bluuebunny/crossref_metadata_2025_split huggingface dataset:
Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations
Authors: Kusano Takaŝi , Naito Manabu , Tanaka Kyoko 
Published: November 2011

SynopsisThe equation to be considered iswhere pi(t), 0≦i≦n, and q(t) are continuous and positive on some half-line [a, ∞). It is known that (*) always has “strictly monotone” nonoscillatory solutions defined on [a, ∞), so that of particular interest is the extreme situation in which such strictly monotone solutions are the only possible nonoscillatory solutions of (*). In this paper sufficient conditions are given for this situation to hold for (*). The structure of the solution space of (*) is also studied.
Travelling waves in an initial-boundary value problem
Authors: Veling E. J. M. 
Published: November 2011

SynopsisIn this paper we consider the initial-boundary value problem for the semihnear diffusion equation ul=uxx+f(u) on the half-line x>0, when for 0<a<1 f(0)=f(a)=f(1)=0 and f(u)<0 on (0, a), f(u)>0 on (a, 1). For a wide class of initial and boundary values a uniformly valid asymptotic expression is given to which the solution converges exponentially. This expression is composed of a travelling wave and a solution of the stationary problem.
Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems
Authors: Carl Bernd 
Published: November 2011

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.
On the Vitali–Hahn–Saks theorem
Authors: Moltó Aníbal 
Published: November 2011

SynopsisIn this paper, a class of Boolean rings containing the class discussed in papers by Seever (1968) and Faires (1976), is defined in such a way that an extension of the classical Vitali–Hahn–Saks theorem holds for exhausting additive set functions. Some new compact topological spaces K for which C(K) is a Grothendieck space are constructed and a Nikodym type theorem is deduced from it. The Boolean algebras of Seever and Faires and those we study here are defined by ‘interpolation properties’ between disjoint sequences in the algebra. We give an example at the end of the paper that illustrates the difficulties arising when we try to find a larger class of Boolean algebras, defined in terms of such properties, for which the Vitali–Hanh–Saks theorem holds.
Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems
Authors: Alikakos Nicholas D. 
Published: November 2011

SynopsisIn §§1 and 2, we consider mainly a system of reaction-diffusion equations with general diffusion matrix and we establish the stabilization of all solutions at t →∞. The interest of this problem derives from two separate facts. First, the sets that are useful for localizing the asymptotics cease to be invariant as soon as the diffusion matrix is not a multiple of the identity. Second, the set of equilibria is connected. In §3, we establish uniform L§ bounds for the solutions of a class of parabolic systems. The unifying feature in the problems considered is the lack of any conventional maximum principles.
Estimates for solutions of the Dirichlet problem for the biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Saint-Venant's principle
Authors: Kondratiev Y. A. , Oleinik O. A. 
Published: November 2011

SynopsisIn this paper energy estimates for solutions of the Dirichlet problem for the biharmonicequation, expressing Saint-Venant's principle in elasticity, are proved. From these integral inequalities, estimates for the maximum modulus of solutions and the gradient of solutions with homogeneous Diriehlet's boundary conditions in a neighbourhood of an irregular boundary point or in a neighbourhood of infinity are derived. These estimates characterize the continuity of solutions and their gradients at these points.
On idempotent affine mappings
Authors: Dawlings R. J. H. 
Published: November 2011

SynopsisLet V be a vector space and End (V) the semigroup of endomorphisms of V. An affine mapping of V is a map A: V → V given by xA = xα + a, where a belongs to End (V) and a is some element of V. Let (V) be the semigroup of affine mappings of V.Let E' denote the non-injective idempotents of End (V) and let ℰ denote the idempotents of (V). In this paper 〈ℰ〉 is determined in terms of 〈E′〉 when End (V) consists of all endomorphisms of V and when End (V) only contains the continuous endomorphisms (in which case we restrict V to being an inner product space).
The varieties of commutative semigroups for which epis are onto
Authors: Higgins P. M. 
Published: November 2011

SynopsisIn a forthcoming paper, N. M. Khan gives a condition for a variety of commutative semigroups V to be saturated in the sense of Howie and Isbell (1967) (i.e. epis are onto for each S ∈ V). We show the necessity of the condition by constructing a non-saturated semigroup which is a member of every commutative variety not satisfying Khan's condition. This determination of the saturated varieties of commutative semigroups enables us then to prove that these varieties form a sublattice of the lattice of varieties of all commutative semigroups.
Lie algebras whose maximal subalgebras are modular
Authors: Varea V. R. 
Published: November 2011

