bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature
Authors: Bridges Thomas J. 
Published: November 2008

AbstractWhen two purely imaginary eigenvalues of opposite Krein signature coalesce, in a Hamiltonian system, a small perturbation can drive them off of the imaginary axis resulting in a linear instability. The most celebrated example of this instability occurs in the restricted 3-body problem at Routh's critical mass ratio. In this paper the collision of eigenvalues is treated as a singularity. A variational form of the Lyapunov–Schmidt method and distinguished parameter ࡃ2-equivariant singularity theory, with the frequency as distinguished parameter, are used to determine the effect of the degeneracy on the branches of periodic solutions in a neighbourhood. Previous results of Meyer and Schmidt[13], Sokol'skij [16] and van der Meer [12] are recovered in the formulation as a co-dimension 1 singularity. The results are extended to include the effect of an additional degeneracy (a co-dimension 2 singularity). The theory is applied to a spinning double pendulum.
A semigroup embedding problem and an arithmetical function
Authors: Howie John M. , Selfridge J. L. 
Published: November 2008

For unexplained terms in semigroup theory see [1] or [4].Let C, D be classes of semigroups such that every finite semigroup in the class C is embeddable in a finite semigroup in the class D. If n ≥ 2 then k is said to be a C – Dcover of n if every semigroup of order n in the class C is embeddable in a semigroup in the class D of order not greater than k. Let be the least C – D cover of n.
On KMS states for self-dual CCR algebras and Bogoliubov automorphism groups
Authors: Ogi Hidekazu 
Published: November 2008

AbstractLet be the self-dual CCR algebra over a triplet (K, r, Γ), where K is assumed to be a Hilbert space, and let {τt}t ∈ R be a Bogoliubov automorphism group of induced by a strongly continuous one-parameter unitary group on K. In this paper, we introduce some continuity for linear functionals on and, under this continuity, we study existence, uniqueness, and non-uniqueness of KMS states for .
On the valence of some classes of harmonic maps
Authors: Lyzzaik Abdallah 
Published: November 2008

AbstractWe give examples which (i) disprove a conjecture of Sheil-Small regarding the valence of harmonic mappings of the unit disc to bounded convex domains, and (ii) answer negatively a question of the author regarding the valence of harmonic mappings with polynomial analytic and co-analytic parts.
The inhomogeneous minimum of binary quadratic forms
Authors: Berend Daniel , Moran William 
Published: November 2008

AbstractAn indefinite binary quadratic form ƒ gives rise to a certain function M on the torus. The properties of M, especially those related to its maximum – the so-called inhomogeneous minimum of ƒ – are the subject of numerous papers. Here we continue this study, putting more emphasis on the general behaviour of M.
Existence of periodic solutions to integro-differential equations of neutral type via limiting equations
Authors: Wu Jianhong , Xia Huaxing 
Published: November 2008

AbstractIn this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov–Razumikhin technique for neutral equations with finite delay to obtain existence of periodic solutions of Volterra neutral integro-differential equations (of infinite delay). Some comparisons between our results and the existing ideas are also provided.
A note on coverage error of bootstrap confidence intervals for quantiles
Authors: Angelis D. De , Hall Peter , Young G. A. 
Published: November 2008

AbstractAn interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of sizen−½, wherendenotes sample size. By way of contrast, the error would beO(n−1)for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved too(n−½)by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage errorO(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-tare also analysed.
On existence varieties of locally inverse semigroups
Authors: Auinger K. , Doyle J. , Jones P. R. 
Published: November 2008

