bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the relative stability of large order statistics
Authors: Hall Peter 
Published: November 2008

AbstractLet X1, X2, … be independent and identically distributed (i.i.d.) random variables and let Xn, r denote the rth largest of X1, X2, …, Xn (so that Xn, r is the (n − r + l)th-order statistic of X1, X2, …, Xn). It is well known that if Xn, l/cn→1 in probability or with probability 1, for some sequence of constants cn, then Xn, r/cn→1 for each r ≥ 1. Therefore if r(n) → ∞ sufficiently slowly, Xn, r(n)/cn→1 for the same sequence of constants cn. In this paper we study behaviour of this type in considerable detail. We find necessary and sufficient conditions on the rate of increase of r(n), n ≤ 1, for the limit theorem Xn, r(n)/cn→1 to hold, and we investigate the rate of convergence in terms of a central limit theorem and a law of the iterated logarithm (LIL). The LIL takes a particularly interesting form, and there are five distinctly different modes of behaviour.
On the comparison of stability criteria in anisotropic materials
Authors: Parry Gareth. P. 
Published: November 2008

AbstractThe convexity of the internal energy, regarded as a function of any tensor strain measure, determines the stability of a material in a particular loading environment. Such convexity criteria reflect properties of the material alone and therefore have the alternative interpretation of constitutive inequalities. An assessment of the relative strengths of these criteria is therefore of interest because it provides an ordering of the constitutive inequalities. Existing comparison theorems, allowing such an assessment, suppose that work-conjugate measures of stress and strain are coaxial. The main content of this paper is a theorem which makes no such supposition and so enables a comparison of criteria of convexity, and an ordering of constitutive inequalities, for arbitrarily anisotropic materials.
A local limit theorem for attractions under a stable law
Authors: Basu Sujit K. , Maejima Makoto 
Published: November 2008

AbstractLet {Xn} be a sequence of independent random variables each having a common d.f. V1. Suppose that V1 belongs to the domain of normal attraction of a stable d.f. V0 of index α 0 ≤ α ≤ 2. Here we prove that, if the c.f. of X1 is absolutely integrable in rth power for some integer r > 1, then for all large n the d.f. of the normalized sum Zn of X1, X2, …, Xn is absolutely continuous with a p.d.f. vn such thatas n → ∞, where v0 is the p.d.f. of Vo.
Analytic functions having distributional boundary values in W′-spaces
Authors: Pathak R. S. 
Published: November 2008

AbstractIt is shown that the functions which are analytic in tubular radial domains and satisfy certain growth conditions have distributional boundary values in the weak topology of (WΩ)′-space. Representation of analytic functions in terms of distributional boundary values are given. Converse results are also obtained. An analytic decomposition theorem is proved. The main theorems are established by means of a number of lemmas concerning WM, WΩ spaces and their dual spaces. Several new lemmas are proved for K{Mp} spaces from which results for WM-spaces can be easily deduced.
ε- and γ-formalisms in the calculus of 4-spinors
Authors: Buchdahl H. A. 
Published: November 2008

AbstractThe calculus of 4-spinors, covariant with respect to arbitrary transformations in a 6-dimensional Riemann space, was presented earlier in a formulation analogous to the so-called ε-formalism in the 2-spinor calculus. Like the latter it is burdened by the appearance of a multiplicity of fractional spin weights and anti-weights as well as the arbitrariness of the trace of the linear spinor connexion. This paper deals in detail with a variant of the calculus which is more akin to the so-called γ-formalism in the 2-spirior calculus; and which is finally extended to be both gauge-invariant and phase-invariant.
Overall properties of a cracked solid
Authors: Hudson J. A. 
Published: November 2008

AbstractThe differential-integral equation of motion for the mean wave in a solid material containing embedded cavities or inclusions is derived. It consists of a series of terms of ascending powers of the scattering operator, and is here truncated after the third term. This implies the second-order interactions between scatterers are included but those of the third order are not.The formulae are specialized to the case of thin cracks, either aligned in a single direction or randomly oriented. Expressions for the overall elastic constants are derived for the case of long wavelengths. These expressions are accurate to the second order in the number density of scatterers.
An extension of the Freiheitssatz
Authors: Baumslag B. , Pride S. J. 
Published: November 2008

