bluuebunny/crossref_metadata_2025_split huggingface dataset:
Local dimension and regular points
Authors: Barlow Martin T. , Taylor S. James 
Published: November 2008

The Hausdorff–Besicovitch dimension of a set A ⊆ ℝd, denoted dim (A), relates to the structure of A in the neighbourhood of its thickest point. If A is irregular then one may wish for an index which will describe the size of A in different places. The obvious definition of the local dimension of A near x isand it is not hard to verify that
The perturbation of relatively open operators with reduced index
Authors: Labuschagne L. E. 
Published: November 2008

AbstractLet X and Y denote normed spaces and T:D(T) ⊂ X → Y a linear transformation. It is shown that even in the case where both X and Y are incomplete, the quantity remains constant under both small and compact perturbation, provided that T is relatively open, R(T) is closed, and the perturbation is made in the right ‘direction’. If in addition and N(T) is topologically complemented, the topological complementation of the kernel is also preserved under small perturbations made in the right ‘direction’ and arbitrary compact perturbation. Various counter-examples are exhibited proving these results to be best possible.
On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums
Authors: Hall R. R. , Wilson J. C. 
Published: November 2008

A number of authors, including Apostol [1], Carlitz [2], Mikolás [5] and Rademacher [9] have obtained linear relations for the Dedekind sums(the inhomogeneous sum) and the homogeneous sumHere denotes the periodic extension into ℝ of the Bernoulli polynomial Bm(X) on [0, 1] given by the relationwith the exception that we define
On random polynomials over finite fields
Authors: Arratia Richard , Barbour A. D. , Tavaré Simon 
Published: November 2008

AbstractWe consider random monic polynomials of degreenover a finite field ofqelements, chosen with allqnpossibilities equally likely, factored into monic irreducible factors. More generally, relaxing the restriction thatqbe a prime power, we consider that multiset construction in which the total number of possibilities of weightnisqn. We establish various approximations for the joint distribution of factors, by giving upper bounds on the total variation distance to simpler discrete distributions. For example, the counts for particular factors are approximately independent and geometrically distributed, and the counts for all factors of sizes 1, 2, …,b, whereb=O(n/logn), are approximated by independent negative binomial random variables. As another example, the joint distribution of the large factors is close to the joint distribution of the large cycles in a random permutation. We show how these discrete approximations imply a Brownian motion functional central limit theorem and a Poisson-Dirichiet limit theorem, together with appropriate error estimates. We also give Poisson approximations, with error bounds, for the distribution of the total number of factors.
On the signature and Euler characteristic of certain four-manifolds
Authors: Johnson F. E. A. , Kotschick† D. 
Published: November 2008

Let M be a smooth closed connected oriented 4-manifold; we shall say that M satisfies Winkelnkemper's inequality when its signature, σ(M), and Euler characteristic, X(M), are related byThis inequality is trivially true for manifolds M with first Betti number b1(M) ≤ 1.
Dyer–Lashof operations in the Hopf ring for complex cobordism
Authors: Turner Paul R. 
Published: November 2008

AbstractWe give a complete description of the additive Dyer-Lashof operations on the Hopf ringwith coefficients in. We re-prove a result of Ravenel and Wilson [9] giving the operations on the elementand give formulae for the operations on the other generators.
On transmission problems for wave propagation in two locally perturbed half-spaces
Authors: Zhang Bo 
Published: November 2008

AbstractIn this paper, we consider transmission problems for wave propagation in two inhomogeneous half-spaces with a locally perturbed hyperplane interface. A radiation condition is obtained for the problem in the framework of the spaces B and B*. It is then used, together with the spaces B, B* and the limiting absorption method to prove the existence of the unique solution to the problem.
A note on the diophantine equation (xm − l) / (x − 1) = yn + l
Authors: Maohua Le 
Published: November 2008

Let ℤ, ℕ, ℚ denote the sets of integers, positive integers and rational numbers, respectively. Solutions (x, y, m, n) of the equation (1) have been investigated in many papers:Let ω(m), ρ(m) denote the number of distinct prime factors and the greatest square free factor of m, respectively. In this note we prove the following results.
Cyclotomic Galois module structure and the second Chinburg invariant
Authors: Snaith Victor P. 
Published: November 2008

