bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Titchmarsh–Weyl m -function
Authors: Harris B. J. 
Published: November 2011

SynopsisThe Weyl theory assets that there exist circles, possibly degenerate, in the complex plane which are associated with Sturm–Liouville equations. Closely related to these circles is the Titchmarch–Weyl m-function which plays a major role in the theory of Sturm-Liouville equations. In this paper, we investigate the asymptotic behaviour of the m-function and derive results of the formfor λ in a certain subset of the compledx plane.
Hyperjacobians, determinantal ideals and weak solutions to variational problems
Authors: Olver Peter J. 
Published: November 2011

SynopsisThe problem of classifying homogeneous null Lagrangians satisfying an nth order divergence identity is completely solved. All such differential polynomials are affine combinations of higher order Jacobian determinants, called hyperjacobians, which can be expressed as higher dimensional determinants of higher order Jacobian matrices. Special cases, called transvectants, are of importance in classical invariant theory. Transform techniques reduce this question to the characterization of the symbolic powers of certain determinantal ideals. Applications to the proof of existence of minimizers of certain quasi-convex variational problems with weakened growth conditions are discussed.
Bounds for the eigenvalues of separated Dirac operators
Authors: Harris B. J. 
Published: November 2011

SynopsisWe develop a systematic method for calculating real numbers Λ1, and Λ2 such that there are no non-trivial solutions of the equationwhich belong to L2(a, ∞) for λ> Λ1, or λ < Λ2. We also give conditions under which this equation has no solutions in L2(a,∞) for any real number λ.
On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
Authors: Jeanjean Louis 
Published: November 2011

Using the ‘monotonicity trick’ introduced by Struwe, we derive a generic theorem. It says that for a wide class of functionals, having a mountain-pass (MP) geometry, almost every functional in this class has a bounded Palais-Smale sequence at the MP level. Then we show how the generic theorem can be used to obtain, for a given functional, a special Palais–Smale sequence possessing extra properties that help to ensure its convergence. Subsequently, these abstract results are applied to prove the existence of a positive solution for a problem of the formWe assume that the functional associated to (P) has an MP geometry. Our results cover the case where the nonlinearity f satisfies (i) f(x, s)s−1 → a ∈)0, ∞) as s →+∞; and (ii) f(x, s)s–1 is non decreasing as a function of s ≥ 0, a.e. x → ℝN.
The lattice of full regular subsemigroups of a regular semigroup
Authors: Johnston Katherine G. , Jones Peter R. 
Published: November 2011

SynopsisAlthough the regular subsemigroups of a regular semigroup S do not, in general, form a lattice in any naturalway, it is shown that the full regular subsemigroups form a complete sublattice LF of the lattice of all subsemigroups; moreover this lattice has many of the nice features exhibited in (the special case of) the lattice of full inverse subsemigroups of an inverse semigroup, previously studied by one of the authors. In particular, LF is again a subdirect product of the corresponding lattices for each of the principal factors of S.A description of LF for completely 0-simple semigroups is given. From this, lattice-theoretic properties of LF may be found for completely semisimple semigroups. For instance, for any such combinatorial semigroup, LF is semimodular.
The number of limit cycles of certain polynomial differential equations
Authors: Blows T. R. , Lloyd N. G. 
Published: November 2011

SynopsisTwo-dimensional differential systemsare considered, where P and Q are polynomials. The question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of P and Q. An algorithm is described for determining a so-called focal basis; this can be implemented on a computer. Estimates can then be obtained for the number of small-amplitude limit cycles. The technique is applied to certain cubic systems; a class of examples with exactly five small-amplitude limit cycles is constructed. Quadratic systems are also considered.
An extension of the Liouville–Green asymptotic formula for oscillatory second-order differential equations
Authors: Cassell J. S. 
Published: November 2011

SynopsisConditions, generalizing the usual Liouville–Green conditions, are obtained under which the equation {r(x)y′}′ + q(x)y = 0, where q and r are positive and have derivatives of a sufficiently high order, has solutions of the form y ∼ (rq)–¼e10. 0 ∼ f (q/r)½ dx as x →∞. A related result is obtained for a system of two first-order equations y′ = A(x)y, where the eigenvalues of A are pure imaginary.
Bifurcations near a multiple eigenvalue of the rectangular plate problem
Authors: Sadovský Zoltán 
Published: November 2011

