bluuebunny/crossref_metadata_2025_split huggingface dataset:
Spectral analysis of the Epstein operator
Authors: Guillot J. C. , Wilcox C. H. 
Published: November 2011

SynopsisThe Epstein operator is defined bywhere x = (x1, …, xn) ∈ Rn, y ∈ R,and H, K, L, M are real constants such that c2(y) > 0. The operator arises in the study of acoustic wave propagation in plane-stratified fluids with sound speed c(y) at depth y. In this paper it is shown that A defines a selfadjoint operator in the Hilbert space ℋ = L2(Rn + 1c−2(y) dx dy) where dx = dx1 … dxn. The spectral family of A is constructed, the spectrum is shown to be continuous and an eigenfunction expansion for A is given in terms of families of improper eigenfunctions.
On a fourth-order singular integral inequality
Authors: Russell A. 
Published: November 2011

SynopsisThe inequality considered in this paper iswhereNis the real-valued symmetric differential expression defined byGeneral properties of this inequality are considered which result in giving an alternative account of a previously considered inequalityto which (*) reduces in the casep=q= 0,r= 1.Inequality (*) is also an extension of the inequalityas given by Hardy and Littlewood in 1932. This last inequality has been extended by Everitt to second-order differential expressions and the methods in this paper extend it to fourth-order differential expressions. As with many studies of symmetric differential expressions the jump from the second-order to the fourth-order introduces difficulties beyond the extension of technicalities: problems of a new order appear for which complete solutions are not available.
Inequalities satisfied by electromagnetic radiation fields
Authors: O'Brien D. M. 
Published: November 2011

SynopsisThis paper presents two inequalities satisfied by any electromagnetic radiation field which is defined in the region outside a smooth, bounded surface and which varies harmonically with time. These inequalities provide an upper bound on the error introduced into the radiation pattern of the field when the field is approximated in numerical calculations. All constants which appear in the inequalities and the error estimate are computable.
Eigenfunction expansions and spectral matrices of singular differential operators
Authors: Hinton Don B. 
Published: November 2011

SynopsisWe consider the eigenfunction expansions associated with a symmetric differential operator M[·] of order 2n with coefficients defined on an open interval (a, b). Each singular endpoint of (a, b) is assumed to be of limit-n type. A direct convergence theory is established for the eigenfunction series expansion of a function y in a set Termwise differentiation of the series is established for the derivatives of order up to n. For O ≤ i ≤ n − 1, the i-fold differentiated series converges absolutely and uniformly to y(i) on compact intervals; the n−fold differentiated series converges to yn in the mean. The expansion theory is valid also when an essential spectrum is present. An explicit formula is given for the calculation of the spectral matrix.
Piecewise continuous solutions of pseudoparabolic equations in two space dimensions
Authors: Begehr Heinrich , Gilbert Robert P. 
Published: November 2011

SynopsisHere the Riemann boundary value problem-well known in analytic function theory as the problem to find entire analytic functions having a prescribed jump across a given contour-is solved for solutions of a pseudoparabolic equation which is derived from the complex differential equation of generalized analytic function theory. The general solution is given by use of the generating pair of the corresponding class of generalized analytic functions which gives rise to a representation for special bounded solutions of the pseudoparabolic equation. These solutions are obtained by linear integral equations one of which is given by a development of the generalized fundamental kernels of generalized analytic functions and which leads to a Cauchy-type integral representation. The bounded solutions are needed to transform the general boundary value problem (of non-negative index) with arbitrary initial data into a homogeneous problem which can easily be solved by the Cauchy-type integral (if the index is zero).
A note on the coordinatisation of implicative (semi-)lattices by Baer semigroups
Authors: Johnson C. S. 
Published: November 2011

SynopsisWe show that a bounded (semi-)lattice is implicative if and only if it can be coordinatised by a (right) Baer semigroup ℛS in which each element of (S) has an idempotent generator f such that fe = efe for all idempotents e with eS ∈ ℛ(S).
The last of the Fibonacci groups
Authors: Havas George , Richardson J. S. , Sterling Leon S. 
Published: November 2011

