bluuebunny/crossref_metadata_2025_split huggingface dataset:
On positive definite differences of multilinear forms and their representation
Authors: Kovačec Alexander 
Published: November 2011

SynopsisWe 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

SynopsisWe 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

SynopsisThe 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.
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

SynopsisEach 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.
A Banach–Stone theorem for spaces of weak* continuous functions
Authors: Cambern Michael 
Published: November 2011

SynopsisIf 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

SynopsisWe consider a system of functional differential equationswhere 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.
A priori bounds for solutions of an elliptic equation
Authors: Faierman M. 
Published: November 2011

SynopsisIn 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

SynopsisThe 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

SynopsisA 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.
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

SynopsisIn 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 gratingwith 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

SynopsisWe investigate the singular problemwhere 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

SynopsisLet 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.
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 problemswith 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.
Orbital compactness and asymptotic behaviour of nonlinear parabolic systems with functionals
Authors: Redlinger Reinhard 
Published: November 2011

SynopsisWeakly 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

SynopsisPeriodic 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.
Norms in product spaces which preserve approximation properties
Authors: Benítez Carlos , Fernández Manuel 
Published: November 2011

SynopsisLet 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

SynopsisWe consider the second order, linear differential equationin 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

SynopsisAn 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

SynopsisThis 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

SynopsisLet m(λ) denote the Titchmarsh–Weyl m-function associated with the differential equationwith 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

SynopsisIn 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].
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 equationis 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.
Linked eigenvalue problems for the p-Laplacian
Authors: Binding P. A. , Huang Y. X. 
Published: November 2011

Linked equations of the formare 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 pointsare uniformly distributed in [0, l)d.
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.
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 typeThe 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.
Global well-posedness and conservation laws for the water wave interaction equation
Authors: Ogawa Takayoshi 
Published: November 2011

Interaction equations of long and short water wave are considered. It is shown that the Cauchy problem foris locally well posed in the largest space where the three conservationscan be justified. HereE(u,v) is the energy functional associated to the system. By these conservation laws, we establish the global well-posedness of the system in the largest class of initial data.
Lower semicontinuity in Sobolev spaces below the growth exponent of the integrand
Authors: Kristensen Jan 
Published: November 2011

Let there be given a non-negative, quasiconvex functionFsatisfying the growth conditionfor somep∈]1, ∞[. For an open and bounded set Ω⊂ℝm, we show that ifthen the variational integralis lower semicontinuous on sequences ofW1, pfunctions converging weakly inW1, q. In the proof, we make use of an extension operator to fix the boundary values. This idea is due to Meyers [26] and Maly [22], and the main contribution here is contained in Lemma 4.1, where a more efficient extension operator than the one in [22] (and in [14]) is used. The properties of this extension operator are in a certain sense best possible.
Periodic trajectories in static space-times
Authors: Greco Carlo 
Published: November 2011

SynopsisLet R ×Nequipped with the warped Lorentzian metricf2dt2⊕(−h), where (N,h) is a Riemannian manifold, andf:N→ ]0, ∞[ is a smooth function. Then R ×Nis called a standard static space-time, and in this paper we look for non-trivial periodic trajectories on R ×NforNcompact.
Blow up for a diffusion-advection equation
Authors: Alikakos Nicholas D. , Bates Peter W. , Grant Christopher P. 
Published: November 2011

SynopsisThese results describe the asymptotic behaviour of solutions to a certain non-linear diffusionadvection equation on the unit interval. The “no flux” boundary conditions prescribed result in mass being conserved by solutions and the existence of a mass-parametrised family of equilibria. A natural question is whether or not solutions stabilise to equilibria and if not, whether they blow up in finite time. Here it is shown that for non-linearities which characterise “fast association” there is a criticalmass such that initial data which have supercritical mass must lead to blow up in finite time. It is also shown that there exist initial data with arbitrarily small mass which also lead to blow up in finite time.
Bifurcation for quasilinear elliptic equations on Rn with natural growth conditions
Authors: Daomin Cao , Gongbao Li , Shusen Yan 
Published: November 2011

