bluuebunny/crossref_metadata_2025_split huggingface dataset:
On a quadratic integral inequality
Authors: Amos R. J. , Everitt W. N. 
Published: November 2011

SynopsisThe inequality considered iswhere p and q are given real-valued coefficients on the interval [a, b), with b ≦ ∝, of the real line; here D is a linear manifold of the Hilbert function space L2(a, b), and μ is a real number characterised in terms of the spectrum of a uniquely determined self-adjoint differential operator in L2(a, b).
A stability problem with algebraic aspects
Authors: Atkinson F. V. 
Published: November 2011

SynopsisWe consider the set S(f) of λ-values for which there exists a function g ∊ L(t0, ∞) such thathas a solution not tending to 0; here f is a fixed function which is positive, non-decreasing and tends to ∞ with t. It is shown that if the jumps of logf(t) at its discontinuities are uniformly bounded, then S(f) is an additive group. This group is determined in some cases; some related groups are noted, which may coincide with S(f).
On the number ofL2-solutions of second order linear differential equations
Authors: Knowles Ian 
Published: November 2011

SynopsisLetddenote the dimension of the vector space consisting of all solutions of the equation − (p(t)y′)′ +q(t)y= 0,a≤t< ∞; that lie in the function spaceL2[a, ∞). By means of certain bounds on the solutions of this equation, sufficiency criteria are obtained for the casesd= 0 andd= 2.
Coupled operator systems and multiparameter spectral theory
Authors: Roach G. F. , Sleeman B. D. 
Published: November 2011

SynopsisIn this paper a spectral theory for completely coupled linear operator systems is developed. These systems take the formwhere Ak, Bk are n × n matrices with operator entries. Λ is an n × n matrix with complex scalar entries and xk is an n × 1 column vector. The main result is a Parseval equality and expansion theorem.
On Schrödinger's factorization method for Sturm-Liouville operators
Authors: Schmincke U.-W. 
Published: November 2011

SynopsisWe consider the Friedrichs extension A of a minimal Sturm-Liouville operator L0 and show that A admits a Schrödinger factorization, i.e. that one can find first order differential operators Bk with where the μk are suitable numbers which optimally chosen are just the lower eigenvalues of A (if any exist). With the help of this theorem we derive for the special case L0u = −u″ + q(x)u with q(x) → 0 (|x| → ∞) the inequalityσd(A) being the discrete spectrum of A. This inequality is seen to be sharp to some extent.
Monotone techniques and semilinear elliptic boundary value problems
Authors: Brown K. J. , Lin S. S. 
Published: November 2011

SynopsisThis paper considers semilinear elliptic boundary value problems of the formwhere the partial derivative ∂f/∂u is bounded above by the least eigenvalue of the linear elliptic operator L. Existence and uniqueness of solutions is proved by using monotone operator theory and sub and supersolution techniques.
A nonlinear singularly perturbed Volterra integrodifferential equation of nonconvolution type
Authors: Jordan G. S. 
Published: November 2011

SynopsisWe consider the nonconvolution initial value problemwhere μ is a small positive parameter, b(t, s) is a given real kernel, and F, g are given real functions. For the convolution case b(t,s) = a(t − s). Lodge, McLeod, and Nohel recently established many qualitative properties of the solution of (+); we extend their results to the general nonconvolution problem. In particular, conditions are given that ensure that the solution of (+) decreases to a limiting value α(μ) > 1 as t → ∞.
Amenability of inverse semigroups and their semigroup algebras
Authors: Duncan J. , Namioka I. 
Published: November 2011

SynopsisIf G is a group, then G is amenable as a semigroup if and only if l1(G), the group algebra, is amenable as an algebra. In this note, we investigate the relationship between these two notions of amenability for inverse semigroups S. A complete answer can be given in the case where the set Es of idempotent elements of S is finite. Some partial results are obtained for inverse semigroups S with infinite Es.
Existence and stability of solutions for semi-linear parabolic systems, and applications to some diffusion reaction equations
Authors: Amann Herbert 
Published: November 2011

