bluuebunny/crossref_metadata_2025 huggingface dataset:
On a Dirichlet–Neumann–Third mixed boundary value problem for the Helmholtz equation
Authors: David M.
Published: November 2011

Synopsis

Existence and uniqueness theorems are proved for the solution of a Dirichlet-Neumann-Third mixed boundary value problem for the Helmholtz equation in ℝ3. The proofs make use of an equivalent system of two integral equations of the second kind.
On a common abstraction of de Morgan algebras and Stone algebras
Authors: Blyth T. S. , Varlet J. C.
Published: November 2011

Synopsis

We consider a common abstraction of de Morgan algebras and Stone algebras which we call an MS-algebra. The variety of MS-algebras is easily described by adjoining only three simple equations to the axioms for a bounded distributive lattice. We first investigate the elementary properties of these algebras, then we characterise the least congruence which collapses all the elements of an ideal, and those ideals which are congruence kernels. We introduce a congruence which is similar to the Glivenko congruence in a p-algebra and show that the location of this congruence in the lattice of congruences is closely related to the subdirect irreducibility of the algebra. Finally, we give a complete description of the subdirectly irreducible MS-algebras.
Liouville theorems for linear elliptic systems
Authors: Weck N.
Published: November 2011

Synopsis

Liouville theorems are obtained for general elliptic PDE-systems ℒU(x): = Σlɑl≦21Aα(x) əαU(x)=0 essentially under the assumption that ℒ satisfies a coerciveness estimate over .
Lp-Theory of degenerate-elliptic and parabolic operators of second order
Authors: Wong-Dzung Baoswan
Published: November 2011

Synopsis

We consider the formal operator given by

in the Banach space X =LP(Rn), 1<p<∞. The coefficients ajk(x),aj(x), and a(x) are real-valued functions, ajkε C2(Rn) has bounded second derivatives, ajε Cl(Rn) has bounded first derivatives, and aεL∞(Rn). Furthermore, we assume that the n × n matrix (ajk(x)) is symmetric and positive semidefinite (i.e. ajk(x)ξjξk≧0 for all (ξ1,…,ξn)εRnandxεRn). We prove that the degenerate-elliptic differential operator given by –Aand restricted to, the minimal realization of –A, is essentially quasi-m-dispersive inLp(Rn), (hence that the minimal realization of +Ais quasi-m-accretive) and that its closure coincides with the maximal realization of –A.
Sphere stratifications and the Gauss map
Authors: Fuster M. C. Romero
Published: November 2011

Synopsis

There is a residual subset of embeddings of an m-manifold, M in Rm+1 (m ≦ 6), for which the induced Maxwell subset on the sphere Sm is a stratified subset. We define and study two different stratifications of this subset and their extensions to the whole Sm: the Gauss stratification and the core stratification. We also find relations between the Euler numbers of the strata of the core stratification and the “exposed” singularities of the Gauss map on M.
An eigenfunction expansion associated with a two-parameter system of differential equations. III
Authors: Faierman M.
Published: November 2011

Synopsis

We continue with the work of earlier papers concerning the use of partial dilferential equations to prove the uniform convergence of the eigenfunction expansion associated witha left definite two-parameter system of ordinary differential equations of the second order.
Nonlinear eigenvalue problems for the whirling of heavy elastic strings, II: new methods of global bifurcation theory
Authors: Alexander J. C. , Antman Stuart S. , Deng Shi-tao
Published: November 2011

Synopsis

This paper treats the global qualitative behaviour of all bifurcating configurations of whirling nonlinearly elastic strings with ends fixed on the axis of rotation.
A nonexistence result for axially symmetric flows with constant angular velocities at infinity
Authors: Elcrat Alan R. , Siegel David
Published: November 2011

Synopsis

If von Kármán's substitution is made in the Navier-Stokes equations, and boundary conditions corresponding to a flow in all of space with constant angular velocities at infinity are imposed, a boundary value problem analgous to those for flow above a rotating disk and between rotating disks is obtained. It is shown here that this problem has no solution.
Steiner triple systems of order 19 constructed from the Steiner triple system of order 9
Authors: Prince Alan R.
Published: November 2011

Synopsis

A standard method of constructing Steiner triple systems of order 19 from the Steiner triple system of order 9 gives rise to 212 different such systems. It is shown that there are just three isomorphism classes amongst these systems. Representatives of each isomorphism class are described and the orders of their automorphism groups are determined.
Conics related by a pentagram: a problem of J. E. Reeve
Authors: Knight A. J.
Published: November 2011

Synopsis

Two non-singular conies ω and α are said to be related by a pentagram if there exist pentads ofdistinct points {Oi} on ω and {Ai} on α (1 ≦ i ≦ 5) such that A1 ≡ O2O4. O3O5, A2 ≡ O3O5. O1O4, A3 ≡ O1O4. O2O5, A4 ≡ O2O5. O1O3 and A5 ≡ O1O3. O2O4. It is shown that relation by a pentagram is a poristic property; and a necessary condition on their mutual projective invariants that two nonsingular conies be so related is derived. Some ramifications are discussed.
Singular differential operators with spectra discrete and bounded below
Authors: Hinton Don B. , Lewis Roger T.
Published: November 2011

