bluuebunny/crossref_metadata_2025_split huggingface dataset:
A note on the image system for a stokeslet in a no-slip boundary
Authors: Blake J. R. 
Published: November 2008

AbstractThe velocity and pressure fields for Stokes's flow due to a point force (‘stokeslet’) in the vicinity of a stationary plane boundary are analysed, using Fourier transforms, to obtain the image system required to satisfy the no-slip condition on the boundary. The image system, which is illustrated by diagrams, is found to consist of a stokeslet equal in magnitude but opposite in sign to the initial stokeslet, a stokes-doublet and a source-doublet, the displacement axes for the doublets being in the original direction of the force. The influence of the wall on the near and far fields is discussed. In the far field it is found that a stokeslet aligned parallel to the wall produces a stokes-doublet far-field, whereas a stokeslet normal to the wall produces a combination of a source-doublet and a stokes-quadrupole far-field. Although results can be alternatively derived by the method of Lorentz (7) using a reciprocal theorem, the present method yields much more clearly the form of the image system.
The propagation of magneto-thermo-viscoelastic plane waves in a parallel union of the Kelvin and Maxwell bodies
Authors: Chandrasekhariah D. S. 
Published: November 2008

AbstractThe propagation of plane waves in a viscoelastic body representing a parallel union of the Kelvin and Maxwell bodies placed in a magneto-thermal field is investigated. It is shown that the longitudinal component of the wave is in general coupled with a transverse component and the wave travels in two families. In particular if the primary magnetic field is either parallel or perpendicular to the direction of wave propagation, the three components of the wave travel unlinked, with either the longitudinal component or the transverse components unaffected by the presence of the electromagnetic field. If the electrical conductivity of the solid is infinite the effect of the primary magnetic field is to increase the values of the material constants. The effect of wave propagation on magnetic permeability is equivalent to an anisotropic rescaling of the primary magnetic field. Some of the results obtained in the earlier works are obtained as particular cases of the more general results derived here.
On the absolute summability and convergence of Fourier series and associated series
Authors: Nayak M. K. 
Published: November 2008

1. We suppose that f(t) is integrable L and periodic with period 2π and we denote the Fourier series of f(t) at the point t = x byWe denote the nth partial sum of the Fourier series by sn. We will prove here a general result (i.e Theorem 1) and some interesting results in connexion with associated series of a Fourier series of the typeWe writeThe object of the present paper is to prove the following theorems. (In all the following cases k is any constant > π if nothing else is mentioned.)
Combinatorial applications of an inequality from statistical mechanics
Authors: Seymour P. D. , Welsh D. J. A. 
Published: November 2008

The main part of this paper shows how an inequality of statistical mechanics has several applications in combinatorial theory.The inequality (known as the FKG inequality) was derived by Fortuin, Kasteleyn and Ginibre(4) in their work on the statistical mechanics of Ising ferromagnets. We first show how it leads to new properties of log supermodular functions, Bernstein polynomials, and log convex sequences.
The law of large numbers for additive arithmetic functions
Authors: Elliott P. D. T. A. 
Published: November 2008

Let f(n) be a real-valued additive arithmetic function, that is to say, that f(ab) = f(a) + f(b) for each pair of coprime integers a and b. Let α(x) and β(x) > 0 be real-valued functions, defined for x ≥ 2. In this paper, we study the frequenciesWe shall establish necessary and sufficient conditions, subject to rather weak growth conditions upon β(x) alone, in order that these frequencies converge to the improper law, in other words, that f(n) obey a form of the weak law of large numbers.
Lower dimensional absolute continuity properties of quasiconformal mappings
Authors: Gehring F. W. 
Published: November 2008

Let Rn denote Euclidean n-space. For p ∈ [0, ∞), the normalized Hausdorff p-dimensional outer measure of a set E ⊂ Rn is defined aswhere the infimum is taken over all countable coverings of E by sets Ej withand(See, for example (4).) Then ℋP (E) measures the p-dimensional size of E. For example, ℋ0 (E) ≤ ∞ if and only if E is finite, in which case ℋ0(E) = card (E). Next if E is an arc or Jordan curve, then ℋ1(E) ≤ ∞ if and only if E is rectifiable, in which case ℋ1(E) = length (E). Finally if p is an integer in [1, n] and if E lies in a p-dimensional hyperplane T in Rn, thenwhere mp denotes the Lebesgue p-dimensional outer measure in T. Thus as p varies from 0 to n, the measures ℋp interpolate in a natural way between the counting measure and Lebesgue outer measure in Rn.
Non-linear angle-sum relations for polyhedral cones and polytopes
Authors: McMullen P. 
Published: November 2008

