bluuebunny/crossref_metadata_2025_split huggingface dataset:
L∞-continuity of Henkin operators solving in certain weakly pseudoconvex domains of ℂ2
Authors: Verdera Joan 
Published: November 2011

SynopsisLet ψ ∈ C2[0,1] be a positive function on (0, 1]. Under certain assumptions on ψ, the setis a pseudoconvex domain with C2-boundary, for which it is possible to construct a Henkin-type operator Hψ = Kψ + Bψ solving in Dψ. The operator Bψ, is L∞-continuous because it has a Riesz potential type kernel, while the L∞-continuity of Kψ depends on the flatness of ψ at 0. Our main result states that Kψ is continuous from L∞(∂Dψ) into L∞(Dψ) if and only if
Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
Authors: Lurie K. A. , Cherkaev A. V. 
Published: November 2011

SynopsisThis paper is a sequel to [1-4]. We consider the problem of G-closure, i.e. the description of the set GU of effective tensors of conductivity for all possible mixtures assembled from a number of initially given components belonging to some fixed set U. Effective tensors are determined here in a sense of G-convergence relative to the operator ∇· D · ∇, of the elements DeU ∈ [5, 6].The G-closure problem for an arbitrary initial set U in the two-dimensional case has already been solved [3, 4]. It remained, however, unclear how to construct, in the most economic way, a composite with some prescribed effective conductivity, or, equivalently, how to describe the set GmU of composites which may be assembled from given components taken in some prescribed proportion. This problem is solved in what follows for a set U consisting of two isotropic materials possessing conductivities D+ = u+E and D− = u−E where 0<u−<u+<∞ and E ( = ii+jj) is a unit tensor.
On regular semigroup rings
Authors: Okniński Jan 
Published: November 2011

SynopsisIt is shown that if A is an algebra over a field, then the regularity of the semigroup algebra A[G] implies that the semigroup G is periodic. This enables us to characterize regular semigroup algebras of semigroups with d.c.c. on principal ideals. Also, regular self-injective semigroup algebras are described.
Multiparameter Sturm theory
Authors: Binding Paul , Browne Patrick J. 
Published: November 2011

SynopsisLet Sturm–Liouville problemswith continuous coefficients and appropriate boundary conditions, be coupled by the eigenvalue λ = (λ1, … λk). When k = 1, there are various oscillation, perturbation and comparison theorems concerning existence and continuous or monotonic dependence of eigenvalues, eigenfunctions and their zeros (i.e. focal points).We attempt a unified theory for such results, valid for general fc, under conditions known as "left" and “right” definiteness. A representative result may be stated loosely as follows: if LD holds then (elementwise) monotonic dependence of p, q and the matrix [ars] forces monotonic dependence of λ. LD is a generalisation of the “polar” case for k = 1, and was originally conceived for a quite different purpose, viz. completeness of eigenfunctions via elliptic partial differential equation theory.
A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions
Authors: Harris B. J. 
Published: November 2011

SynopsisIn an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equationhas the asymptotic expansionas |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.We show that if the real valued function q admits the expansionin a neighbourhood of 0, then
A system of order 2 in which small sub-harmonics and large sub-harmonics coexist
Authors: Obi Chike 
Published: November 2011

SynopsisThis paper establishes the coexistence of small and large subharmonics in a special case of the ordinary non-linear differential equationof order 2, where κ, ε are small parameters, λ>0 is a parameter independent of κ, ε, h(t) has the least period 2π andIt is divided into three sections. In Section 1 a general analysis of the periodic solutions of (.), classified into small, medium or large, is given. In Section 2 the general theory of Section 1 is applied to the special form of (.) where k = vε1+s, v>0, s>0 constants, to obtain results from which we extract in Section 2 a theorem (Section 3) on the coexistence of a small periodic solution of order 1, several small sub-harmonics and several large sub-harmonics of the special caseof (.), where Q≧1 is an integer.
Convergence criteria for Aronszajn's method and for the Bazley-Fox method
Authors: Brown R. D. 
Published: November 2011

