bluuebunny/crossref_metadata_2025 huggingface dataset:
Denseness of norm-attaining operators into strictly convex spaces
Authors: Acosta M. D.
Published: November 2011

We show that no infinite-dimensional Banach space provided with a strictly convex norm satisfies Lindenstrauss's property B. This is a generalization of previous results by Lindenstrauss for rotund spaces isomorphic to C0 and by Gowers for ℓp (1 < p < ∞). Also, there is an appropriate complex version of the announced result that works for all the C-strictly convex spaces. As a consequence, the Hardy space H1, any infinite-dimensional complex L1(μ), and, in general, any infinite-dimensional predual of a von Neumann algebra lacks Lindenstrauss's property B.
Minimizing properties of arbitrary solutions to the Ginzburg–Landau equation
Authors: Comte M. , Mironescu P.
Published: November 2011

We consider the Ginzburg–Landau type equation

whereGis a smooth bounded domain in ℝ2,g ∊ C∞(∂G;ℝ2/ {0}), andε> 0 is a small parameter. We prove the uniqueness of solutions to this equation under some non-vanishing assumptions onuε, or under conditions on the boundary functiong.
On a class of Noetherian algebras
Authors: Jespers E. , Okniński J.
Published: November 2011

A class of Noetherian semigroup algebrasK[S]is described. In particular, we show that, for any submonoidSof the semigroupMnof all monomialn × nmatrices over a polycyclic-by-finite groupG, K[S]is right Noetherian if and only ifSsatisfies the ascending chain condition on right ideals. This is then used to prove that every prime homomorphic image of a semigroup algebra of a finitely generated Malcev nilpotent semigroupSsatisfying the ascending chain condition on right ideals is left and right Noetherian.
Convergence of blow-up solutions of nonlinear heat equations in the supercritical case
Authors: Matos J.
Published: November 2011

In this paper, we study the blow-up behaviour of the radially symmetric non-negative solutions u of the semilinear heat equation with supercritical power nonlinearity up (that is, (N – 2)p> N + 2). We prove the existence of non-trivial self-similar blow-up patterns of u around the blow-up point x = 0. This result follows from a convergence theorem for a nonlinear parabolic equation associated to the initial one after rescaling by similarity variables.
The wave equation, O(2, 2), and separation of variables on hyperboloids
Authors: Kalnins E. G. , Miller W.
Published: November 2011

Synopsis

We classify group-theoretically all separable coordinate systems for the eigenvalue equation of the Laplace-Beltrami operator on the hyperboloid = 1, finding 71 orthogonal and 3 non-orthogonal systems. For a number of cases the explicit spectral resolutions are worked out. We show that our results have application to the problem of separation of variables for the wave equation and to harmonic analysis on the hyperboloid and the group manifold SL(2, R). In particular, most past studies of SL(2, R) have employed only 6 of the 74 coordinate systems in which the Casimir eigenvalue equation separates.
Transformations of second order ordinary and partial difierential operators
Authors: Ahlbrandt Calvin D. , Hinton Don B. , Lewis Roger T.
Published: November 2011

Synopsis

Liouville type transformations are given for symmetric linear ordinary and partial differential operators of second order. Explicit formulas are given for the coefficients of the transformed operators. As a corollary to the general theory we obtain an “Atkinson form” for certain first order vector partial differential operators. This leads to a generalization of the concept of “g-unitary” transformations. Applications to oscillation and spectral theories are included.
On the range and inversion of fractional integrals in weighted spaces
Authors: Andersen Kenneth F.
Published: November 2011

Synopsis

The weight functions w(x) for which the Riemann fractional integral operator Iα is bounded from the Lebesgue space Lp(wp) into Lq(wq), l/q = l/p −, have been characterized by Muckenhoupt and Wheeden. In this paper, we prove an inversion formula for Iα in the context of these weighted spaces and we also characterize the range of Iα as a subset of Lq(wq) Similar results are proved for other fractional integrals. These results may be viewed as weighted analogues of certain results of Stein and Zygmund, Herson and Heywood, Heywood, and Kober who considered the unweighted case, w(x) = l.
On the essential spectra of linear 2nth order differential operators with complex coefficients
Authors: Race David
Published: November 2011

Synopsis

In this paper, a formally J-symmetric, linear differential expression of 2nth order, with complex-valued coefficients, is considered. A number of results concerning the location of the essential spectrum of associated operators are obtained. These are extensions of earlier work dealing with complex Strum-Liouville operators, and include results which, in the real case, are due to Birman, Glazman and others. They lead to criteria, for the non-emptiness of the regularity field, of the corresponding minimal operator-a condition which is needed in the theory of J-selfadjoint extensions.
An eigenfunction expansion associated with a two-parameter system of differential equations. II
Authors: Faierman M.
Published: November 2011

Synopsis

We continue with the work of an earlier paper concerning the use of partial differential equations to prove the uniform convergence of the eigenfunction expansion associated with a left definite two-parameter system of ordinary differential equations of the second order.
Existence, uniqueness and asymptotic expansion of the solution of a multipoint boundary-value problem with parameters for a singularly-perturbed system of integro-differential equations
Authors: Hristova S. G. , Bainov D. D.
Published: November 2011