Synopsis

A weighted, formally self-adjoint ordinary differential operator l of order 2n is considered, and conditions are given on the coefficients of l which ensure that all self-adjoint operators associated with l have a spectrum which is discrete and bounded below. Both finite and infinite singularities are considered. The results are obtained by the establishment of certain conditions which imply that l is non-oscillatory.
Equivalent norms and Schauder bases in anisotropic Besov spaces
Authors: Long Tran Due , Triebel Hans
Published: November 2011

Synopsis

The paper deals with equivalent norms and Schauder bases in anisotropic Besov spaces where 1≦p <∞, = (s1,…, sn), and 0 < sk <1.
A generalisation of the inverse spectral theorem of Levitan and Gasymov
Authors: Thurlow Christine
Published: November 2011

Synopsis

In the Inverse Spectral Theorem in the form given by Levitan and Gasymov, necessary and sufficient conditions are given for a non-decreasing function, p(ℷ), to be the spectral function of a Sturm–Liouville problem. In these conditions, p(ℷ) is compared with the spectral function for the particular Strum–Liouville problem

If the method of Levitan and Gasymov's proof is slightly adapted, the necessary and sufficient conditions can be stated in a more general form in which p(ℷ) is compared with the spectral function for any problem of the form

wherehOis real and qo(x) locally integrable.
Problèmes elliptiques du 2ème ordre non sous forme divergence
Authors: Lions Pierre-Louis
Published: November 2011

Synopsis

We prove existence and uniqueness results for the solution of nonlinear elliptic boundary value problems, where the linear part of the equation is given by a second-order elliptic operator not in divergence form.
The stability problem for transformations of the circle
Authors: Cenzer Douglas
Published: November 2011

Synopsis

Let I be the group of rotations of the circle and suppose that a map f from I into I is “almost linear”. More precisely, let ε be a positive real number and suppose that d(f(x)+f(y), f(x + y))<ε for all x and y in I; f is said to be an ε-homomorphism. If ε is sufficiently small, then a homomorphism h from I into I can be constructed such that d(f(x), h(x))≦ε for all x in I. This result is refined and generalized in several ways.
Positive solutions of superlinear boundary value problems
Authors: Voss Heinrich
Published: November 2011

Synopsis

Using a fixed point theorem on operators expanding a cone in a Banach space we prove the existence of positive solutions of superlinear boundary value problems

At the same time we get bounds (or even inclusions) of positive solutions.
Liouville theorems for elliptic systems and nonlinear equations of fourth order
Authors: Goyal Vinod B. , Schaefer Philip W.
Published: November 2011

Synopsis

Liouville theorems are obtained for fourth order elliptic systems of the form Δ2U + B Δ U + AU = 0 and for fourth order nonlinear equations of the form Δ2u−q(x) Δu + p(x)f(u) = 0 as a consequence of two related subharmonic functions, the mean value property of subharmonic functions, and a basic Green identity.
Monotone techniques and some existence-uniqueness theorems for two point boundary value problems
Authors: Lin Song-Sun
Published: November 2011

Synopsis

In this paper we study the existence and uniqueness of the two point boundary value problems −(p(x)u′(x))′ = f(x, u(x), u′(x)), xε(0, 1), u′(0)−cu(0) = 0 = u′(1) + du(1), where ∂f/∂u is bounded. above by the least eigenvalue of associated linear problems and ∂f/∂u is bounded. By using monotone techniques to investigate the equivalent problem −(p(x)u′(x))′ + r(x)u(x) = f(x, u(x), u′(x)) + r(x)u(x) where r ε C[0, 1] we show that

gives the optimal bounds for ∂f/∂u and ∂f/u′ when c and d are nonnegative constants.
Explicit solutions for a class of dual integral equations
Authors: Anderssen R. S. , de Hoog F. R. , Rose L. R. F.
Published: November 2011

Synopsis

An explicit solution is derived for the dual integral equations

when A(ξ) takes the form

It is then shown how the basic technique can be adapted to derive explicit solutions for more general forms of A(ξ) such as

and

and linear combinations of such sums.
On the zeros of solutions to nonlinear hyperbolic equations
Authors: Yoshida Norio
Published: November 2011

Synopsis

We consider the hyperbolic equation uxy + c(x, y, u) =f(x, y) and the wave equation

We show that, under suitable conditions, there are bounded domains in which every solution to certain problems has a zero. Characteristic initial value problems and initial boundary value problems are considered.
Tight stable surfaces, II
Authors: Coghlan Leslie
Published: November 2011

Synopsis

Kuiper has proved that there is no tight topological immersion of RP2 into E3. Thus any continuous tight map RP2 → E3 has to have singular points. In this note we consider tight C∞-stable maps of RP2 and the torus into E3; i.e. maps with the simplest possible singularities (Whitney pinchpoints) and transversal crossings. We classify the forms that the outer part of such maps can take; we prove also some facts about the inner part. The result about the outer part of C℞-stable tight maps RP2 → E3 establishes the first half of Banchoff's conjectured classification of such mappings.
Functions with finite intersections with analytic functions
Authors: Buczolich Zoltán
Published: November 2011