SynopsisConvergence criteria are derived for Aronszajn's method and for the Bazley-Fox C*C method applied to self-adjoint eigenvalue problems of the form Bx = λx. These criteria generalise previously used criteria and are seen to be, in a certain restricted sense, the best possible. The framework used is general enough to allow approximations where the intermediate problems are not finite dimensional perturbations of the base problem.
The nilpotency index of the radicals of group algebras of finite groups whose Sylow 3-subgroups are extra-special of order 27 of exponent 3
Authors: Koshitani Shigeo 
Published: November 2011

SynopsisLet J(FG) be the Jacobson radical of the group algebra FG of a finite groupG with a Sylow 3-subgroup which is extra-special of order 27 of exponent 3 over a field F of characteristic 3, and let t(G) be the least positive integer t with J(FG)t = 0. In this paper, we prove that t(G) = 9 if G has a normal subgroup H such that (|G:H|, 3) = 1 and if H is either 3-solvable, SL(3,3) or the Tits simple group 2F4(2)'.
A distributional approach to Namias' fractional Fourier transforms
Authors: Kerr Fiona H. 
Published: November 2011

SynopsisA fractionalisation of the Fourier transform was developed formally by Namias. By workingin ℐ, we found that this theory could be made mathematically rigorous. Here we extend our previous results to the space ℐ′ to consider fractional powers of the distributional Fourier transform. The paper concludes with an application to an ordinary differential equation which shows how a distributional approach can sometimes be more useful than a classical approach.
Decomposition matrices for spin characters of symmetric groups
Authors: Morris A. O. , Yaseen A. K. 
Published: November 2011

SynopsisMethods are developed for determining the decomposition matrices for the spin characters of the symmetric groups Snfor an odd primep. Some general results are obtained which are non-trivial modifications of the corresponding results for ordinary characters. The methods are used to determine the decomposition matrices for 3 ≦ n ≦ ll, andp= 3 but with an interesting ambiguity in the casen= 9. The second author will deal separately with the casesp= 5, 7, 11.
A shooting argument with oscillation for semilinear elliptic radially symmetric equations
Authors: Jones C. K. R. T. , Küpper T. , Plakties H. 
Published: November 2011

SynopsisA new method is developed for finding radially symmetric solutions of semilinear elliptic problems by phase space methods. The basic idea is to formulate a shooting argument from initial conditions at r = 0 which involves encoding the oscillation information about the trajectories under consideration. The main theorem is applied to a particular nonlinearity and produces a cascade of solutions wherein the multiplicity increases with the number of zeros.
Non-immersibility of a space form as a totally umbilical hypersurface
Authors: Okumura Masafumi , Takahashi Hiroshi 
Published: November 2011

SynopsisSuppose that a space form is immersed into another Riemannian manifold as a totally umbilical hypersurface with constant mean curvature. Then, in the ambient manifold, the lengthof the curvature tensor, that of the Ricci tensor and the scalar curvature must satisfy an inequality. In this paper the authors proved the inequality. As applications of the inequality, some immersibility problems are investigated. For example, it is proved that if a space form is immersed in an Einstein manifold as a totally umbilical hypersurface, then the Einstein manifold has constant sectional curvature along the hypersurface. Moreover, it is proved that a space form cannot be immersed into some Kaehlerian manifolds as a totally umbilical hypersurface with constant mean curvature.
Existence and uniqueness of heteroclinic orbits for the equation λu‴ + u′ = f(u)
Authors: Toland J. F. 
Published: November 2011

SynopsisIffis a continuous even function which is decreasing on (0,∞) and such that±α are its only zeros and are simple, then in three-dimensional phase spacethe unstable manifold of the equilibrium u = −α and the stable manifold of u = α are both two dimensional. If λ<0 it is shown that there is a unique bounded orbit of the equation λu‴ + u′ = f(u), and that this is a heteroclinic orbit joining these two equilibria. Other results on the existence and uniqueness of heteroclinic orbits are also established when f is not even and when f is not monotone on (0, ∞).
Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire
Authors: Tahraoui R. 
Published: November 2011