Synopsis

An asymptotic expansion in powers of the small parameter of the solution of a singularly-perturbed system of integro-differential equations with a non-linear boundary condition set at several points of the interval considered is constructed and verified.
Extensions of states of C* -algebras, II
Authors: Archbold R. J. , Bunce J. W. , Gregson K. D.
Published: November 2011

Synopsis

Let A be a unital C*-algebra and let B be an abelian C*-subalgebra containing the identity of A. For any pure state h of B let Fh be the set of states of A which restrict to h on B. Necessary and sufficient conditions are given for an element x in A to have the property that, for each h, x is unable to distinguish between distinct elements of Fh. By specializing, this leads to a new proof of a theorem giving necessary and sufficient conditions for Fh to be a singleton for each h.

It is also shown that if A is postliminal and π(B) is a maximal abelian C*-subalgebra of π(B) for each irreducible representation π of A then Fh is a Choquet simplex for each h.
A non-linear Goursat problem for a 4th order polyvibrating equation
Authors: Borzymowski Andrzej
Published: November 2011

Synopsis

In the paper the existence is proved of a solution of a non-linear Goursat problem for a 4th order partial differential equation with the boundary conditions given on four curves emanating from a common point. The problem is reduced to a system of integro-functional equations and then Schauder's fixed point theorem is applied.
Existence and uniqueness for two-point boundary value problems
Authors: Baxley John V. , Brown Sarah E.
Published: November 2011

Synopsis

Boundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.
Superassociative systems with given semigroup of inner right translations
Authors: Länger H.
Published: November 2011

Synopsis

Letnbe some fixed positive integer and let (A,f) be some fixed algebra of typen+ 1. (A,f) is called ann-dimensional superassociative system iff(f(x0,…,xn), ȳ) =f(x0,f(x1, ȳ), …,f(xn, ȳ)) for anyx0, …,xn∈Aand for any ȳ ∈An. The semigroup ({f(., ā) | ā ∈An},∘) is called the semigroup of inner right translations of (A,f). In the present note a theorem is derived in order to determine alln-dimensional superassociative systems with a given semigroup of inner right translations. As an example, using this method all two-element superassociative systems are determined.
A lower bound for electrostatic capacity in the plane
Authors: Fraenkel L. E.
Published: November 2011

Synopsis

This note presents a lower bound, in terms of the diameter ratio of the inner and outer conductors, for the electrostatic capacity of certain two-dimensional condensers. We use double Steiner symmetrization to prove that the minimizing condenser consists of a line segment placed symmetrically within a circle; the capacity of this condenser is known explicitly.
Completely simple semigroups: free products, free semigroups and varieties
Authors: Jones P. R.
Published: November 2011

Synopsis

The class CS of completely simple semigroups forms a variety under the operations of multiplication and inversion (x−1 being the inverse of x in its ℋ-class). We determine a Rees matrix representation of the CS-free product of an arbitrary family of completely simple semigroups and deduce a description of the free completely simple semigroups, whose existence was proved by McAlister in 1968 and whose structure was first given by Clifford in 1979. From this a description of the lattice of varieties of completely simple semigroups is given in terms of certain subgroups of a free group of countable rank. Whilst not providing a “list” of identities on completely simple semigroups it does enable us to deduce, for instance, the description of all varieties of completely simple semigroups with abelian subgroups given by Rasin in 1979. It also enables us to describe the maximal subgroups of the “free” idempotent-generated completely simple semigroups T(α, β) denned by Eberhart et al. in 1973 and to show in general the maximal subgroups of the “V-free” semigroups of this type (which we define) need not be free in any variety of groups.
Dissipative Sturm-Liouville operators
Authors: Knowles Ian
Published: November 2011

Synopsis

Consider the differential expression

wherepandw> 0 are real-valued andqis complex-valued onI. A number of criteria are established for certain extensions of the minimal operator generated by τ in the weighted Hilbert spaceto be maximal dissipative.
Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems
Authors: Díaz J. I. , Herrero M. A.
Published: November 2011

Synopsis

We obtain existence and uniqueness of solutions with compact support for some nonlinear elliptic and parabolic problems including the equations of one-dimensional motion of a non-newtonian fluid. Precise estimates for the support of these solutions are obtained, and the optimality of our hypotheses is discussed.
Integrable-square solutions of a singular ordinary differential equation
Authors: Gilbert Richard C.
Published: November 2011

Synopsis

Absolutely square integrable solutions are determined for the equation= λywhere the ζn−r(x) are holomorphic in a sector of the complex plane and have asymptotic expansions asxapproaches infinity. It is shown that the number of such solutions depends upon the roots of the characteristic equation and their multiplicity, and upon the sign of the derivative of the characteristic polynomial. Application is made to formally symmetric ordinary differential operators.
Estimate of the number of eigenvalues for an operator of Schrödinger type
Authors: Fleckinger J.
Published: November 2011