AbstractIt is shown that the internal and external angles at the faces of a polyhedral cone satisfy various bilinear relations. The first two of these are related to the Gauss–Bonnet and Steiner parallel formulae for spherical polytopes, while the third is completely new. However, the proofs are basically combinatorial in nature, rather than differential geometric, as in the more classical treatments. These relations lead to inversion formulae, analogous to Euler-type relations, for certain functions defined on polytopes and polyhedral cones. As a result, various new relations involving quermassintegrals and Grassmann angles are found; there is also an application to lattice polytopes.
A remark on the K-theory of BГq
Authors: Whitley Alan 
Published: November 2008

1. In (4) Bott and Heitsch discussed certain classifying spaces of importance in the study of foliations of various types. For example they studied the space BГq which helps to classify real foliations of codimension q and proved that a canonical mapinduces an injection in integral cohomology for q ≥ 2. Similar results hold for classifying spaces BUГq and BSГq related to complex and oriented foliations respectively. The object of this paper is to demonstrate that the canonical maps referred to above also induce injections in integral K-theory.
A new formula for cumulants
Authors: Good I. J. 
Published: November 2008

Let θ be ann-dimensional random vector with components θ1, θ2, …, θnand let itscumulantsbe defined as usual by the identitywherex1,x2, …,xnare purely imaginary variables,Edenotes expectation, andLet θ(1), θ(2), …, θ(R) be independent and identically distributed (i.i.d.) random vectors each with the same distribution as θ, whereR=r1+r2+ … +rn= |r|, theorderof the cumulantKr. Let θ* have the components
A class of approximate exterior rotating solutions of Einstein's equations
Authors: Islam Jamal N. 
Published: November 2008

AbstractA class of approximate stationary vacuum solutions are obtained by expanding the metric in powers of a certain parameter, and by solving explicitly the first few orders in terms of two harmonic functions ø and ψ. These solutions, to the order considered, reduce to the Weyl solutions when ψ = 0 and yield the Papapetrou solutions when ø = 0, and contain a subclass that is asymptotically flat and has non-zero mass. The physical interpretation and the possibility of proceeding further are briefly discussed.
A model for the two-way propagation of water waves in a channel
Authors: Bona Jerry L. , Smith Ronald 
Published: November 2008

Global existence, uniqueness and regularity of solutions and continuous dependence of solutions on varied initial data are established for the initial-value problem for the coupled system of equationsThis system has the same formal justification as a model for the two-way propagation of (one-dimensional) long waves of small but finite amplitude in an open channel of water of constant depth as other versions of the Boussinesq equations. A feature of the analysis is that bounds on the wave amplitude η are obtained which are valid for all time.
Applications of Leray–Schauder degree theory to problems of hydrodynamic stability
Authors: Benjamin T. Brooke 
Published: November 2008

AbstractA previous application of the theory, to the nonlinear boundary-value problem for steady flows of a viscous fluid in a bounded domain, is first retraced in order to verify a general theorem concerning the indices of multiple solutions. Then, in §5, the bearing of the theorem on questions of the bifurcation of steady flows is discussed, and the conclusion is drawn that a transcritical form of bifurcation is virtually universal in practice. In §6 it is proved that a flow represented by a solution with index i = – 1 is necessarily unstable, and hence it appears that lack of uniqueness generally implies the existence of an unstable steady flow.
On a Gaussian process related to multivariate probability density estimation
Authors: Silverman B. W. 
Published: November 2008

The multivariate Gaussian process with the same variance/covariance structure as the multivariate kernel density estimator in Euclidean space of dimension d is considered. An exact result is obtained for the limit in probability of the maximum of the normalized process. In addition weak and strong bounds are placed on the asymptotic behaviour of the maximum of the process over a multidimensional interval which is allowed to increase as the sample size increases. All the bounds obtained on the process areOnly the uniform continuity of the underlying density is assumed; the conditions on the kernel are also mild.
Spinors in Hilbert space
Authors: Plymen R. J. 
Published: November 2008