AbstractWe study the second Chinburg invariant of a Galois extension of number fields. The Chinburg invariant lies in the class-group of the integral group-ring of the Galois group of the extension. A procedure is given whereby to evaluate the invariant in the case of the real cyclotomic case of regular prime power conductor and their subextensions of p-power degree. The invariant is shown to be zero in the latter cases, which yields new examples giving an affirmative answer to a question of Chinburg ([1], p. 358) which has come to be known as ‘Chinburg's Second Conjecture’ ([3], §4·2).
Cubic systems with four real line invariants
Authors: Kooij Robert E. 
Published: November 2008

A polynomial system is a real autonomous system of ordinary differential equations on the plane with polynomial nonlinearities:with aij, bij ∈ ℝ and where x = x(t) and y = y(t) are real-valued functions.The problem of analysing limit cycles (isolated periodic solutions) in polynomial systems was first discussed by Poincaré[16]. Then, in the famous list of 23 mathematical problems stated in 1900, Hilbert[9] asked in the second part of the 16th problem for an upper bound for the number of limit cycles for nth degree polynomial systems, in terms of n. Recently, it has been proved that, given a particular choice of coefficients for a system of form (1·1), the number of limit cycles is finite. This result is known as Dulac's theorem, see Ecalle[8] or Il'yashenko[10]. However, it is unknown whether or not there exists an upper bound for the number of limit cycles in system (1·1) in terms of n. Even for quadratic systems (i.e. polynomial systems with quadratic nonlinearities) this remains an open question.
Some remarks on Gauss sums associated with kth powers
Authors: Montgomery H. L. , Vaughan R. C. , Wooley T. D. 
Published: November 2008

Estimates for rational trigonometric sums are of great importance in analysing the local aspects of many additive problems. Indeed, bounds for the sumsin which e(α) denotes exp (2πiα), play a fundamental rôle in the application of the Hardy–Littlewood method to Waring's problem (see [11]), and also in the analysis of the local solubility of systems of additive equations (see, for example, [2]). When k ≥ 2 is an integer, and p is a prime number it is well known (see [5] or [11, lemma 4·3]) that
Homotopical algebra and triangulated categories
Authors: Grandis Marco 
Published: November 2008

AbstractWe study here the connections between the well known Puppe-Verdier notion of triangulated category and an abstract setting for homotopical algebra, based on homotopy kernels and cokernels, which was expounded by the author in [11, 13[.We show that a right-homotopical category A (having well-behaved homotopy cokernels, i.e. mapping cones) has a sort of weak triangulated structure with regard to the suspension endofunctor σ, called σ-homotopical category. If A is homotopical and h-stable (in a sense related to the suspension-loop adjunction), this structure is also h-stable, i.e. satisfies ‘up to homotopy’ the axioms of Verdier[29[ for a triangulated category, excepting the octahedral one which depends on some further elementary conditions on the cone endofunctor of A. Every σ-homotopical category can be stabilized, by two universal procedures, respectively initial and terminal.
Asymptotic distribution of the zeros of Faber polynomials
Authors: Kuijlaars A. B. J. , Saff E. B. 
Published: November 2008

AbstractUsing potential theoretic methods and exploiting the connection with eigenvalues of Toeplitz matrices, we investigate the limiting behaviour of zeros of Faber polynomials generated by a Laurent series. Our results build upon fundamental work of J. L. Ullman. For example, we show that if E is a compact set with simply connected complement and connected interior whose boundary is either (i) not a piecewise analytic curve or (ii) a piecewise analytic curve but with a singularity other than an outward cusp, then the equilibrium distribution for E is a limit measure of the sequence of normalized zero counting measures for the Faber polynomials associated with E.
Counterexamples to the modified Weyl–Berry conjecture on fractal drums
Authors: Lapidus Michel L. , Pomerance Carl 
Published: November 2008