Synopsis

We obtain an asymptotic estimate for the number of eigenvalues less than λ of an operator of Schrödinger type

defined on an unbounded domain.
An analogue of Langton's theorem on valuative criteria for vector bundles
Authors: Mehta V. B. , Ramanathan A.
Published: November 2011

Synopsis

We prove in this paper that on a non-singular projective variety, the χ-semistable functor is proper and the χ-stable functor is separated. This result was proved for μ-stability and μ-semistability by Langton. An essential part of our proof consists in defining a notion of stability between the μ and χ definitions and then proceeding by induction.
On successive coefficients of close-to-convex functions
Authors: Elhosh M. M.
Published: November 2011

Synopsis

A coefficient difference bound for k-fold symmetric and close-to-convex functions in the unit disc is established in this paper.
Finite projective double Stone algebras
Authors: Düntsch Ivo
Published: November 2011

Synopsis

We characterize the finite projective double Stone algebras, and also make some observations concerning infinite projective double Stone algebras.
On positive definite differences of multilinear forms and their representation
Authors: Kovačec Alexander
Published: November 2011

Synopsis

We study the evaluation of multilinear forms under arbitrary rearrangements of the entries of increasing n-tuples x(1), x(2),…, x(m), and we show that the difference of two such multilinear forms under certain circumstances can be written as a sum of obviously definite forms.
On the Schrödinger equation with time-dependent electric fields
Authors: Iório Rafael José , Marchesin Dan
Published: November 2011

Synopsis

We prove existence and uniqueness of solutions of i(∂ψ/∂t) = (−Δ+x1g(t)+q(x))ψ, ψ(x, s) = ψs (x) in ℝ3 for potentials q(x) including the Coulomb case. Existence and completeness of the wave operators is established for g(t) periodic with zero mean and q(x) short-range, smooth in the x1 direction. We characterize scattering and bound states in terms of the period operator.
Gravitational theory in atomic scale units in Dirac cosmology
Authors: Davidson W.
Published: November 2011

Synopsis

The implication of Dirac's large numbers hypothesis (LNH) that there are two cosmological spacetime metrics, gravitational (E) and atomic (A), is used to formulate the gravitational laws for a general mass system in atomic scale units within such a cosmology. The metric is constrained to be asymptotic to the cosmological A metric at large distance. The gravitational laws are illustrated in application to the case of a single spherical mass immersed in the smoothed out expanding universe. The condition is determined for such a metric to apply approximately just outside a typical member of a cosmic distribution of such masses. Conversely, the condition is given when the influence of the universe as a whole can be neglected outside such a mass. In the latter situation, which applies in particular to stars, a Schwarzschild-type metric is derived which incorporates variable G in accordance with the LNH. The dynamics of freely moving particles and photons in such a metric are examined according to the theory and observational tests are formulated.
H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
Authors: Tartar Luc
Published: November 2011

Synopsis

New mathematical objects, called H-measures, are introduced for studying oscillations and concentration effects in partial differential equations. Applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach.
Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity
Authors: Jiang Song
Published: November 2011

Synopsis

We consider the initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity in ℝ+; and prove a global existence-uniqueness theorem for small smooth data. The asymptotic behaviour is simultaneously obtained.
Combinatorial results relating to products of idempotents in finite full transformation semigroups
Authors: Howie John M. , Lusk Ewing L. , McFadden Robert B.
Published: November 2011

Synopsis

Each singular element α of the full transformation semigroup on a finite set is generated by the idempotents of defect one. The length of the shortest expression of α as a product of such idempotents is given by the gravity function g(α).We use certain consequences of a result by Tatsuhiko Saito to explore connections between the defect and the gravity of α, and then determine the number of elements that have maximum gravity. Finally, we obtain formulae for the number of elements of small gravity. Such elements must have defect 1, and we determine their number within each ℋ-class. Many of the results obtained were suggested, and all have been verified, by programs written in PROLOG, a logic programming language very well suited for algebraic calculations.
Discrete spectrum of perturbed Dirac systems with real and periodic coefficients
Authors: Buffoni Boris
Published: November 2011

Synopsis

This paper deals with the number of eigenvalues which appear in the gaps of the spectrum of a Dirac system with real and periodic coefficients when the coefficients are perturbed. The main results provide an upper bound and a condition under which exactly one eigenvalue appears in a given gap.
SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type
Authors: McIntosh Ian
Published: November 2011

It is shown how to derive SL(n + 1)-invariant equations which reduce to scalar Lax equations for an operator of order n + 1. The existence of these systems explains the Miura transformation between modified Lax and scalar Lax equations. In particular we study an SL(2)-invariant system with a certain space of solutions lying over the solution space of a Korteweg-de Vries equation described by G. B. Segal and G. Wilson. This enables us to write down some solutions of this SL(2)-invariant system in terms of θ-functions of a hyperelliptic Riemann surface.
A Banach–Stone theorem for spaces of weak* continuous functions
Authors: Cambern Michael
Published: November 2011

