bluuebunny/crossref_metadata_2025_split huggingface dataset:
Classical approximations to Gibbs states
Authors: Davies E. B. 
Published: November 2008

AbstractWe obtain two approximate representations of a one-particle Gibbs state, both of which become asymptotically exact in trace norm as m → ∞. The second representation is an integral of pure coherent states over phase space, and can therefore be regarded as a classical approximation to the Gibbs state. We also obtain a version of the second representation applicable to the microcanonical ensemble.
Periodic groups generated by finite amalgams
Authors: Hickin Kenneth K. , Phillips Richard E. , Plotkin J. M. 
Published: November 2008

The following embedding theorem was proved in the paper (7). Let Π be a set of primes and P, H and K periodic Π-groups satisfyingThen there is a period Π-group J generated by isomorphic copies of H and K such that P ≤ J.
Generalized Nörlund means and consistency theorems
Authors: Maddox I. J. 
Published: November 2008

It was recently shown in (1), corollary 1, that if (I) = (N, q) then I and (N, q) were consistent. By I we denote the unit infinite matrix, and (N, q) denotes a general complex Nörlund mean. The summability field (A) of any infinite matrix A = (ank) is defined aswhere c is the space of convergent sequences. The summability field of (N, q) is, for simplicity, written as (N, q) instead of ((N, q)).
On elastic waves from a finite line-source
Authors: Viswanathan K. 
Published: November 2008

AbstractHazebroek's problem of a finite line-source in an infinite elastic medium is reconsidered. Here the object is to present a simpler method of solution by treating bhe line-source as equivalent to an appropriate distribution of point sources over the surface of a prolate spheroid which degenerates into this line in the limit when its minor axis tends to zero. This is achieved by using the property of Green's functions. The solution thus obtained is verified to be identical with that derived by Hazebroek.
Norm and spectral radius for algebraic elements of a Banach algebra
Authors: Young N. J. 
Published: November 2008

The purpose of this note is to show that, for any algebraic element a of a Banach algebra and certain analytic functions f, one can give an upper bound for ‖f(a)‖ in terms of ‖a‖ and the spectral radius ρ(a) of a. To illustrate the nature of the result, consider the norms of powers of an element a of unit norm. In general, the spectral radius formulacontains all that can be said (that is, the limit ρ(a) can be approached arbitrarily slowly). If we have the additional information that a is algebraic of degree n we can say a good deal more. In the case of a C*-algebra we have the neat result that, if ‖a‖ ≤ 1,(see Theorem 2), while for a general Banach algebra we have at least
Constitutive surfaces in fluid mechanics
Authors: Sewell M. J. , Porter D. 
Published: November 2008

AbstractThe new concept of a constitutive surface is introduced into inviscid fluid mechanics, with special reference to compressible gas dynamics and to shallow water theory. The detailed shape of such surfaces is calculated, including the manner of their transition across singularities where the Mach or Froude number passes through unity. The calculation draws upon recent work describing the transition of a Legendre transformation through its singularity. For example, mass flow Q, total energy h and flow stress P are always related by part of a ‘swallowtail’ surface, regardless of the particular motion.The addition of dynamical conditions defines particle history tracks which always lie on constitutive surfaces even for unsteady flow, except that they may jump from one part to another of such a surface when shock waves or hydraulic jumps are passed through.Illustrations given include the steady flow of a general gas through a standing normal shock, general shallow water theory, and flow along a sloping-sided channel. Connections with existing literature are described.
How to solve a quadratic equation in integers
Authors: Grunewald Fritz J. , Segal Daniel 
Published: November 2008

In answer to a question posed by J. L Britton in (2), we sketch in this note an effective procedure to decide whether an arbitrary quadratic equationwith rational coefficients, has a solution in integers. A similar procedure will in fact decide whether such an equation over a (suitably specified) algebraic number field k has a solution in any (suitably specified) order in k; but we shall not burden the exposition by giving chapter and verse for this claim.
Characterizing the rate of convergence in the central limit theorem. II
Authors: Hall Peter 
Published: November 2008