SynopsisIn this paper we study diffusion-reaction equations arising in the theory of chemical reactions. We prove the global existence and uniqueness of a solution without any restriction for the Lewis number and the Biot numbers. In addition, it is shown that there is at least one stationary state which is globally asymptotically stable (in a rather strong sense) provided the Thiele number is sufficiently small. These results are obtained as special cases from much more general results on semilinear parabolic systems, derived below.
Baer semigroup coordinatizations of modular lattices
Authors: Blyth T. S. 
Published: November 2011

SynopsisIn the coordinatization of lattices by Baer semigroups, two notable gaps that remain to be filled concern the coordinatization of modular and distributive lattices. In this paper we present coordinatizations of modular lattices. In a subsequent paper we shall deal with the distributive case. Here we show that a bounded lattice L is modular if and only if L can be coordinatized by a Baer semigroup S such that if eS, fS ∊ R(S) then there exist idempotents ē, ∊ S such that ēS = eS, S = fS and e¯, commute; equivalently, if and only if L can be coordinatized by a Baer semigroup S such that if eS, fS ∊ R(S) with e idempotent then there is an idempotent such that S = fS and e = ee.
Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments
Authors: Philos Ch. G. 
Published: November 2011

SynopsisThis paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative of the unknown function x defined bywhere r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.
Positivity results for determinantal operators
Authors: Binding Paul , Browne Patrick J. 
Published: November 2011

SynopsisLet Vrs, s = 1 …, K be Hermitian operators on Hilbert spaces Hr, r = 1, …, k. For x = x1⊗…⊗xk ∊ H1⊗…⊗Hk we define Δx by the formal determinantal expansion Δx = ⊗det{Vrsxr}. Δ is extended to all of H by linearity and continuity. The paper presents results concerning positivity properties of Δ on decomposable tensors.
High frequency solutions of the delta wing equations
Authors: Hargrave B. A. 
Published: November 2011

SynopsisUniformly valid asymptotic approximations are presented for solutions of the angular equations associated with the problem of diffraction by a plane angular sector. Error estimates are provided for all approximations. The asymptotic variable is related to the number of zeros of the solutions of the angular equations and expressions for the eigenvalues of the equations are presented in decoupled form.
Periodic solutions of ordinary differential equations with one-sided growth restrictions
Authors: Mawhin J. , Walter W. 
Published: November 2011

SynopsisThe existence of periodic solutions is proved for first order vector ordinary and functional differential equations when the right-hand side satisfies a one-sided growth restriction of Wintner type together with some conditions of asymptotic nature. Special cases in the line of Landesman-Lazer and of Winston are explicited.
Dirichlet, Neumann and mixed Dirichlet-Neumann boundary value problems for Uxy = 0 in rectangles
Authors: Abdul-Latif Ali I. 
Published: November 2011

SynopsisIt is well known that the Dirichlet problem for hyperbolic equations is a classical “not well posed” problem. Here we consider the Dirichlet, Neumann and mixed Dirichlet-Neumann boundary value problems for the hyperbolic equation uxy = 0 in all positions of the square and a class of rectangles. We also get a partial answer to the problem which deals with a ray that moves from any point on the boundary of a rectangle and is reflected on the boundary such that the angle between every ray and its reflection is π/2.
A class of symmetric ordinary differential operators whose deficiency numbers differ by an integer†
Authors: Gilbert Richard C. 
Published: November 2011

SynopsisFormulas are determined for the deficiency numbers of a formally symmetric ordinary differential operator with complex coefficients which have asymptotic expansions of a prescribed type on a half-axis. An implication of these formulas is that for any given positive integer there exists a formally symmetric ordinary differential operator whose deficiency numbers differ by that positive integer.
Perturbation of nonlinear partial differential variational inequalities, II
Authors: Stroescu Elena 
Published: November 2011

SynopsisThis paper is devoted to the study of the weak respectively strong convergence of solutions of a variational inequality, with nonlinear partial differential operators of the generalized divergence form and of semimonotone type, under a perturbation of the domain of definition. In this study we use abstract convergence theorems given by Stroescu and Vivaldi, convergence concepts defined according to Stummel and compactness theorems of the natural imbedding of the Cartesian product of Sobolev spaces into the direct sum of Lp spaces, also by Stummel.
Complementary variational principles for free molecular channel flow
Authors: Cole R. J. 
Published: November 2011

