bluuebunny/crossref_metadata_2025_split huggingface dataset:
The space group corepresentations of antiferromagnetic NiO
Authors: Cracknell A. P. , Joshua S. J. 
Published: November 2008

AbstractThe geometry of the Brillouin zone of antiferromagnetic NiO (Cc2/c) is studied. The corepresentations of the magnetic little group are deduced for the points and lines of symmetry. The magnon symmetries are investigated and the selection ruies for two magnon electric dipole and magnetic dipole absorption are deduced.
A note on magnetohydrodynamic duct flow
Authors: Butler G. F. 
Published: November 2008

AbstractThis paper is concerned with the problem of the flow of an incompressible electrically conducting fluid along a rectangular duet under a transverse magnetic field. The case in which the walls perpendicular to the field are perfectly conducting and those parallel to the field are non-conducting has been considered by Hunt (1), who derives the solution in two ways; as the limiting cases of the flows with (a) non-conducting walls parallel and thin walls of arbitrary conductivity perpendicular to the field, and (b) thin walls of arbitrary conductivity parallel and perfectly conducting walls perpendicular to the field. We show that these two limiting solutions derived by Hunt are in fact equivalent. In addition, we extend the solution of case (b) above by removing the thin wall restriction.
A Tauberian theorem for absolute summability
Authors: Das G. 
Published: November 2008

Let be the given infinite series with {sn} as the sequence of partial sums and let be the binomial coefficient of zn in the power series expansion of the function (l-z)-σ-1 |z| < 1. Now let, for β > – 1,converge for 0 ≤ x < 1. If fβ(x) → s as x → 1–, then we say that ∑an is summable (Aβ) to s. If, further, f(x) is a function of bounded variation in (0, 1), then ∑an is summable |Aβ| or absolutely summable (Aβ). We write this symbolically as {sn} ∈ |Aβ|. This method was first introduced by Borwein in (l) where he proves that for α > β > -1, (Aα) ⊂ (Aβ). Note that for β = 0, (Aβ) is the same as Abel method (A). Borwein (2) also introduced the (C, α, β) method as follows: Let α + β ╪ −1, −2, … Then the (C, α, β) mean is defined by
Mean field approximations to Couette flow and its stability
Authors: Bradley Roy 
Published: November 2008

AbstractThe preferred-mode method of Roberts (11) is applied to the stability of liquid contained between coaxial cylinders, the inner of which is rotating. Accordingly the velocity field of a steady Taylor vortex is approximated by a truncated Fourier series and the steady state corresponding to a chosen wave number is obtained. The stability of a steady state so obtained is investigated:(a) With respect to an axisymmetric perturbation associated with a Taylor vortex of a different axial wave number, so that a stable or ‘ preferred ’ steady state is determined. This is done for a narrow gap, η (the ratio of the radii of the cylinders) = 0·95, for Taylor numbers up to 40%, and for a wide gap, η = 0·5, up to 30% beyond the critical values.(b) For a narrow gap, η = 0·95, with respect to a non-axisymmetric perturbation of a different axial wave number. The solutions obtained for the steady states are found to be stable to such perturbations for a range of Taylor numbers 40% beyond the critical value.
On hearing the shape of a drum: further results
Authors: Stewartson K. , Waechter R. T. 
Published: November 2008

1. Introduction. The underlying problem is to deduce the shape of a drum or plane uniform membrane from the knowledge of its spectrum of eigenvalues ωn = i√λn. It has been shown by Kac(3) that some progress is possible on establishing the leading terms of the asymptotic expansion of the trace function for small positive t. In particular, for a simply connected membrane Ω bounded by a smooth convex curve Γ for which the displacement satisfies the wave equation ∇2ø = ∂2ø/∂t2 and Dirichlet conditions on Γwhere |Ω| = area of Ω, L = length of Γ, and the constant ⅙ is determined (apart from a factor) on integrating the curvature of the boundary; moreover, if Ω is permitted to have a finite number of smooth convex holes then the constant becomes ⅙(1–r), where r = number of holes.
Harmonic analysis of scalar and vector fields inn
Authors: Smith J. Denmead 
Published: November 2008