AbstractA locally inverse semigroup is a regular semigroup S with the property that eSe is inverse for each idempotent e of S. Motivated by natural examples such as inverse semigroups and completely simple semigroups, these semigroups have been the subject of deep structure-theoretic investigations. The class ℒ ℐ of locally inverse semigroups forms an existence variety (or e-variety): a class of regular semigroups closed under direct products, homomorphic images and regular subsemigroups. We consider the lattice ℒ(ℒℐ) of e-varieties of such semigroups. In particular we investigate the operations of taking meet and join with the e-variety CS of completely simple semigroups. An important consequence of our results is a determination of the join of CS with the e-variety of inverse semigroups – it comprises the E-solid locally inverse semigroups. It is shown, however, that not every e-variety of E-solid locally inverse semigroups is the join of completely simple and inverse e-varieties.
Bounded distortion and dimension for non-conformal repellers
Authors: Falconer K. J. 
Published: November 2008

AbstractWe obtain an expression for the dimension of a mixing repeller of a non-conformal mapping analogous to the well-known Bowen-Ruelle formula for conformal repellers. The dimension is given in terms of a generalized pressure defined in the context of the thermodynamic formalism. In the course of the paper we develop a subadditive version of the thermodynamic formalism that is suited to our needs and also obtain a ‘bounded distortion’ principle applicable to the non-conformal situation.
Duality of induction and restriction for abelian twisted covariant systems
Authors: Echterhoff Siegfried 
Published: November 2008

AbstractLet (A, G, α, τ) be a twisted covariant system such that G/Nτ is abelian, and let Nτ ⊆ M ⊆ H be closed subgroups of G. We show that inducing covariant representations from A ⋊α, τM to A ⋊α, τH is in a certain sense dual to restricting representations from (A⋊α, τG)⋊άM┴ to (A⋊α, τG)⋊άH┴, and that, similarly, restricting representations from A⋊α, τH to A⋊α, τM is dual to inducing representations from (A⋊τG)⋊άH┴ to (A ⋊α, τG)⋊άM┴.
Properties (V) and (w V) on C(Ω X)
Authors: Bator Elizabeth M. , Lewis Paul W. 
Published: November 2008

A formal series Σxn in a Banach space X is said to be weakly unconditionally converging, or alternatively weakly unconditionally Cauchy (wuc) if Σ|x*(xn)| < ∞ for every continuous linear functional x* ∈ X*. A subset K of X* is called a V-subset of X* iffor each wuc series Σxn in X. Further, the Banach space X is said to have property (V) if the V-subsets of X* coincide with the relatively weakly compact subsets of X*. In a fundamental paper in 1962, Pelczynski [10] showed that the Banach space X has property (V) if and only if every unconditionally converging operator with domain X is weakly compact. In this same paper, Pelczynski also showed that all C(Ω) spaces have property (V), and asked if the abstract continuous function space C(Ω, X) has property (F) whenever X has property (F).
Applications of the Birkhoff–Hopf theorem to the spectral theory of positive linear operators
Authors: Eveson Simon P. , Nussbaum Roger D. 
Published: November 2008

This paper may be regarded as a sequel to our earlier paper [19], where we give an elementary and self-contained proof of a very general form of the Hopf theorem on order-preserving linear operators in partially ordered vector spaces (reproduced here as Theorem 1·1).Versions of this theorem and related ideas have been used by various authors to study both linear and nonlinear integral equations (Thompson [41], Bushell [9, 11], Potter [38, 39], Eveson [16, 17], Bushell and Okrasiriski [12, 13]); the convergence properties of nonlinear maps (Nussbaum [32, 33]); so-called DAD theorems (Borwein, Lewis and Nussbaum [8]) and in the proof of weak ergodic theorems (Fujimoto and Krause [20], Nussbaum [34]).
Equivariant homology
Authors: Austin David M. , Braam Peter J. 
Published: November 2008

AbstractThis paper studies the homology of the homotopy quotient of a G-manifold. We start by formulating a complex based on differential forms to compute this homology. This leads to a topological version of integration formulas over fibred products of G-manifolds. In particular the TQFT formulas studied by Witten and Atiyah–Jeffrey now appear as a pairing of homology and cohomology classes. We compare our construction with both the double complex of Axelrod and Witten and with the distributional complex of Duflo and Vergne.
Vassiliev invariants and the Hopf algebra of chord diagrams
Authors: Willerton Simon 
Published: November 2008