Let Ω be a non-empty open set in ℝn with finite ‘volume’ (n-dimensional Lebesgue measure). Let be the Laplacian operator. Consider the eigenvalue problem (with Dirichlet boundary conditions):where λ ∈ ℝ and u is a non-zero member of (the closure in the Sobolev space H1(Ω) of the set of smooth functions with compact support contained in Ω). It is well known that the values of λ∈ℝ for which (1·1) has a non-zero solution are positive and form a discrete set. Moreover, for each λ, the associated eigenspace is finite dimensional. Let the spectrum of (1·1) be denoted where 0 < λ1 ≤ λ2 ≤ … and where the multiplicity of each λ in the sequence is the dimension of the associated eigenspace. Let
Countable partitions of Euclidean space
Authors: Schmerl James H. 
Published: November 2008

Erdös has asked whether the plane ℝ2, or more generally n-dimensional Euclidean space ℝn, can be partitioned into countably many sets none of which contains the vertices of an isosceles triangle. Assuming the Continuum Hypothesis (CH), Davies[2] (for n = 2) and Kunen[10] (for arbitrary n) proved that such partitions exist. Assuming Martin's Axiom, Erdös and Komjáth proved in [5] that such partitions exist for n = 2. We will prove here, without additional set-theoretic hypotheses, that there are such partitions in all dimensions.Let ‖x‖ denote the usual Euclidean norm of a point x ∈ ℝn, so that ‖x − y‖ is the distance between x and y.
Uniqueness theorems for left-symmetric enveloping algebras
Authors: Bolgar J. R. 
Published: November 2008

AbstractLet L be a Lie algebra over a field of characteristic zero. We study the uni versai left-symmetric enveloping algebra U(L) introduced Dan Segal in [9]. We prove some uniqueness results for these algebras and determine their automorphism groups, both as left-symmetric algebras and as Lie algebras.
Transfer maps for fibrations
Authors: Dwyer W. G. 
Published: November 2008

Let f: E → B be a fibration with fibre F over a connected space B. If F is homotopy equivalent to a finite complex, Becker and Gottlieb [2, 3] and others have constructed a transfer mapwhere for simplicity X+ denotes the suspension spectrum of the space obtained from X adding a disjoint basepoint. One key property of τ(f) is the fact that the composite map f+. τ(f): B+ → B+ induces a map on integral homology which is multiplication the Euler characteristic X(F).
Geometrical conditions for the stability of orbits in planar systems
Authors: Garcia R. A. , Gasull A. , Guillamon A. 
Published: November 2008

AbstractGiven a vector field X on the real plane, we study the influence of the curvature of the orbits of ẋ = X┴(x) in the stability of those of the system x˙ = X(x). We pay special attention to the case in which this curvature is negative in the whole plane. Under this assumption, we classify the possible critical points and give a criterion for a point to be globally asymptotically stable. In the general case, we also provide expressions for the first three derivatives of the Poincaré map associated to a periodic orbit in terms of geometrical quantities.
Modular symbols for 1(N) and elliptic curves with everywhere good reduction
Authors: Cremona J. E. 
Published: November 2008

AbstractThe modular symbols method developed by the author in 4 for the computation of cusp forms for 0(N) and related elliptic curves is here extended to 1(N). Two applications are given: the verification of a conjecture of Stevens 14 on modular curves parametrized by 1(N); and the study of certain elliptic curves with everywhere good reduction over real quadratic fields of prime discriminant, introduced by Shimura and related to Pinch's thesis 10.
Modular structure of algebras of unbounded operators
Authors: Inoue Atsushi 
Published: November 2008

AbstractA systematic analysis of standard systems and modular systems for which one can develop TomitaTakesaki theory for algebras of unbounded operators is presented. Such systems arise in the Wightman quantum field theory. The connection between such systems and the theory of local nets of von Neumann algebras initiated by Araki and HaagKastler is discussed.
Singular n-tuples and Hausdorff dimension. II
Authors: Baker R. C. 
Published: November 2008