AbstractIt is shown that a real scalar function innwhich is of classCnand either has zero mean on all spheres of unit radius, or has zero mean in all balls of unit radius admits a unique expansion in terms of eigenfunctions of the Laplacian operator. In a similar manner, a suitably smooth vector-valued function innwhich has zero flux through all spheres cf unit radius is shown to be decomposable as the sum of a solenoidal part and a series of conservative parts that are eigenfunctions of the Laplacian. Applications are given, including some in complex analysis.
An eigenvalue problem for elastic contact with finite friction
Authors: Spence D. A. 
Published: November 2008

AbstractThe two-dimensional indentation of an elastic half space by a rigid punch under a slowly applied normal load is considered, for the case in which there is a finite coefficient of friction μ between the surfaces. The contact area is then divided into an inner adhesive region −c<x<cin which the surface displacements are known, surrounded by regionsc< |x| < 1 in which the friction is limiting and the lateral displacement (which must increase in proportion to the overall load) is not known in advance. The problem is formulated in terms of a coupled pair of singular integral equations for the normal and shear stresses σ and τ at the surface; these are combined to give a single homogeneous Fredholm equation with positive kernel for a quantity π proportional to the difference τ – μσ in the adhesive region. The largest eigenvalue of this equation, for which π > 0, gives the adhesive boundarycin terms of μ and Poisson's ratio ν. A similarity transformation shows thatchas the same value for both flat-faced and power law punches.
Measures vanishing off the symmetric maximal ideals of M(G)
Authors: Graham Colin C. 
Published: November 2008

AbstractWe show that if μ is a measure on the LCA group G whose Gelfand transform vanishes off the set Σ of symmetric maximal ideals, then μ µ M0(G), that is, then the Fourier-Steiltjes transform of μ vanishes at infinity. This result is then used to show μ µ L1(G)½.
Inextensible Riesz spaces
Authors: Fremlin D. H. 
Published: November 2008

My aim in this paper is to give an abstract characterization of the C∞ spaces described in (6) or (9), and to develop some of the remarkable special properties of these spaces. Although the subject is in some ways highly specialized, inextensible and sequentially inextensible spaces seem common enough (they include all spaces of the forms Rx and L0) to be worth studying, and I have already employed them in the proof of more general results (1).In the first section I set out those properties that can be described in simple Riesz space terms; much of this work has already been published in slightly different forms. In the second part I go on to questions that arise when we impose a topology on an inextensible Riesz space. Finally, in the third section, I discuss some problems, arising from the work before, which are related to the famous measurable cardinal problem.
Physical interpretation of N.U.T. metric
Authors: Sackfield A. 
Published: November 2008

AbstractA metric is constructed, which represents the gravitational field of two spherical static bodies of masses +b and −b, together with a massless source of angular momentum between them. When the separation of the two masses is allowed to tend to infinity the N.U.T. metric can be obtained from the limiting process. This supports the view that the N.U.T. solution represents a static Schwarzschild body together with a rotating semi-infinite spike of pure angular momentum.
The groups of the generalized Petersen graphs
Authors: Frucht Roberto , Graver Jack E. , Watkins Mark E. 
Published: November 2008

1.Introduction. For integersnandkwith 2 ≤ 2k <n, thegeneralized Petersen graph G(n, k)has been defined in (8) to have vertex-setand edge-setE(G(n, k))to consist of all edges of the formwhereiis an integer.All subscripts in this paper are to be read modulo n, where the particular value ofnwill be clear from the context. ThusG(n, k)is always a trivalent graph of order 2n, andG(5, 2) is the well known Petersen graph. (The subclass of these graphs withnandkrelatively prime was first considered by Coxeter ((2), p. 417ff.).)
Greatest common divisor of several polynomials
Authors: Barnett S. 
Published: November 2008