SynopsisA collisionless gas flows through a finite rectangular duct which reflects molecules diffusely. The transmission probability Q of the duct involves the solution of a pair of coupled integral equations. Complementary variational principles have been employed which supply upper and lower bounds to Q. Numerical calculations have been made for a variety of duct shapes and compared, where appropriate, to those of other authors.
Multiplicity and bifurcation of periodic solutions in ordinary differential equations
Authors: Laloux B. 
Published: November 2011

SynopsisOne considers the linear differential systems where is a (not necessarily diagonal) matrix and one relates the computation of a general multiplicity defined from this system to the corresponding multiplicity of some eigenvalues of . Then applying these conclusions, one gives simple conditions ensuring the existence of odd or even periodic solutions for systems having the form .
A classification of the solutions of a differential equation according to their asymptotic behaviour
Authors: Elias Uri 
Published: November 2011

SynopsisThe solutions of the differential equationLny+p(x)y= 0, whereLny= ρn(ρn−1… (ρ1(ρ0y)′)′ …)′ andp(x) is of one sign, are classified according to their behaviour asx→ ∞. The solution space is decomposed into disjoint, non-empty setsSk, 0≦K≦n, such that (−1)n−kp(x)≦0. We study the growth properties and the density of the zeros of the solutions which belong to the different setsSk, the structure of the sets and its connection with (k,n−k)-disfocality.
Anti-isomorphisms of completely 0-simple semigroups
Authors: Houghton C. H. 
Published: November 2011

SynopsisConditions for the existence of anti-isomorphisms and anti-automorphisms of completely 0-simple semigroups are derived and a method is given for the enumeration of finite 0-simple and simple semigroups up to isomorphism and anti-isomorphism.
The Poincaré–Bendixson theorem for certain differential equations of higher order
Authors: Smith Russell A. 
Published: November 2011

SynopsisBy adapting its well-known proof, the Poincaré–Bendixson theorem, on the existence of periodic orbits of plane autonomous systems, is extended to vector differential equations of the form f(D)x + bφ(g(D)x) = 0. The only restrictions placed on the vector function φ(y) are that its Jacobian matrix should be continuous and lie within a suitably chosen ellintic ball.
Regularität in der nichtlinearen Spektraltheorie
Authors: Weyer Jürgen 
Published: November 2011

SynopsisA non-linear spectral theory is developed which includes the spectral theory of linear operators and the theory of (maximal) monotone operators. In this nonlinear theory certain polytone operators will play the role of the linear or monotone operators. The concept of λ-polytonicity allows the characterization of regular points in terms of maximality. Furthermore, properties of the spectrum of non-linear operators are discussed in terms of the corresponding properties of their linearizations and vice versa.
Mutually conjugate solutions of formally self-adjoint differential equations
Authors: Hill J. M. , Nillsen R. V. 
Published: November 2011

SynopsisLet L be a formally self-adjoint linear differential operator of order m with strictly positive leading coefficient and let m = 2n + 1 if m is odd, m = 2n if m is even. Let y1, y2,…, yn be n given mutually conjugate solutions of Ly = 0 on I, where I is some interval, whose Wronskian is non-zero on I. Then L = (−1)nQ*Q or L = (−1)nQ*DQ where Q is a differential operator of order n, Q* is the adjoint operator and D denotes differentiation. This fact is used to construct further solutions yn+1,−, ym of Ly = 0 so that y1,…, ym is a basis for the solutions of Ly = 0 and for which yi and yn+j are mutually conjugate if i ≠ j. If y1 ≠ 0 on I the degree of L may be lowered by 2 to obtain a formally self-adjoint operator L1 for which mutually conjugate solutions are constructed. If this process is continued a factorization result is obtained which is related to a result of Pólya.
Two series inequalities
Authors: Copson E. T. 
Published: November 2011