AbstractWe obtain upper and lower bounds of the same order of magnitude for the error between the distribution of a sum of independent and identically distributed random variables, and a normal approximation by a portion of a Chebychev-Cramér series. Our results are sufficiently general to contain the familiar characterizations by Ibragimov(4), Heyde and Leslie (3) and Lifshits(5), and complement some of those obtained earlier by the author (2).
3-primary exponents
Authors: Neisendorfer Joseph A. 
Published: November 2008

The purpose of this paper is to show that 3n annihilates the 3-primary component of the homotopy groups of the 2n + 1-dimensional sphere. In the terminology of (2) and (3), S2n+1 has exponent 3n at 3.In fact, a stronger result is proved. Localize at 3 and let Ω2nS2n + 1〈2n + 1〉 denote the 2n-fold loop space of the 2n + 1-connected cover of S2n+1. Then Ω2nS2n + 1〈2n + 1〉 has a null homotopic 3n-th power map.
Homomorphs and wreath product extensions
Authors: Förster Peter 
Published: November 2008

A homomorph is a class of (finite soluble) groups closed under the operation Q of taking epimorphic images. (All groups considered in this paper are finite and soluble.) Among those types of homomorphs that have found particular interest in the theory of finite soluble groups are formations and Schunck classes; the reader is referred to (2), § 2, for a definition of those classes. In the present paper we are interested in homomorphs satisfying the following additional closure property:(W0) if A is abelian with elementary Sylow subgroups, then each wreath product A G (with respect to an arbitrary permutation representation of G) with G ∊ is contained in .
Asymptotic analysis of the Cooke-Noble integral equation
Authors: Rose L. R. F. 
Published: November 2008

Those mixed boundary-value problems which can usefully be treated analytically often lead to the following mathematical problem. Two functions u(x), σ(x), defined over the interval ([0, ∞), take prescribed values over complementary portions of that interval; specifically, letwhere p(x) is usually a simple function, for example a constant or a power of x. There exists a relation between u(x) and σ(x) which can be most simply expressed as a relation between their Hankel transforms. Using a circumflex to denote the Hankel transform, for example withwhere Jv denotes as usual the Bessel function of the first kind of order v, we can state that relation between u and σ as follows:where A(ξ) is a known function, determined at an earlier stage of the analysis. The problem is to derive u(x) for (xє [ 0, a), or σ(x) for x є (a, ∞).
The singularities of H-space
Authors: Tod K. P. 
Published: November 2008

The non-linear graviton construction of Penrose (9) and the ℋ-space construction of Newman (6) are two complementary techniques for constructing complex four dimensional space-times with quadratic metric and anti-self-dual curvature tensor.In the former, the space-time is the space of holomorphic sections of a complex fibre space obtained by deforming part of flat twistor space. In the latter the space-time is the space of regular solutions of a differential equation, the good cut equation.Pathologies arise in the non-linear graviton construction when the normal bundle of a holomorphic section changes. This is reflected in the ℋ-space construction by a change in the character of the solutions of the linearized good cut equation, the Newman equation.
On a theorem of Wielandt concerning simply primitive groups
Authors: Jones G. A. , Soomro K. D. 
Published: November 2008

Let G be a simply primitive permutation group on a set Ω of order p2, where p is a prime (necessarily odd). In theorem 27·2 of (9), Wielandt states without proof:Theorem A. (i) ¦G¦ is not divisible by p3;(ii) if G has a pair of Sylow p-subgroups with nontrivial intersection, then G has an imprimitive subgroup of index 2 which is the direct product of two intransitive groups.
On subordinated distributions and random record processes
Authors: Embrechts P. , Omey E. 
Published: November 2008

AbstractConsider a sequence of i.i.d. random variables attached to the points of an independent point process. The random record process is the process of epochs of successive maxima in this sequence. Various limit theorems are proved for the distribution of times to successive records and interrecord times. Some new results on the tail-behaviour of subordinated distributions are needed.
On a conjecture of Watson
Authors: Raka Madhu 
Published: November 2008