SynopsisAll the Fibonacci groups in the family F(2, n) have been either fully identified or determined to be infinite, bar one, namely F(2, 9). Using computer-aided techniques it is shown that F(2, 9) has a quotient of order 152.5741, and an explicit matrix representation for a quotient of order 152.518 is given. This strongly suggests that F(2, 9) is infinite, but no proof of such a claim is available.
Energy stability for the flow between rotating, coaxial disks
Authors: Elcrat Alan R. 
Published: November 2011

SynopsisA stability condition is derived for solutions of the Von Kárman-Batchelor equations for the flow of a viscous, incompressible fluid between rotating, coaxial (infinite) disks. The rigid motion solution which arises when the angular velocities of the disks are equal is stable with respect to perturbations which go to zero sufficiently rapidly at infinity, for all values of the Reynolds number. If the angular velocities are sufficiently close the stability condition derived applies to perturbations whose “deformation energy” is sufficiently confined to a “core” region.
The existence of eigenvalues of infinite multiplicity for the Schrödinger operator
Authors: Thurlow Christine R. , Eastham Michael S.P. 
Published: November 2011

SynopsisIt is shown that eigenvalues of infinite multiplicity can exist for the Schrödinger equation holding in the whole N-dimensional space RN(N ≧ 2). In the example which is constructed, the potential is separable and bounded in RN, and the method is an application of inverse spectral theory.
On the separation property of symmetric ordinary fourth-order differential expressions
Authors: Das Jyoti , Sett Jayasri 
Published: November 2011

SynopsisConditions are given on the coefficients p, q and r of the fourth-order, symmetric differentia expressionwhere y ∈ L2(0, ∞) and L[y] ∈ L2(0, ∞), such that some or all of the individual terms in L[y] are also in L2(0, ∞).
Wiener processes on manifolds of maps
Authors: Baxendale Peter 
Published: November 2011

SynopsisThe solutions of stochastic differential equations are used to construct Markov processes on the Banach manifold C(S, M) of continuous maps from a compact metric space S into a smooth complete finite dimensional Riemannian manifold M. In the special case where S is a single point the construction gives a large class of diffusion processes on the manifold M, including (under certain curvature conditions) the Brownian motion process.
An example of “secondary bifurcation” in a non-autonomous two-point boundary value problem
Authors: Clément Ph. , vanKan J. 
Published: November 2011

SynopsisWe consider the continuation of positive solutions of -u" = λs(x)f(u), with appropriate boundary conditions and with positive s and f. We show by an example that bifurcation may occur from the curve of these positive solutions.
Point transfer matrices for the Schrödinger equation: the algebraic theory
Authors: Gordon N. A. , Pearson D. B. 
Published: November 2011

This paper deals with the theory of point interactions for the one-dimensional Schrödinger equation. The familiar example of the δ-potential V(x) = gδ(x−x0), for which the transfer matrix across the singularity (point transfer matrix) is given byis extended to cover cases in which the transfer matrix M(z) is dependent on the (complex) spectral parameter z, and which can be obtained as limits of transfer matrices across finite intervals for sequences of approximating potentials Vn.The case of point transfer matrices polynomially dependent on z is treated in detail, with a complete characterization of such matrices and a proof of their factorization as products of point transfer matrices linearly dependent on z.The theory presented here has applications to the study of point interactions in quantum mechanics, and provides new classes of point interactions which can be obtained as limiting cases of regular potentials.
Spectral properties of compact multiparameter operators
Authors: Binding Paul , Browne Patrick J. , Turyn Lawrence 
Published: November 2011

SynopsisLetbe, for each λ∈ℝk, a compact symmetric operator on a complex Hilbert space. Let the“fundamental” eigenset Z be denned by the relation λ∈Z if and only if W(λ) has maximal eigenvalue one. Conditions are given for Z to be the boundary of an open convex set P. A detailed investigation is given of the structure of P, including its recession cone and its representations as intersections of half-spaces.
A stable method for an inverse problem in acoustic scattering by an obstacle with an impedance boundary condition
Authors: Smith Robert T. 
Published: November 2011