AbstractGiven a polynomial a(λ) with degree n, and polynomials b1(λ), …, bm(λ) of degree not greater than n – 1, then the degree k of the greatest common divisor of the polynomials is equal to the rank defect of the matrix R = [b1(A), b2(A), …, bm(A)], where A is a suitable companion matrix of a(λ). Furthermore, it is shown that if the first k rows of R are expressed as linear combinations of the remaining n – k rows (which are linearly independent) then the greatest common divisor is given by the coefficients of row k + 1 in these expressions. A simple expression is derived for R and a permutation of the columns of this matrix establishes a direct connexion with controllability of a constant linear control system. Finally, when m = 1 a relationship between the corresponding R and Sylvester's matrix is exhibited.
On the forced surface waves due to a vertical wave-maker in the presence of surface tension
Authors: Rhodes-Robinson P. F. 
Published: November 2008

AbstractThe classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.
On dual summability methods
Authors: Kuttner B. 
Published: November 2008

1. Let A be a summability method given by the sequence-to-sequence transformationWe suppose throughout that, for each nconverges; this is a much weaker assumption than the regularity of A. Then we defineWe also suppose throughout that the sequence {sk} is formed by taking the partial sums of the series Σak; that is to say thatLet A' denote the summability method given by the series-to-sequence transformationFollowing Lorent and Zeller (4), (5), we describe A, A' as dual summability methods. We recall that formally,
On Teh's construction of orders in Abelian groups
Authors: Minassian Donald P. 
Published: November 2008

AbstractA claim of H. H. Teh on Archimedean full orders ((2), ‘only if’ of Theorem 2, p. 480) fails. His statement (p. 478, line 5) that the direct product of n copies of the additive rational numbers admits no full order of Archimedean rank more than n is proved without Hahn's embedding theorem. A few other remarks are made.
Wave-front singularities for two-dimensional anisotropic elastic waves
Authors: Payton Robert G. 
Published: November 2008

AbstractWave-front singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d–½ where d measures distance away from the front. However, in certain exceptional cases singularities of order d–-n where n = ¼, ⅔, ¾, may be encountered.
Discrete spectra criteria for singular differential operators with middle terms
Authors: Hinton Don B. , Lewis Roger T. 
Published: November 2008

Let l be the differential operator of order 2n defined bywhere the coefficients are real continuous functions and pn > 0. The formally self-adjoint operator l determines a minimal closed symmetric linear operator L0 in the Hilbert space L2 (0, ∞) with domain dense in L2 (0, ∞) ((4), § 17). The operator L0 has a self-adjoint extension L which is not unique, but all such L have the same continuous spectrum ((4), § 19·4). We are concerned here with conditions on the pi which will imply that the spectrum of such an L is bounded below and discrete.
Stationary gravity waves on non-uniform free streams: jet-like streams
Authors: Peregrine D. H. , Smith Ronald 
Published: November 2008

AbstractThe basic state considered in this paper is a parallel flow of a jet-like character with the centre of the jet being at or near a free surface which is horizontal. Stationary surface gravity waves may exist on such a flow, and a number of examples are looked at for small amplitude waves. Explicit solutions are given for ‘top-hat’ profile jets and for two-dimensional flows. Asymptotic solutions are developed for stationary waves of large wave-number.
The Schwarzian derivative and estimates of functions analytic in the unit disc
Authors: Essén Matts , Keogh F. R. 
Published: November 2008

Suppose that w is analytic in the open unit disc Δ in the z-plane. The Schwarzian derivative of w is defined by(for basic properties of {w, z} we refer to Hille ((3), p. 375)). Let denote the class of functions w which are analytic in Δ and satisfy the conditions
On a class of Volterra and Fredholm non-linear integral equations
Authors: Bushell P. J. 
Published: November 2008

This paper concerns the existence and uniqueness of non-negative solutions of non-linear Volterra integral equations of the typeandwhere the kernel function k(.,.) is non-negative and sufficiently smooth, and either 0 < p < 1 or – 1 < p < 1. We will consider also the corresponding Fredholm equationsand
Deterministic epidemic waves
Authors: Atkinson C. , Reuter G. E. H. 
Published: November 2008