In 1913, É. Cartan discovered that the special orthogonal groupSO(k) has a ‘two-valued’ representation (i.e. a projective representation) on a complex vector spaceSof dimension 2n, wherek= 2nor 2n+ 1. The projective representation in question lifts to a true representation of the double cover Spin (k) ofSO(k). We restrict attention to the casek= 2n. Under the action of Spin (2n),Sbreaks up into 2 irreducible subspaces:The vectors inSare calledspinors(relative toSO(2n)), those inS+orS−are calledhalf-spinors(4).
On eigenstresses in a semi-infinite solid
Authors: Aderogba K. 
Published: November 2008

AbstractA uniform eigenstrain is prescribed within a spherical subregion of an isotropic linearly elastic half-space. Combining an application of potential theory with the stress-function approach of Papkovitch and Neuber, and starting with Eshelby's well-known solution for the homogeneous infinite solid, it is shown that the residual problem of potential to be solved is the determination of Boussinesq's first and second three-dimensional logarithmic potentials of volume distributions. Although explicit results are supplied only for the case of a spherical inclusion, the dependence of the solution on the infinite solid solution holds good for an arbitrarily shaped transforming inclusion. This can be established on the basis of the principle of superposition, considering that an arbitrary volume is essentially made up from an infinite spectrum of spherical regions.
The ideal structure of the Stone-Čech compactification of a group
Authors: Baker J. W. , Milnes P. 
Published: November 2008

Let S be both a topological space and a semigroup. For s ∈ S, define the maps λs and ρs of S to S byWe shall say that S is a right-topological (resp. left-topological) semigroup if ρs (resp. λs) is continuous for each s in S. We denote by Λ(S) the setthis is a subsemigroup of S.
The variances of a sequence
Authors: Maddox I. J. 
Published: November 2008

In statistical problems, use is often made of the variance s2 of a finite sequence of numbers x1, x2, …, xn, wherex¯ being the arithmetic mean of x1, x2, …, xn. The object of this note is to introduce a generalized variance for an infinite sequence x = (xk) and to examine some of its properties.
On non-uniqueness of the order of saturation
Authors: Kuttner B. , Sahney B. 
Published: November 2008

1. Let X be a normed linear space of periodic functions (of period 2π), which includes the class of trigonometric polynomials. We restrict ourselves throughout to functions f ∈ X. Let D) = (dn, k) be the matrix of a regular sequence-to-sequence transformation. (We could also consider sequence-to-function transformations, in which case n is replaced by a continuous variable.) We suppose that, for all n,Let {Ln(x)} be the D transform of the Fourier series of f(x). If f(x) is a constant, it follows from (1) that, for all n, Ln(x) = f(x). However, it is often found that, roughly speaking, except in this trivial case, Ln(x) cannot tend to f(x) (in the topology given by the norm) with more than a certain degree of rapidity. This leads to the concept of ‘saturation’, which was first introduced by Favard (1) and Zamanski (8) and which has since been investigated by many authors (see (2), (3), (4), (5), (6), (7)). This is defined as follows.
Continuity properties of compact right topological groups
Authors: Milnes Paul 
Published: November 2008

AbstractCompact right topological groups appear naturally in topological dynamics. Some continuity properties of the one arising as an enveloping semigroup from the distal function are considered here (and, by way of comparison, the enveloping semigroups arising from two almost automorphic functions are discussed). The continuity properties are established either explicitly or by citing a theorem which is proved here and gives some characterizations of almost periodic functions. One characterization is proved using the result (essentially due to W. A. Veech) that a distal, almost automorphic function is almost periodic. A proof of this last result is also given.
Homogeneous line-segment processes
Authors: Cowan Richard 
Published: November 2008

SummaryA number of formulae of an integral geometric character are presented for the most general planar, homogeneous line-segment process, one in which a given segment length and orientation may depend upon (a) the point process of segment midpoints and (b) the lengths and orientations of other segments. The sense in which these formulae have a probabilistic/statistical interpretation is made precise. For the general process, two interpretations are given; one requires the theory of Palm distributions whilst the other depends upon ergodic results. When additional structure for the process is assumed, the integral geometric formulae lead to interesting, non-intuitive sampling formulae.
Bifurcation of rotating circular cylindrical elastic membranes
Authors: Haughton D. M. , Ogden R. W. 
Published: November 2008