Synopsis

We prove that for every dense Gδ set H, there exists a continuous function f, such that f intersects every analytic function in finitely many points and f is infinitely differentiable exactly at the points of H. This answers a problem of S. Agronsky, A. M. Bruckner, M. Laczkovich and D. Preiss. They proved a result which implies that every continuous function with finite intersections with analytic functions is infinitely differentiable at the points of a dense Gδ set.
Diffusive logistic equations with indefinite weights: population models in disrupted environments
Authors: Cantrell Robert Stephen , Cosner Chris
Published: November 2011

Synopsis

The dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form ut = d Δu + [m(x) — cu]u in Ω × (0, ∞), where u represents the population density, c, d > 0 are constants describing the limiting effects of crowding and the diffusion rate of the population, respectively, and m(x) describes the local growth rate of the population. If the environment ∞ is bounded and is surrounded by uninhabitable regions, then u = 0 on ∂∞× (0, ∞). The growth rate m(x) is positive on favourablehabitats and negative on unfavourable ones. The object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled. The models are shown to possess a unique, stable, positive steady state (implying persistence for the population) provided l/d> where is the principle positive eigenvalue for the problem — Δϕ=λm(x)ϕ in Χ,ϕ=0 on ∂Ω. Analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat. In the limit as the diffusion rate d ↓ 0, the solutions tend toward the positive part of m(x)/c, and if m is discontinuous develop interior transition layers. The analysis uses bifurcation and continuation methods, the variational characterisation of eigenvalues, upper and lower solution techniques, and singular perturbation theory.
Exact estimates of the conductivity of a binary mixture of isotropic materials
Authors: Lurie K. A. , Cherkaev A. V.
Published: November 2011

Synopsis

This paper describes the set GmU of effective conductivity tensors of mixtures generated by two isotropic materials taken in prescribed proportions m1 and m2 We describe microstructures which realise any point of GmU for n-dimensional space.
The Ljapunov equation and an application to stabilisation of one-dimensional diffusion equations
Authors: Nambu Takao
Published: November 2011

Synopsis

A Ljapunov equationXL − BX = Cappears in stabilisation studies of linear systems. Here, the operatorsL, B, andCare given linear operators working in infinite-dimensional Hilbert spaces, which are derived from a specific control system. We have so far considered the case whereLis a general elliptic operator of order 2 in a bounded domain of an Euclidean space. WhenLis instead a self-adjoint elliptic operator working in an interval of ℝ1, we derive here a stronger geometrical character of the solutionXto the Ljapunov equation. The result is applied to stabilisation of one-dimensional diffusion equations.
Left approximate identities in algebras of compact operators on Banach spaces
Authors: Dixon P. G.
Published: November 2011

Synopsis

We study the existence of left approximate units, left approximate identities and bounded left approximate identities in the algebras (X)of all compact operators on a Banach space X and ℱ(X)− of all operators uniformly approximable by finite rank operators. In the case of bounded left approximate identities, necessary and sufficient conditions on X are obtained. In the other cases, sufficient conditions are obtained, together with an example of non-existence using a space constructed by Szankowski. The possibility of the sufficient conditions being also necessary depends on the question of whether every compact set is contained in the closure of the image of the unit ball under an operator in (X)(or ℱ(X)−). Sufficient conditions on X are obtained for this to be true, but it is conjectured that the answer for general X is negative.
Elementary operators
Authors: Brešar M. , Šemrl P.
Published: November 2011

We introduce the concept of an elementary operator between two algebras, and thereby extend the study of operators of the form

where ai, bi are fixed elements in an algebra. Elementary operators on some classes of algebras are considered and their general form is described in some special cases.
On various semiconvex relaxations of the squared-distance function
Authors: Zhang K.
Published: November 2011

For the Euclidean squared-distance functionf(·) = dist2(·, K), withK ⊂ MN×n, we show thatKis convex if and only iff(·)equals either its rank-one convex, quasiconvex or polyconvex relaxations. We also establish that if (i)Kis compact and contractible or (ii) dimC(K) = k < Nn, Kis convex if and only iffequals one of the semiconvex relaxations when dist2(P, K)is sufficiently large, and for case (i),P ∈MNxn; for case (ii),P ∈ Ek—a k-dimensional plane containingC(K). We also give some estimates of the difference between dist2(P, K)and its semiconvex relaxations. Some possible extensions to more generalp-distance functions are also considered.
Lower semicontinuhy of positive quadratic forms
Authors: Simon Barry
Published: November 2011

Synopsis

We develop various facets of the theory of quadratic forms on a Hilbert space suggested by a criterion of Kato which characterizes closed forms in terms of lower semicontinuity.
Eigenvalues of regular differential operators
Authors: Benzinger Harold E.
Published: November 2011

Synopsis

It is shown that the fine structure of the asymptotic estimates for the eigenvalues of a large class of ordinary differential operators, can be described in terms of the Fourier coefficients of a function of class L2.
On a gradient-like integro-differential equation
Authors: Hale Jack K. , Rybakowski Krzysztof P.
Published: November 2011