SynopsisWe consider the bifurcation problem of the Föppl–Kármán equations for a thin elastic rectangular plate near a multiple eigenvalue allowing for a small perturbation parameter related to the aspect ratio of the plate. The first step in the study is to introduce equivalent operator equations in the energy spaces of the problem which explicitly contain the perturbation parameter. By dealing partially with a general formulation, we obtain the main results for the double eigenvalue andZ2⊓Z2symmetry of bifurcation equations. We are chiefly interested in the degenerate cases of bifurcation equations.
Critical semilinear biharmonic equations in RN
Authors: Noussair Ezzat S. , Swanson Charles A. , Jianfu Yang 
Published: November 2011

SynopsisAn existence theorem is obtained for a fourth-order semilinear elliptic problem in RNinvolving the critical Sobolev exponent (N + 4)/(N − 4), N>4. A preliminary result is that the best constant in the Sobolev embeddingL2N/(N–4)(RN) is attained by all translations and dilations of (1 + ∣x∣2)(4-N)/2. The best constant is found to be
On Sommerfeld radiation conditions for the diffraction problem with two unbounded media
Authors: Roach G. F. , Zhang Bo 
Published: November 2011

SynopsisA radiation condition is obtained, and is then used together with weighted Sobolev spaces and the limiting absorption method to establish the unique existence of solutions to the diffraction problem for the wave propagation in the case where the propagation speed is piecewise constant, and the surface separating two media is unbounded.
On an extension of Copson's inequality for infinite series
Authors: Brown B. M. , Evans W. D. 
Published: November 2011

SynopsisIn 1979 Copson proved the following analogue of the Hardy-Littlewood inequality: if is a sequence of real numbers such that are convergent, where Δan = an+1 – an and Δ2an = Δ(Δan), then is convergent and the constant 4 being best possible. Equality occurs if and only if an = 0 for all n. In this paper we give a result that extends Copson's result to inequalities of the formwhere Mxn =–Δ(pn_l Δxn_l)+qnxn (n = 0, 1, …). The validity of such an inequality and the best possible value of the constant K are determined in terms of the analogue of the Titchmarsh-Weyl m-function for the difference equation Mxn = λwnxn (n = 0, 1, …).
On the question of whether f″+ e−zf′ + B(z)f = 0 can admit a solution f ≢ 0 of finite order
Authors: Gundersen Gary G. 
Published: November 2011

SynopsisWe show that if B(z) is either (i) a transcendental entire function with order (B)≠1, or (ii) a polynomial of odd degree, then every solution f≠0 to the equation f″ + e−zf′ + B(z)f = 0 has infinite order. We obtain a partial result in the case when B(z) is an even degree polynomial. Our method of proof and lemmas for case (i) of the above result have independent interest.
A remark on comparison results via symmetrization
Authors: Alvino A. , Lions P.L. , Trombetti G. 
Published: November 2011

SynopsisIn this paper, we study the converse of comparison results for solutions to linear second-order elliptic equations. Namely, in the inequalities proved by G. Talenti and others, we study the case of equality and prove that “equalities are achieved only in the spherical situation”. We also present some applications of these results to semilinear elliptic equations.
On integral transforms whose kernels are solutions of singular Sturm–Liouville problems
Authors: Zayed Ahmed I. 
Published: November 2011

SynopsisIn this paper we investigate integral transforms of type , where φ(x, s) is the solution of the singular Sturm–Liouville problem: y″ + (s2 – q(x))y = 0, 0≦x <∞ with y(0) cos α + y′(0)sin α = 0, y(x) is bounded at ∞, and dp is the spectral measure. If F(s) = sk for some k = 0, 1, 2, …, then f(x) may not exist since, in general, φ(x, s) is not even in . One aim of this paper is to investigate the Abel summability of these integrals. In the special case where q(x) = 0 and α = π/2, then φ(x, s) = cos sx and dp = ds, while if α = 0, then φ(x, s) = −sin sx/s and dp = s2ds. It is known thatwhere the values of these integrals are interpreted as the Abel limits of these integrals or as the Fourier transform of some tempered distributions. Another aim of this paper is to derive the analogue of these results for the general kernel φ(x, s), and then apply that to the theory of asymptotic expansions.
Parameter ranges for the existence of solutions whose state components have specified nodal structure in coupled multiparameter systems of nonlinear Sturm–Liouville boundary value problems
Authors: Cantrell Robert Stephen 
Published: November 2011