AbstractThis paper is closely related to Bar-Natan's work, and fills in some of the gaps in [1]. Following his analogy of the extension of knot invariants to knots with double points to the notion of multivariate calculus on polynomials, we introduce a new notation which facilitates the formulation of a Leibniz type formula for the product of two Vassiliev invariants. This leads us to see how Bar-Natan's co-product of chord diagrams corresponds to multiplication of Vassiliev invariants. We also include a proof that the multiplication in is a consequence of Bar-Natan's 4T relation.The last part of this paper consists of a proof that the space of weight systems is a sub-Hopf algebra of the space *, by means of the canonical projection.
On ground states for CCR algebras and Bogoliubov automorphism groups
Authors: Ogi Hidekazu 
Published: November 2008

AbstractLet ACCR(L) be the CCR algebra over a Hubert space L, and let {σt}t∈R be a Bogoliubov automorphism group of ACCR(L) induced by a strongly continuous one-parameter unitary group on L. In this paper, we introduce some continuity for linear functionals on ACCR(L) and, under this continuity, we study existence, uniqueness, and non-uniqueness of ground states for {ACCR(L), {σt}t∈R}.
The geometry of open continuous mappings having two valences between Riemann surfaces
Authors: Lyzzaik Abdallah 
Published: November 2008

AbstractAn open continuous function from an open Riemann surface with finite genus and finite number of boundary components into a closed Riemann surface is termed a (p, q)-map, 0 < q < p, if it has a finite number of branch points and assumes every point in the image surface either p or q times, counting multiplicity, with possibly a finite number of exceptions.The object of this paper is to prove that the geometry of any (p, q)-map resembles that of a (p, q)-map whose q-set (the set of image points of f that are taken on exactly q times, counting multiplicity), constitutes a finite set of Jordan arcs or curves (loops). This leads to interesting geometrie results regarding (p, q)-maps without exceptional points. Further, it yields that every (p, q)-map is homotopic to a simplicial (p, q)-map having the same covering properties.
Complemented copies of l1, in Lp(μ;E)
Authors: Mendoza José 
Published: November 2008

AbstractLet E be a Banach space, let (Ω, Σ, μ) a finite measure space, let 1 < p < ∞ and let Lp(μ;E) the Banach space of all E-valued p-Bochner μ-integrable functions with its usual norm. In this note it is shown that E contains a complemented subspace isomorphic to l1 if (and only if) Lp(μ; E) does. An extension of this result is also given.
The ideal structure of some Banach algebras
Authors: Filali M. 
Published: November 2008

AbstractLet G be a locally compact group and let Ĝ be its character group. Among other results, the minimal left ideals of L∞(G)* and LUC(G)* are all found when G is abelian. The main tool used for this study is the set of (topological) χ-invariant functionals (χ∈Ĝ), defined in this paper.
Spectral representation and scattering theory for the wave equation with two unbounded media
Authors: Roach G. F. , Zhang Bo 
Published: November 2008

AbstractIn this paper, we establish the generalized eigenfunction expansions for wave propagation in inhomogeneous, penetrable media in ℝn(n ≥ 2) with an unbounded interface. We then use them together with the method of stationary phase to prove the existence of the wave operators and to obtain the representations of the wave operators in terms of the generalized Fourier transforms.
Julia sets of rational functions are uniformly perfect
Authors: Hinkkanen A. 
Published: November 2008

AbstractLetfbe a rational function of degree at least two. We shall prove that the Julia setJ(f) offis uniformly perfect. This means that there is a constantc∈(0, 1) depending onfonly such that wheneverz∈J(f) and 0 <r< diamJ(f) thenJ(f) intersects the annulus.
Safe numerical bounds for the Titchmarsh–Weyl m(λ)-function
Authors: Brown B. M. , Kirby V. G. , Evans W. D. , Plum M. 
Published: November 2008