Synopsis

Under appropriate conditions on b and a function g with 2k +1 simple zeros, the equation

has a maximal compact invariant set Ab,g in C([−1,0]R), consisting of the zeros of g and the one-dimensional unstable manifolds of these zeros. For k =2, it is shown that there may be a saddle connection in the flow on Ab,g for some g. This implies that the zeros of g as elements of the flow on Ab,g cannot be given the natural order of the reals.
A note on non-abelian homological algebra and endomorphism near-rings
Authors: Lockhart R.
Published: November 2011

Synopsis

One possible generalisation of homological algebra to non-abelian structures is suggested.
On the boundary value problems of electro- and magnetostatics
Authors: Picard Rainer
Published: November 2011

Synopsis

The classically well-known relation between the number of linearly independent solutions of the electro- and magnetostatic boundary value problems (harmonic Dirichlet and Neumann vector fields) and topological characteristics (genus and number of boundaries) of the underlying domain in 3-dimensional euclidean space is investigated in the framework of Hilbert space theory. It can be shown that this connection is still valid for a large class of domains with not necessarily smooth boundaries (segment property). As an application the inhomogeneous boundary value problems of electro- and magnetostatics are discussed.
Hermite–Birkhoff interpolation by Hermite–Birkhoff splines
Authors: Goodman T. N. T.
Published: November 2011

Synopsis

We consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E. Similarly the allowable discontinuities of the piecewise polynomials are specified by a finite incidence matrix F. We first find necessary conditions on (E, F) for the problem to be poised, that is to have a unique solution for any given data. The main result gives sufficient conditions on (E, F) for the problem to be poised, generalising a well-known result of Atkinson and Sharma. To this end we prove some results involving estimates of the numbers of zeros of the relevant piecewise polynomials.
Expansion problems with irregular multipoint boundary conditions
Authors: Freiling Gerhard
Published: November 2011

Synopsis

Using asymptotic estimates for the Green's function of irregular multipoint eigenvalue problems, we state sufficient conditions for the uniform convergence of the expansion of functions into a series of eigenfunctions.
Existence of conjugate points for second and fourth order differential equations
Authors: Müller-Pfeiffer E.
Published: November 2011

Synopsis

The paper presents sufficient conditions on the coefficients of second and fourth order differential equations to ensure that there exists at least one pair of conjugate points on an interval (a, b), −∞≦ a <b ≦ ∞. Oscillation criteria related to the equation (p(x)y″)″ + q(x)y = 0, 0 < x < ∞, are proved with no sign restrictions on q(x).
Non-existence of eigenvalues of Dirac operators
Authors: Kalf Hubert
Published: November 2011

Synopsis

Absence of non-trivial square integrable solutions of the Dirac equation

for values of λ in half-rays is proved under local conditions on q, curl b, and the radial derivative of q. The Coulomb potential is admitted. Another result does not contain any growth condition on the radial derivative of q. It states that there are no solutions of integrable square other than the trivial solution if λ ε ℝ\ [−1, 1] and
Oscillatory and asymptotic properties of a class of operator-differential inequalities
Authors: Myshkis A. D. , Bainov D. D. , Zahariev A. I.
Published: November 2011

Synopsis

The present paper studies some asymptotic (including oscillatory) properties of the solutions of operator-differential inequalities of the form

where

(the latter symbol denotes the space of locally summable functions).

As an application of the results obtained, theorems are proved for the asymptotic behaviour of the solutions of certain classes of functional-differential and integro-differential neutral-type equations.
Associated Laguerre and Hermite polynomials
Authors: Askey Richard , Wimp Jet
Published: November 2011

Synopsis

Explicit orthogonality relations are found for the associated Laguerre and Hermite polynomials. One consequence is the construction of the [n − 1/n] Padé approximation to Ψ(a + 1, b; x)/Ψ(a, b; x), where Ψ(a, b; x) is the second solution to the confluent hypergeometric differential equation that does not grow rapidly at infinity.
Semicontinuous envelopes of polyconvex integrals
Authors: Acerbi Emilio , Buttazzo Giuseppe
Published: November 2011

Synopsis

We answer some questions about the semicontinuity inL∞and inLpof functionals defined onW1,n(Ωℝn) as integrals of non-convex functions of the gradient matrix, and we give a conjecture for the general case.
On the traction problem for linear elastostatics in exterior domains
Authors: Padula Mariarosaria
Published: November 2011

Synopsis

In this note, we study the well-posedness of the exterior traction value problem for linear anisotropic non-homogeneous elastostatics. We prove existence and continuous dependence upon the data. In particular, in the isotropic homogeneous case, provided the body force is “simple”, we show that solutions tend to zero uniformly at large spatial distances.
Doubly-null-concordant simple even-dimensional knots
Authors: Kearton C.
Published: November 2011

Synopsis

The simple 2q-knots, q ≧ 5, for which contains no ℤ-torsion, have been classified in terms of Hermitian duality pairings on their homology and homotopy modules. In this paper, a necessary and sufficient condition is given for such a knot to be doubly-null-concordant.
The deficiency indices of powers of second order expressions with large leading coefficient
Authors: Read Thomas T.
Published: November 2011