SynopsisIn this paper, we study problems of the form:We obtain some existence and regularity results when Ω is either a ball or an annulus, without convexity hypothesis on g. We then apply these results to some shear problems in nonlinear elasticity.
Regularity of plate equations with control concentrated in interior curves
Authors: Jaffard Stéphane , Tucsnak Marius 
Published: November 2011

SynopsisWe consider initial and boundary-value problems modelling the vibration of a plate with piezoelectric actuator. The usual models lead to the Bernoulli–Euler and Kirchhoff plate equations with right-hand side given by a distribution concentrated in an interior curve. We obtain regularity results which are stronger than those obtained by simply using the Sobolev regularity of the right-hand side. By duality, we obtain new trace regularity properties for the solutions of plate equations. Our results provide appropriate function spaces for the control of plates provided with piezoelectric actuators.
An eigenvalue problem for generalized Laplacian in Orlicz—Sobolev spaces
Authors: Mustonen Vesa , Tienari Matti 
Published: November 2011

Let m: [ 0, ∞) → [ 0, ∞) be an increasing continuous function with m(t) = 0 if and only if t = 0, m(t) → ∞ as t → ∞ and Ω C ℝN a bounded domain. In this note we show that for every r > 0 there exists a function ur solving the minimization problemwhere Moreover, the function ur is a weak solution to the corresponding Euler–Lagrange equationfor some λ > 0. We emphasize that no Δ2-condition is needed for M or M; so the associated functionals are not continuously differentiable, in general.
Monotone convergence theorems for variational triples with applications to intermediate problems
Authors: Brown R. D. 
Published: November 2011

SynopsisThe variational eigenvalue problem for a real quadratic form b with respect to a positive definite form a on a vector space V may be represented by the triple (b, a, V). Methods of intermediate problems provide approximations from below to the lower eigenvalues of (b, a, V) using monotone increasing sequences of such triples. It is shown that every such approximation method is canonically equivalent to Weinstein's method. General convergence theorems are proved for such methods. These results generalise known convergence results for increasing sequences of quadratic forms. The results are applied to some specific approximation methods and are illustrated using a differential eigenvalue problem.
A computer proof of relations in a certain class of groups
Authors: Robertson Edmund F. , Rutherford Kevin 
Published: November 2011

SynopsisA gp-toolkit consisting of computer implementations of various group theory methods, in particular a Tietze transformation program, was designed. Special cases of a conjecture were solved by the gp-toolkit. Examination of the method used by the gp-toolkit to deduce relations showed that a general approach had been employed. We present a proof verifying that the conjecture is true which is a straightforward generalisation of the method discovered by the gp-toolkit.
Immersing projective spaces in Euclidean space
Authors: Crabb M. C. 
Published: November 2011

SynopsisUsing theKOℝ/2-theoretic obstruction theory developed in [4] and [5], necessary and sufficient conditions are derived for quaternionic projective spaces ℍPkand odd-dimensional complex projective spaces ℂP2k+1, of real dimensionmsay, to immerse in Euclidean space ℝ2m−1in the range l ≦ 14. The results refine those obtained by Davis and Mahowald ([10, 11]) and earlier authors.
The closure of the generalised eigenspace of a class of infinitesimal generators
Authors: Lunel S. M. Verduyn 
Published: November 2011

SynopsisIn this paper we study the fine geometric structure of a class of strongly continuous semigroups that satisfy the following property: the resolvent of the infinitesimal generator can be represented as the quotient of entire functions of finite exponential type. This class includes the solution map for functional differential equations and certain partial differential equations. In particular, we present necessary and sufficient conditions for one-to-oneness of the solution map and for completeness of the system of generalised eigenfunctions of the generator.
An exterior boundary-value problem for the Maxwell equations with boundary data in a Sobolev space
Authors: Hähner Peter 
Published: November 2011