SynopsisWe consider the following eigenvalue problem:We prove the existence of H1(Rn)∩L∞(Rn) bifurcation at λ=0 but only require aij(x, t) (i,j= 1, 2, …,n) and f(x, t) to satisfy certain conditions in theneighbourhood of Rn × {0}.
Weak continuity and weak lower semicontinuity for some compensation operators
Authors: Pedregal Pablo 
Published: November 2011

SynopsisWe study a special class of linear differential operators well-behaved with respect to weakconvergence. Questions related to weak lower semicontinuity, associated Young measures, weak continuity and quasi-convexity are addressed. Specifically, it is shown that the well-known necessary conditions for weak lower semicontinuity are also sufficient in this case. Some examples are given, including a discussion on how well the operator curl fits inthis context.
A class of C∞-integrable Hamiltonian systems
Authors: Oliva W. M. , Castilla M. S. A. C. 
Published: November 2011

SynopsisWe discuss the C∞ complete integrability of Hamiltonian systems of type q = —grad V(q) = F(q), in which the closure of the cone generated (with nonnegative coefficients) by the vectors F(q), q ϵ ℝn, does not contain a line. The components of the asymptotic velocities are first integrals and the main aim is to prove their smoothness as functions of the initial conditions. The Toda-like system with potential V(q)=ΣNi=1 exp(fi∣ q) is a special case of the considered systems ifthe cone C(f1,…,fN)={ΣNi=1cifi,ci≧0} does notcontain a line. In any number of degrees of freedom, if C(f1,…,fN) has amplitude not too large (ang (fi, fj ≦π/2i,j=1,2,…, N), the first integrals are C∞ functions. In two degrees of freedom, without restriction on the amplitude of the cone, C∞-integrability is proved even in a case in which it is known that there is no other meromorphic integral of motion independent of energy. In three degrees of freedom the C∞-integrability of a deformation of the classic nonperiodic Toda system is proved. Some other examples are also discussed.
Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry
Authors: Melbourne I. , Chossat P. , Golubitsky M. 
Published: November 2011

SynopsisIn this paper we show that in O(2) symmetric systems, structurally stable, asymptoticallystable, heteroclinic cycles can be found which connect periodic solutions with steady states and periodic solutions with periodic solutions. These cycles are found in the third-order truncated normal forms of specific codimension two steady-state/Hopf and Hopf/Hopf mode interactions.We find these cycles using group-theoretic techniques; in particular, we look for certainpatterns in the lattice of isotropy subgroups. Once the pattern has been identified, the heteroclinic cycle can be constructed by decomposing the vector field on fixed-point subspaces into phase/amplitude equations (it is here that we use the assumption of normal form). The final proof of existence (and stability) relies on explicit calculations showing that certain eigenvalue restrictions can be satisfied.
Homoclinic orbits for a class of Hamiltonian systems
Authors: Rabinowitz Paul H. 
Published: November 2011

SynopsisConsider the second order Hamiltonian system:where q ∊ ℝn and V ∊ C1 (ℝ ×ℝn ℝ) is T periodic in t. Suppose Vq (t, 0) = 0, 0 is a local maximum for V(t,.) and V(t, x) | x| → ∞ Under these and some additional technical assumptions we prove that (HS) has a homoclinic orbit q emanating from 0. The orbit q is obtained as the limit as k → ∞ of 2kT periodic solutions (i.e. subharmonics) qk of (HS). The subharmonics qk are obtained in turn via the Mountain Pass Theorem.
Boundary conditions for general ordinary differential operators and their adjoints
Authors: Evans W. D. , Ibrahim Sobhy E. 
Published: November 2011

SynopsisA characterisation is obtained of all the regularly solvable operators and their adjoints generated by a general differential expression in . The domains of these operators are described in terms of boundary conditions involving the solutions of Mu = λwu and the adjoint equation . The results include those of Sun Jiong [15] concerning self-adjoint realisations of a symmetric M when the minimal operator has equal deficiency indices: if the deficiency indices are unequal the maximal symmetric operators are determined by the results herein. Another special case concerns the J -self-adjoint operators, where J denotes complex conjugation, and for this we recover the results of Zai-jiu Shang in [16].