Synopsis

The deficiency index of each power of the differential expression M[y] = w−1(−(py′)′ + qy), defined on [a, ∞), is calculated exactly in terms of the behaviour of a simple function of p and w for a large class of expressions satisfying a hypothesis which requires that p be large compared with w and q. In general, not all powers of M are limit-point.
On Malcev algebras in which all subideals are ideals
Authors: Elduque Alberto
Published: November 2011

Synopsis

Malcev algebras in which the relation of being an ideal is transitive are studied as well as those Malcev algebras in which every subalgebra satisfies that condition. These algebras are closely related to those in which right multiplication by any element is semisimple and they are used to determine Malcev algebras with a relatively complemented lattice of subalgebras.
Approximate identities in extensions of topologically nilpotent Banach algebras
Authors: Dixon P. G. , Willis G. A.
Published: November 2011

Synopsis

In commutative Banach algebras with factorisation, the existence of an identity (bounded approximate identity) modulo a topologically nilpotent radical implies the existence of a global identity (bounded approximate identity), respectively.
The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions II
Authors: Rutter John W.
Published: November 2011

Synopsis

We give here an abelian kernel (central) group extension sequence for calculating, for a non-simply-connected space X, the group of pointed self-homotopy-equivalence classes . This group extension sequence gives in terms of , where Xn is the nth stage of a Postnikov decomposition, and, in particular, determines up to extension for non-simplyconnected spaces X having at most two non-trivial homotopy groups in dimensions 1 and n. We give a simple geometric proof that the sequence splits in the case where is the generalised Eilenberg–McLane space corresponding to the action ϕ: π1 → aut πn, and give some information about the class of the extension in the general case.
Existence and boundedness of a minimiser for a constrained minimisation problem on Rn with limiting exponent
Authors: Yaotian Shen , Shusen Yan
Published: November 2011

Synopsis

We use the concentration compactness principle to study the existence of a minimiser of the minimisation problem where u =(u1, …, uN), . We also prove the boundedness of the minimiser of l1 by using the reverse Holder inequality.
Convergence in Lotka–Volterra-type delay systems without instantaneous feedbacks
Authors: Kuang Yang , Smith Hal L.
Published: November 2011

Synopsis

Most of the convergence results appearing so far for delayed Lotka–Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka–Volterra-type system if some of the delays are small, and initial functions are small and smooth, then the convergence of its positive steady state follows that of the undelayed system or the corresponding system whose instantaneous negative feedback dominates. In particular, we establish explicit expressions for allowable delay lengths for such convergence to sustain.
Local and global existence results for anisotropic Hele–Shaw flows
Authors: Deckelnick Klaus , Elliott Charles M.
Published: November 2011

In this paper we study a moving boundary problem for an anisotropic two-phase Hele–Shaw flow. Using a regularization technique, we prove existence of a local solution. Under suitable conditions on the initial free boundary we obtain a global solution and study its asymptotic behaviour.
Stratified path spaces and fibrations
Authors: Hughes Bruce
Published: November 2011

The main objects of study are the homotopically stratified metric spaces introduced by Quinn. Closed unions of strata are shown to be stratified forward tame. Stratified fibrations between spaces with stratifications are introduced. Paths that lie in a single stratum, except possibly at their initial points, form a space with a natural stratification, and the evaluation map from that space of paths is shown to be a stratified fibration. Applications to mapping cylinders and to the geometry of manifold stratified spaces are expected in future papers.
A study of Jacobians in Hardyd–Orlicz spaces
Authors: Iwaniec Tadeusz , Verde Anna
Published: November 2011

We study the Jacobian determinants J = det(∂fi/∂xj) of mappings f: Ω ⊂ ℝn → ℝn in a Sobolev–Orlicz space W1,Φ (Ω,ℝn). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy–Orlicz spaces ℌp (Ω). Other nonlinear quantities involving the Jacobian, such as J log |J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.
On the motion of a vortex filament in an external flow according to the localized induction approximation
Authors: Nishiyama Takahiro
Published: November 2011

A vector equation which gives the velocity of a vortex filament embedded in an inviscid incompressible flow is considered. It comprises terms representing effects from the localized self-induction and from the external flow. The initial value problem is proved to have at least a solution for a suitable external flow term.
On equations of KP-type
Authors: Iório Rafael José , Nunes Wagner Vieira Leite
Published: November 2011

We discuss the local Cauchy problem for the generalised Kadomtsev–Petviashvili equation, namely , in the periodic and nonperiodic settings.
Fragmentation–diffusion model. Existence of solutions and their asymptotic behaviour
Authors: Laurençot Philippe , Wrzosek Dariusz
Published: November 2011

An infinite system of reaction–diffusion equations that represents a particular case of the discrete coagulation–fragmentation model with diffusion is studied. The reaction part of the model describes the rate of clusters break-up into smaller particles. Diffusion constants are assumed to be different in each equation and concentration-dependent fragmentation coefficients are considered. Existence of solutions is studied under fairly general assumptions on fragmentation coefficients and initial data. Uniqueness in the class of mass-preserving solutions is proved. Convergence of solutions to spatially homogeneous equilibrium state is obtained.
Geodesic spheres and Jacobi vector fields on Sasakian space forms
Authors: Blair David E. , Vanhecke Lieven
Published: November 2011

