit cycles for this degenerate case requires us to investigate not the first but the second variationM2of the displacement function. We prove that up to three limit cycles can emerge from the period annulus surrounding the centre. This implies that the cyclicity of period annuli of nearby systems inandQ4is at most three as well. Our approach relies upon the possibility of deriving appropriate Picard–Fuchs equations satisfied by the four independent integrals included inM2.
Spectral properties of the Orr-Sommerfeld problem
Authors: Langer Heinz , Tretter Christiane
Published: November 2011

In this paper, we study the Orr–Sommerfeld problem on a finite interval. It is shown that the eigenfunctions and associated functions form a Bari basis in a suitable Hilbert space if the unperturbed velocity profile u is sufficiently smooth. To this end, the Orr–Sommerfeld problem is considered as a bounded perturbation of a certain self-adjoint spectral problem.
The asymptotic form of the spectral function in Sturm–Liouville problems with a large potential like −xc(c ≦ 2)
Authors: Eastham M. S. P.
Published: November 2011

A new formula is given for the spectral function in singular Sturm–Liouville problems where the potential is like – (const.)xc(0 < c ≦ 2). The formula is used to answer an open question concerning the asymptotic form of the spectral function.
The Riemann problem for a resonant nonlinear system of conservation laws with Dirac-measure solutions
Authors: Hu Jiaxin
Published: November 2011

The Riemann problem for a resonant nonlinear system of conservation laws is considered here. The Riemann solution was constructed by employing the viscosity approximation approach. One kind of new discontinuity, which is called the Dirac-contact wave, appeared in the Riemann solution. Because the strict hyperbolicity as well as the genuine nonlinearity of the system considered failed, the solution we obtained in this paper is not unique for some initial data. An additional condition was explored to guarantee the uniqueness of the Riemann problem.
Variational perturbative methods and bifurcation of bound states from the essential spectrum
Authors: Ambrosetti Antonio , Badiale Marino
Published: November 2011

This paper consists of two main parts. The first deals with a perturbative method in critical point theory and can be seen as the generalisation and completion of some earlier results. The second part is concerned with applications of the abstract setup to the existence of bound states of a class of elliptic differential equations that branch off from the infimum of the essential spectrum.
On the different convex hulls of sets involving singular values
Authors: Dacorogna B. , Tanteri C.
Published: November 2011

We give a representation formula for the convex, polyconvex and rank one convex hulls of a set of n × n matrices with prescribed singular values.
Gradient-like parabolic semiflows on BUC(ℝN)
Authors: Daners Daniel , Merino Sandro
Published: November 2011

We prove that a class of weighted semilinear reaction diffusion equations onRNgenerates gradient-like semiflows on the Banach space of bounded uniformly continuous functions onRN. IfN= 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.
Generators and factorisations of transformation semigroups
Authors: Higgins Peter M. , Howie John M. , Ruškuc Nikola
Published: November 2011

IfEis the set of idempotents andGthe group of units within a full transformation semigroup ℐx, thenEG = GE = ℐxifXis finite. The question of identifying the subsemigroupEG = GE = 〈G∪E〉in the case whereXis infinite leads to an investigation of interrelations among various naturally occurring subsemigroups ofℐX. In the final section it is shown that precisely two additional elementsµ, vare needed in order thatG∪E∪{µ, v}should generateℐx.
A difference scheme for a stiff system of conservation laws
Authors: Yong Wen-An
Published: November 2011

A stiff system of conservation laws is analysed using a difference method. The existence of entropy-satisfying BV-solutions to the initial value problems is established. Furthermore, we show that the solutions converge to the solutions of the corresponding equilibrium system as the relaxation time tends to zero.
An eigenvalue problem for generalized Laplacian in Orlicz—Sobolev spaces
Authors: Mustonen Vesa , Tienari Matti
Published: November 2011

Let m: [ 0, ∞) → [ 0, ∞) be an increasing continuous function with m(t) = 0 if and only if t = 0, m(t) → ∞ as t → ∞ and Ω C ℝN a bounded domain. In this note we show that for every r > 0 there exists a function ur solving the minimization problem

where Moreover, the function ur is a weak solution to the corresponding Euler–Lagrange equation

for some λ > 0. We emphasize that no Δ2-condition is needed for M or M; so the associated functionals are not continuously differentiable, in general.
Monotone convergence theorems for variational triples with applications to intermediate problems
Authors: Brown R. D.
Published: November 2011