Synopsis

If X is a compact Hausdorff space and E a dual Banach space, let C(X, Eσ*) denote the Banach space of continuous functions F from X to E when the latter space is provided with its weak * topology, normed by . It is shown that if X and Y are extremally disconnected compact Hausdorff spaces and E is a uniformly convex Banach space, then the existence of an isometry between C(X, Eσ*) and C(Y, Eσ*) implies that X and Y are homeomorphic.
Periodic solutions to functional differential equations
Authors: Arino O. A. , Burton T. A. , Haddock J. R.
Published: November 2011

Synopsis

We consider a system of functional differential equations

where G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.
Remark on the Dirichlet problem for harmonic maps from the disc into the 2-sphere
Authors: Qing Jie
Published: November 2011

Synopsis

In this paper we prove a theorem concerning existence and nonexistence of minimising harmonic maps in each connected component using the framework of Brezis, Coron and Soyeur.
A priori bounds for solutions of an elliptic equation
Authors: Faierman M.
Published: November 2011

Synopsis

In the general theory of non-selfadjoint elliptic boundary value problems involving an indefinite weight function, there arises the problem of obtaining a priori estimates for solutions about points of discontinuity of the weight function. Here we deal with this problem for the case where the weight function vanishes on a set of positive measure.
Cardinal interpolation with shifted three-directional box splines
Authors: Binev Peter , Jetter Kurt
Published: November 2011

Synopsis

The question of “correctness” of cardinal interpolation with shifted three-directional box splines is solved for arbitrary orders of the directional vectors. It is shown that the corresponding symbol can be viewed as a collection of curves with certain properties (convexity, increasing argument, etc.) which are investigated in detail. The method of proof involves an induction argument which is based on properties of the exponential Euler splines (studied in [6]).
Centre manifolds for partial differential equations with delays
Authors: Lin Xiaodong , So Joseph W.-H. , Wu Jianhong
Published: November 2011

Synopsis

A centre manifold theory for reaction-diffusion equations with temporal delays is developed. Besides an existence proof, we also show that the equation on the centre manifold is a coupled system of scalar ordinary differential equations of higher order. As an illustration, this reduction procedure is applied to the Hutchinson equation with diffusion.
On the growth of the relative volume of a tube with its radius
Authors: Giménez Fernando
Published: November 2011

Synopsis

In this paper we obtain some theorems of Bishop–Gromov type for tubes about a submanifold and semitubes about a real hypersurface of a Riemannian or Kaehler manifold with curvature bounded either from below or from above.
Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain
Authors: Bruno Oscar P. , Reitich Fernando
Published: November 2011

Synopsis

In this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials. This corresponds to a two-dimensional quasi-periodic boundary value problem for the Helmholtz equation. We prove that solutions behave analytically with respect to variations of the interface. The interest of this result is both theoretical – the legitimacy of power series expansions in the parameters of the problem has indeed been questioned – and, perhaps more importantly, practical: we have found that the solution can be computed on the basis of this observation. The simple algorithm that results from such boundary variations is described. To establish the property of analyticity of the solution for the grating

with respect to the height δ, we present a holomorphic formulation of the problem using surface potentials. We show that the densities entering into the potential theoretic formulation are analytic with respect to variations of the boundary, or, in other words, that the integral operator that results from the transmission conditions at the interface is invertible in a space of holomorphic functions of the variables (x, y, δ). This permits us to conclude, in particular, that the partial derivatives of u with respect to δ at δ = 0 satisfy certain boundary value problems for the Helmholtz equation, in regions with plane boundaries, which can be solved in a closed form.
A global estimate for the gradient in a singular elliptic boundary value problem
Authors: del Pino Manuel A.
Published: November 2011

Synopsis

We investigate the singular problem

where Ω is a bounded smooth domain, k a bounded, nonnegative measurable function and v Ω 0. For the solution u to this problem, which is shown to exist if k(x) > 0 on some subset of Ω with positive measure, a uniform bound for |∇u| in Ω is derived when k(x) ≧ ψ (dist (x, ∂Ω)) with ψ (s)/sv ∈ Lp(0, a) for some a > 0, p > 1.
Differentiable functions on algebras and the equation grad (w) = M grad (v)
Authors: Waterhouse William C.
Published: November 2011

Synopsis

Let U be a convex open set in a finite-dimensional commutative real algebra A. Consider A-differentiable functions f: U → A. When they are C2 as functions of their real variables, their A-derivatives are again A-differentiable, and they have second-order Taylor expansions. The real components of such functions then have second derivatives for which the A-multiplications are self-adjoint. When A is a Frobenius algebra, that condition (a system of second-order differential equations) actually forces a real function on U to be a component of some such f. If v is a function of n real variables, and M is a constant matrix, then the requirement that M∇(u) should equal ∇(w) for some w usually falls into this setting for a suitable A, and the quite special properties of such v, w can be deduced from known properties of A-differentiable functions.
A centre manifold theorem for hyperbolic PDEs
Authors: Renardy Michael
Published: November 2011

Synopsis

A version of the centre manifold theorem is established which is suitable for quasilinear hyperbolic equations. As an application, the Benard problem for a viscoelastic fluid is discussed.
Stability of bundles with a given filtration on a smooth curve
Authors: Ballico E.
Published: November 2011