SynopsisIn 1932, Hardy and Littlewood proved the inequalitiesThe best possible values of the constants K1 and K2 being 1 and 4 respectively. The object of this paper is to prove analogous results for infinite series in which the derivative of the real function f is replaced by the finite differenceof a sequence {an} of real numbers.
On the possibility of defining the Chapman–Kolmogorov semi-group on L∞
Authors: Devinatz Allen , Malliavin Paul 
Published: November 2011

SynopsisIf the diffusion matrix coefficient of an Itô stochastic differential equation is everywhere non-singular, then the corresponding Chapman-Kolmogorov semi-group may be defined on L∼(Rn), the space of Lebesgue equivalence classes of essentially bounded Borei measurable functions. However, if the diffusion matrix is singular at some points of Rn, it is not clear that this can always be done. We show that in certain situations it is possible to do so.
Nodal cubic surfaces
Authors: Edge W. L. 
Published: November 2011

SynopsisThe cubic surfaces in, save for the elliptic cone, are, whatever their singularities, projections of del Pezzo's non-singular surface F, of order 9 in. It is explained how, merely by specifying the geometrical relation of the vertex of projection to F, each cubic surface is obtainable “at a stroke”, without using spaces of intermediate dimensions.
On a class of systems of singular integral equations on a bounded domain
Authors: Džuraev A. 
Published: November 2011

SynopsisA class of systems of two-dimensional singular integral equations with even kernels over bounded domains in the plane is studied. The applications include integral equations with the Bergman kernel function. The method of investigation is the following: the integral equation is reduced to a Riemann type boundary value problem for a first order elliptic system. This is solved by means of one-dimensional singular integral equations over the boundary curve. An adjoint problem is formulated, the Noetherian theorems are established, and a formula for the index is given.
Some ergodic theorems
Authors: Dunford Nelson 
Published: November 2011

SynopsisA general ergodic theorem is proved for semi-group operators onB-spaceX. In particularXmay be a Lebesgue spaceLp(S, Σ, μ) where (S, Σ, μ) is a positive measure space.The discussion is based on the theory of semi-groups as developed by Hille [6] and results in the theory of product measures [3]. The reader need only be familiar with the basic concepts of these theories, as all pertinent results used in this note are proved as they are needed.
On the variation of Teichmüller's metric
Authors: Gardiner Frederick P. 
Published: November 2011

SynopsisThe main result of this article is the calculation of the first derivative of Teichmüller's metric from an inequality of Reich and Strebel. Furthermore, from the same inequality one is able to calculate information about the difference quotient for the second derivative. From the techniques used here it does not seem possible to determine whether the metric isC2.
On the point spectra of complex Sturm—Liouville operators
Authors: Knowles Ian , Race David 
Published: November 2011

SynopsisIn this paper, the formally J-symmetric Sturm—Liouville operator with complex-valued coefficients is considered, and as a preliminary two criteria are established for the J-selfadjointness of certain of its extensions. The main purpose of the work is to give results on the location of the point spectra of such operators. Some of the results are extensions of results known for real-valued coefficients, whilst others are new.
Baer semigroup coordinatisations of distributive lattices
Authors: Blyth T. S. 
Published: November 2011

SynopsisIn a previous publication we investigated certain idempotent residuated mappings and showed how these could be used to provide a solution to the problem of finding a Baer semigroup coordinatisation of bounded modular lattices. Here we use essentially the same idempotents to provide a coordinatisation of bounded distributive lattices. Specifically, we prove that a bounded lattice L is distributive if and only if it can be coordinatised by a Baer semigroup S such that if eS, fS, gS ∈ R(S) with eS ∩ fS = eS ∩ gS then there are idempotents ē, , ∈ S such that ēS = eS, S = fS, S = gS and ē commutes with both and .
Genetic algebras for some inbreeding systems
Authors: Holgate P. 
Published: November 2011

SynopsisThe paper deals with genetic algebras for populations in which given fractions of the population practise specified types of inbreeding. It is shown that the technique of linearising the quadratic transformation of genetic type frequencies, which has been studied for triangular algebras, can be extended to a much wider class, including those for inbreeding systems.
Differential Operators of infinite order
Authors: Hille Einar 
Published: November 2011

