bluuebunny/crossref_metadata_2025_split huggingface dataset:
L2-norm inequalities for the differentiation operator on compact intervals
Authors: Gillman David W. , Kaper Hans G. , Kwong Man Kam 
Published: November 2011

SynopsisIn this paper we establish the best possible value of the constant K in the inequality ∥f ′ ∥2 ≦ K ∥f∥ ∥f″∥ for functions f that are defined and twice continuously differentiable on a compact interval [a, b] ⊂ ℝ and whose first derivative vanishes at some point in [a, b].
On the k-invariants of iterated loop spaces
Authors: Arlettaz Dominique 
Published: November 2011

SynopsisThe purpose of this paper is to give universal bounds for the order of the Postnikov k-invariants of infinite loop spaces. This is done by giving universal bounds for the order of the k-invariants of m-connected r-fold loop spaces in dimensions ≦ r + 2m. An application of the result provides information on the Hurewicz homomorphism between the algebraic K-theory of aring and the homology of its general linear group.
A proof of characterisation of oscillation for higher-order neutral differential equations of mixed type by the Laplace transform
Authors: Arino O. , Attar M. A. El 
Published: November 2011

Consider the general expression of such equations in the formwhereAi, Bj, ∊ ℝ, δo= 0dn/ 0,dnaren-derivatives,n≧ l, the σj'S and δj,'s respectively, are ordered as an increasing family with possibly positive and negative terms. These are the deviating arguments. In this paper, we provide a proof of this result based on the use of the Laplace transform. Our method involves new results regarding the exponential growth of positive solutions for such equations.
Dilation method and smoothing effects of solutions to the Benjamin–Ono equation
Authors: Hayashi Nako , Kato Keiichi , Ozawa Tohru 
Published: November 2011

In this paper we study smoothing effects of solutions to the Benjamin–Ono equationwhere H is the Hilbcrt transform defined byWe prove that ifφ∈H2and (x∂x)4φ then the solutionuof(BO) belongs to, where
Critical diffusion exponents for self-similar blow-up solutions of a quasilinear parabolic equation with an exponential source
Authors: Budd Chris J. , Galaktionov Victor A. 
Published: November 2011

We study the self-similar solutions of the quasilinear parabolic equationWe show that there is an exponentsuch that if σ> then the equation admits a countable set {uk(x, t)} of self-similar blow-up solutions. These solutions have the formwhere T> 0 is a finite blow-up time, θ(ξ) solves a nonlinear ODE and each function uk(x, t) is nonconstant in a neighbourhood of the origin and has exactly k maxima and minima for x ≧ 0. There is a further critical exponent σ = ф such that if σ > ф there is a second set of self-similar solutions which are constant (in x) in a neighbourhood of the origin. We conjecture (and provide formal arguments and numerical evidence for) the existence of an infinite sequence σk→σ∞ of critical values, such that σ1 = 0 and uk exists only in the range σ>σk (when σ> 0 the equation has no nontrivial self-similar solutions). The proof of existence when σ>σ∞(σ>ф) is obtained by a combination of comparison and dynamical systems arguments and relates the existence of the self-similar solutions to a homoclinic bifurcation in an appropriate phase-space.
Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝN
Authors: Dao-Min Cao , Huan-Song Zhou 
Published: November 2011

We consider the following problemwhere for all ≦f(x,u)≦c1up-1 + c2u for all x ∈ℝN,u≧0 with c1>0,c2∈(0, 1), 2<p<(2N/(N – 2)) if N ≧ 3, 2 ≧ + ∝ if N = 2. We prove that (*) has at least two positive solutions ifand h≩0 in ℝN, where S is the best Sobolev constant and
Cauchy problem for hyperbolic conservation laws with a relaxation term
Authors: Klingenberg Christian , Lu Yun-guang 
Published: November 2011

This paper considers the Cauchy problem for hyperbolic conservation laws arising in chromatography:with bounded measurable initial data, where the relaxation term g(δ, u, v) converges to zero as the parameter δ > 0 tends to zero. We show that a solution of the equilibrium equationis given by the limit of the solutions of the viscous approximationof the original system as the dissipation ε and the relaxation δ go to zero related by δ = O(ε). The proof of convergence is obtained by a simplified method of compensated compactness [2], avoiding Young measures by using the weak continuity theorem (3.3) of two by two determinants.
Optimal existence and uniqueness in a nonlinear diffusion–absorption equation with critical exponents
Authors: Chaves M. , Vazquez J. L. , Walias M. 
Published: November 2011