LetXbe a smooth projective curve of genusg ≥2. Here we construct stable vector bundles onXequipped with a filtration with suitable numerical properties and with stable graded subquotients.
A degree theoretic approach to N-species periodic competition systems on the whole ℝN
Authors: Du Yihong
Published: November 2011

Previous fixed-point index calculation results (see [4] and [7]) exploited in the study of population systems on bounded domains are no longer applicable to systems on the whole ℝn, due mainly to the lack of compactness. In this paper, we develop fixed-point index calculation techniques for non-compact operators so that they are applicable to systems on the whole ℝn. We illustrate the use of our fixed-point index calculation results by a simple representative model, namely, the Lotka–Volterra N-species periodic competition system on the whole ℝn.
Holomorphically embedded discs with rapidly growing area
Authors: Globevnik Josip
Published: November 2011

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.
Travelling-waves for the FKPP equation via probabilistic arguments
Authors: Harris Simon C.
Published: November 2011

We outline a completely probabilistic study of travelling-wave solutions of the FKPP reaction-diffusion equation that are monotone and connect 0 to 1. The necessary asymptotics of such travelling-waves are proved using martingale and Brownian motion techniques. Recalling the connection between the FKPP equation and branching Brownian motion through the work of McKean and Neveu, we show how the necessary asymptotics and results about branching Brownian motion combine to give the existence and uniqueness of travelling waves of all speeds greater than or equal to the critical speed.
Global unique existence of a positive solution for a system of equations in electrochemistry
Authors: Chae Dongho , Imanuvilov Oleg Yu.
Published: November 2011

In this paper we prove global-in-time existence and uniqueness of a positive solution for the system of nonlinear partial differential equations arising from an electrochemistry model. The powers of nonlinearity are allowed to be arbitrary positive integers, and our domain is any bounded subdomain of ℝ2 with a smooth boundary.
Maximum and anti-maximum principles for singular Sturm–Liouville problems
Authors: Duhoux M.
Published: November 2011

The maximum and anti-maximum principles are extended to the case of eigenvalue Sturm–Liouville problems

with boundary conditions of Dirichlet type (if possible) on a bounded interval [a, b]. The function r is assumed to be continuous and > 0 on ]a, b[, but the function 1/r is not necessarily integrable on [a, b]. The conditions on the functions p, m and h depend on the integrability or nonintegrability of 1/r on [a, c] and/or [c, b], for some c ∈ ]a, b[. The weight function m is not necessarily of constant sign.
Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation
Authors: Kapitula Todd
Published: November 2011

The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the work of Kapitula and Maier-Paape.
Sharp inequalities for maximal functions associated with general measures
Authors: Grafakos L. , Kinnunen J.
Published: November 2011

Sharp weak type (1,1) and Lp estimates in dimension one are obtained for uncentred maximal functions associated with Borel measures which do not necessarily satisfy a doubling condition. In higher dimensions, uncentred maximal functions fail to satisfy such estimates. Analogous results for centred maximal functions are given in all dimensions.
BV solutions and relaxation limit for a model in viscoelasticity
Authors: Luo Tao , Natalini Roberto
Published: November 2011

Global existence of uniformly bounded BV entropy solutions to a 2 × 2 quasilinear system with relaxation, arising in viscoelasticity, is established by using special fractional step versions of Godunov and Glimm schemes for arbitrarily large initial data. Thanks to the uniform estimates obtained, we prove the convergence of solutions to the corresponding equilibrium limit as the relaxation parameter tends to zero.
Global weak solutions for elastic equations with damping and different end states
Authors: Luo Tao , Yang Tong
Published: November 2011

In this paper, we study global weak solutions for elastic equations with damping using the compensated compactness method. When the two end states at ± ∞ are not equal, the selfsimilar solutions for the corresponding parabolic equation are used to get the entropic estimates for both the L∞ and L2 cases.
Smooth solutions of a nonhomogeneous iterative functional differential equation
Authors: Si Jian-Guo , Cheng Sui Sun
Published: November 2011

This paper is concerned with an iterative functional differential equation x(t) = c1x(t) + c2x[2](t) + … cmχ[m](t) + F(t), where x[i](t) is the i-th iterate of the function x(t). By means of Schauder's Fixed Point Theorem, we establish a local existence theorem for smooth solutions which also depend continuously on the forcing function F(t).
Orbital compactness and asymptotic behaviour of nonlinear parabolic systems with functionals
Authors: Redlinger Reinhard
Published: November 2011