SynopsisWe treat the time-harmonic Maxwell equations in an exterior domain with prescribed boundary data [n, E] in the Sobolev space of square integrable tangential fields with square integrable surface divergence. By using boundary integral equation methods, existence and uniqueness results are established. Furthermore, we investigate the completeness of electric and magnetic dipoles distributed on an inner surface in this Sobolev space.
Dissipative decomposition of ordinary differential equations
Authors: Olver Peter J. , Shakiban Chehrzad 
Published: November 2011

SynopsisA general decomposition theorem that allows one to express uniquely arbitrary differential polynomials in one independent and one dependent variable as a combination of conservative, dissipative and higher order dissipative pieces is proved. The decomposition generalises the Rayleigh dissipation law for linear equations.
Unstable atomicity of ΩSpin(r)
Authors: Mahmud Zafer 
Published: November 2011

SynopsisWe determine the homomorphism induced, in Z2-cohomology, by a map f: ΩSpin(r) → ΩSpin(r). As a corollary we show that ΩSpin(r), r ≧ 9 is 2-atomic, where a space X is 2-atomic if any map f: X ≧X is either a mod 2 homotopy equivalence or f*: H*(X, Z2) → H*(X, Z2) is nilpotent.
Ergodic actions of group extensions on von Neumann algebras
Authors: Thomsen Klaus 
Published: November 2011

SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.
Transition systems
Authors: Mischaikow Konstantin 
Published: November 2011

SynopsisThe concept of a transition system is extended to a parametrised family of differential equationswhere x ∊ ℝn and λ ∊ Λ = [0, l]m, an m-cube. Furthermore, algebraic formulae for comparing connection matrices at the various parameter values are obtained. Finally, several applications of these techniques are indicated.
Vanational elliptic problems involving noncoercive functionals
Authors: Ramos Miguel , Sanchez Luis 
Published: November 2011

SynopsisWe consider the nonlinear elliptic problem at resonance, Δu + λ1u + f(x, u) = h(x) in Ω, u = 0 on ∂Ω, where Ω is a bounded smooth domain in ℝN, λl is the first eigenvalue of –Δ in Ω and h(x) is orthogonal to the first eigenfunction. We give some conditions of solvability in terms of the primitive of f with respect to u.
A space of slowly decreasing functions with pleasant Fourier transforms
Authors: Fraenkel L. E. 
Published: November 2011

SynopsisThe space in question is Aµ(R):=L1(R) + Bµ(R), where Bµ(R) is a Banach space that contains the “tails” (the dominant parts for large values of |x|) of certain slowly decreasing functions from R to R. Functions in Bµ(R) are of bounded variation, and the norm involves their variation and a weighting function. Theorems are proved only for Bµ(R), because those for L1(R) are known. The results concern the convolution of a function in Bµ(R) with one in L1(R), the Fourier transform acting on Bµ(R), and the signum rule for the Hilbert transform of functions in Bµ(R).
On a comparison theorem via symmetrisation
Authors: Kesavan S. 
Published: November 2011

SynopsisTalenti's theorem allows us to estimate the norms of the solution of an elliptic boundary value problem posed on a bounded open set Ω in terms of those of the “symmetrised” problem posed on Ω*, the ball centred at 0 and such that |Ω| = |Ω*|. We are interested in the limiting case when equality is achieved between the norms of the two solutions. We show then that Ω = Ω* and that the solution is radially symmetric and decreasing. The novelty of this exposition is that the method used is very elementary compared to the usual arguments.
Heat equation on a hemisphere
Authors: van den Berg M. 
Published: November 2011

SynopsisConsider the following heat conduction problem: let Hm−1 be a hemisphere of Sm−1 and suppose that Hm−1 has temperature 1 at time t = 0, while the boundary of Hm−1 is kept at temperature 0 for all time t>0. We obtain a combinatorial formula and a uniform estimate for the amount of heat in Hm−1 at time t.
Comparison results in second order quasilinear Dirichlet problems
Authors: Payne L. E. , Webb J. R. L. 
Published: November 2011