SynopsisWe examine the case of plane, time-harmonic acoustic waves in two dimensions, scattered by an obstacle on the surface of which an impedance boundary condition is imposed. A stable method is developed for solving the inverse problem ofdetermining both the shape of the scatterer and the surface impedance from measurements of the asymptotic behaviour of the scattered waves at low frequencies. We accomplish this by minimizing an appropriate functional over a compact set of admissible boundary curves and admissible impedances.
Singular perturbation of a nonlinear problem with multiple solutions
Authors: Lefevere Anne-Marie 
Published: November 2011

SynopsisA nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().
Is elasticity the proper asymptotic theory for materials with small viscosity and capillarity?
Authors: Boldrini Jose L. 
Published: November 2011

SynopsisWe consider the equations for the isothermal motion of a one-dimensional unbounded body composed of a material with viscosity and capillarity. Using a technique derived from the theory of compensated compactness, we find conditions which guarantee that, as viscosity and capillarity approach zero, the solutions to these equations converge to a solution to the corresponding equations in elasticity.
The Palais–Smale conditions for the Yang–Mills functional
Authors: Wilkins D. R. 
Published: November 2011

SynopsisWe consider the Yang–Mills functional denned on connections on a principal bundle over a compact Riemannian manifold of dimension 2 or 3. It is shown that if we consider the Yang–Mills functional as being defined on an appropriate Hilbert manifold of orbits of connections under the action of the group of principal bundle automorphisms, then the functional satisfies the Palais–Smale condition.
On the semigroups of order-decreasing finite full transformations
Authors: Umar Abdullahi 
Published: November 2011

SynopsisLet Singn be the subsemigroup of singular elements of the full transformation semigroup on a totally ordered finite set with n elements. Let be the subsemigroup of all decreasing maps of Singn. In this paper it is shown that is a non-regular abundant semigroup with n − 1 -classes and . Moreover, is idempotent-generated and it is generated by the n(n − 1)/2 idempotents in J*n−1. LetandSome recurrence relations satisfied by J*(n, r) and sh (n, r) are obtained. Further, it is shown that sh (n, r) is the complementary signless (or absolute) Stirling number of the first kind.
Linear initial value problems with a singular perturbation of hyperbolic type
Authors: Geel R. 
Published: November 2011

SynopsisThis paper deals with initial value problems in ℝ2 which are governed by a hyperbolic differential equation containing a small positive factor ε in front of the second order part of the differential operator. Pointwise a priori estimates for the solution are established by means of an energy integral method. With the help of these estimates it is shown that the solution admits an asymptotic expansion into powers of ε which is uniformly valid in compact subsets of ℝ2. All results are obtained under the assumption that the characteristics of the first order part of the differential operator satisfy a so-called “timelike” condition. A discussion of the concepts “timelike” and “spacelike” is given.
Dual solutions in mixed convection
Authors: Wilks G. , Bramley J. S. 
Published: November 2011

SynopsisDual similarity solutions in the context of mixed convection are presented. In contrast to the Falkner–Skan solutions the bifurcation point is found to be distinct from the point of vanishing skin friction. The eigenvalue problem arising out of a stability analysis of these solutions is examined numerically. The numerical evidence would seem to indicate that the margin of stability is associated with the onset of reverse flow as opposed to the bifurcation point, as conjectured by Banks and Drazin in 1973.
A limit-point criterion for 2n-th order symmetric differential expressions
Authors: Schultze Bernd 
Published: November 2011

SynopsisA perturbation theorem for symmetric differential expressions is given and applied to even-order expressions. We assume the coefficients p0(t), pn(t) to be eventually positive and to have real powers of t as dominating terms. Then we are able to admit for the absolute values of the other coefficients a rate of growth depending on the growth of both of the coefficients p0, pn in order to obtain minimal deficiency indices.
On uniform boundedness properties in exhausting additive set function spaces
Authors: Moltó Aníbal 
Published: November 2011

SynopsisValdivia (1978) introduced the class of suprabarrelled spaces, and (1979) deduced some uniform boundedness properties for scalar valued exhausting additive set functions on a σ-algebra from the suprabarrelledness of certain spaces. In this paper, it is shown that those uniform boundedness properties hold for G-valued exhausting additive set functions, G being a commutative topological group, on a larger class of Boolean algebras. Such properties are proved in Valdivia (1979) by means of duality theory arguments and ‘sliding hump’ methods, whereas here they are derived from the Baire category theorem. This generalization enables us to find a wide class of compact topological spaces K such that the subspaces of C(K) which satisfy a mild property are suprabarrelled.
The simplicity of near-rings of mappings
Authors: Meldrum J. D. P. , Zeller Mike 
Published: November 2011