Synopsis

Weakly coupled semilinear parabolic systems of the form with homogeneous boundary conditions are studied. The nonlinear function g: C([−r, 0] × Ω ℝn) → ℝn is assumed to be locally Lipschitz continuous with r≧0 a given real number and Ω ⊂ ℝm a bounded domain, , ut for t ≧ 0 is denned by ut (σ, ξ) = u(t + σ, ξ), − r ≦σ ≦ 0 ξ ∊Ω and A is a uniformly elliptic second order diagonal operator. Let u be a bounded classical solution. We first establish precompactness results for the orbit of u in several function spaces. Using these results and assuming that a Liapunov function V is known for the corresponding ordinary functional differential equation ż =g(zt), we then show under some general conditions that the limit set ω+ (as t→∞) of u consists of spatially homogeneous functions only. Moreover, ω+ is invariant with respect to z = g(z,) and V = 0 on ω+. The proof uses a Liapunov function for the full system whichis obtained from V via a simple construction (cf. (3.3)). The theory is illustrated with an example.
Non-autonomous equations related to polynomial two-dimensional systems
Authors: Alwash M. A. M. , Lloyd N. G.
Published: November 2011

Synopsis

Periodic solutions of certain one-dimensional non-autonomous differential equations are investigated (equation (1.4)); the independent variable is complex. The motivation, which is explained in the introductory section, is the connection with certain polynomial two-dimensional systems. Several classes of coefficients are considered; in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. In particular, we need to know when there is a full neighbourhood of periodic solutions. We give a number of sufficient conditions and investigate the implications for the corresponding two-dimensional systems.
Odd-order differential expressions with positive supporting coefficients
Authors: Schultze Bernd
Published: November 2011

Synopsis

The deficiency indices (mean deficiency index) and the essential spectrum for a class of odd order ordinary differential expressions are determined. The considered expressions are relatively bounded or relatively compact perturbations of symmetric expressions with odd order terms having as coefficients real powers of the independent variable.
A construction of symmetric differential expressions with non-empty essential spectrum
Authors: Schultze Bernd
Published: November 2011

Synopsis

A simple method is given for the construction of real symmetric differential expressions that are not in the limit-point case but have the real half-line as essential spectrum.
Norms in product spaces which preserve approximation properties
Authors: Benítez Carlos , Fernández Manuel
Published: November 2011

Synopsis

Let E1 and E2 be real normed linear spaces such that the dimension of any of them is at least 2. We prove that the norms in E1 × E2 which verify a simple property of monotonicity with regard to the initial norms in E1 and E2 are the only norms in E1 × E2 which preserve best linear approximations, in the sense that ifyk ∊ Lk is best approximation to xk from the linear subspace Lk, (k = 1,2), then (y1, y2) is best approximation to (x1, x2) from L1 × L2.
The form of the spectral functions associated with a class of Sturm–Liouville equations with integrable coefficient
Authors: Harris B.J.
Published: November 2011

Synopsis

We consider the second order, linear differential equation

in the case where, roughly, q ∊ L1 [0, ∞). We devise a representation for the spectral function, τ(t), associated with (*) which is valid for t sufficiently large. Our results are the best possible.
U-algebras and the Hahn–Banach extension theorem
Authors: Lavrič Boris
Published: November 2011

Synopsis

An Archimedean unital f-algebra A is called a U-algebra if, for every a∊A, there exists an invertible element u∊A such that a = u |a|. Characterisations of a U-algebra are established. As an application, an extension theorem of Hahn–Banach type on modules over a U-algebra and over the complexification of a Dedekind complete unital f-algebra is given.
Comparison and stability of solutions to a class of quasilinear parabolic problems
Authors: Chipot Michel , Rodrigues José-Francisco
Published: November 2011

Synopsis

This paper presents new comparison and uniqueness results for the solutions of parabolic quasilinear boundary value problems with (and without) obstacles. A stability result in L1(Ω) yields the asymptotic stabilisation in this space, when t → ∞) towards the corresponding elliptic problem.
An inverse problem involving the Titchmarsh–Weyl m-function
Authors: Harris B.J.
Published: November 2011

Synopsis

Let m(λ) denote the Titchmarsh–Weyl m-function associated with the differential equation

with Neumann boundary condition at 0. In the case q ∊ CM[0, ε) for some integer M and ε > 0 we prove the following result (Theorem 2.1): If for some integer ŋ ≧ 3 we know that Im {λ(ŋ + l)/2m0(λ)} = 0 on the ray λ = |λ| eiπ/ŋ, then q(v) (0) = 0 for all v in the set {0, 1, … M} for Which ≢ ŋ − 2 mod ŋ.
Amenability of weighted discrete convolution algebras on cancellative semigroups
Authors: Grønbæk Niels
Published: November 2011

Synopsis

In this paper we apply a theorem of Khelemskiĭ and Sheĭnberg, characterising amenability by means of bounded approximate identities, to weighted discrete convolution algebras. In doing this we give a condition for a weighted discrete convolution algebra to have a bounded approximate identity. Under the condition that the semigroup (S,.) is one-sided cancellative, we prove that, if some weighted discrete convolution algebra on S is amenable, then (S,.) is actually a group. We further characterise all amenable weighted discrete convolution algebras on groups, thus extending a well-known theorem of B. E. Johnson [9].
Point interactions on bounded domains
Authors: Caspers Wim , Sweers Guido
Published: November 2011