In the well-known deterministic model for the spread of an epidemic, one considers a population of uniform density along a line and divides the population into three classes: susceptible but uninfected, infected and infectious, infected but removed. If we denote space and time variables by s, t and let x(s, t), y(s, t), z(s, t) be the proportions of the population at (s, t) in these three classes, then x + y + z = 1 and we suppose thatHere Ῡ(s, t) denotes a space average ∫ y(s + σ) p(σ) dσ, where p is a probability density function; b is the removal rate; the scale of t has been adjusted to remove a constant that would otherwise occur in (1).
A simple proof of an identity of Good
Authors: Groeneveld J. , Kampen N. G. Van 
Published: November 2008

Recently, Good discovered the following curious identity (1). Let θ be a real-valued random variable having cumulants Km ≡ Km(θ) (m = 1, 2, …). Take a set of m statistically independent variables θ(1), θ(2), …, θ(m), each with the same distribution as θ, and form the random variablewhere ω is any primitive mth root of unity (e.g. ω = e2πi/m). Thenwhere 〈.〉 denotes expectation.
The forced two dimensional oscillations of a rigid strip in smooth contact with a semi-infinite elastic solid
Authors: Wickham G. R. 
Published: November 2008

AbstractIn this paper we investigate a time harmonic plane strain problem in a homogeneous isotropic semi-infinite elastic solid with mixed boundary conditions on its surface. The boundary is free from applied stress apart from on an infinite strip where the tangential components of stress are zero, and the normal component of displacement is a prescribed function. By reducing the mixed boundary value problem to the solution of a Fredholm integral equation of the second kind, an existence theorem is proved and a simple low frequency asymptotic formula relating the normal stress to the prescribed displacement is derived rigorously. The results are applied to the forced heaving and rocking motion of a rigid cylindrical body in smooth contact with an elastic half space. Some further applications to scattering problems are suggested.
Weakly compactly generated locally convex spaces
Authors: Hunter Richard J. , Lloyd John 
Published: November 2008

AbstractLocally convex spaces which are generated by a weakly compact subset (or a sequence of weakly compact subsets) and their subspaces are studied. Various characterizations and the permanence properties of these spaces are obtained. Certain results valid for weakly compactly generated Banach spaces are extended. These spaces are shown to have sequential properties which extend well-known properties of separable locally convex spaces.
Harmonic balance and the Hopf bifurcation
Authors: Allwright D. J. 
Published: November 2008

SummaryA form of the Hopf bifurcation theorem specially suited to systems in block-diagram form has been developed, which allows one to deal with high or infinite order linear elements solely in terms of their transfer functions. The results are proved by the method of harmonic balance, and, for general non-linear systems, lead to criteria for the existence and stability of bifurcated orbits generalizing those derived by various authors for systems of ordinary differential equations. In the particular case of control loops with a single non-linearity, a simple addition to the Nyquist diagram of the loop determines the amplitude and frequency of bifurcated orbits, and whether they occur when the equilibrium is stable or unstable. The analysis is independent of the central manifold theorem, and of Floquet theory.
Overstable convection in a horizontally heated rotating fluid
Authors: Daniels P. G. , Stewartson K. 
Published: November 2008

AbstractFluid is contained in a rotating annulus of rectangular cross-section which is subject to a radial temperature gradient along the base and is insulated around its upper surfaces. If E is an Ekman number, which is assumed small, a finite amplitude cellular motion of wavelength ∼ E⅓ develops near the inner sidewall of the annulus by an exchange process if the local Rayleigh number, R, exceeds its critical value Rc and the Prandtl number of the fluid, σ, is greater than a critical value, σc (Daniels and Stewartson(5)). In the present study we consider the remaining range of values 0 < σ < σc for which overstability is preferred, occurring at a value of the Rayleigh number, Rc0, less than Rc. Disturbances to the basic flow near the sidewall now oscillate in time with frequency ∼ E⅓ and are amplified if R exceeds Rc0, the vertical cellular velocity attaining values ∼ E in a region of extent ∼ E near the sidewall. On the time-scale ∼ E disturbances take the form of two wave-like components which travel in opposite directions with the characteristic group velocity of the system. The first is simply convected away from the sidewall into the stably stratified interior and decays, while the second travels towards the sidewall where it is reflected. The reflexion coefficient is determined by the dynamics of an E⅓ boundary layer where an oscillatory motion is generated by the incident wave.
A counter-example in summability theory
Authors: Kuttner B. 
Published: November 2008