Let n be a natural number, with n ≥ 2. Let Kn denote the set of θ in Euclidean space Rn for which θ1, …, θn, 1 are linearly independent over the rational numbers. We denote points of the set of integer n-tuples Zn by x, y,…. We writeInner product is denoted by θø. In Rl, ‖θ‖ denotes distance to the nearest integer.
An integral of hypergeometric type
Authors: Slater L. J. 
Published: November 2008

In a recent paper (2) I gave some integrals which represented general transformations of hypergeometric series of both ordinary and basic types. In this paper I give the most general form of this kind of integral, from which all the previously known general basic transformations can be deduced.In the usual notation for basic series,where x may be a function of n, for example, and Π is written for ‘Idem (a; b)' means that the expression immediately preceding is to be repeated with b written in place of a and a written in place of b.
The interaction of alpha-particles and the binding energy of 8Be
Authors: Edwards S. F. 
Published: November 2008

AbstractA calculation of the binding energy of 8Be is given, based upon the separation of the eight nucleons into two groups of four, using Gaussian functions and a Yukawa central force. The calculation is considerably simplified by the use of an integral identity between the Gaussian potential and the Yukawa potential. The energy is calculated with a Gaussian potential, and the identity used to convert the result to that which would have been obtained by direct use of the Yukawa potential. The results of the variational calculation show that unless the saturation conditions usually adopted in the theory of heavy nuclei are abandoned, there can be no binding, confirming an earlier result of Margenau, obtained with a Gaussian potential. The results do not depend essentially on the range of the force, nor on the central two-body type of force adopted. When the old saturation conditions are abandoned, quite reasonable results are obtained. The magnitude of the energies due to the exchange of single particles and pairs of particles indicates that the force between alpha-particles is not additive. A discussion of the saturation conditions and of the alpha-particle model in the light of the results is given.
On the second-order correction terms to values of gravity measured at sea
Authors: Worsley Beatrice H. 
Published: November 2008

AbstractThe motion of a pendulum on a periodically accelerated support has been studied by means of an electronic computing machine. The results have been applied to the problem of calculating the second-order correction to measurements of gravity made at sea with the Vening Meinesz three-pendulum apparatus. It is found that the correction for a single horizontal acceleration under typical conditions is likely to be more than twice that found analytically by Browne. His correction for vertical acceleration is valid for a wide range of frequency of the disturbing motion.
Products of flows
Authors: Arrowsmith D. K. 
Published: November 2008

AbstractThe aim of the paper is to exhibit the structure of products of flows that are suspensions of diffeomorphisms and show their relationship with suspensions of product diffeomorphisms.The problem is important for applications of the following type. Suppose we have two dynamical systems each with a stable attractor. If the systems are brought into contact, as, for example, in the way a forced oscillation is imposed upon a natural oscillation in synchronization theory, then this is represented by taking the product flow to find the resulting behaviour of the joint system. However, the product of two stable attractors is no longer stable in general, and therefore it is important to analyse why, in order to understand what new stable attractors can arise from perturbations.
On summability domains
Authors: Kalton N. J. 
Published: November 2008

We denote by ω the space of all complex sequences with the topology given by the semi-normswhere δn(x) = xn. An FK-space, E, is a subspace of ω on which there exists a complete metrizable locally convex topology τ, such that the inclusion (E, τ) ⊂ ω is continuous; if τ is given by a single norm then E is a BK-space.
Capillary-gravity waves over a sloping beach
Authors: Allwood D. A. 
Published: November 2008

AbstractIt is shown how the solution for the velocity potential may be determined when the effect of surface tension is included in the linearized theory of surface waves over a sloping beach. In particular, two independent standing wave solutions are found, both of which have finite amplitude at the shoreline. The results agree with those of previous writers when the surface tension force tends to zero.
A partial evaluator for the untyped lambda-calculus
Authors: Gomard Carsten K. , Jones Neil D. 
Published: November 2008