The Laplacian operator Δ on a bounded domain Ω in ℝn containing 0, with Dirichlet boundary condition, is perturbed by a pseudopotential δ, the Dirac measure at 0. Such a perturbation will be defined in Lp(ℝ) for n = 2, 1 <lt; p < ∞, and for n = 3, < p < 3, and is shown to be the generator of an analytic semigroup. Thus solutions of the corresponding evolutionary system are well defined. The necessary estimates involve the Gagliardo– Nirenberg inequality and the Kato inequality.
Blow-up behaviour for nonlinearly perturbed semilinear parabolic equations
Authors: Bricher Stephen
Published: November 2011

The blow-up behaviour of radially symmetric classical solutions to the quasilinear parabolic equation

is analysed assuming k(u) and Q(u) are small perturbations of {k, Q} ≡ {1, up},p > 1. Moreover, it is proved that the asymptotic behaviour near blowup of solutions to the semilinear equation ut = Δu + up, and in particular the final-time profile, is stable with respect to small quasilinear perturbations of the elliptic operator.
On the fixpoints of composite entire functions of finite order
Authors: Langley J. K.
Published: November 2011

Suppose that f and g are transcendental entire functions such that the composition F = f(g) has finite order, and suppose that Q is a nonconstant rational function. We show that N(r, 1/(F – Q)) ≠ o(T(r, F)). The theorem is related to results of Bergweiler, Goldstein and others.
Stability of the interface in a model of phase separation
Authors: Masi A. De , Orlandi E. , Presutti E. , Triolo L.
Published: November 2011

The paper is concerned with the asymptotic behaviour of the solutions to a nonlocal evolution equation which arises in models of phase separation. As in the Allen–Cahn equations, stationary spatially nonhomogeneous solutions exist, which represent the interface profile between stable phases. Local stability of these interface profiles is proved.
Linked eigenvalue problems for the p-Laplacian
Authors: Binding P. A. , Huang Y. X.
Published: November 2011

Linked equations of the form

are studied on a bounded smooth domain in RN for λ ∈ R2. Existence and uniqueness of solutions are discussed for fi homogeneous of order p – 1 in ui, generalising the ‘Klein Oscillation Theorem’ when p = 2, N = 1. Bifurcation from the principal eigenvalue is also considered for nonhomogeneous perturbations fi of order greater than p – 1.
Equidistribution of values of rational functions (mod p)
Authors: Odoni R. W. K. , Spain P. G.
Published: November 2011

Let R1(x),…, Rd(x) be rational functions in Iℚ(x), such that 1, R1(x),…, Rd(x) are linearly independent over Iℚ. For almost all primes p, their mod p reductions, are well-defined rational functions over Fp and are linearly independent over Fp We show that asymptotically the points

are uniformly distributed in [0, l)d.
Gradient estimates and heat kernel estimates
Authors: Qian Zhongmin
Published: November 2011

In the first part of this paper, Yau's estimates for positive L-harmonic functions and Li and Yau's gradient estimates for the positive solutions of a general parabolic heat equation on a complete Riemannian manifold are obtained by the use of Bakry and Emery's theory. In the second part we establish a heat kernel bound for a second-order differential operator which has a bounded and measurable drift, using Girsanov's formula.
Positive solutions of certain elliptic systems with density-dependent diffusions
Authors: Ahn Inkyung , Li Lige
Published: November 2011

Results are obtained on the existence of positive solutions to the following elliptic system:

in a bounded region Ω in Rn with a smooth boundary, where the diffusion terms φ ψ are non-negative functions and the system could be degenerate, β γ are strictly increasing functions, k,σ ≧ 0 are constants. We assume also that the growth rates f, g satisfy certain monotonicities. Applications to biological interactions with density-dependent diffusions are given.
Renormalisation of finitely ramified fractals
Authors: Metz Volker
Published: November 2011

Transition probabilities are calculated which make the construction of diffusions on finitely ramified fractals straightforward. In contrast to former approaches using Brouwer's Fixed Point Theorem, we consider an approximation procedure based on the iteration of a nonlinear mapL. Physically, this is done by ‘coarse-graining-renormalisation of finite electric resistor networks’. Mathematically, it is a convergence problem for quotients of Dirichlet forms on finite graphs. These graphs approximate finitely ramified fractals. The basic tool is a contraction theorem for the renormalisation mapLwhich allows the use of known results about nested fractals for non-nested (p.c.f. self-similar) ones. In general, the above contraction is not strict because several linear independent fixed points occur.
On the regularity of very weak minima
Authors: Giachetti Daniela , Leonetti Francesco , Schianchi Rosanna
Published: November 2011

We consider very weak minimisers u of variational integrals ∫ F(x, Du(x)) dx and very weak solutions u of nonlinear elliptic systems div A(x, u, Du) = 0; we prove higher integrability for the gradient Du without any homogeneity on ξ→A(x,u,ξ) thus improving on a result by Iwaniec and Sbordone.
A theorem on lower semicontinuity of integral functionals
Authors: Li Zhiping
Published: November 2011