Let Qn be a real indefinite quadratic form in n variables x1, x2,…, xn, of determinant D ≠ 0 and of type (r, s), 0 < r < n, n = r + s. Let σ denote the signature of Qn so that σ = r − s. It is known (see e.g. Blaney(4)) that, given any real numbers c1 c2, …, cn, there exists a constant C depending upon n and σ only such that the inequalityhas a solution in integers x1, x2, …, xn. Let Cr, s denote the infimum of all such constants. Clearly Cr, s = Cs, r, so we need consider non-negative signatures only. For n = 2, C1, 1 = ¼ follows from a classical result of Minkowski on the product of two linear forms. When n = 3, Davenport (5) proved that C2, 1 = 27/100. For all n and σ = 0, Birch (3) proved that Cr, r = ¼. In 1962, Watson(18) determined the values of Cr, s for all n ≥ 21 and for all signatures σ. He proved thatWatson also conjectured that (1·2) holds for all n ≥ 4. Dumir(6) proved Watson's conjecture for n = 4. For n = 5, it was proved by Hans-Gill and Madhu Raka(7, 8). The author (12) has proved the conjecture for σ = 1 and all n. In the preceding paper (13) we proved that C5, 1 = 1. In this paper we prove Watson's conjecture for σ = 2, 3 and 4.
Multiple images of stochastic processes
Authors: Berman Simeon M. 
Published: November 2008

AbstractA simple sufficient condition is given for a stochastic process x(t), 0 ≤ t ≤ 1, to have the following property: There is an integer m ≥ 2 such that for any non-degenerate subinterval J ⊂ [0, 1], there exist m disjoint subintervals I1, …, Im ⊂ J such that the intersection of the images of I1,…, Im under the mapping by x(·) has positive Lebesgue measure, almost surely. There is also a version for vector random fields; and the main result is shown to apply to large classes of processes.
Some applications of Maz'ja's uniqueness theorem to a class of linear water wave problems
Authors: Hulme Andrew 
Published: November 2008

AbstractThis paper describes a criterion which, if satisfied, guarantees uniqueness of solution for the problem involving the radiation or diffraction of small amplitude water waves by a totally submerged body. This criterion was originally stated by a Russian mathematician, V. G. Maz'ja, although his work does not appear to be widely known. For this reason a brief outline of Maz'ja's proof is given here, together with a discussion of the condition to be satisfied by the submerged body.Maz'ja's criterion is not satisfied by all submerged bodies and so his result does not provide a general proof of uniqueness. However, the criterion is satisfied in some important cases and examples are presented here. The partial nature of this result is due entirely to the method of proof and not to any intrinsic difficulty with the underlying hydrodynamics.
The transient behaviour of the Moran model in population genetics
Authors: Donnelly Peter 
Published: November 2008

AbstractThis paper presents an alternative analysis of the behaviour of the Moran model. Using some of the techniques developed in the study of interactive particle systems, a process which is dual to the Moran model is constructed. Exact analysis of this dual process is considerably easier than for the original model. Because of the relationship between the two processes it is then possible to find the distribution of the Moran model.
A dualizing complex for Stanley–Reisner rings
Authors: Gräbe Hans-Gert 
Published: November 2008

AbstractIn this paper we construct a (multihomogeneous) dualizing complex for A [Δ], the Stanley–Reisner ring of Δ over an arbitrary commutative noetherian ring A with identity, admitting a dualizing complex. In addition, some consequences are discussed.
Projections and embeddings of locally convex operator spaces and their duals
Authors: Fourie Jan H. , Ruckle William H. 
Published: November 2008

AbstractLet E, F be Hausdorff locally convex spaces. In this note we consider conditions on E and F such that the dual space of the space Kb (E, F) (of quasi-compact operators) is a complemented subspace of the dual space of Lb (E, F) (of continuous linear operators). We obtain necessary and sufficient conditions for Lb(E, F) to be semi-reflexive.
Complex strict and uniform convexity and hyponormal operators
Authors: Mattila Kirsti 
Published: November 2008

Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. The (spatial) numerical range of an operator TεB(X) is defined as the setIf V(T) ⊂ ℝ, then T is called hermitian. More about numerical ranges may be found in [8] and [9].
Generalized translations associated with an unbounded self-adjoint operator
Authors: Fishel B. 
Published: November 2008