Synopsis

Using explicit equations for Jacobi vector fields on a Sasakian space form, we characterise such spaces by means of the shape operator of small geodesic spheres.
An example of H1-unboundedness of solutions to strongly elliptic systems of partial differential equations in a laminated geometry
Authors: Le Dret Hervé
Published: November 2011

Synopsis

In this paper, a counterexample is given to the H1-boundedness of solutions to a sequence of systems of linear partial differential equations uniformly satisfying a strict Legendre–Hadamard condition and whose coefficients depend on one direction only. This counterexample is relevant for the theory of homogenisation of laminated elastic materials.
Trend to spatial homogeneity for solutions to semilinear damped wave equations
Authors: Solà-Morales J. , València M.
Published: November 2011

Synopsis

The semilinear damped wave equations

subject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.
Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains
Authors: Fortunato Donato , Jannelli Enrico
Published: November 2011

Synopsis

We consider the boundary value problem

where Ω ⊂ ℝn is a bounded domain, n≧3, 2* = 2n/(n − 2) is the critical exponent for the Sobolev embedding and λ is a real positive parameter. We prove the existence of infinitely many solutions of (*) when Ω exhibits suitable symmetries.
A Laplace transform relevant to holomorphic semigroups
Authors: Rebarber R.L.
Published: November 2011

Synopsis

A Laplace transform is developed for functions which are holomorphic in the complex wedge Ω = {z| |arg (z)| < σ}, where 0 ≦ σ < π. The resulting transform will be holomorphic in a complementary wedge of the form Ωa = {a+ z||arg (z)|< (π/2) +σ for some a. This Laplace transform is shown to be an isomorphism between two appropriate spaces. The spanning properties of sets of the form {eλkS}k∊I in the domain space are studied. These results are then applied to a control problem.
Radial entire solutions to even order semilinear elliptic equations in the plane
Authors: Kusano Takaŝi , Naito Manabu , Swanson Charles A.
Published: November 2011

Synopsis

Semilinear elliptic equations of the form

are considered, where Δm is the m-th iterate of the two-dimensional Laplacian Δ, p(t) is continuous in [0, ∞), and f(u is continuous and positive either in (0, ∞) or in ℝ.

Our main objective is to present conditions on p and f which imply the existence of radial entire solutions to (*), that is, those functions of class C2m(ℝ2) which depend only on |x| and satisfy (*) pointwise in ℝ2.

First, necessary and sufficient conditions are established for equation (*), with p(t) > 0 in [0, ∞), to possess infinitely many positive radial entire solutions which are asymptotic to positive constant multiples of |x|2m−2 log |x as |x| → ∞. Secondly, it is shown that, in the case p(t < 0, in [ 0, ∞) and f(u) > 0 is nondecreasing in ℝ, equation (*) always has eventually negative radial entire solutions, all of which decrease at least as fast as negative constant multiples of |x|2m−2 log |x| as |x| → ∞. Our results seem to be new even when specialised to the prototypes

where γ is a constant.
Sturmian theory for nonself-adjoint differential equations of second order
Authors: Müller-Pfeiffer E.
Published: November 2011

Synopsis

The Sturm–Picone comparison theorem is extended to nonself-adjoint differential equations considered on non-compact intervals.
An analytical study of bifurcation problems for equations involving Fredholm mappings
Authors: Tan N.X.
Published: November 2011

Let us consider equations in the form

where Λ is an open subset of a normed space. For any fixed λ ∊ Λ, T, L(λ,.) and M(λ,.) are mappings from the closure D0 of a neighbourhood D0 of the origin in a Banach space X into another Banach space Y with T(0) = L(λ, 0) = M(λ, 0) = 0. Let λ be a characteristic value of the pair (T, L) such that T − L(λ,.) is a Fredholm mapping with nullity p and index s, p> s≧ 0. Under sufficient hypotheses on T, L and M, (λ, 0) is a bifurcation point of the above equations. Some well-known results obtained by Crandall and Rabinowitz [2], McLeod and Sattinger [5] and others will be generalised. The results in this paper are extensions of the results obtained by the author in [7].
Comparison principles for strongly coupled reaction diffusion equations in unbounded domains
Authors: Tuma E.
Published: November 2011

Synopsis

Comparison principles for systems of reaction–diffusion equations in unbounded domains and coupledvia both reaction and diffusion terms are considered. Applications are made to the FitzHugh–Nagumo equations and models of coupled nerve fibres.
Maximal torsional rigidity: some qualitative remarks
Authors: Tahraoui R.
Published: November 2011

We give an existence result and some qualitative remarks about the optimisation of the torsional rigidity of a beam.
Characterisation of correctness of cardinal interpolation with shifted three-directional box splines
Authors: Zhou Ding-Xuan , Jetter Kurt
Published: November 2011

Cardinal interpolation by integer translates of shifted three-directional box splines is studied. It is shown that, for arbitrary orders, k, l, m ∈ N of the directional vectors, this problem is correct if and only if the shift vector is taken from the hexagonal shift region (modulo translation with respect to the lattice Z2). This confirms a conjecture of S. D. Riemenschneider [9], and settles the problem studied in [5] for the special case k = l = m in full generality. The method of proof is from homotopy theory.
On the uniform stability for a ‘food-limited’ population model with time delay
Authors: So Joseph W.-H. , Yu J. S.
Published: November 2011