Synopsis

The variational eigenvalue problem for a real quadratic form b with respect to a positive definite form a on a vector space V may be represented by the triple (b, a, V). Methods of intermediate problems provide approximations from below to the lower eigenvalues of (b, a, V) using monotone increasing sequences of such triples. It is shown that every such approximation method is canonically equivalent to Weinstein's method. General convergence theorems are proved for such methods. These results generalise known convergence results for increasing sequences of quadratic forms. The results are applied to some specific approximation methods and are illustrated using a differential eigenvalue problem.
A computer proof of relations in a certain class of groups
Authors: Robertson Edmund F. , Rutherford Kevin
Published: November 2011

Synopsis

A gp-toolkit consisting of computer implementations of various group theory methods, in particular a Tietze transformation program, was designed. Special cases of a conjecture were solved by the gp-toolkit. Examination of the method used by the gp-toolkit to deduce relations showed that a general approach had been employed. We present a proof verifying that the conjecture is true which is a straightforward generalisation of the method discovered by the gp-toolkit.
Immersing projective spaces in Euclidean space
Authors: Crabb M. C.
Published: November 2011

Synopsis

Using theKOℝ/2-theoretic obstruction theory developed in [4] and [5], necessary and sufficient conditions are derived for quaternionic projective spaces ℍPkand odd-dimensional complex projective spaces ℂP2k+1, of real dimensionmsay, to immerse in Euclidean space ℝ2m−1in the range l ≦ 14. The results refine those obtained by Davis and Mahowald ([10, 11]) and earlier authors.
The closure of the generalised eigenspace of a class of infinitesimal generators
Authors: Lunel S. M. Verduyn
Published: November 2011

Synopsis

In this paper we study the fine geometric structure of a class of strongly continuous semigroups that satisfy the following property: the resolvent of the infinitesimal generator can be represented as the quotient of entire functions of finite exponential type. This class includes the solution map for functional differential equations and certain partial differential equations. In particular, we present necessary and sufficient conditions for one-to-oneness of the solution map and for completeness of the system of generalised eigenfunctions of the generator.
An exterior boundary-value problem for the Maxwell equations with boundary data in a Sobolev space
Authors: Hähner Peter
Published: November 2011

Synopsis

We treat the time-harmonic Maxwell equations in an exterior domain with prescribed boundary data [n, E] in the Sobolev space of square integrable tangential fields with square integrable surface divergence. By using boundary integral equation methods, existence and uniqueness results are established. Furthermore, we investigate the completeness of electric and magnetic dipoles distributed on an inner surface in this Sobolev space.
Dissipative decomposition of ordinary differential equations
Authors: Olver Peter J. , Shakiban Chehrzad
Published: November 2011

Synopsis

A general decomposition theorem that allows one to express uniquely arbitrary differential polynomials in one independent and one dependent variable as a combination of conservative, dissipative and higher order dissipative pieces is proved. The decomposition generalises the Rayleigh dissipation law for linear equations.
On the planar rank-one convexity condition
Authors: Parry G. P.
Published: November 2011

I discuss implications of the rank-one convexity condition in a particular case.
Unstable atomicity of ΩSpin(r)
Authors: Mahmud Zafer
Published: November 2011

Synopsis

We determine the homomorphism induced, in Z2-cohomology, by a map f: ΩSpin(r) → ΩSpin(r). As a corollary we show that ΩSpin(r), r ≧ 9 is 2-atomic, where a space X is 2-atomic if any map f: X ≧X is either a mod 2 homotopy equivalence or f*: H*(X, Z2) → H*(X, Z2) is nilpotent.
Ergodic actions of group extensions on von Neumann algebras
Authors: Thomsen Klaus
Published: November 2011

Synopsis

We consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.
Transition systems
Authors: Mischaikow Konstantin
Published: November 2011

Synopsis

The concept of a transition system is extended to a parametrised family of differential equations

where x ∊ ℝn and λ ∊ Λ = [0, l]m, an m-cube. Furthermore, algebraic formulae for comparing connection matrices at the various parameter values are obtained. Finally, several applications of these techniques are indicated.
Vanational elliptic problems involving noncoercive functionals
Authors: Ramos Miguel , Sanchez Luis
Published: November 2011