Delsarte [2], Povzner [9], Levitan [8], Leblanc [7], Dunford and Schwartz [3] (p. 1626) and Hutson and Pym [5] have discussed generalized translation operators (GTO) ‘associating with a differential operator’. The latter authors have also considered the topic in an abstract setting-the GTO ‘associates’ with a compact operator in a normed space. GTO are to have properties generalizing those of the translation operators defined by members of a group on a vector space E of functions defined on the group:(πεE, s and t are group elements). In the case of a locally compact topological group the integration spaces E = L1,L2,L∞, for a Haar measure of the group, are of especial interest.
A computation of the Littlewood exponent of stochastic processes
Authors: Blei Ron C. , Kahane J.-P. 
Published: November 2008

A stochastic process X = {X(t): t ∈ [0, 1]} on a probability space (Ω, , ℙ) is said to have finite expectation if the function defined on the measureable rectangles in Ω × [0, 1] byfor A ∈ and (s, t) ⊂ [0, 1] gives rise to a complex measure in each of its two coordinates (see [1], definition 1·1). Equivalently, X has finite expectation ifis finite. The function defined by (1), effectively a generalization of the Doléans measure (see e.g. [4] pp. 33–35), is extendible to a bona fide complex measure on Ω × [0, 1] if and only if its ‘total variation’
A geometric criterion for decomposition and multivalence
Authors: Abu-Muhanna Y. , Lyzzaik A. 
Published: November 2008

AbstractWe give a quite general geometric criterion for a function analytic in the unit disc to be a polynomial of a univalent function, and hence a criterion for multivalence. We believe that this is the essence why multivalent close-to-convex functions enjoy the latter decomposition property. As another application, we study, as suggested by T. Sheil-Small ‘9’, the geometry of classes of analytic functions which arise from his recent investigation of multivalent harmonic mappings.
The packing measure of the graphs and level sets of certain continuous functions
Authors: Rezakhanlou Fraydoun 
Published: November 2008

AbstractThe relationship between the local growth of a continuous function and the packing measure of its level sets and of its graph is studied. For the Weierstrass function with b an integer such that b ≥ 2 and with 0 < α < 1, and for x ∈ Range (W) outside a set of first category, the level set W−1(x) has packing dimension at least 1 − α. Furthermore, for almost all x ∈ Range (W), the packing dimension of f is at most 1 − α. Finer results on the occupation measure and the size of the graph of a continuous function satisfying the Zygmund Λ-condition are obtained.
Characterization of matrix probability distributions by mean residual lifetime
Authors: Jupp P. E. 
Published: November 2008

The mean residual lifetime of a real-valued random variable X is the function e defined byOne of the more important properties of the mean residual lifetime function is that it determines the distribution of X. See, for example, Swartz [10]. References to related characterizations are given by Galambos and Kotz [3], pages 30–35. It was established by Jupp and Mardia[6] that this property holds also for vector-valued X. As (1·1) makes sense if X is a random symmetric matrix, it is natural to ask whether the property holds in this case also. The purpose of this note is to show that, under certain regularity conditions, the distributions of such matrices are indeed determined by their mean residual lifetimes.
Presentations for (G, s)-transitive graphs of small valency
Authors: Weiss Richard 
Published: November 2008

Given a groupG, a subgroupHand an elementa∈G, we define Γ(G, H, a) to be the graph on the set of left-cosets ofHinG, where two left-cosetsg1Handg2Hare adjacent whenever. We will consider this construction only in the case thatThe first of these conditions assures that adjacency is a symmetric relation (i.e. that Γ(G, H, a) is an undirected graph) and the second assures that Γ(G, H, a) is connected.
Fitting functors in finite solvable groups: II
Authors: Beidleman James C. , Brewster Ben , Hauck Peter 
Published: November 2008

This paper is a continuation of [1], where we introduced the concept and investigated the basic properties of Fitting functors for finite solvable groups. We recall that a map f which assigns to each finite solvable group G a non-empty set f(G) of subgroups of G is called a Fitting functor if the following property is satisfied: whenever α: G → H is a monomorphism with α(G) ⊴ H, thenThe most prominent examples of conjugate Fitting functors are provided by injectors of Fitting classes. However, Fitting functors f in general do not behave as nicely as injectors. For instance, f(G) need not consist of pronormal subgroups of a group G (cf. [1], 4·3).
Coupled stationary bifurcations in non-flux boundary value problems
Authors: Armbruster D. , Dangelmayr G. 
Published: November 2008

AbstractCoupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov–Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in ℂ2 of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.
Some sign properties of symmetric functions
Authors: Hunter D. B. , Macdonald I. G. 
Published: November 2008

AbstractThis paper is concerned with the sign properties of the S-functions sλ for real arguments. We show first that sλ is indefinite if any part of the partition λ is odd. Thus it is only if all parts of λ are even that sλ can possibly be positive definite or semi-definite. In this case we show that sλ(x) is positive provided that at least l(λ) of the components of x are non-zero, where l(λ) is the number of parts of the partition λ.
KMS states for reduced groups, theta functions and the Powers–Størmer construction
Authors: Hannabuss K. C. 
Published: November 2008

AbstractKMS states of a twisted convolution algebra of Schwartz functions on a vector group are classified and related to KMS states of twisted L1-algebras for certain subquotients. The KMS states for the subquotient algebras are also related to Fock states of vector groups. In the particular case of the subquotient Tn × ℤn of ℚ2n this links the Fock space construction of the theta functions with their appearance in KMS states of loop groups and in the Kac character formula.
The function field abstract prime number theorem
Authors: Cohen Stephen D. 
Published: November 2008

For arithmetical semigroups modelled on the positive integers, there is an ‘abstract prime number theorem’ (see, for example, [1]). In order to study enumeration problems in the several arithmetical categories whose prototype instead is the ring of polynomials in an indeterminate over a finite field of order q, Knopfmacher[2, 3] introduced the following modification. An additive arithmetical semigroup G is a free commutative semigroup with an identity, generated by a countable set of ‘primes’ P and admitting an integer-valued degree mapping ∂ with the properties(i) ∂(l) = 0,∂(p) > 0 for p∈P;(ii) ∂(ab) = ∂(a) + ∂(b) for all a, b in G;(iii) the number of elements in G of degree n is finite. (This number will be denoted by G(n).)
Far field patterns and inverse scattering problems for imperfectly conducting obstacles
Authors: Angell T. S. , Colton David , Kress Rainer 
Published: November 2008

AbstractWe first examine the class of far field patterns for the scalar Helmholtz equation in ℝ2 corresponding to incident time harmonic plane waves subject to an impedance boundary condition where the impedance is piecewise constant with respect to the incident direction and continuous with respect to x ε ∂ D where ∂ D is the scattering obstacle. We then examine the class of far field patterns for Maxwell's equations in subject to an impedance boundary condition with constant impedance. The results obtained are used to derive optimization algorithms for solving the inverse scattering problem.
The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field
Authors: Flynn Eugene Victor 
Published: November 2008

AbstractAn embedding of the Jacobian variety of a curve of genus 2 is given, together with an explicit set of defining equations. A pair of local parameters is chosen, for which the induced formal group is defined over the same ring as the coefficients of . It is not assumed that has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field (of characteristic ╪ 2, 3, or 5).
Selections of multivalued maps and shape domination
Authors: Sanjurjo José M. R. 
Published: November 2008

AbstractSome results are presented which establish connections between shape theory and the theory of multivalued maps. It is shown how to associate an upper-semi-continuous multivalued map F: X → Y to every approximative map f = {fk, X → Y} in the sense of K. Borsuk and it is proved that, in certain circumstances, if F is ‘small’ and admits a selection, then the shape morphism S(f) is generated by a map, and if F admits a coselection then S(f) is a shape domination.
On the computational complexity of the Jones and Tutte polynomials
Authors: Jaeger F. , Vertigan D. L. , Welsh D. J. A. 
Published: November 2008

AbstractWe show that determining the Jones polynomial of an alternating link is #P-hard. This is a special case of a wide range of results on the general intractability of the evaluation of the Tutte polynomial T(M; x, y) of a matroid M except for a few listed special points and curves of the (x, y)-plane. In particular the problem of evaluating the Tutte polynomial of a graph at a point in the (x, y)-plane is #P-hard except when (x − 1)(y − 1) = 1 or when (x, y) equals (1, 1), (−1, −1), (0, −1), (−1, 0), (i, −i), (−i, i), (j, j2), (j2, j) where j = e2πi/3