LetIbe a set and letH(i)(i∈I) be non-trivial groups. IfJis a subset ofI, we denote the free product of theH(j)(j∈J) byH(J). We denoteH(I) simply byH.LetRbe a cyclically reduced element ofHof length at least two, and letLet μ:H→Gbe the natural homomorphism. IfJis a subset ofIsuch thatR∉H(J), we callH(J)a Magnus subgroup, or occasionallythe J-Magnus subgroup(ofHwith respect toR). We will say that the Freiheitssatz holds if μ|Mis an injection for each Magnus subgroupM. Magnus (4) showed that the Freiheitssatz holds if theH(i)are free, and this was extended by Pride (5) to the case where theH(i)are locallyfullyresidually free. In this paper we prove Theorem 1.The Freiheitssatz holds if the H(i)are locally residually free.
Bol loops of order pq
Authors: Niederreiter Harald , Robinson Karl H. 
Published: November 2008

AbstractThe main results of this paper show that for any odd primes p and q with q dividing p2 − 1 there exist non-associative Bol loops of order pq. The construction is sufficiently flexible so as to allow the resulting loops to be either Bruck loops or non-Bruck loops. It also permits the determination of isotopy classes among the loops constructed. All Bol loops of order 15 are determined.
Some best-approximation theorems in tensor-product spaces
Authors: Light W. A. , Cheney E. W. 
Published: November 2008

We begin by describing a concrete example from the class of problems to be considered. A continuous bivariate function f defined on the square |t| ≤ 1, |s| ≤ 1 is to be approximated by a tensor-product form involving univariate functions. For example, the approximation may be prescribed to have the formin which the Ti are the Tchebycheff polynomials, and the coefficient functions xi(t) and yi(s) are to be chosen to achieve a good or best approximation. Will a best approximation exist? If so, how can it be obtained?
Infinite intensity mixtures of point processes
Authors: Daley D. J. 
Published: November 2008

AbstractLet the stationary point processN(·) be the mixture of scaled versions of a stationary orderly point processN1(·) of unit intensity with mixing distributionG(·), so thatWithN(·) has finite or infinite intensity asis finite or infinite, and it is Khinchin orderly when the function γ(·) is slowly varying at infinity. Conditions forN(·) to be orderly involve bothG(·) and the Palm distribution ofN1(·).
Representing elements of π1M3 by fibred knots
Authors: Harer John 
Published: November 2008

Every smooth, closed, orientable manifold of dimension 3 contains a fibred knot, i.e. an imbedded circle K such that M – K is the total space of a fibre bundle over S1 whose fibre F is standard near K. This means the boundary of the closure of F is K so that K is null-homologous in M. A natural problem suggested by Rolfsen (see (2), problem 3·13) is to determine which elements of π1M3 may be represented by fibred knots. We deal with this by proving theTheorem. The collection of all elements of π1 M3 which can be represented by fibred knots is exactly the commutator subgroup [π1 M3, π1 M3].
Strategies for compounds of partizan games
Authors: Fraenkel Aviezri S. , Tassa Uzi 
Published: November 2008

AbstractIn this paper we define two order relations between every two partizan games with possible draw positions. We use these relations to prove two ‘simplest form’ theorems, and to describe an algorithm for computing the simplest form of the ‘finite games’ which are an extension of Conway's short games.
Free subgroups of certain one-relator groups defined by positive words
Authors: Baumslag Gilbert 
Published: November 2008

Let ℒ be the class of those groupsGwhich can be presented in the formwhereuandvare positive words in the given generators. Here a wordwis termed positive if only non-negative powers ofa,b,…,coccur inw. If each generator occurs with exponent sum zero inuv-1, we term the ℒ-groupGa-group. This classcontains, in particular, the classXof those groupsGwhich can be presented in the formwhereuandvare positive words, and where [u,v] is the commutatoruvu-1v-1.
An irreducible 4-string braid with unknotted closure
Authors: Morton H. R. 
Published: November 2008

Every oriented knot or link in S3 can be represented in many ways as the closure of a braid β ∈ Bn, the braid group on n strings, for some n. Braids β ∈ Bn, γ ∈ Bm are called closure-equivalent if and are equivalent as oriented knots. It is a well-known result of Markov, see, for example, (l), that β and γ are closure equivalent if and only if there is a sequence of elementary (Markov) moves in which β ∈ Bn is replaced by(a) a conjugate in Bn, or , or(c) β1 ∈ Bn−1, where ,and the process repeated until γ is reached.
Wavefronts and parallels in Euclidean space
Authors: Bruce J. W. 
Published: November 2008