Synopsis

We consider the nonlinear elliptic problem at resonance, Δu + λ1u + f(x, u) = h(x) in Ω, u = 0 on ∂Ω, where Ω is a bounded smooth domain in ℝN, λl is the first eigenvalue of –Δ in Ω and h(x) is orthogonal to the first eigenfunction. We give some conditions of solvability in terms of the primitive of f with respect to u.
Genera of rationally equivalent integral binary quadratic forms
Authors: Earnest A. G.
Published: November 2011

Synopsis

A formula is given for the number of genera of primitive integral binary quadratic forms of discriminant D which lie in a rational equivalence class. In particular, necessary and sufficient conditions for the genus and rational equivalence class to coincide are given in terms of the prime factorisation of D.
A space of slowly decreasing functions with pleasant Fourier transforms
Authors: Fraenkel L. E.
Published: November 2011

Synopsis

The space in question is Aµ(R):=L1(R) + Bµ(R), where Bµ(R) is a Banach space that contains the “tails” (the dominant parts for large values of |x|) of certain slowly decreasing functions from R to R. Functions in Bµ(R) are of bounded variation, and the norm involves their variation and a weighting function. Theorems are proved only for Bµ(R), because those for L1(R) are known. The results concern the convolution of a function in Bµ(R) with one in L1(R), the Fourier transform acting on Bµ(R), and the signum rule for the Hilbert transform of functions in Bµ(R).
On a comparison theorem via symmetrisation
Authors: Kesavan S.
Published: November 2011

Synopsis

Talenti's theorem allows us to estimate the norms of the solution of an elliptic boundary value problem posed on a bounded open set Ω in terms of those of the “symmetrised” problem posed on Ω*, the ball centred at 0 and such that |Ω| = |Ω*|. We are interested in the limiting case when equality is achieved between the norms of the two solutions. We show then that Ω = Ω* and that the solution is radially symmetric and decreasing. The novelty of this exposition is that the method used is very elementary compared to the usual arguments.
The travelling wave fronts of nonlinear reaction–diffusion systems via Friedlin's stochastic approaches
Authors: Zhao Huaizhong
Published: November 2011

In this paper we study the asymptotic behaviour of reaction–diffusion systems with a small parameter by using then-dimensional Feynman–Kac formula and large deviation theory. The generalised solutions are introduced in Section 2. We obtain the travelling wave joining an unstable steady state and an asymptotically stable steady state of a diffusionless dynamical system in a reaction–diffusion system with nonlinear ergodic interactions, and a special case with nonlinear reducible interactions.
Symmetry and convergence properties for non-negative solutions of nonautonomous reaction–diffusion problems
Authors: Hess Peter , Poláčik P.
Published: November 2011

Nonautonomous parabolic equations of the form ut − Δu = f(u, t) on a symmetric domain are considered. Using the moving-hyperplane method, it is proved that any bounded nonnegative solution symmetrises as t → ∞. This is then used to show that for nonlinearities periodic in t, any non-negative bounded solution approaches a periodic solution.
On semigroup algebras of cancellative commutative semigroups
Authors: Kelarev A. V.
Published: November 2011

Synopsis

A cancellative commutative semigroup s and a hereditary radical ρ are constructed such that ρ is S-homogeneous but not S-normal. This answers a question which arose in the literature.
Heat equation on a hemisphere
Authors: van den Berg M.
Published: November 2011

Synopsis

Consider the following heat conduction problem: let Hm−1 be a hemisphere of Sm−1 and suppose that Hm−1 has temperature 1 at time t = 0, while the boundary of Hm−1 is kept at temperature 0 for all time t>0. We obtain a combinatorial formula and a uniform estimate for the amount of heat in Hm−1 at time t.
Positive solutions of elliptic equations involving supercritical growth
Authors: Merle F. , Peletier L. A.
Published: November 2011

Synopsis

Positive radial solutions of elliptic equation involving supercritical growth are analysed as their supremum norm tends to infinity. It is shown that they converge, uniformly away from the origin, as well as inH1, to the unique singular solution.
Comparison results in second order quasilinear Dirichlet problems
Authors: Payne L. E. , Webb J. R. L.
Published: November 2011