AbstractThis article describes theoretical and practical aspects of an implemented self-applicable partial evaluator for the untyped lambda-calculus with constants and a fixed point operator. To the best of our knowledge, it is the first partial evaluator that is simultaneously higher-order, non-trivial, and self-applicable.Partial evaluation produces aresidual programfrom a source program and some of its input data. When given the remaining input data the residual program yields the same result that the source program would when given all its input data. Our partial evaluator produces a residual lambda-expression given a source lambda-expression and the values of some of its free variables. By self-application, the partial evaluator can be used to compile and to generate stand-alone compilers from a denotational or interpretive specification of a programming language.An essential component in our self-applicable partial evaluator is the use of explicitbinding time information.We use this to annotate the source program, marking asresidualthe parts for which residual code is to be generated and marking aseliminablethe parts that can be evaluated using only the data that is known during partial evaluation. We give a simple criterion,well-annotatedness,that can be used to check that the partial evaluator can handle the annotated higher-order programs without committing errors.Our partial evaluator is simple, is implemented in a side-effect free subset of Scheme, and has been used to compile and to generate compilers and a compiler generator. In this article we examine two machine-generated compilers and find that their structures are surprisingly natural.
Fixed points and frontiers: a new perspective
Authors: Hunt Sebastian , Hankin Chris 
Published: November 2008

AbstractAbstract interpretation is the collective name for a family of semantics-based techniques for compile-time analysis of programs. One of the most costly operations in automating such analyses is the computation of fixed points. The frontiers algorithm is an elegant method, invented by Chris Clack and Simon Peyton Jones, which addresses this issue.In this article we present a new approach to the frontiers algorithm based on the insight that frontiers represent upper and lower subsets of a function's argument domain. This insight leads to a new formulation of the frontiers algorithm for higher-order functions, which is considerably more concise than previous versions.We go on to argue that for many functions, especially in the higher-order case, finding fixed points is an intractable problem unless the sizes of the abstract domains are reduced. We show how the semantic machinery of abstract interpretation allows us to place upper and lower bounds on the values of fixed points in large lattices by working within smaller ones.
Equivalence in functional languages with effects
Authors: Mason Ian , Talcott Carolyn 
Published: November 2008

AbstractTraditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the call-by-value lambda calculus results in a language with a rich equational theory, satisfying many of the usual laws. Combined with other recent work, this provides evidence that expressive, mathematically clean programming languages are indeed possible.
Theoretical PearlsEnumerators of lambda terms are reducing
Authors: Barendregt Henk 
Published: November 2008

AbstractA closed λ-termEis called anenumeratorifHere ⋀0is the set of closed λ-terms,. is the set of natural numbers and the ⌜n⌝ are the Church's numerals λfx.fnx. Such anEis calledreducingif, moreoverAn ingenious recursion theoretic proof by Statman will be presented, showing that every enumerator is reducing. I do not know any direct proof.
A domain-theoretic approach to functional and logic programming
Authors: Silbermann Frank S. K. , Jayaraman Bharat 
Published: November 2008

AbstractThe integration of functional and logic programming languages has been a topic of great interest in the last decade. Many proposals have been made, yet none is completely satisfactory especially in the context of higher order functions and lazy evaluation. This paper addresses these shortcomings via a new approach: domain theory as a common basis for functional and logic programming. Our integrated language remains essentially within the functional paradigm. The logic programming capability is provided by set abstraction (via Zermelo-Frankel set notation), using the Herbrand universe as a set abstraction generator, but for efficiency reasons our proposed evaluation procedure treats this generator's enumeration parameter as a logical variable. The language is defined in terms of (computable) domain-theoretic constructions and primitives, using the lower (or angelic) powerdomain to model the set abstraction facility. The result is a simple, elegant and purely declarative language that successfully combines the most important features of both pure functional programming and pure Horn logic programming. Referential transparency with respect to the underlying mathematical model is maintained throughout. An implicitly correct operational semantics is obtained by direct execution of the denotational semantic definition, modified suitably to permit logical variables whenever the Herbrand universe is being generated within a set abstraction. Completeness of the operational semantics requires a form of parallel evaluation, rather than the more familiar left-most rule.