Let Σ denote the set of all seriesof complex numbers. By a ‘summability method’, say A, we mean a function from some subset (the set of ‘A -summable series’) of Σ into the set of complex numbers. We will use the language generally associated with this definition, and will take for granted the case in which A is (C, 1). A summability method A will be called linear if, whenever a, b are A -summable, then so is λa + μb (where λ, μ are any complex constants) and if the. A -sums of a, b, λa + μb are then related in the natural way. We call A regular if, whenever a converges to σ, it is A -summable to σ. If A is a regular summability method, then any condition P on the series (1) will be called a Tauberian condition for A if any A -summable series which satisfies P is convergent.
Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes
Authors: Beem John K. , Ehrlich Paul E. 
Published: November 2008

AbstractWe consider globally hyperbolic spacetimes (M, g) of dimension ≥ 3 satisfying the curvature condition Ric (g) (v, v) ≥ 0 for all non-spacelike tangent vectors v in TM. This curvature condition arises naturally as an energy condition in cosmology. Suppose (M, g) admits a smooth globally hyperbolic time function h: M → such that for some t0, the Cauchy surface h−1(t0) satisfies the strict curvature condition Ric (g) (v, v) > 0 for all non-spacelike v attached to h−1(t0). Then M admits a metric g′ conformal to g satisfying the strict curvature condition Ric (g′) (v, v) > 0 for all non-spacelike v in TM. If the curvature and strict curvature conditions are restricted to null vectors, the analogous result may be obtained. Similar results may also be obtained for the scalar curvature in dimension ≥ 2 and for non-positive Ricci curvature.
Some results concerning linear codes and (k, 3)-caps in three-dimensional Galois space
Authors: Hill Raymond 
Published: November 2008

AbstractThe packing problem for (k, 3)-caps is that of finding (m, 3)r, q, the largest size of (k, 3)-cap in the Galois space Sr, q. The problem is tackled by exploiting the interplay of finite geometries with error-correcting codes. An improved general upper bound on (m, 3)3 q and the actual value of (m, 3)3, 4 are obtained. In terms of coding theory, the methods make a useful contribution to the difficult task of establishing the existence or non-existence of linear codes with certain weight distributions.
On the exterior problems of acoustics: II
Authors: Ursell F. 
Published: November 2008

AbstractThe exterior problems of acoustics can be reduced to the solution of Fredholm integral equations of the second kind in many different ways. Some of these equations break down at certain values of the wavenumber but this difficulty can be reduced or even removed altogether by choosing a different (usually more complicated) integral equation. The present paper is concerned with a class of equations proposed recently by D. S. Jones. It is shown that the proof of one of his principal results can be much shortened.
Subsequence principles for vector-valued random variables
Authors: Garling D. J. H. 
Published: November 2008

1. Introduction. Révész(8) has shown that if (fn) is a sequence of random variables, bounded in L2, there exists a subsequence (fnk) and a random variable f in L2 such that converges almost surely whenever . Komlós(5) has shown that if (fn) is a sequence of random variables, bounded in L1, then there is a subsequence (A*) with the property that the Cesàro averages of any subsequence converge almost surely. Subsequently Chatterji(2) showed that if (fn) is bounded in LP (where 0 < p ≤ 2) then there is a subsequence (gk) = (fnk) and f in Lp such thatalmost surely for every sub-subsequence. All of these results are examples of subsequence principles: a sequence of random variables, satisfying an appropriate moment condition, has a subsequence which satisfies some property enjoyed by sequences of independent identically distributed random variables. Recently Aldous(1), using tightness arguments, has shown that for a general class of properties such a subsequence principle holds: in particular, the results listed above are all special cases of Aldous' principal result.