Synopsis

In [6] and [9] two different methods are given for comparing solutions of Dirichlet problems for second order quasilinear elliptic equations on convex regions. In this paper a general comparison technique is outlined—one which contains the methods of [6] and [9] as special cases. This technique is then applied to a number of special examples, comparisons with known results are given and a number of possible extensions are indicated.
On equichordal curves
Authors: Cieślak Waldemar
Published: November 2011

Synopsis

In this paper we consider equichordal curves in ℝn. We extend the notion of chordal area to all equichordal curves and introduce a notion of *-chordal area. We establish results connected with the length, *-chordal area and extended chordal area. Moreover, we give a Crofton-type integral formula for plane equichordal curves and derive an isoperimetric inequality for *-chordal area. The paper is based on the results of F. J. Craveiro de Carvalho and S. A. Robertson [2].
The Ap condition and a positive, linear operator
Authors: Sinnamon Gordon
Published: November 2011

Synopsis

A positive, linear operator is exhibited which is bounded on the mixed weighted Lebesgue space if and only if the weight w satisfies the Ap condition of Muckenhoupt.
Linear second order elliptic equations with Venttsel boundary conditions
Authors: Luo Yousong , Trudinger Neil S.
Published: November 2011

Synopsis

We prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.
A problem in neural networks
Authors: Amick C. J.
Published: November 2011

Synopsis

In this paper we consider a simple model for coupled nonlinear oscillators in a continuous medium. There is shown to exist a maximal branch of phaselocked solutions connecting the trivial one to a limiting singular solution.
A free boundary problem arising in some reacting–diffusing system
Authors: Hilhorst D. , Nishiura Y. , Mimura M.
Published: November 2011

Synopsis

We prove the well-posedness for a one-dimensional free boundary problem arising from some reaction diffusion system. The interfacial point hits a boundary point in finite time or remains inside for all time. In the large diffusion limit, the system is reduced to ordinary differential equations of finite dimension.
Poincaré–Bendixson theory for certain reaction–diffusion boundary-value problems
Authors: Smith Russell A.
Published: November 2011

The paper studies orbits in a function space described by solutions of a system of reaction–diffusion equations in a bounded domain with a boundary condition of homogeneous Robin type. The omega-limit set of a bounded semi-orbit is shown to have a simple structure, provided that certain hypotheses are satisfied. For a two-dimensional system of Fitz-Hugh Nagumo type, these hypotheses yield explicit sufficient conditions for the existence of at least one periodic trajectory.
The structure of the singularities of holomorphic matrices
Authors: Pandolfi L.
Published: November 2011

Synopsis

In this paper we consider a holomorphic matrix H(z) over a possibly unbounded region Ω and we study its properties in the neighbourhoods of a boundary point z0 of Ω (it may be z0 = ∞ if Ω is unbounded and z0 may not be an isolated singularity). Applications to systems theory and, in particular, to the theory of delay systems are presented. In this case the properties of completability, small solutions observability and zeros at z0 = ∞ are investigated.
On the codegree of negative multiples of the Hopf bundle
Authors: Crabb M. C. , Knapp K.
Published: November 2011

Synopsis

Let H be the Hopf line bundle over the complex projective space of complex dimension k – 1. We determine the codegree of the virtual bundle –nH in the range l ≦ n ≦ k. This codegree has geometric significance as a stable James number.
Global versus local admissibility criteria for dynamic phase boundaries
Authors: Fan Haitao
Published: November 2011

Synopsis

The nonuniqueness of solutions of Riemann problems for a system of conservation laws of mixed type which are admissible according to kinetic relation criteria or travelling wave criteria is proved. The above-mentioned admissibility criteria all consist of local restrictions on points of discontinuity of weak solutions. An example is given which has more than one solution admissible by these local admissibility criteria, but has only one solution, the one-phase solution, satisfying the vanishing viscosity criterion. The entropy rate criterion, however, prefers the two-phase solution.
An inverse problem for the heat equation
Authors: Ramm A. G.
Published: November 2011

Synopsis

Uniqueness of the solution to the following inverse problem is established. Given the heat equation, the initial temperature, the boundary regime at the left end of a finite rod and the measurements of the temperature at an intermediate point of the rod, find the temperature at the right end of the rod.
Foldings of star manifolds
Authors: Farran H. R. , El-Kholy E. , Robertson S. A.
Published: November 2011

Synopsis

This paper is a sequel to [4]. Its purpose is to show that the concept of isometric foldings of Riemannian manifolds can be extended to a much wider class of manifolds without losing the main structure theorem. We present here what we believe to be a definitive form of the folding concept for smooth manifolds.