SynopsisThe set of solutions to the two-parameter systemhas been shown in a preceding paper of the author to exhibit a topological-functional analytic structure analogous to the structure of solution sets for nonlinear Sturm–Liouville boundary value problems. As the parameter λ and µ are varied, transitions in the solution set occur, first from trivial solutions to solutions (u, 0) with u having n nodes on (a, b) or solutions (0, v) with v having m nodes on (a, b), and then to solutions of the form (u, v), where u has n nodes on (a, b) and v has m nodes on (a, b), with n possibly different from m. Moreover, each transition is global in an appropriate bifurcation theoretic sense, with preservation of nodal structure. This paper explores these phenomena more closely, focusing on the range of parameters (λ, µ) for the existence of solutions (u, v) with u having n nodes on (a, b) and v having m nodes on (a, b) and its dependence on the assumptions placed on the coupling functions f and g. The principal tools of the analysis are the Alexander–Antman Bifurcation Theorem and a priori estimate techniques based on the maximum principle.
On polynomial interpolation at the points of a geometric progression
Authors: Schoenberg I. J. 
Published: November 2011

SynopsisThis note pursues two aims: the first is historical and the second is factual.1. We present James Stirling's discovery (1730) that Newton's general interpolation series with divided differences simplifies if the points of interpolation form a geometric progression. For its most important case of extrapolation at the origin. Karl Schellbach (1864) develops his algorithm of q-differences that also leads naturally to theta-functions. Carl Runge (1891) solves the same extrapolation at the origin, without referring to the Stirling-Schellbach algorithm. Instead, Runge uses “Richardson's deferred approach to the limit” 20 years before Richardson.2. Recently, the author found a close connection to Romberg's quadrature formula in terms of “binary” trapezoidal sums. It is shown that the problems of Stirling, Schellbach, and Runge, are elegantly solved by Romberg's algorithm. Numerical examples are given briefly. Fuller numerical details can be found in the author's MRC T.S. Report #2173, December 1980, Madison, Wisconsin. Thanks are due to the referee for suggesting the present stream-lined version.
On the L2 nature of solutions of nth order symmetric differential equations and McLeod's conjecture
Authors: Paris R. B. , Wood A. D. 
Published: November 2011

SynopsisWe investigate the integrable square properties of solutions of linear symmetric differential equations of arbitrarily large order 2m, whose coefficients involve a real multiple ɑr of certain positive real powers β of the independent variable x. Information on the L2 nature is obtained by variation of parameters from Meijer function solutions of an associated homogeneous equation of hypergeometric type. When the coefficients of the differential expressions are positive, it is possible, by a suitable choice of ɑr, β and m, to obtain between m and 2m —1 linearly independent solutions in L2(0, ∞). This proves a conjecture of J. B. McLeod that the deficiency index can take values between m and 2m —1 for such operators.
Some Pontrjagin rings, I
Authors: Hubbuck J. R. 
Published: November 2011

SynopsisThe H-spaces considered have no homology p-torsion and are rationally equivalent as H-spaces to products of even dimensional Eilenberg–Maclane spaces. We obtain conditions which ensure that if the cohomology with coefficients in the ring of integers localized at the prime p is a polynomial algebra, then the Pontrjagin ring with these same coefficients is polynomial. A topological consequence is that BSUP has just one homotopy associative, homotopy commutative H-structure.
Asymptotic theory and deficiency indices for differential equations of odd order
Authors: Eastham M. S. P. 
Published: November 2011

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. The theory is applied to the evaluation of the deficiency indicesN+andN−associated with symmetric differential expressions of odd order. General conditions on the coefficients are given under which all possible values ofN+andNsubject to |N+−N| ≦ 1 are realized.
The number of positive solutions of a non-linear problem with discontinuous non-linearity
Authors: Douchet Jacques 
Published: November 2011

SynopsisFor the non-linear problemwhere f is a discontinuous function at 1, we show that the number of non-trivial positive solutions, for a given real number λ≧0, is related to the graph of a continuous function g. Then, by studying the function g it is possible in some special cases to give, for any λ≧0, the minimal or exact number of non-trivial positive solutions.
On a Dirichlet–Neumann–Third mixed boundary value problem for the Helmholtz equation
Authors: David M. 
Published: November 2011