SynopsisA subalgebra M of a Lie algebra L is called modular in L if M is a modular element in the lattice of the subalgebras of L. Our aim is to study the finite-dimensional Lie algebras all of whose maximal subalgebras are modular. We characterize these algebras over any field of characteristic zero.
On small cancellation theory over H.N.N. extensions
Authors: Perraud J. 
Published: November 2011

SynopsisSmall cancellation theory has been extended to symmetrized subsets of free products, amalgamated free products and Higman-Neumann-Neumann (H.N.N.) extensions. We though that it was possible to obtain results on decision problems if we could define small cancellation conditions for finite subsets.Sacerdote and Schupp (1974) defined the small cancellation condition C'(l/6) for symmetrized subsets of an H.N.N. extension. We define this condition for finite subsets, with the following properties:For each finite subset X, there is a symmetrized subset X1 with the same normal closure and, if X1 satisfies C'(l/6), then X satisfies C'(l/6).For some H.N.N. extensions, we can decide whether any finite subset satisfies C'(l/6), and, in this case, we can solve the word problem for the corresponding quotient.
Absence of singular continuous spectrum for two-body Schrödinger operators with long-range potentials (a new proof)
Authors: Cycon Hans L. 
Published: November 2011

SynopsisWe prove the absence of singular continuous spectra for Schrödinger operators − Δ + V with long-range potential V such that V and (1 + r)1+ε(∂/∂r) V is (− Δ)-compact by using a modified “Mourre type” estimate and by Kato-Lavine's H-smoothness theory.
On the compatibility of the natural order on a regular semigroup
Authors: Blyth T. S. , Gomes Gracinda M. S. 
Published: November 2011

SynopsisA notable achievement in the algebraic theory of semigroups has been the discovery by Nambooripad of the natural order on a regular semigroup. He has shown that this order is compatible with multiplication if and only if the semigroup is locally inverse, in the sense that every local submonoid is an inverse semigroup. In this paper we determine precisely when the natural order is compatible on the right (respectively left) with multiplication; this is so if and only if every local submonoid is ℒ-unipotent (respectively ℛ-unipotent).
Growth of localized disturbances on a vortex sheet
Authors: Craik A. D. D. 
Published: November 2011

SynopsisLinearized local disturbances on a vortex sheet are known to develop singularities after a finite term in some cases but not in others. A simple test for the appearance of such singularities is given in terms of the Fourier transform of the initial disturbance. Such singularities are a consequence of the artificiality of the vortex sheet model and should not be regarded as physically meaningful.
A note on expansions for the two-dimensional, compressible, laminar boundary layer equations near a point of zero skin friction
Authors: Wilks G. 
Published: November 2011

SynopsisThe first non-arbitrary coefficient, α12, of the Buckmaster expansions is evaluated in the context of the extended Goldstein-Stewartson theory. Leading terms of the next order contributions to the skin friction and heat transfer coefficients are also obtained.
On holomorphic extensions from spheres in ℂ2
Authors: Globevnik Josip 
Published: November 2011

SynopsisA theorem of Rudin states that if B is the open unit ball in ℂN, N > 1, if 0<ρ < 1, if is the family of all complex lines in ℂN at a distance ρ from the origin and if f ∈ C(∂B) is such that for every Λ∈ the function f|Λ∂B has a continuous extension to Λ ∩ B which is holomorphic in Λ ∩ B, then f has a continuous extension to B which is holomorphic in B. In this paper we show that when N = 2, the theorem still holds if is replaced by a considerably smaller family.
On optimal mild solutions of non-homogeneous differential equations in Banach spaces
Authors: Zaidman S. 
Published: November 2011

SynopsisConsider mild solutions on the real line of non-homogeneous differential equations in a Banach space: u′(t) = Au(t) + f(t), where A is the infinitesimal generator of a C0-semigroup.We prove an existence result for optimal solutions (as defined in the text) in reflexive spaces and an uniqueness fact in uniformly convex B-spaces.
Equations de Schrödinger non linéaires en dimension deux
Authors: Cazenave Thierry 
Published: November 2011