The theory discussed here is based on the idea of a 1-spread [2], where the role of geodesies on a Riemannian manifold is assumed by smooth, unoriented and unparametrised curves on a smooth manifold. The absence of metrical structure forces a fresh approach to the basic definitions. A crucial feature of the Riemannian theory does survive, however, in this general setting: a 1-spread on a sufficiently smooth manifold M induces a 1-spread on sufficiently small spheres surrounding any point of M. With the help of this fact, we are able to construct an inductive definition of “star folding” f:M → N between smooth manifolds M and N, and to retain the theorem that the manifold M is stratified by the “folds”, each of which has the character of a “totally geodesic” submanifold with respect to the above-mentioned curves.
Multiple transition layers in a singularly perturbed differential-delay equation
Authors: Mallet-Paret John , Nussbaum Roger D.
Published: November 2011

Synopsis

The singularly perturbed differential-delay equation

is studied for a class of step-function nonlinearities f. We show that in general the discrete system

does not mirror the dynamics of (*), even for small ε, but that rather a different system

does. Here F is related to, but different from, f, and describes the evolution of transition layers. In this context, we also study the effects of smoothing out the discontinuities of f.
Symmetry sets of piecewise-circular curves
Authors: Giblin P. J. , Banchoff T. F.
Published: November 2011

Synopsis

Piecewise-circular (PC) curves are made up of circular arcs and segments of straight lines, joined so that the (undirected) tangent line turns continuously. PC curves have arisen in various applications where they are used to approximate smooth curves. In a previous paper, the authors introduced some of their geometrical properties. In this paper they investigate the ‘symmetry sets’ of PC curves and one-parameter families of such curves. The symmetry set has also arisen in applications (this time to shape recognition) and its mathematical properties for smooth curves have been investigated by Bruce, Giblin and Gibson. It turns out that the symmetry sets of general one-parameter families of plane curves are mirrored remarkably faithfully by the symmetry sets arising from the much simpler class of PC curves.
Schrödinger-Poisson systems in dimension d ≦ 3: The whole-space case
Authors: Nier F.
Published: November 2011

Synopsis

After a study made for bounded domains and in the periodic case, we investigate the variational formulation of Schrödinger-Poisson systems set on the whole space ℝd,d≦ 3. This variational formulation leads to a uniqueness result, while the existence of a solution is proved only for ‘small data’ because of the lack of coerciveness. The end of this paper briefly presents the extension of this formalism to a physically relevant problem where the potential is periodic in one direction.
Homogenisation and θ — 2 convergence
Authors: Alexandre Radjesvarane
Published: November 2011

We introduce a new concept of convergence for bounded sequences of functions in L2(Ω), called θ – 2 convergence, where Ω is an open set of ℝn and θ a C2 diffeomorphism of ℝn. This tool enables us to deal with homogenisation problems in some nonperiodic perforated domains. In particular, it provides a simple proof, and extensions, of a recent result of M. Briane.
Homogenisation of Dirichlet problems for monotone operators in varying domains
Authors: Casado-Díaz Juan
Published: November 2011

We study the asymptotic behaviour, for a sequence of varying open sets Ωn, of the solutionsunof nonlinear Dirichlet problems for a monotone Leray–Lions operator. The method is based on the comparison between the gradient ofunand the corrector for thep-Laplacian corresponding to the same geometry as the monotone operator. The representation of the limit problem and a corrector result are obtained.
Young measures in a nonlocal phase transition problem
Authors: Ren Xiaofeng , Winter Matthias
Published: November 2011

A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for Young measures and the principle of concentration-compactness. The regularity of such global minimisers is discussed, and the nonlocal variational problem is also considered on asymptotic tubes.
Shape optimisation problems governed by nonlinear state equations
Authors: Bucur Dorin , Trebeschi Paola
Published: November 2011

The purpose of this paper is to give a compactness-continuity result for the solution of a nonlinear Dirichlet problem in terms of its domain variation. The topology in the family of domains is given by the Hausdorff metric and continuity is obtained under capacity conditions. A generalisation of Sverak's result in iV-dimensions is deduced as a particular case.