Given a smooth plane curve or surface in ℝ3 its parallels consist of those curves or surfaces a fixed distance d down the normals in a fixed direction. Generically they have Legendre singularities. We are concerned here with the way in which these parallels change as we alter the distance d. (Alternatively the manner in which wave-fronts change as they evolve from an initial smooth wavefront.)This problem was considered in (1) by V. I. Arnold. In a very beautiful paper he describes the generic evolution of wavefronts but does not prove that for a generic initial wavefront in ℝ2 or ℝ3 the evolution is of the type described there. This we do here, using the tool of transversality. A more positive outcome of our investigation is that some of Arnold's generic forms do not occur (those corresponding to A2 singularities).
Finite particle systems and infection models
Authors: Donnelly Peter , Welsh Dominic 
Published: November 2008

Infinite particle systems on lattices have been extensively studied in recent years. The main questions of interest concern the ergodic and limiting behaviour of these processes, and their relationship with the dimension of the underlying lattice. A comprehensive review is given by Durrett(6).One of the more tractable of these processes is the voter model introduced by Clifford and Sudbury(3) and much studied since, see for example the monograph by Griffeath(8), or the papers by Harris(11), Holley and Liggett(13), Bramson and Griffeath(1) and (2) or, for a more general approach, Kelly(16).In this paper we consider the case where the underlying spatial structure is finite and examine the transient behaviour of the voter process and also the infection process introduced by Williams and Bjerknes(21).
Best approximation in LP (I, X)
Authors: Khalil Roshdi 
Published: November 2008

Let T be a measure space and m a finite measure on T. The space of p-Bochner integrable functions defined on T with values in a Banach space X is denoted by Lp(T, X). It is well known (1) that Lp (T, X) is a Banach space under the normA subspace E in a Banachh space F is said to be proximinal if for each xF there is at least one xE such thatThe element y is called best approximant of x in E.
Some combinatorial series identities
Authors: Srivastava H. M. , Raina R. K. 
Published: November 2008

AbstractWhile expanding upon the work of H. M. Srivastava [6] on generalizations of an interesting identity of Carlson, R. G. Buschman and H. M. Srivastava [2] proved a number of double-series identities and listed various cases of reducibility of certain hypergeometric series in two variables (cf. [1], p. 150, equation (29)). The object of the present paper is to derive three new classes of combinatorial series identities (contained in Theorems 1, 2 and 3 below) which unify and extend the results of these earlier papers ([2], [6]). A multiple-series analogue of one of the combinatorial series identities presented here is also recorded.
On the connectedness of a random graph
Authors: Grimmett G. R. , Keane M. , Marstrand J. M. 
Published: November 2008

AbstractLet p = (p(i): i ≥ 0) be a sequence of numbers satisfying 0 ≤ p(i) < 1 for i = 0,1,2,…, and let G be a random graph with vertex set ℤ = {…, — 1, 0, 1,…} and with edge set defined as follows: for each pair i, j of vertices, where i ≤ j, there is an edge joining i and j with probability p(j — i), independently of the presence or absence of all other edges. We explore the connectedness of G, showing that G is almost surely connected if and only if Σip(i) = ∞ and the (positive) greatest common divisor of the set {i ≥ 1: p(i) < 0} equals 1; if one of these two conditions fails to hold then G is almost surely disconnected. Corresponding results hold in higher dimensions, for random graphs defined on the vertex sets ℤd where d ≥ 2.
Limit distributions for coefficients of iterates of polynomials with applications to combinatorial enumerations
Authors: Flajolet P. , Odlyzko A. M. 
Published: November 2008

AbstractThis paper studies coefficientsyh, nof sequences of polynomialsdefined by non-linear recurrences. A typical example to which the results of this paperapply is that of the sequencewhich arises in the study of binary trees. For a wide class of similar sequences a general distribution law for the coefficientsyh, nas functions ofnwithhfixed is established. It follows from this law that in many interesting cases the distribution is asymptotically Gaussian near the peak. The proof relies on the saddle point method applied in a region where the polynomials grow doubly exponentially ash→ ∞. Applications of these results include enumerations of binary trees and 2–3 trees. Other structures of interest in computer science and combinatorics can also be studied by this method or its extensions.
Graphs in the plane invariant under an area preserving linear map and general continuous solutions of certain quadratic functional equations
Authors: McCarthy P. J. , Crampin M. , Stephenson W. 
Published: November 2008