SynopsisThis paper is devoted to the study of some non linear Schrödinger equations in two dimensions, arising in non linear optics; in particular, it is concerned with solutions to the Cauchy problem. The problem of global existence and regularity of the solutions, the asymptotic behaviour of global solutions, and the blow-up of non global solutions are studied.
On the divergence in rth mean of a class of eigenfunction expansions
Authors: Pitts C. G. C. 
Published: November 2011

SynopsisWe consider the expansion of a function in Lr (the class of measurable functions whose rth powers are Lebesgue integrable over some interval) in terms of the eigenfunctions arising from a singular Sturm-Liouville problem defined over an infinite or semi-infinite interval. We show that if l ≦ r ≦ inline1 or if r ≧ 4 there exists f in Lr whose eigenfunction expansion is divergent in the rth mean sense, and that the terms of the series form an unbounded sequence in Lr The result extends some work of Askey and Wainger concerning the Hermite series expansions of functions in Lr(–∞, ∞).
Subgroups of SL2ℤ generated by elementary matrices
Authors: Tuler Randy 
Published: November 2011

SynopsisAn elementary matrix has ones down the main diagonal and at most one element off the diagonal that differs from zero. We study the subgroups of SL2ℤ generated by sets of elementary matrices. Specifically, we give a stringent condition that the entries of a matrix belonging to such a group must satisfy.
Semilinear elliptic equations in unbounded domains of Rn
Authors: Donato Patrizia , Migliaccio Lucia , Schianchi Rosanna 
Published: November 2011

SynopsisWe study, in unbounded domains Ω⊂Rn, an elliptic semilinear problem with homogeneous boundary conditions. We assume that the nonlinear term f(x, u, Du) satisfies some condition of quadratic growth with respect to Du. We prove, in the framework of weighted Sobolev spaces, that, if and are respectively a subsolution and a supersolution of our problem, then there exists a least solution ū and a greatest solution û in the ordered interval and we obtain some multiplicity results.
Some subsemigroups of infinite full transformation semigroups
Authors: Howie J. M. 
Published: November 2011

SynopsisAs in an earlier paper by the author, three cardinal numbers, the shift, the defect and the collapse, are associated with each element of the full transformation semigroup ℑ(X), where X is an infinite set. It is shown that the elements of finite shift and non-zero defect form a subsemigroup F of ℑ(X). Moreover, if E(F) denotes the set of idempotents in F then 〈E(F)〉 = F, but (E(F))n ⊂F for every finite n. For each infinite cardinal m not exceeding ∣X∣ the set Qm of balanced elements of weight m, i.e. those with shift, defect and collapse all equal to m, forms a subsemigroup of ℑ(X). Moreover, (E(Qm))4=Qm,(E(Qm))3⊂Qm.
On the number of solutions of right-definite problems with a convergent Dirichlet integral
Authors: Eastham M. S. P. 
Published: November 2011

SynopsisA recently developed asymptotic theory of higher-order differential equations is applied to problems of right-definite type to determine the numbers M+, M− of linearly independent solutions with a convergent Dirichlet integral, M+ and M− referring to the usual upper and lower λ.-half-planes. Particular attention is given to the phenomenon noted by Karlsson in which one of M+ and M− is maximal but not the other. Conditions are given under which M+ (say) is maximal and M− is the same, one less, and two less.
Geršgorin theory and the definiteness of determinantal operators
Authors: Farenick D. R. , Browne Patrick J. 
Published: November 2011

SynopsisLet Aij, l≦j≦k, be bounded Hermitean operators on Hilbert spaces Hi, 1≦i≦k, and let be the induced operators on . An important operator for multiparameter theory is δ: H →H denned by δ = det the determinant being expanded formally. Various definiteness properties of δ are critical for multiparameter spectral theory.We use the operators Aij to construct a numerical matrix δ(δ) upon which we use Geršgorin theory to investigate the non-singularity and definiteness of δ. Diagonal dominance properties of the array [Aij] are also discussed.
Finitely generated GEn-rings
Authors: Mason A. W. 
Published: November 2011