We study the existence and uniqueness of non-negative solutions of the nonlinear parabolic equationposed inQ=RN× (0, ∞) with general initial datau(x, 0) =u0(x) ≧ 0. We find optimal exponential growth conditions for existence of solutions. Similar conditions apply for uniqueness, but the growth rate is different. Such conditions strongly depart from the linear casem= 1,ut= Δu–u, and also from the purely diffusive caseut= Δum.
Almost-Lp-projections and Lp isomorphisms
Authors: Cambern Michael , Jarosz Krzysztof , Wodinski Georg 
Published: November 2011

SynopsisLp -summands and Lp -projections in Banach spaces have been studied by E. Behrends, who showed that for a fixed value of p, l ≦ p ≦ ∞, p ≠ 2, any two Lp -projections on a given Banach space E commute. Here we introduce the notion of almost-Lp -projections, and we establish a result which generalises Behrends' theorem, while also simplifying its proof. Almost-Lp-projections are then applied to the study of small-bound isomorphisms of Bochner LP -spaces. It is shown that if the Banach space E satisfies a geometric condition which, in the finite-dimensional case, reduces to the absence of non-trivial Lp-summands, then for separable measure spaces, the existence of a small-bound isomorphism between Lp (λ1, E) and LP(λ2, E) implies that these Bochner spaces are, in fact, isometric.
Existence of conjugate points for self-adjoint linear differential equations
Authors: Došlý Ondřej 
Published: November 2011

SynopsisThe conjecture of Muller-Pfeiffer [4] concerning the oscillation behaviour of the differential equation (–l)n(p(x)y(n))(n) + q(x)y = 0 is proved, and a similar conjecture concerning the more general differential equation ∑nk=0(−l)k(Pk(x)y(k)(k + q(x)y= 0 is formulated.
Multiple solutions of a nonlinear boundary value problem
Authors: Troy William C. 
Published: November 2011

SynopsisWe consider a system of nonlinear differential equations derived from a model for the self-trapping of light. We prove that there is a parameter range for which there is a fundamental mode solution. Further, given any positive integer N, there also exists a parameter range over which the boundary value problem has N solutions. The first of these is a fundamental mode solution while the next N — 1 solutions represent additional modes.
The Dirichlet problem for harmonic maps from the disc into the 2-sphere
Authors: Soyeur Alain 
Published: November 2011

SynopsisWe consider the Dirichlet problem for harmonic maps from the discD2into the sphereS2, with prescribed boundary values γ:∂D2→S2, and we prove that if γ is not a rational function, one can find infinitely many nonhomotopic harmonic maps which agree with γon ∂D2.
Instability of a class of dispersive solitary waves
Authors: Souganidis P. E. , Strauss W. A. 
Published: November 2011

SynopsisThis paper studies the stability and instability properties of solitary wave solutions φ(x – ct) of a general class of evolution equations of the form Muttf(u)x=0, which support weakly nonlinear dispersive waves. It turns out that, depending on their speed c and the relation between the dispersion (i.e. the order of the pseudodifferential operator) and the nonlinearity, travelling waves maybe stable or unstable. Sharp conditions to that effect are given.
Elliptic equations on manifolds and isoperimetric inequalities
Authors: Cianchi Andrea 
Published: November 2011

SynopsisWe consider linear and nonlinear elliptic equations in divergence form on Riemannian manifolds with or without boundary. In the former case we impose a homogeneous Neumann boundary condition. By making use of isoperimetric inequalities for manifolds, we obtain a priori sharp estimates for the decreasing rearrangement of the solutions to such equations. These estimates enable us to derive bounds for suitable norms of the solutions and of their gradients.
A rigorous proof of an exponentially small estimate for a boundary value arising from an ordinary differential equation
Authors: Byatt-Smith J. G. B. , Davie A. M. 
Published: November 2011