AbstractRecent efforts have been focused on using numerical methods to estimate the Titchmarsh–Weyl m-coefficient. In this paper we look at interval analytic methods to provide provable bounds for these values.
A partition of non-synthesis for a quotient algebra of A(Z)
Authors: Salinger D. L. 
Published: November 2008

Let A(Z) be the Banach algebra of Fourier-Lebesgue coefficients: a function f is an element of A(Z) if it is the Fourier transformof some function fεL1(T), where T, as usual, denotes the circle group. We write
An application of distribution theory to Martin's method in potential scattering
Authors: Whipp A. T. 
Published: November 2008

AbstractIn order to study the convergence of a series arising from the use of Martin's method in potential scattering a framework consisting of a modifidation to Schwartz's formulation of distribution theory is set up. This modification makes essential use of norms on the spaces of test functions and linear functionals. By making the norm on the space of test functions satisfy extra axioms a bound is obtained on the norm of a generalized convolution of two linear functionals, and this bound is used to prove the convergence of the series. The proof of convergence is generalized to cover the multi-channel problem. The method used may also be applied to many other physical problems.
Bohr-Sommerfeld orbits and quantizable symplectic manifolds
Authors: Simms D. J. 
Published: November 2008

The phase space of a finite dimensional classical Hamiltonian system is a C∞ differentiable manifold M which carries a C∞ differential 2-form ω which is closed, dω = 0, and non-singular in the sense that there is a bijective map α→ Xα from covariant vector fields to contravariant vector fields satisfying the identitySuch a pair (M, μ) is called a symplectic manifold.
On the elliptic ball stability criterion for ordinary differential equations
Authors: Smith Russell A. 
Published: November 2008

AbstractIt is proved that the elliptic ball criterion is a necessary condition on the matrix M(t) for the linear feedback control equation f(D)x + BM(t)g(D)x = 0 to have a special kind of quadratic Lyapunov function. That it is also a sufficient condition has already been proved elsewhere. These two facts lead to a comparison theorem which enables the existence of a quadratic Lyapunov function for one equation to be deduced from that for another equation.
An evaluation of a link polynomial
Authors: Lipson A. S. 
Published: November 2008

There exists for each oriented link L in the 3-sphere a unique 2-variable Laurent polynomial defined uniquely by the following:(i) PU = 1 for the unknot U(ii) ,where L+, L− and L0 are identical outside a ball and inside are as shown in Figure 1. See [1] and [2].
The Shot Effect for Showers
Authors: Whittaker J. M. 
Published: November 2008

1. A well-known theorem on probability may be stated as follows. Let λdt be the chance that a certain event will happen in time dt, so that λT is the average number of occurrences of the event in an interval T. If we take a large number of repetitions of the interval T the actual numbers of occurrences will fluctuate about the mean λT, being say λT + x′, λT + x″,…. Then the theorem states thatThe ejection of an α-particle by a radioactive substance is an event of the type contemplated and the theorem was applied to this physical problem by von Schweidler in 1905. Much similar work, both theoretical and experimental, has been done at intervals since then*.
Implementing the evaluation transformer model of reduction on parallel machines
Authors: Burn G. L. 
Published: November 2008

AbstractThe evaluation transformer model of reduction generalizes lazy evaluation in two ways: it can start the evaluation of expressions before their first use, and it can evaluate expressions further than weak head normal form. Moreover, the amount of evaluation required of an argument to a function may depend on the amount of evaluation required of the function application. It is a suitable candidate model for implementing lazy functional languages on parallel machines.In this paper we explore the implementation of lazy functional languages on parallel machines, both shared and distributed memory architectures, using the evaluation transformer model of reduction. We will see that the same code can be produced for both styles of architecture, and the definition of the instruction set is virtually the same for each style. The essential difference is that a distributed memory architecture has one extra node type for non-local pointers, and instructions which involve the value of such nodes need their definitions extended to cover this new type of node.To make our presentation accessible, we base our description on a variant of the well-known G-machine, an abstract machine for executing lazy functional programs.
Explicit substitutions
Authors: Abadi M. , Cardelli L. , Curien P.-L. , Lévy J.-J. 
Published: November 2008