SummaryBifurcation from a finitely deformed circular cylindrical configuration of a rotating circular cylindrical elastic membrane is examined. It is found (for a physically realistic choice of elastic strain-energy function) that the angular speed attains a maximum followed by a minimum relative to the increasing radius of the cylinder for either a fixed axial extension or fixed axial force.At fixed axial extension (a) a prismatic mode of bifurcation (in which the cross-section of the cylinder becomes uniformly non-circular) may occur at a maximum of the angular speed provided the end conditions on the cylinder allow this; (b) axisyim-metric modes may occur before, at or after the angular speed maximum depending on the length of the cylinder and the magnitude of the axial extension; (c) an asymmetric or ‘wobble’ mode is always possible before either (a) or (b) as the angular speed increases from zero for any length of cylinder or axial extension. Moreover, ‘wobble’ occurs at lower angular speeds for longer cylinders.At fixed axial force the results are similar to (a), (b) and (c) except that an axisym-metric mode necessarily occurs between the turning points of the angular speed.
On the effect of magneto-thermo-elastic interactions on the cooling process of an infinite circular cylinder
Authors: Bakshi Sachindra Kumar 
Published: November 2008

AbstractThe paper deals with the problem of investigating the effect of magneto-thermo-elastic interactions on the cooling process of an infinite circular cylinder when its boundary is subjected to a time-decaying temperature. The Hooke–Duhamel law of elasticity, the equation of heat conduction together with the electromagnetic equations of Maxwell supplemented by Ohm's law have been used to solve the problem. It is found that the Laplace transformation serves as an important tool for the solution of the problem.
Local limit theorems for the maxima of discrete random variables
Authors: Anderson C. W. 
Published: November 2008

Let , where the Xi, i = 1, 2, … are independent identically distributed random variables. Classical extreme value theory, described for example in the books of do Haan(6) and Galambos(3) gives conditions under which there exist constants an > 0 and bn such thatwhere G(x) is taken to be one of the extreme value distributions G1(x) = exp (− e−x), G2(x) = exp (− x−a) (x > 0, α > 0) and G3(x) = exp (−(− x)α) (x < 0, α > 0).
The decomposition of crystal families
Authors: Jarratt J. D. 
Published: November 2008

In the course of their enumeration of all 4-dimensional space groups, Brown, Bülow, Neubüser, Wondratschek and Zassenhaus have introduced concepts appropriate to the study of n-dimensional crystallography for n ≥ 4 (see (2), (3)). One such concept is that of a crystal family. Families seem to be particularly useful as a framework within which to study higher dimensional crystallography, primarily because they determine a classification of all the standard crystallographic objects and overcome the traditional confusion over crystal systems (see (2); pp. 16–17, (9)). In this paper, techniques are developed for the determination of all rationally decomposable families in a given dimension from the indecomposable families of lower dimensions. These techniques place emphasis on three geometric invariants of families: the decomposition pattern; the canonical decomposition pattern; and the number of free parameters. This, it is felt, further reinforces their position as fundamental objects. The key result (Theorem 5.4) is:a family uniquely determines, and is uniquely determined by, the constituent families in the canonical decomposition.
Convex curves in which a triangle can revolve
Authors: Croft H. T. 
Published: November 2008

We shall be considering plane closed convex curves Γ (whose interior plus boundary will be denoted by Σ ≡ Σ(Γ)) in which we can inscribe a large set (in various senses to be made precise) of equilateral triangles or e-triangles for short; and in particular an e-triangle of side-length 1 is called an E-triangle or just an E. More formally we define the sets to be the sets of closed convex Γ for which, respectively:: each point of Γ is the vertex of some inscribed E;: Γ contains the vertices of some E in each orientation in the plane;: an E can be moved round continuously, through angle 2π, with all vertices on Γ throughout.
The form of the tangent-developable at points of zero torsion on space curves
Authors: Cleave J. P. 
Published: November 2008