SynopsisLet G be a group and S a group of automorphisms of G. The simplicity of the near-ring, MS(G), of zero preserving functions on G which commute with the elements of S, is investigated. The relationship between simplicity, 2-primitivity and containment relations among the stabilizers of elements of G is explored.
Perturbation of two-point boundary value problems with eigenvalue parameter in the boundary conditions
Authors: Turyn Lawrence 
Published: November 2011

SynopsisWe discuss smooth changes of eigenvalues under perturbation of the boundary value problems given in the title. The simple eigenvalue criterion is developed in the setting of Banach spaces, so very general perturbations of both the differential equation and the boundary conditions are allowed. Further, we need no assumptions about self-adjointness of the original or perturbed problems. The discussion is concluded with the application of the simple eigenvalue criterion to two examples.
The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space
Authors: Dawlings R. J. H. 
Published: November 2011

Let H be a separable Hilbert space and let CL(H) be the semigroup of continuous, linear maps from H to H. Let E+ be the idempotents of CL(H). Let Ker ɑ and Im ɑ be the null-space and range, respectively, of an element ɑ of CL(H) and let St ɑ be the subspace {x∊H: xɑ = x} of H. It is shown that 〈E+〉 = I∪F∪{i}, whereand ι is the identity map. From the proof it is clear that I and F both form subsemigroups of 〈E+〉 and that the depth of I is 3. It is also shown that the depths of F and 〈E+〉 are infinite.
Periodic solutions of time-dependent, semilinear evolution equations of compact type
Authors: Sager Herbert C. 
Published: November 2011

SynopsisWe establish the existence of solutions in a weak sense ofwhere t Є J = [0, T] and′ = d/dt. It is supposed that the unbounded, linear operators A(t) generate analytic and compact semigroups on a Hilbert space H and that B(t, x) are bounded linear operators. The function f(t, x) with values in H may have asymptotically sublinear growth.We prove the existence of a periodic solution with the help of Schauder’s fixed point theorem.Accordingly, we first verify that the corresponding linearized version of (0.1),has a unique solution for each square integrable ψ(t), provided that the homogeneous problem has only the zero solution.
Discrete and shift Kolmogorov type inequalities
Authors: Ditzian Z. 
Published: November 2011

SynopsisThe operators Δhf ≡ f(x) on function spaces and Δxn ≡ xn+1–xn on sequence spaces replace derivatives to yield analogues of the Kolmogorov inequality. Estimates for best constants are given for many spaces and for a few the best constants are actually given.
Singularities of solutions for first order quasilinear hyperbolic systems
Authors: Da-tsin(Li Ta-tsien) Lee , Jia-hong Shi 
Published: November 2011

SynopsisIn this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.
Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces
Authors: Webb G. F. 
Published: November 2011

SynopsisThe following theorem is proved: Let S(t), t≧0 be a dynamical system in an infinite dimensional Banach space X such that S(t) = S1(t)+S2(t) for t≧0, where (1) uniformly in bounded sets of x in X, and (2) S2(t) is compact for t sufficiently large. Then, if the orbit {S(t)x: t ≧0} of x ∈ X is bounded in X, it is precompact in X. Applications are made to an age dependent population model, a non-linear functional differential equation on an infinite interval, and a non-linear Volterra integrodifferential equation.
The inverse scattering problem for a cylinder
Authors: Colton David 
Published: November 2011

SynopsisLet D be a bounded simply connected domain in the plane and Ω the unit disk. Let F(Θ;k) be the far field pattern arising from the scattering of an incoming plane wave by the obstacle D and let an(k) denote the nth Fourier coefficient of F. Then if f conformally maps ℝ2\D onto ℝ2\Ω, a “moment” problem is derived which expresses an(k) in terms of f−1 for small values of the wave number k. The solution of this moment problem then gives the Laurent coefficients of f−1 and hence ∂D.
On a class of interpolation series
Authors: Hille Einar 
Published: November 2011