In this paper, we provide sufficient conditions which guarantee the uniform stability as well as asymptotic stability of the positive equilibrium for a food limited population model with time delay.
Practical persistence in ecological models via comparison methods
Authors: Cantrell Robert Stephen , Cosner Chris
Published: November 2011

A basic question in mathematical ecology is that of deciding whether or not a model for the population dynamics of interacting species predicts their long-term coexistence. A sufficient condition for coexistence is the presence of a globally attracting positive equilibrium, but that condition may be too strong since it excludes other possibilities such as stable periodic solutions. Even if there is such an equilibrium, it may be difficult to establish its existence and stability, especially in the case of models with diffusion. In recent years, there has been considerable interest in the idea of uniform persistence or permanence, where coexistence is inferred from the existence of a globally attracting positive set. The advantage of that approach is that often uniform persistence can be shown much more easily than the existence of a globally attracting equilibrium. The disadvantage is that most techniques for establishing uniform persistence do not provide any information on the size or location of the attracting set. That is a serious drawback from the applied viewpoint, because if the positive attracting set contains points that represent less than one individual of some species, then the practical interpretation that uniform persistence predicts coexistence may not be valid. An alternative approach is to seek asymptotic lower bounds on the populations or densities in the model, via comparison with simpler equations whose dynamics are better known. If such bounds can be obtained and approximately computed, then the prediction ofpersistence can be made practical rather than merely theoretical. This paper describes how practical persistence can be established for some classes of reaction–diffusion models for interacting populations. Somewhat surprisingly, themodels need not be autonomous or have any specific monotonicity properties.
Self-induced compactness in Banach spaces
Authors: Casazza P. G. , Jarchow H.
Published: November 2011

We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has a negative answer, in general, for approximable operators. We further construct a Banach space failing the bounded compact approximation property, though all of its duals have the metric compact approximation property.
Cesàro averaging operators on Hardy spaces
Authors: Andersen Kenneth F.
Published: November 2011

It is shown that the Cesàro averaging operatorℜα > – 1, satisfies an inequality which immediately implies that it is bounded on certain Hardy spaces including Hp, 0 < p < ∞. This answers an open question of Stempak, who introduced these operators and obtained their boundedness on Hp, 0 < p ≦ 2, for ℜα ≧ 0. The operator which is conjugate to on H2 is also shown to be bounded on Hp for 1 < p < ∞ and ℜα = – 1. This extends a result of Stempak who obtained this boundedness for 2 ≦ p≦ ∞ and ℜα ≧:0.
Jacobi's elliptic functions and Lagrangian immersions
Authors: Chen Bang-Yen
Published: November 2011

First, we establish a sharp inequality between the squared mean curvature and the scalar curvature for a Lagrangian submanifold in a nonflat complex-space-form. Then, by utilising the Jacobi's elliptic functions en and dn, we introduce three families of Lagrangian submanifolds and two exceptional Lagrangian submanifolds Fn, Ln in nonflat complex-space-forms which satisfy the equality case of the inequality. Finally, we obtain the complete classification of Lagrangian submanifolds in nonflat complex-space-forms which satisfy this basic equality.
On the algebra of a free monoid
Authors: Crabb M. J. , McGregor C. M. , Munn W. D. , Wassermann S.
Published: November 2011

Let denote a subring of the complex field that contains 1 and is closed under complex conjugation. It is shown that, with respect to the involution induced by word-reversal, the algebra over of a free monoid admits a trace and a separating family of star matrix representations. From the existence of a trace it is deduced that the aforementioned involution is special, in the sense of Easdown and Munn. Similar results hold for the algebra over of a free monoid with involution.
Stochastic generalised KPP equations
Authors: Davies I. M. , Truman A. , Zhao H. Z.
Published: November 2011

We classify multiplicative white noise perturbationsk(·)dw, of generalised KPP equations and their effects on deterministic approximate travelling wave solutions by the behaviour of, the solutions of the stochastic generalised KPP equations converge to deterministic approximate travelling waves and if

being an associated potential energy, Фsa solution of the corresponding classical mechanical equations of Newton,Dbeing a certain domain inR1×Rrthen the white noise perturbations essentially destroy the wave structure and force the solutions to die down.

For the case

(suppose the existence of the limit) we show that there is a residual wave form but propagating at a different speed from that of the unperturbed equations. Numerical solutions are included and give good agreement with theoretical results.
Existence and uniqueness of the global admissible solution for a viscoelastic model with relaxation
Authors: Zhao Huijiang
Published: November 2011

This paper examines the Cauchy problem for a viscoelastic model with relaxation

with discontinuous, large initial data, where ½ ≦ μ <1, δ > 0 are constants. We first give a definition of admissible (or entropic) solutions to the system. Under this definition, we prove the existence, uniqueness and continuous dependence of the global admissible solution for the system. Our methods are essentially due to Kruzkov, and the requirement that f(u) is not badly degenerate (more precisely, meas {x: f″(x) = 0} = 0), needed previously when considering the global existence problem for the same system, is removed.
Homogenisation of transport kinetic equations with oscillating potentials
Authors: Frenod E. , Hamdache K.
Published: November 2011