A tangent-developable is a surface generated by the tangent lines of a space curve. The intersection of a tangent-developable with the normal plane at a point P of the curve generally has a cusp at that point. Thus the tangent-developable of a space curve has a cuspidal edge along the curve. The classical derivation of this phenomenon takes the trihedron (t, n, b) at P as coordinate axes to which the curve is referred. Then the intersection of the part of the tangent-developable generated by tangent lines at points close to P with the normal plane at P (i.e. the plane through P containing n and b) is given parametrically by power serieswhere K, T are the curvature and torsion, respectively, of the curve at P and s is arc-length measured from P ((2) p. 68). It is tacitly understood in this analysis that curvature and torsion are both defined and non-zero.
Characteristic classes for permutation representations
Authors: Segal G. B. , Stretch C. T. 
Published: November 2008

To a finite-dimensional real representation V of a finite group G there are associated its Stiefel–Whitney classes wk (V) (k = 1, 2, 3, …) in the cohomology groups Hk(G; ). ( is the field with two elements.) The total Stiefel-Whitney classin the ring H*(G; is natural with respect to G in the obvious sense, and, in addition,(a) exponential, i.e. w(V ⊕ W) = w(V).w(W),and(b) stable, i.e. w(V) = 1 when F is a trivial representation.
On the asymptotic behaviour of sample spacings
Authors: Hawkes John 
Published: November 2008

SummarySuppose that we are given a random sample of size n chosen according to the uniform distribution on the unit interval. Let Zn(x) = Zn(x, ω) be the length of the unique left-closed and right-open sample spacing that contains x. The purpose of this paper is to examine the almost sure, and exceptional, growth rates of the process {Zn}. The typical maximum growth rate and the growth rate of the maximum can be of quite different orders of magnitude as is shown by the following two results.Theorem 2. With probability one we havefor almost all x.Theorem 3. With probability one we have
The structure of the solution set for the Yang-Mills equations
Authors: Arms Judith M. 
Published: November 2008

AbstractThe solution set for the (sourceless) Yang-Mills equations on a spacetime with compact Cauchy surface is a smooth manifold (i.e. the equations are linearization stable) except at solutions that are symmetric. At such symmetric solutions, the structure is described by a homogeneous quadratic form. The degeneracy space for this form is tangent to a manifold of symmetric solutions. Symmetry breaking occurs for perturbations in the nondegenerate directions of the quadratic form. The terms ‘symmetry’ and ‘stability’ in the present work are compared to these terms as used elsewhere in the literature.
Towards a characterization of smooth braids
Authors: Johnson D. L. 
Published: November 2008

The braid group on n + 1 strings has the presentationwhere xi corresponds to the single crossing of the i string over the i + 1 string, and rij is a commutator when i < j − 1, and a braid relator when i = j − 1. B1 is the trivial group and B2 is infinite cyclic; we shall assume n ≥ 2 throughout.
Improved packing of equal circles on a sphere and rigidity of its graph
Authors: Tarnai T. , Gáspár Zs. 
Published: November 2008

AbstractHow must n equal non-overlapping circles be packed on a sphere so that the angular diameter of the circles will be as great as possible? In the paper, the conjectured solutions of this problem for n = 18, 27, 34, 35, 40 are improved on the basis of an idea of Danzer. Using the theory of bar structures it is ascertained that, in these cases, the edge-length of the graphs of the circle-packings can be increased till, in the graphs, additional edges appear which prevent further motions apart from rigid motions. The cases of n = 17 and 32 are also dealt with and there are references to the possibilities of further applications of the method applied in this paper (n = 59, 80, 110, 122).
On non-uniqueness of the order of saturation (II)
Authors: Kuttner B. 
Published: November 2008

1. In this paper, the notation and terminology of [2] will be used throughout. As in [2], we consider the space of bounded measurable functions of period 2π, with the sup norm. We let K0ρ denote the subspace consisting of those functions in the space considered which have the further property that the conjugate function belongs to Lrρ 1. Again as in [2], we consider regular summability methods given by a sequence-to-sequence matrix transformation D = (dnk), whereand where, for fixed n,
Exact Brans-Dicke-Bianchi type-V solutions
Authors: Lorenz-Petzold D. 
Published: November 2008

AbstractSpatially homogeneous cosmological models of the Bianchi type-V are considered in the Brans-Dicke scalar-tensor theory of gravitation. Exact solutions are given in the vacuum case as well as for models filled with dust, radiation or stiff matter.