SynopsisSuslin and Cohn have proved that the polynomial ring Z[t1, …,td], where Z is the ring of rational integers and d >0, is a GEn-ring if and only if n ≧ 3. (A commutative ring R with identity is called a GEn-ring if and only if SLn(R) is generated by elementary matrices, where n ≧ 2.) In this paper we consider the following question:Given algebraic numbers α1, …,αd, for which n (if any) is the ring A =Z [α1, …,αd a GEn-ring?By standard results from algebraic K-theory it follows that (a) A is GEn for all n ≧ 2, (b) A is not GEn for any n ≧ 2, or (c) A is GEn if and only if n ≧ 3. Examples of each type are provided. In particular, it is shown that if each αi is real or at least one αi is not an algebraic integer, then A is of type (a).
Global higher bifurcations in coupled systems of nonlinear eigenvalue problems
Authors: Cantrell Robert Stephen 
Published: November 2011

SynopsisCoexistent steady-state solutions to a Lotka–Volterra model for two freely-dispersing competing species have been shown by several authors to arise as global secondary bifurcation phenomena. In this paper we establish conditions for the existence of global higher dimensional n-ary bifurcation in general systems of multiparameter nonlinear eigenvalue problems which preserve the coupling structure of diffusive steady-state Lotka–Volterra models. In establishing our result, we mainly employ the recently-developed multidimensional global multiparameter theory of Alexander–Antman. Conditions for ternary steady-state bifurcation in the three species diffusive competition model are given as an application of the result.
Existence for the modified Kassoy problem
Authors: Bebernes J. , Troy W. 
Published: November 2011

SynopsisWe prove that there exists an ᾱ > 0 such that for each 0 ≦ α ≦ ᾱ, there is at least one β = β(α) < 0 such that y“ − (x/2)y' + ey − 1 =0, y(0) = α, y'(0) = β has a solution y(x, α,β) satisfying the asymptotic property y(x, α,β)∼ −2 In x + Kα as x → ∞.
On the fixed point index in locally convex spaces
Authors: Furi M. , Pera M. P. 
Published: November 2011

SynopsisLet E be a Hausdorff locally convex space, Q a convex closed subset of E and U an open subset of Q. We develop an index theory for a class of locally compact maps f: U → E for which the usual assumption f(U) ⊂ Q is replaced by an appropriate “pushing condition”. Moreover, from this index theory, we deduce a general continuation principle and some global results for nonlinear eigenvalue problems.
Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications
Authors: Kawashima Shuichi 
Published: November 2011

SynopsisWe study the large-time behaviour of solutions to the initial value problem for hyperbolic-parabolic systems of conservation equations in one space dimension. It is proved that under suitable assumptions a unique solution exists for all time t ≧ 0, and converges to a given constant state at the rate t − ¼ as t → ∞. Moreover, it is proved that the solution approaches the superposition of the non-linear and linear diffusion waves constructed in terms of the self-similar solutions to the Burgers equation and the linear heat equation at the rate t − ½ +α, α > 0, as t →∞. The proof is essentially based on the fact that for t → ∞ the solution to the hyperbolic-parabolic system is well approximated by the solution to a semilinear uniformly parabolic system whose viscosity matrix is uniquely determined from the original system. The results obtained are applicable straightforwardly to the equations of viscous (or inviscid) heat-conductive fluids.
On a counterexample of a rank 1 convex function which is not polyconvex in the case N = 2
Authors: Aubert G. 
Published: November 2011

SynopsisJ. M. Ball has introduced the notion of polyconvexity to study nonlinear problems in elasticity and he has shown that polyconvexity implies rank 1 convexity. In this paper we prove by a counterexample that the converse of this implication is false in two dimensions.
Studies in multiplicative solutions to linear differential equations
Authors: Arscott F. M. 
Published: November 2011

SynopsisGiven an ordinary linear differential equation whose singularities are isolated, a solution is called multiplicative for a closed path C if, when continued analytically along C, it returns to its starting-point merely multiplied by a constant. This paper first classifies such paths into three types, then investigates combinations of two such paths, in which a number of qualitatively different situations can arise. A key result is also given relating to a three-path combination. There are applications to special functions and Floquet theory for periodic equations.
Volterra integral equations and a new Gronwall inequality (Part I: The linear case)
Authors: Norbury J. , Stuart A. M. 
Published: November 2011