SynopsisExistence and uniqueness theorems are proved for the solution of a Dirichlet-Neumann-Third mixed boundary value problem for the Helmholtz equation in ℝ3. The proofs make use of an equivalent system of two integral equations of the second kind.
On a common abstraction of de Morgan algebras and Stone algebras
Authors: Blyth T. S. , Varlet J. C. 
Published: November 2011

SynopsisWe consider a common abstraction of de Morgan algebras and Stone algebras which we call an MS-algebra. The variety of MS-algebras is easily described by adjoining only three simple equations to the axioms for a bounded distributive lattice. We first investigate the elementary properties of these algebras, then we characterise the least congruence which collapses all the elements of an ideal, and those ideals which are congruence kernels. We introduce a congruence which is similar to the Glivenko congruence in a p-algebra and show that the location of this congruence in the lattice of congruences is closely related to the subdirect irreducibility of the algebra. Finally, we give a complete description of the subdirectly irreducible MS-algebras.
Lp-Theory of degenerate-elliptic and parabolic operators of second order
Authors: Wong-Dzung Baoswan 
Published: November 2011

SynopsisWe consider the formal operator given byin the Banach space X =LP(Rn), 1<p<∞. The coefficients ajk(x),aj(x), and a(x) are real-valued functions, ajkε C2(Rn) has bounded second derivatives, ajε Cl(Rn) has bounded first derivatives, and aεL∞(Rn). Furthermore, we assume that the n × n matrix (ajk(x)) is symmetric and positive semidefinite (i.e. ajk(x)ξjξk≧0 for all (ξ1,…,ξn)εRnandxεRn). We prove that the degenerate-elliptic differential operator given by –Aand restricted to, the minimal realization of –A, is essentially quasi-m-dispersive inLp(Rn), (hence that the minimal realization of +Ais quasi-m-accretive) and that its closure coincides with the maximal realization of –A.
Sphere stratifications and the Gauss map
Authors: Fuster M. C. Romero 
Published: November 2011

SynopsisThere is a residual subset of embeddings of an m-manifold, M in Rm+1 (m ≦ 6), for which the induced Maxwell subset on the sphere Sm is a stratified subset. We define and study two different stratifications of this subset and their extensions to the whole Sm: the Gauss stratification and the core stratification. We also find relations between the Euler numbers of the strata of the core stratification and the “exposed” singularities of the Gauss map on M.
A nonexistence result for axially symmetric flows with constant angular velocities at infinity
Authors: Elcrat Alan R. , Siegel David 
Published: November 2011

SynopsisIf von Kármán's substitution is made in the Navier-Stokes equations, and boundary conditions corresponding to a flow in all of space with constant angular velocities at infinity are imposed, a boundary value problem analgous to those for flow above a rotating disk and between rotating disks is obtained. It is shown here that this problem has no solution.
Steiner triple systems of order 19 constructed from the Steiner triple system of order 9
Authors: Prince Alan R. 
Published: November 2011

SynopsisA standard method of constructing Steiner triple systems of order 19 from the Steiner triple system of order 9 gives rise to 212 different such systems. It is shown that there are just three isomorphism classes amongst these systems. Representatives of each isomorphism class are described and the orders of their automorphism groups are determined.
Conics related by a pentagram: a problem of J. E. Reeve
Authors: Knight A. J. 
Published: November 2011

SynopsisTwo non-singular conies ω and α are said to be related by a pentagram if there exist pentads ofdistinct points {Oi} on ω and {Ai} on α (1 ≦ i ≦ 5) such that A1 ≡ O2O4. O3O5, A2 ≡ O3O5. O1O4, A3 ≡ O1O4. O2O5, A4 ≡ O2O5. O1O3 and A5 ≡ O1O3. O2O4. It is shown that relation by a pentagram is a poristic property; and a necessary condition on their mutual projective invariants that two nonsingular conies be so related is derived. Some ramifications are discussed.
Singular differential operators with spectra discrete and bounded below
Authors: Hinton Don B. , Lewis Roger T. 
Published: November 2011

SynopsisA weighted, formally self-adjoint ordinary differential operator l of order 2n is considered, and conditions are given on the coefficients of l which ensure that all self-adjoint operators associated with l have a spectrum which is discrete and bounded below. Both finite and infinite singularities are considered. The results are obtained by the establishment of certain conditions which imply that l is non-oscillatory.
A generalisation of the inverse spectral theorem of Levitan and Gasymov
Authors: Thurlow Christine 
Published: November 2011