AbstractThe requirement that the graph of a function be invariant under a linear map is equivalent to a functional equation of f. For area preserving maps M(det (M) = 1), the functional equation is equivalent to an (easily solved) linear one, or to a quadratic one of the formfor all Here 2C = Trace (M). It is shown that (Q) admits continuous solutions ⇔ M has real eigenvalues ⇔ (Q) has linear solutions f(x) = λx ⇔ |C| ≥ 1. For |c| = 1 or C < – 1, (Q) only admits a few simple solutions. For C > 1, (Q) admits a rich supply of continuous solutions. These are parametrised by an arbitrary function, and described in the sense that a construction is given for the graphs of the functions which solve (Q).
Characterizations of invariant distributions
Authors: Brown Timothy C. , Cartwright Donald I. , Eagleson G. K. 
Published: November 2008

AbstractLet (S, ρ) be a separable metric space and G a group of transformations of S. Necessary and sufficient conditions for a distribution on S to be invariant under G are derived in terms of the behaviour of the convolution of a random transformation from G and a random element of S.
A simpler proof of Levinson's theorem
Authors: Conrey J. B. , Ghosh A. 
Published: November 2008

In this paper we present a proof of the mean-value theorem required by Levinson to show that at least one-third of the zeros of ζ(s) are on the critical line. As in Levinson [3], letwhere Χ(s)=ζ(s)/ζ(1−s) is the usual factor from the functional equation, and letwhereandwhere
Conservation laws and null divergences
Authors: Olver Peter J. 
Published: November 2008

AbstractIt is shown that P, depending on x, u and derivatives of u, satisfies Div P ≥ 0 for all such x, u, if and only if Div p = Φ(x) ≥ 0 where Φ is independent of u. Applications to theories of continuum thermomechanics are discussed.
Distances in Gaussian point sets
Authors: Clifford Peter , Green N. J. B. 
Published: November 2008

AbstractThe joint distribution of the n(n− l)/2 distances between n normally distributed points in d dimensions is studied. Moment generating functions and probability density functions are obtained. It is shown that when n = d the squared distances are jointly exponentially distributed subject only to the constraint that a valid n point configuration is prescribed. In the case n = d = 3 the distributions of the ordered distance are obtained explicitly.
Projective actions, invariant sigma-curves and quadratic functional equations
Authors: McCarthy Patrick J. 
Published: November 2008

AbstractThe quadratic functional equation f(f(x)) *–Tf(x) + Dx = 0 is equivalent to the requirement that the graph be invariant under a certain linear map The induced projective map is used to show that the equation admits a rich supply of continuous solutions only when L is hyperbolic (T2 > 4D), and then only when T and D satisfy certain further conditions. The general continuous solution of the equation is given explicitly in terms of either (a) an expression involving an arbitrary periodic function, function additions, inverses and composites, or(b) suitable limits of such solutions.
Nonlinear random equations with maximal monotone operators in Banach spaces
Authors: Kravvaritis Dimitrios 
Published: November 2008

Let X be a real Banach space, X* its dual space and ω a measurable space. Let D be a subset of X, L: Ω × D → X* a random operator and η:Ω →X* a measurable mapping. The random equation corresponding to the double [L, η] asks for a measurable mapping ξ: Ω → D such thatRandom equations with operators of monotone type have been studied recentely by Kannan and Salehi [7], Itoh [6] and Kravvarits [8].
Central limit theorems for sums of extreme values
Authors: Csörgoő Sándor , Mason David M. 
Published: November 2008

AbstractGiven a sequence of non-negative independent and identically distributed random variables, we determine conditions on the common distribution such that the sum of appropriately normalized and centred upperknextreme values based on the firstnrandom variables converges in distribution to a normal random variable, wherekn→ ∞ andkn/n → 0 asn→ ∞. The probabilistic problem is motivated by recent statistical work on the estimation of the exponent of a regularly varying distribution function. Our main tool is a new Brownian bridge approximation to the uniform empirical and quantile processes in weighted supremum norms.
Knot surgery and primeness
Authors: Acuña Francisco González , Short Hamish 
Published: November 2008