AbstractThe λσ-calculus is a refinement of the λ-calculus where substitutions are manipulated explicitly. The λσ-calculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λ-calculus and concrete implementations.
Using transformations in the implementation of higher-order functions
Authors: Nielson Hanne Riis , Nielson Flemming 
Published: November 2008

AbstractTraditional functional languages do not have an explicit distinction between binding times. It arises implicitly, however, as one typically instantiates a higher-order function with the arguments that are known, whereas the unknown arguments remain to be taken as parameters. The distinction between ‘known’ and ‘unknown’ is closely related to the distinction between binding times like ‘compile-time’ and ‘run-time’. This leads to the use of a combination of polymorphic type inference and binding time analysis for obtaining the required information about which arguments are known.Following the current trend in the implementation of functional languages we then transform the run-time level of the program (not the compile-time level) into categorical combinators. At this stage we have a natural distinction between two kinds of program transformations: partial evaluation, which involves the compile-time level of our notation, and algebraic transformations (i.e., the application of algebraic laws), which involves the run-time level of our notation.By reinterpreting the combinators in suitable ways we obtain specifications of abstract interpretations (or data flow analyses). In particular, the use of combinators makes it possible to use a general framework for specifying both forward and backward analyses. The results of these analyses will be used to enable program transformations that are not applicable under all circumstances.Finally, the combinators can also be reinterpreted to specify code generation for various (abstract) machines. To improve the efficiency of the code generated, one may apply abstract interpretations to collect extra information for guiding the code generation. Peephole optimizations may be used to improve the code at the lowest level.
A categorical understanding of environment machines
Authors: Asperti Andrea 
Published: November 2008

AbstractIn the last two decades, category theory has become one of the main tools for the denotational investigation of programming languages. Taking advantage of the algebraic nature of the categorical semantics, and of the rewriting systems it suggests, it is possible to use these denotational descriptions as a base for research into more operational aspects of programming languages.This approach proves to be particularly interesting in the study and the definition of environment machines for functional languages. The reason is that category theory offers a simple and uniform language for handling terms and environments (substitutions), and for studying their interaction (through application).Several examples of known machines are discussed, among which the Categorical Abstract Machine of Cousineau et al. (1987) and Krivine's machine. Moreover, as an example of the power and fruitfulness of this approach, we define two original categorical machines. The first one is a variant of the CAM implementing a λ-calculus with both call-by-value and call-by-name as parameters passing modes. The second one is a variant of Krivine's machine performing complete reduction of λ-terms.
Distributed random number generation
Authors: Burton F. Warren , Page Rex L. 
Published: November 2008

AbstractIn a functional program, a simple random number generator may generate a lazy list of random numbers. This is fine when the random numbers are consumed sequentially at a single point in the program. However, things are more complicated in a program where random numbers are used at many locations, such as in a large simulation. The programmer should not need to worry about providing separate generators with a unique seed at each point where random numbers are used. At the same time, the programmer should not need to coordinate the use of a single stream of random numbers in many parts of the program, which can be particularly difficult with lazy evaluation or parallel processing.We discuss several techniques for distributing random numbers to various parts of a program, and some methods of allowing different program components to evaluate random numbers locally. We then propose a new approach in which a random number sequence can be split at a random point to produce a pair of random number sequences that can be used independently at different points in the computation.The approach can also be used in distributed procedural programs, where it is desirable to avoid dealing with a single source of random numbers. The approach has the added advantage of producing repeatable results, as might be needed in debugging, for example.