SynopsisIn the Inverse Spectral Theorem in the form given by Levitan and Gasymov, necessary and sufficient conditions are given for a non-decreasing function, p(ℷ), to be the spectral function of a Sturm–Liouville problem. In these conditions, p(ℷ) is compared with the spectral function for the particular Strum–Liouville problemIf the method of Levitan and Gasymov's proof is slightly adapted, the necessary and sufficient conditions can be stated in a more general form in which p(ℷ) is compared with the spectral function for any problem of the formwherehOis real and qo(x) locally integrable.
The stability problem for transformations of the circle
Authors: Cenzer Douglas 
Published: November 2011

SynopsisLet I be the group of rotations of the circle and suppose that a map f from I into I is “almost linear”. More precisely, let ε be a positive real number and suppose that d(f(x)+f(y), f(x + y))<ε for all x and y in I; f is said to be an ε-homomorphism. If ε is sufficiently small, then a homomorphism h from I into I can be constructed such that d(f(x), h(x))≦ε for all x in I. This result is refined and generalized in several ways.
Liouville theorems for elliptic systems and nonlinear equations of fourth order
Authors: Goyal Vinod B. , Schaefer Philip W. 
Published: November 2011

SynopsisLiouville theorems are obtained for fourth order elliptic systems of the form Δ2U + B Δ U + AU = 0 and for fourth order nonlinear equations of the form Δ2u−q(x) Δu + p(x)f(u) = 0 as a consequence of two related subharmonic functions, the mean value property of subharmonic functions, and a basic Green identity.
Monotone techniques and some existence-uniqueness theorems for two point boundary value problems
Authors: Lin Song-Sun 
Published: November 2011

SynopsisIn this paper we study the existence and uniqueness of the two point boundary value problems −(p(x)u′(x))′ = f(x, u(x), u′(x)), xε(0, 1), u′(0)−cu(0) = 0 = u′(1) + du(1), where ∂f/∂u is bounded. above by the least eigenvalue of associated linear problems and ∂f/∂u is bounded. By using monotone techniques to investigate the equivalent problem −(p(x)u′(x))′ + r(x)u(x) = f(x, u(x), u′(x)) + r(x)u(x) where r ε C[0, 1] we show thatgives the optimal bounds for ∂f/∂u and ∂f/u′ when c and d are nonnegative constants.
Explicit solutions for a class of dual integral equations
Authors: Anderssen R. S. , de Hoog F. R. , Rose L. R. F. 
Published: November 2011

SynopsisAn explicit solution is derived for the dual integral equationswhen A(ξ) takes the formIt is then shown how the basic technique can be adapted to derive explicit solutions for more general forms of A(ξ) such asandand linear combinations of such sums.
On the zeros of solutions to nonlinear hyperbolic equations
Authors: Yoshida Norio 
Published: November 2011

SynopsisWe consider the hyperbolic equation uxy + c(x, y, u) =f(x, y) and the wave equationWe show that, under suitable conditions, there are bounded domains in which every solution to certain problems has a zero. Characteristic initial value problems and initial boundary value problems are considered.
Tight stable surfaces, II
Authors: Coghlan Leslie 
Published: November 2011

SynopsisKuiper has proved that there is no tight topological immersion of RP2 into E3. Thus any continuous tight map RP2 → E3 has to have singular points. In this note we consider tight C∞-stable maps of RP2 and the torus into E3; i.e. maps with the simplest possible singularities (Whitney pinchpoints) and transversal crossings. We classify the forms that the outer part of such maps can take; we prove also some facts about the inner part. The result about the outer part of C℞-stable tight maps RP2 → E3 establishes the first half of Banchoff's conjectured classification of such mappings.
Functions with finite intersections with analytic functions
Authors: Buczolich Zoltán 
Published: November 2011

SynopsisWe prove that for every dense Gδ set H, there exists a continuous function f, such that f intersects every analytic function in finitely many points and f is infinitely differentiable exactly at the points of H. This answers a problem of S. Agronsky, A. M. Bruckner, M. Laczkovich and D. Preiss. They proved a result which implies that every continuous function with finite intersections with analytic functions is infinitely differentiable at the points of a dense Gδ set.