The aim of this paper is to prove some new results towards answering the question: When does Dehn surgery on a knot give a non-prime manifold? This question has been raised on several occasions (see for instance [5] or [4]; concerning the latter see below). Recall that a 3-manifold is prime if, in any connected sum decompositionone of M1, M2 is S3. (For standard definitions of low-dimensional topology see [2] or [16].)
Asymptotically optimal sampling schemes for periodic functions
Authors: Dahmen W. , Micchelli C. A. , Smith P. W. 
Published: November 2008

In this paper we are concerned with the following question: Given a function class , the space of L2-one periodic complex valued functions, when does sampling a function give optimal information for approximation? To make this question precise, we introduce the quantity, where A is any mapping from ℝN and I is any continuous linear mapping from into ℝN.
Global analogues of the Brown–Grossman proper homotopy groups of an end
Authors: Hernandez L. J. , Porter T. 
Published: November 2008

AbstractThe Brown–Grossman proper homotopy groups at an end of a locally compact Hausdorff space,X, were introduced by E. M. Brown in 1974. In this note we define and study ‘global’ versions of these groups and compare these global groups with the groups ‘at infinity’. We also obtain several interlocking exact sequences relating these groups with the Hurewicz and Steenrod homotopy groups ofX.
Additivity and superadditivity in Lp-spaces
Authors: Bernau S. J. 
Published: November 2008

AbstractA simple proof is given that if X is a normed vector lattice, 1 ≼ p ≼ ∞, and the norm in X is p-additive, then the norm is p-superadditive if p < ∞. If p = ∞, then X satisfies Kakutani's classical M-space condition. The proof uses duality but is otherwise elementary.
On the global attractivity in a generalized delay-logistic differential equation
Authors: Gopalsamy K. 
Published: November 2008

The purpose of this article is to derive a set of ‘easily verifiable’ sufficient conditions for the local asymptotic stability of the trivial solution ofand then examine the ‘size’ of the domain of attraction of the trivial solution of the nonlinear system (1·1) with a countable number of discrete delays.
Laws of the iterated logarithm for sums of the middle portion of the sample
Authors: Haeusler Erich , Mason David M. 
Published: November 2008

AbstractLet X1, X2, …, be a sequence of independent random variables with common distribution function F in the domain of attraction of a stable law and, for each n ≥ 1, let X1, n ≤ … ≤ Xn, n denote the order statistics based on the first n of these random variables. It is shown that sums of the middle portion of the order statistics of the form , where (kn)n ≥ 1 is a sequence of non-negative integers such that kn → ∞ and kn/n → 0 as n → ∞ at an appropriate rate, can be normalized and centred so that the law of the iterated logarithm holds. The method of proof is based on the almost sure properties of weighted uniform empirical processes.
Singularities of convex-polygonally generated shape-densities
Authors: Le Hui-Lin 
Published: November 2008

AbstractIn earlier papers Kendall and Le[3,4] made a geometrical study of the structure and singularities of a convex-polygonally generated shape-density for any convex polygon K. The present work describes the singular tessellation T(K) in algebraic terms, and obtains explicit formulae for the ‘jump functions’ of m̃ across every edge of the tessellation. These results, combined with earlier work by Le[5] on the basic tile, make it possible to find m̃ explicitly in every tile by what we have called the ‘stepping-stone’ method. In a closing section the exact order of the differential singularity is found at the tile boundaries.
Multivariate Landau–Kolmogorov-type inequality
Authors: Ditzian Z. 
Published: November 2008

AbstractAssuming that the nth iterate of the Laplacian Δnf belongs to L∞(ℝ), we show for 0 < k < 2n thatwhere ∂/∂ξi is the derivative in the ei direction. The result is also extended to other Banach spaces of functions on ℝd.
Topological conjugation of Lorenz maps by β-transformations
Authors: Glendinning Paul 
Published: November 2008

AbstractNecessary and sufficient conditions for a Lorenz map to be topologically conjugate to a piecewise linear map with constant slope (a β-transformation) are given, first in terms of kneading invariants of the maps and then in terms of the topological entropy restricted to basic sets. The dynamics of β-transformations is also described.