SynopsisThis paper deals with a class of interpolation series of the formcalled R-series. It is equiconvergent with the Dirichlet seriesIf the nth Legendre polynomial for the interval (0,1) is denoted by (−1)nLn(t), then the bilinear formulaserves as generating function for the Rn(z). It also leads in easy steps to R-series expansions for rational functions.Lagrange [7] has shown that a function holomorphic and of finite rate of growth in a right half-plane can be expanded in an R-series whose abscissa of convergence is limited by the rate of growth of f(z). The converse problem is attacked in Theorem 2 below where it is shown that
The periodic quasigeostrophic equations: existence and uniqueness of strong solutions
Authors: Bennett A. F. , Kloeden P. E. 
Published: November 2011

SynopsisThe periodic quasigeostrophic equations are a coupled system of a second order elliptic equation for a streamfunction and first order hyperbolic equations for the relative potential vorticity and surface potential temperatures, on a three-dimensional domain which is periodic in both horizontal spatial co-ordinates. Such equations are used in both numerical and theoretical studies in meteorology and oceanography. In this paper Schauder estimates and a Schauder fixed point theorem are used to prove the existence and uniqueness of strong, that is classical, solutions of the periodic quasigeostrophic equations for a finite interval of time, which is inversely proportional to the sum of the norms of the initial vorticity and surface temperatures.
Dissipative operators with finite dimensional damping
Authors: Röh Harald 
Published: November 2011

SynopsisLetG: ε(G)⊂ℋ → ℋ be a maximal dissipative operator with compact resolvent on a complex separable Hilbert space ℋ andT(t) be theCosemigroup generated byG. A spectral mapping theorem σ(T(t))\{0} = exp (tσ(G))/{0} together with a condition for 0 ε σ(T(t)) are proved if the set {xε ⅅ(G) | Re (Gx, x) = 0} has finite codimension in ε(G) and if some eigenvalue conditions forGare satisfied. Proofs are given in terms of the Cayley transformationT= (G+I)(G−I)−1ofG. The results are applied to the damped wave equationutt+ γutx+uxxxx+ ßuxx= 0, 0 ≦t< ∞ 0 <x< 1, β, γ ≧ 0, with boundary conditionsu(0,t) =ux(0,t) =uxx(1,t) =uxxx(1,t) = 0.
The approximation of exterior Neumann problems in a halfspace by means of problems with compact boundary
Authors: Becker Ronald I. , New Ronald 
Published: November 2011

SynopsisThis paper describes a proof that the solutions of Neumann problems for the exterior of spheres {x ∊ ℝ3∣ converge to the solutions of the exterior problem for the halfspace {x ∊ ℝ3 } x1 ≧ 0} as b → ∞ provided that the boundary data converge in a certain sense. The method requires that there be some dissipation which can be arbitrarily small. Fredholm integral equations are set up for the boundary data, and these are solved by means of Neumann series for large b. Estimates on the terms of the series (which involve singular integrals), in terms of b, allow the convergence proof to be carried through.The procedure of expressing problems with infinite boundaries in terms of problems with finite boundaries allows the implementation of an effective numerical procedure for determining, for example, the entire near-field of a baffled piston, a problem whose solution has proved elusive for many years.
The mod 2 homology of the space of loops on the exceptional Lie group
Authors: Kono Akira , Kozima Kazumuto 
Published: November 2011

SynopsisThe Hopf algebra structure of H*(ΩG, F2) and the action of the dual Steenrod algebra are completely and explicitly determined when G isone of the connected, simply connected, exceptional, simple Lie groups. The approach is homological, using connected coverings and spectral sequences.
On the geometric properties of Vandermonde's mapping and on the problem of moments
Authors: Kostov V. P. 
Published: November 2011

SynopsisIn this paper we prove that the domain of hyperbolicity of the polynomial xn + λ2nn−2+λ3xn−3+ … + λn,λiϵR intersected by the half-space λ2 ≧ – 1, has the property of Whitney, i.e., every two points of this set can be connected by a piecewise-smooth curve belonging to it, whose length is ≦C times greater than the euclidian distance between the points, where the constant C does not depend on the choice of the points. Parallel with this, we show that the values x1≦x2≦…≦xn of a random variable are uniquely determined by the corresponding probabilities and by thefirst n moments.