SynopsisThe equationhas a solution y(t) which is non-oscillating on the interval (0, ∞) and has the asymptotic expansionEach term of this expansion is even in t so that formally is zero to all orders of ɛ. The estimate of has been obtained by Byatt-Smith [3] who corrects (2) in the complex plane near t = i where the series ceases to be valid. This requires asolution of the equationthe equation for the first Painlevé transcedent. Here we prove rigorously that this method gives the correct asymptotic estimatewhereThe proof involves converting (1) and (3) to integral equations. The existence and uniqueness of these integral equations are established by use of the contraction mapping theorem. We also prove that the appropriate solution to (3) provides a uniformly valid approximation to (2) over a suitably defined region of the complex plane.We also consider the connection problem for the oscillatory solutions of (1) which have asymptotic expansionswhere Ã+, Ã− φ+, and φ− are constants. The connection problem is to determine the asymptotic expansion at +∞ of a solution which has a given asymptotic expansion at −∞. In other words, we wish to find (Ã+,φ+) as a function of Ã−and φ−. We prove that there is a unique solution to the connection problem, provided Ã− is small enough, and obtain bounds on the estimate of Ã+
On the Titchmarsh-Weyl M(λ)-coefficient and spectral density for a Dirac system
Authors: Clemence Dominic P. 
Published: November 2011

SynopsisFor a Dirac system on the line, we study the Jost solutions and the existence of half-bound states. A characterisation of this phenomenon is given in terms of the M(λ)-function, which supplements a well-known spectral characterisation for the system. As a corollary, we deduce the spectral density behaviour at the spectral gap endpoints, which is shown to depend on the possible existence of half-bound states.
Boundary value problems of the Ginzburg–Landau equations
Authors: Yang Yisong 
Published: November 2011

SynopsisFor a domain Ω in the Euclidean space Rd (d = 2, 3) existence of weak solutions for both interior and exterior Dirichlet boundary value problems of the Ginzburg-Landau equations are established without any restriction on the range of the coupling constant λ, thesize of Ω, or the boundary data. For the critical choice λ = 1, we prove the existence of confined multivortices in a bounded domain by a constructive monotone iteration method.
On blow-up and degeneracy for the semilinear heat equation with source
Authors: Galaktionov V. A. 
Published: November 2011

SynopsisThe asymptotic behaviour of the solution of the semilinear parabolic equation ut = uxx + (1 + u)ln2(l + u) for t > 0, x ∊[−π, π ], ux(t, ± π) = 0 for t > 0 and u(0, x) = u0(x) ≧ 0 in [−π, π], which blows up at a finite time T0, is investigated. It is proved that for some two-parametric set of initial functions u0 the behaviour of u(t, x) near t = T0 is described by the approximate self-similar solution va(t, x) = exp {(T0 −t)−1 cos2 (x/2)} − 1, satisfying the first order nonlinear Hamilton–Jacobi equation vt, = (vx)2 /(1 + v) + (1 + v) ln2 (1 + v). Some open problems of degeneracy near a finite blow-up time for other semilinear or quasilinear parabolic equations with source ut, = Δu + (1 + u) lnβ (1 + u) (β >1), ut, = Δu + uβ(β > l), ut = Δu + eu; ut = ∇. (lnσ(1 + u)∇u)+ (1 + u)lnβ(1 + u) (σ > 0, β > 1) are discussed.
Stability of discontinuous steady states in shearing motions of a non-Newtonian fluid
Authors: Nohel John A. , Pego Robert L. , Tzavaras Athanasios E. 
Published: November 2011

SynopsisWe study the nonlinear stability of discontinuous steady states of a model initial-boundary value problem in one space dimension for incompressible, isothermal shear flow of a non-Newtonian fluid driven by a constant pressure gradient. The non-Newtonian contribution to the shear stress is assumed to satisfy a simple differential constitutive law. The key feature is a non-monotone relation between the total steady shear stress and shear strain-rate that results in steady states having, in general, discontinuities in the strain rate. We show that every solution tends to a steady state as t → ∞, and we identify steady states that are stable.
On dichotomic maps for a class of differential-difference equations
Authors: Carvalho L. A. V. , Cooke K. L. 
Published: November 2011