A general lower semicontinuity theorem, in which not only mappings uM and PM but also the integrands fM depend on M, is proved for integrands f,fM under certain general hypotheses. These include thai f(x, u. P) is convex with respect to P and fM converge to f locally uniformly, but fM(x, u. P) are not required to be convex with respect to P and fM(x,·,·) do not even need to be lower semicontintious. Some more usable criteria for lower semicontinuity of integral funetionals are also given as corollaries of the main theorem.
Exponential formulae in quantum stochastic calculus
Authors: Holevo A. S.
Published: November 2011

The rigorous definition of time-ordered exponentials, solving quantum linear stochastic differential equations, is extended to Boson and Fermion stochastic calculi with infinitely many degrees of freedom. The relation to the classicalmultiplicative stochastic integral, solving the Doleans exponential equation, is discussed.
A global branch of positive solutions above the continuous spectrum for problems with indefinite nonlinearities
Authors: Küpper Tassilo , Tertikas Achilles
Published: November 2011

We prove the existence and bifurcation of a global branch of positive solutions for a nonlinear Neumann eigenvalue problem on the half axis [0, ∞). The nonlinearity is assumed to have a superlinear growth multiplied by a weight function changing sign. This leads to the existence of nontrivial solutions above the continuous spectrum of the linearised problem.
Regular and singular Sturm–Liouville problems with coupled boundary conditions
Authors: Bailey P. B. , Everitt W. N. , Zettl A.
Published: November 2011

Eigenvalues of both regular and singular Sturm–Liouville (S–L) problems with general coupled self-adjoint boundary conditions are characterised. This characterisation, although elementary, appears to be new even in the regular case. The singular characterisation is an exact parallel of the regular one and reduces to it. One application yields inequalities among the eigenvalues of different coupled boundary conditions. This is a far-reaching extension, even in the regular case, of the well-known relationship among the periodic and semiperiodic eigenvalues.
Exact multiplicity results for boundary value problems with nonlinearities generalising cubic
Authors: Korman Philip , Li Yi , Ouyang Tiancheng
Published: November 2011

Using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type

The first result concerns the case when the nonlinearity is independent ofxand behaves like a cubic inu.The second one deals with a class of nonlinearities with explicitxdependence.
Some remarks about relaxation problems in the Calculus of Variations
Authors: Flores-Bazán Fabián
Published: November 2011

We study variational problems for the functional F(u) = ∫Ω f(x, u(x), Lu(x)) dx where u∈uo + V, with Vbeing any closed linear subspace of W2.P(Ω) containing W2.p.0(Ω), Ω is a bounded open set, p > 1, L is a differential operator of second order. We determine the greatest lower semicontinuous function majorised by F for the weak topology of W2.p, for its sequential version if f satisfies no coercivity assumption, showing that in both cases the relaxed functional is expressed in terms of the function ξ↦ f**(x, u, ξ). Finally, an existence result in case f (not necessarily convex) depending only on the Laplacian, is given
Riemann problem for a class of 2 × 2 hyperbolic conservation laws
Authors: Zhu Changjiang
Published: November 2011

In this paper we prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 hyperbolic conservation laws, which is neither necessarily strictly hyperbolic nor necessarily genuinely nonlinear.
A global continuation theorem and bifurcation from infinity for infinite-dimensional dynamical systems
Authors: Ward James R.
Published: November 2011

A general continuation theorem for isolated sets in infinite-dimensional dynamical systems is proved for a class of semiflows. This result is then used to prove the existence of continua of full bounded solutions bifurcating from infinity for systems of reaction—diffusion equations.
Global smooth solution of the nonisentropic gas dynamics system
Authors: Zhu Changjiang
Published: November 2011

In this paper, a sufficient condition (H) is given on initial values for which there is a unique smooth global in time solution of the initial value problem for a special nonisentropic gas dynamics system.
The Cauchy problem for the system of Zakharov equations arising from ion-acoustic modes
Authors: Boling Guo , Guangwei Yuan
Published: November 2011

In this paper the initial value problem for a class of Zakharov equations arising from ion-acoustic modes is discussed. Without assuming the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicatea prioriestimates.
Stable periodic solutions of a spatially homogeneous nonlocal reaction–diffusion equation
Authors: Poláčik Peter , Šošovička Vladimir
Published: November 2011

Nonlocal reaction–diffusion equations of the form ut = uxx + F(u, α(u)), where are considered together with Neumann or Dirichlet boundary conditions. One of the main results deals with linearisation at equilibria. It states that, for any given set of complex numbers, one can arrange, choosing the equation properly, that this set is contained in the spectrum of the linearisation. The second main result shows that equations of the above form can undergo a supercritical Hopf bifurcation to an asymptotically stable periodic solution.
A quasilinear elliptic equation in ℝN
Authors: Alvarez O.
Published: November 2011

A quasilinear elliptic equation in ℝN of Hamilton-Jacobi-Bellman type is studied. An optimal criterion for uniqueness which involves only a lower bound on the functions is given. The unique solution in this class is identified as the value function of the associated stochastic control problem.
On convexity properties of homogeneous functions of degree one
Authors: Dacorogna Bernard , Haeberly Jean-Pierre
Published: November 2011

We provide an explicit example of a function that is homogeneous of degree one, rank-one convex, but not convex.