SynopsisIn [6] and [9] two different methods are given for comparing solutions of Dirichlet problems for second order quasilinear elliptic equations on convex regions. In this paper a general comparison technique is outlined—one which contains the methods of [6] and [9] as special cases. This technique is then applied to a number of special examples, comparisons with known results are given and a number of possible extensions are indicated.
On equichordal curves
Authors: Cieślak Waldemar 
Published: November 2011

SynopsisIn this paper we consider equichordal curves in ℝn. We extend the notion of chordal area to all equichordal curves and introduce a notion of *-chordal area. We establish results connected with the length, *-chordal area and extended chordal area. Moreover, we give a Crofton-type integral formula for plane equichordal curves and derive an isoperimetric inequality for *-chordal area. The paper is based on the results of F. J. Craveiro de Carvalho and S. A. Robertson [2].
A free boundary problem arising in some reacting–diffusing system
Authors: Hilhorst D. , Nishiura Y. , Mimura M. 
Published: November 2011

SynopsisWe prove the well-posedness for a one-dimensional free boundary problem arising from some reaction diffusion system. The interfacial point hits a boundary point in finite time or remains inside for all time. In the large diffusion limit, the system is reduced to ordinary differential equations of finite dimension.
The structure of the singularities of holomorphic matrices
Authors: Pandolfi L. 
Published: November 2011

SynopsisIn this paper we consider a holomorphic matrix H(z) over a possibly unbounded region Ω and we study its properties in the neighbourhoods of a boundary point z0 of Ω (it may be z0 = ∞ if Ω is unbounded and z0 may not be an isolated singularity). Applications to systems theory and, in particular, to the theory of delay systems are presented. In this case the properties of completability, small solutions observability and zeros at z0 = ∞ are investigated.
On the codegree of negative multiples of the Hopf bundle
Authors: Crabb M. C. , Knapp K. 
Published: November 2011

SynopsisLet H be the Hopf line bundle over the complex projective space of complex dimension k – 1. We determine the codegree of the virtual bundle –nH in the range l ≦ n ≦ k. This codegree has geometric significance as a stable James number.
Global versus local admissibility criteria for dynamic phase boundaries
Authors: Fan Haitao 
Published: November 2011

SynopsisThe nonuniqueness of solutions of Riemann problems for a system of conservation laws of mixed type which are admissible according to kinetic relation criteria or travelling wave criteria is proved. The above-mentioned admissibility criteria all consist of local restrictions on points of discontinuity of weak solutions. An example is given which has more than one solution admissible by these local admissibility criteria, but has only one solution, the one-phase solution, satisfying the vanishing viscosity criterion. The entropy rate criterion, however, prefers the two-phase solution.
Foldings of star manifolds
Authors: Farran H. R. , El-Kholy E. , Robertson S. A. 
Published: November 2011

SynopsisThis paper is a sequel to [4]. Its purpose is to show that the concept of isometric foldings of Riemannian manifolds can be extended to a much wider class of manifolds without losing the main structure theorem. We present here what we believe to be a definitive form of the folding concept for smooth manifolds.The theory discussed here is based on the idea of a 1-spread [2], where the role of geodesies on a Riemannian manifold is assumed by smooth, unoriented and unparametrised curves on a smooth manifold. The absence of metrical structure forces a fresh approach to the basic definitions. A crucial feature of the Riemannian theory does survive, however, in this general setting: a 1-spread on a sufficiently smooth manifold M induces a 1-spread on sufficiently small spheres surrounding any point of M. With the help of this fact, we are able to construct an inductive definition of “star folding” f:M → N between smooth manifolds M and N, and to retain the theorem that the manifold M is stratified by the “folds”, each of which has the character of a “totally geodesic” submanifold with respect to the above-mentioned curves.
Multiple transition layers in a singularly perturbed differential-delay equation
Authors: Mallet-Paret John , Nussbaum Roger D. 
Published: November 2011

SynopsisThe singularly perturbed differential-delay equationis studied for a class of step-function nonlinearities f. We show that in general the discrete systemdoes not mirror the dynamics of (*), even for small ε, but that rather a different systemdoes. Here F is related to, but different from, f, and describes the evolution of transition layers. In this context, we also study the effects of smoothing out the discontinuities of f.