We consider the homogenisation of transport kinetic equations with a highly periodic oscillating external field. The external field, acting on the particles, consists of a sum of a field deriving from a periodic potential and a bounded periodic perturbation. For the profile function generated by the oscillating solution of the problem, we derive a kinetic model with transmission boundary conditions in the energy variable. In some cases, for example when the field is not perturbed, we deduce a transport kinetic equation with memory effect satisfied by the weak-* limit of the sequence of solutions.
Periodic oscillations of forced pendulums with very small length
Authors: Fonda Alessandro , Zanolin Fabio
Published: November 2011

We prove the existence of an arbitrarily large number of periodic solutions for a class of nonlinear differential equations generalising the dynamics of a forced pendulum with small length.
Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3, Part I: countably normed spaces on polyhedral domains
Authors: Guo Benqi , Babuška Ivo
Published: November 2011

This is the first of a series of three papers devoted to the regularity of solutions of elliptic problems on nonsmooth domains in ℝ3. The present paper introduces various weighted spaces and countably weighted spaces in the neighbourhood of edges and vertices of polyhedral domains, and it concentrates on exploring the structure of these spaces, such as the embeddings of weighted Sobolev spaces, the relation between weighted Sobolev spaces and weighted continuous function spaces, and the relations between the weighted Sobolev spaces and countably weighted Sobolev spaces in Cartesian coordinates and in the spherical and cylindrical coordinates. These well-defined spaces are the foundation for the comprehensive study of the regularity theory of elliptic problems with piecewise analytic data in ℝ3, which are essential for the design of effective computation and the analysis of the h – p version of the finite element method for solving elliptic problems in three-dimensional nonsmooth domains arising from mechanics and engineering.
A gradient estimate on a manifold with convex boundary
Authors: Qian Zhongmin
Published: November 2011

We present a simple probability approach for establishing a gradient estimate for a solution of an elliptic equation on a compact Riemannian manifold with convex boundary, or on a noncompact complete manifold. Our method can also be applied to derive a similar gradient estimate for a nonlinear parabolic equation, and an abstract gradient estimate for a Markov semigroup.
Unique continuation properties of the nonlinear Schrödinger equation
Authors: Zhang Bing-Yu
Published: November 2011

Consider the unique continuation problem for the nonlinear Schrödinger (NLS) equation

By using the inverse scattering transform and some results from the Hardy function theory, we prove that if u ∈ C(R; H1(R)) is a solution of the NLS equation, then it cannot have compact support at two different moments unless it vanishes identically. In addition, it is shown under certain conditions that if u is a solution of the NLS equation, then u vanishes identically if it vanishes on two horizontal half lines in the x–t space. This implies that the solution u must vanish everywhere if it vanishes in an open subset in the x–t space.
On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem
Authors: Dancer E. N. , Wei Juncheng
Published: November 2011

We discuss the existence of positive solutions of some singularity perturbed elliptic equations on convex domains with nonlinearity changing sign. In particular, we obtain solutions with both a boundary layer and a sharp interior peak.
Lowersemicontinuity of energy clusters
Authors: Morgan Frank
Published: November 2011

We discuss existence and lowersemicontinuity for clusters of materials minimising an energy given by a collection of norms φij on the interfaces between regions Ri and Rj. Following Ambrosio and Braides, we exhibit a problem for which the triangle inequality holds but existence fails, and we state a new sufficient condition for lowersemicontinuity, which may be necessary.
Dynamic boundary conditions for the Navier–Stokes equations
Authors: Grobbelaar-Van Dalsen Maríe , Sauer Niko
Published: November 2011

Synopsis

When a symmetric rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. These equations at the boundary contain a time derivative and thus are of a dynamic nature. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity and pressure fields of the fluid motion and the angular velocity of the rigid body.

In this paper we formulate the physical problem for the case of rotation about an axis of symmetry as an abstract ordinary differential equation in two Banach spaces in which the velocity field is the only unknown. To achieve this, a method for the elimination of the pressure field, which also occurs in the boundary condition, is developed. Existence and uniqueness results for the abstract equation are derived with the aid of the theory of B-evolutions and the associated theory of fractional powers of a closed pair of operators.
Evolution equations with dynamic boundary conditions
Authors: Hintermann Thomas
Published: November 2011

Synopsis

In this paper, we study boundary problems with dynamic boundary conditions, that is, with boundary operators containing time derivatives. The equations under consideration are transformed into abstract Cauchy problems x – Cx = f and x(0) = x0. Abstract theoretical results concerning the operators C are obtained by the study of a naturally arising pseudodifferential operator. For existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations, we then apply the theory of semigroups in Banach spaces. Some examples of semilinear and quasilinear problems, to which our results apply, are given.
On the existence of weak solutions for a nonlinear time dependent Dirac equation
Authors: Dias João-Paulo , Figueira Mário
Published: November 2011

Synopsis

In this paper we prove the existence of a weak solution of the Cauchy problem for the nonlinear Dirac equation in ℝ × ℝ

where X(r) is the characteristic function of a compact interval of ]0, + ∞[