SynopsisWe present a generalisation of the continuous Gronwall inequality and show its use in bounding solutions of discrete inequalities of a form that arise when analysing the convergence of product integration methods for Volterra integral equations. We then use these ideas to prove convergence of a numerical method which is effective in approximating Volterra integral equations of the second kind with weakly singular kernels.
Some general constructions of tight mappings
Authors: Coghlan Leslie 
Published: November 2011

SynopsisWe present several general methods of constructing tight hypersurfaces f: Mn → En+1, n ≧ 2. We prove a smoothing lemma, which allows us to approximate tight continuous hypersurfaces by C∞ tight ones. We show that given a tight immersion or C∞-stable map f: M2 → E3 of a compact surface M2 other than S2, there is a tight C∞-stable map g: M2 # RP2:→ E3. We prove that given C∞ tight immersions f: Mn → En+1 and g: Nn → En+1 of compact n-manifolds Mn and Nn into En+1, there is a tight C∞ immersion of Mn # Nn into En+1. Two other methods involve hypersurfaces of rotation and sets in En+1 at a fixed distance from a tightly embedded n-manifold with boundary in En. One consequence of these methods is that the outer part of C∞ tight hypersurfacesf: Mn → En+1, n ≧ 3, is far more complicated than in the case of tight surfaces in En. For example, given any C∞n-manifold M with boundary tightly embedded in En, there is a tight immersion f:Nn → En+1 of a closed n-manifold having M as a topset. Kuiper's theorem describing tight immersions of surfaces into E3 does not generalise to the case of hypersurfaces f: Mn → En+1, n ≧ 3, without substantial restrictions on Mn and/or f.
The perturbed test function method for viscosity solutions of nonlinear PDE
Authors: Evans Lawrence C. 
Published: November 2011

SynopsisThe method of viscosity solutions for nonlinear partial differential equations (PDEs) justifies passages to limits by in effect using the maximum principle to convert to the corresponding limit problem for smooth test functions. We describe in this paper a “perturbed test function” device, which entails various modifications of the test functions by lower order correctors. Applications include homogenisation for quasilinear elliptic PDEs and approximation of quasilinear parabolic PDEs by systems of Hamilton-Jacobi equations.
Weighted norm inequalities involving gradients
Authors: Carton-Lebrun C. , Heinig H. P. 
Published: November 2011

SynopsisLetthen, for certain weight functionsuandvand indicesp,q, it is shown that ∥Tαf∥q, u≦C∥grad f ∥p, v'q>n/ α holds. For α=l,p=qandu=v≡ l this reduces to a result of M. Weiss. In addition we establishn-dimensional weighted Hardy—Littlewood type inequalities ofthe formfor large classes of weights.
On a characterisation of Dirac measures
Authors: Escobedo Miguel 
Published: November 2011

SynopsisAssume f ∈ C(RM, SN−1) (M ≧ 1, N ≧ 1) is periodic with period one in each variable and satisfies:Then, every probability measure on [0, 1)M such thatis a Dirac measure at some point of [0, 1)M.
Multiplicity results for nonlinear elliptic equations involving critical Sobolev exponent
Authors: Capozzi A. , Palmieri G. 
Published: November 2011

SynopsisIn this paper we study the following boundary value problemwhere Ω is a bounded domain in Rn, n≧3, x ∈Rn, p* = 2n/(n – 2) is the critical exponent for the Sobolev embedding is a real parameter and f(x, t) increases, at infinity, more slowly than .By using variational techniques, we prove the existence of multiple solutions to the equations (0.1), in the case when λ belongs to a suitable left neighbourhood of an arbitrary eigenvalue of −Δ, and the existence of at least one solution for any λ sufficiently large.
Weighted norm inequalities for the Hankel- and -transformations
Authors: Emara S. A. , Heinig H. P. 
Published: November 2011

SynopsisWe give conditions on pairs of non-negative weight functions u and v which are sufficient that, for 1<p, q <∞,where T is the Hankel-or the K-transformation.The proofs are based on a weighted Marcinkiewicz interpolation theorem for linear operators. In the case that T is the Hankel transformation and 1<p≦q <∞, the result is similar to a weighted estimate of Heywood and Rooney [9], but with different weight conditions.