SynopsisThe differential operators in question are of the form G(DZ) where G(w)is an entire function of order at most 1/n and minimal type while Dz is a linear differential operator of order n with coefficients which are entire ( = integral) functions of z, usually polynomials. This class of operators form a natural generalization of the class G(d/dz) studied during the first half of the century Muggli, Polya, Ritt and others. The class G(DZ) was introduced by the present author and his pupils in the 1940s. In fact, the present paper is partly based on a MS from that period, mostly devoted to the special casebut also containing generalizations, some of which were later worked out by Klimczak. A basic tool in this paper is the characteristic seriesExamples are given showing that the domain of absolute convergence of such a series need neither be convex nor of finite connectivity, a question which has puzzled the author for forty odd years. Characteristic series arising from regular or singular boundary value problems for the operator Dz are used to study the inversion problemfor given F(z). In particular it is shown that exp (Dx)[W(z)] = 0 has the unique solution W(z) ≡ 0. Some singular boundary value problems are considered briefly.
Proof of a conjecture of Offord
Authors: Erdös Paul 
Published: November 2011

SynopsisIf z1, z2 … zn are complex numbers satisfying |zi−zj|≧1 for all i, j then the number of the 2n sums where ει = ±1, which lie in any circle of radius r cannot exceed αr2n/n3/2 where αr depends only on r.
From B-completeness to countable codimensional subspaces via the closed graph theorem
Authors: Saiflu H. , Tweddle I. 
Published: November 2011

SynopsisWe show that for some closed graph theorems each countable codimensional subspace of a domain space may also serve as a domain space. This provides a general principle from which we are able to extract some of the known results on the inheritance of topological vector space properties by subspaces of countable codimension. We make use of a result of Savgulidze and Smoljanov on B-completeness for which we provide a new and simpler proof.
Liouville theorems for a class of fourth order elliptic equations
Authors: Goyal Vinod B. , Schaefer Philip W. 
Published: November 2011

SynopsisLiouville type theorems are obtained for bounded entire solutions of equations of the form Δ2u − q(x)Δu + p(x)u = 0 by means of subharmonic functionals and Green type inequalities.
Reflection of singularities of solutions to the wave equation and the leading singularity of the scattering kernel
Authors: Alber H. D. 
Published: November 2011

SynopsisIn this paper the reflection of singularities of solutions to the wave equation is studied using progressing wave expansions. The results are used to calculate the leading singularity of the Lax–Phillips scattering kernel, thus generalizing earlier results of Majda.
m (λ)-functions for complex Sturm-Liouville operators
Authors: Race David 
Published: November 2011

SynopsisIn this paper, the formally J-symmetric Sturm-Liouville operator with complex-valued coefficients is considered and a generalisation of the Weyl limit-point, limit-circle dichotomy is sought by means of m (λ )-functions. These functions are then used to give an explicit description of all the associated J-selfadjoint operators with separated boundary conditions in the limit-circle case. A formulation of the eigenvalues of these operators, and a characterisation of which extensions are non-well-posed, are also found. Finally, the limit-point case is studied, mainly by means of an example.
Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
Authors: Fulton Charles T. 
Published: November 2011

SynopsisIn this paper I extend the analysis of regular problems containing the eigenvalue parameter in the boundary conditions given by Walter (1973) and myself (1977) to singular problems which involve the eigenvalue parameter linearly in a regular or a limit-circle boundary condition at the left endpoint. The formulation of the limit-circle boundary conditions follows that given in another paper by the present author in 1977, and has the advantage that a λ-dependent boundary condition at a regular endpoint becomes a special case of a λ-dependent boundary condition at a limit-circle endpoint. The simplicity of the spectrum is also built into the formulation given, and the spectral function is shown to have bounded total variation over (−∞, ∞) which is known in terms of the parameters of the λ-dependent boundary condition independently of the limit-circle/limit-point classification at the right endpoint. The theory is applied to the constant coefficient equation in [0, ∞) and the Bessel equation of order zero in (0, ∞), explicit formulae for the spectral function being obtained in each case. Finally, the question is posed as to whether the classical Weyl theory for problems not involving λ in the boundary conditions can also be formulated so as to involve spectral functions having bounded total variation.