SynopsisStability and asymptotic stability of the null solution of the differential-difference equation (E)x′(t) = f(x(t), x(t − r)), f: RNxRN → RN, f(0, 0) = 0, are studied by means of an extension of the Liapunov–Razumikhin method. Let V: RN → R be a differentiate map, let C = C(+ −r, 0=, RN), and let x(t, ψ) denote the solution of (E) with initial condition ψ in C at t = 0. For t ≧ 0 let xt(ψ) be defined by xt,(ψ)(θ) = x(t + θ, ψ), −r ≦θ ≦0. Let V′ (ψ) be the variation of V along the solution x(t, ψ). We say that V is dichotomic with respect to (E) if there exist T ≧0 and Ω, a neighbourhood of the origin in C, such that if ψ is in the closure of the set where V′ (xT(ψ)) >; 0, then V(x(T, ψ)) ≦ V(x(s, ψ)) for some s, −r ≦ sT. It is proved that if V is positive definite, continuously differentiable, and dichotomic, then the null solution of (E) is stable. A concept of strict dichotomic map is introduced and used to prove asymptotic stability. A number of examples are given to illustrate the applications of the method.
A note on a paper of Atkinson concerning the asymptotics of an eigenvalue problem with interior singularity
Authors: Harris B.J. 
Published: November 2011

SynopsisIn [2] Atkinson considers the asymptotic form of the eigenvalues of the linear differentialequationwhere a < 0 < b and y satisfies appropriate conditions at a andb. In particular Atkinson considers where q is singular at 0. In this case q(x) = xK, his results cover the case l ≦ K < . We extend Atkinson's results to cover more singular q, in the power case 1 ≦K <
Bounded solutions of linear periodic abstract parabolic equations
Authors: Lunardi Alessandra 
Published: November 2011

SynopsisWe study the asymptotic behaviour of the parabolic evolution operatorG(t,s) associated with a family of generators of analytic semigroups {A(t);t∊ ℝ} in general Banach space, under the periodicity assumptionA(t) =A(t+T). We find new maximal regularity results for the bounded solutions of abstract nonhomogeneous parabolic equations in unbounded time intervals.
A singular perturbation problem for nonlinear damped hyperbolic equations
Authors: Biler Piotr 
Published: November 2011

SynopsisWe consider damped nonlinear hyperbolic equations utt + Aut + αAu + βA2u + G(u) = 0, where A is a positive operator and G is the Gateaux derivative of a convex functional. We examine the asymptotic behaviour of solutions and the convergence of strong solutions to these equations when the parameter β tends to zero.
Some Newman-type theorems for maps from Riemannian manifolds into manifolds
Authors: Hai-bao Duan 
Published: November 2011

SynopsisLetf: Mm→Nnbe a map from a Riemannianm-manifold(Mm, d)into ann-manifold Nn. The major purpose of this paper is to give a lower bound for the numberby examining the behaviour of the cohomology homomorphisms induced byf. This idea will be used to generalise the classical Newman theorem and present a geometric background for a well-known non-embedding theorem in topology.
A remark on the nodal regions of the solutions of some superlinear elliptic equations
Authors: Benci Vieri , Fortunato Donato 
Published: November 2011

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

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

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

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

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

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

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

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

SynopsisWe use a direct, geometric approach to study the free surface boundary conditions for stationary flows of viscous liquids. The free surface problem is characterised by a mapping on smooth variations of a given configuration; this mapping has a simple structure, which we determine by computing its differential, and studying it in terms of the space dimension and the surface tension coefficient. Applications are given to problems of existence, uniqueness and regularity in free surface flows.
Some interior and exterior boundary-value problems for the Helmholtz equation in a quadrant
Authors: Meister E. , Penzel F. , Speck F.-O. , Teixeira F. S. 
Published: November 2011

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

SynopsisIn this paper we obtain new results which relate the number of conjugacy classes of л-elements of a finite group and an arbitrary subgroup, which are analogous to some results about normal subgroups. We also prove some new results which show the relationship between class numbers and splitting theorems. Our proofs only involve elementary techniques.
Generalised factorisation for a class of Jones form matrix functions
Authors: Câmara M. C. , Lebre A. B. , Speck F.-O. 
Published: November 2011

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

SynopsisSolution branches of a semilinear elliptic problem with Neumann boundary conditions are studied at its corank-2 bifurcation points. It is shown that generally there are exactly four different nontrivial solution branches passing through a corank-2 bifurcation point. The bifurcating solution branches are parametrised via a nonsingular enlarged problem. Branch switching at bifurcation points is incorporated with a continuation method.