bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the right lower circular density of two-dimensional Jordan curves in the plane
Authors: Larman D. G. 
Published: November 2008

We use J(a, b) to denote a Jordan curve of positive two-dimensional measure in the plane, with end-points a and b. If υ is a point of J(a, b), we define the right lower arc density at υ bywhere J( υ, υ′) is the largest arc, whose left-end point is υ, which is contained in the disc c(υ, r).
The influence of surface tension on the reflection of water waves by a plane vertical barrier
Authors: Evans D. V. 
Published: November 2008

AbstractIn this paper the effect of surface tension is included in a well-known problem in the theory of two-dimensional infinitesimal water waves. The problem is that of the reflection of waves from a fixed vertical barrier immersed to a depth a into deep water. It is shown how the solution for the velocity potential may be determined uniquely when simple assumptions are made concerning the behaviour of the free surface near the barrier. In particular, expressions are derived for the reflection coefficient, defined as the ratio of the amplitude of the reflected wave to that of the incident wave, at infinity, and the transmission coefficient, defined similarly. It is shown how these coefficients, for small values of the surface tension force, tend to the values obtained by Ursell (4) when surface tension is ignored. The related problem of a completely immersed vertical barrier extending to a distance a from the surface may be solved in a similar manner. Expressions for the reflection and transmission coefficients for this case are given.
On the scattering of short surface waves by a finite dock
Authors: Leppington F. G. 
Published: November 2008

AbstractA sinusoidal travelling wave-train is at normal incidence upon a two-dimensional finite dock fixed on the surface of a body of water of great depth, and the problem investigated herein is that of finding the limiting form of the induced velocity potential for short waves. Of particular interest are the amplitudes of the wave-trains reflected and transmitted towards infinity by such an obstacle. The potential is expressed as a sum of coupled semi-infinite dock potentials, whence results a pair of weakly coupled integral equations for the solution. This formulation of the problem is shown to be amenable to an approximate solution for large wave-numbers, and the first few terms are derived in formal expansions for the reflection and transmission coefficients.
A uniqueness theorem for magnetohydrodynamic duct flows
Authors: Hunt J. C. R. 
Published: November 2008

AbstractWe analyse the steady, fully developed, laminar flows of uniform, electrically conducting, incompressible fluids along arbitrarily shaped ducts of constant cross-section under the action of transverse magnetic fields to show that these flows are uniquely specified by certain parameters, namely: either the pressure drop along the duct per unit length or the volume flow rate and either the electric current leaving the walls of the duct at each point where the duct is connected to an external electrical circuit or the electric potential at these points. The most important, and novel, feature of the analysis is the proof that no secondary flow can exist in these fully developed flows. The analysis includes the special cases where the walls of the duct are non-conducting, and where the fluid is non-conducting (e.g. Poiseuille flow); in the latter case the uniqueness of the flow has not previously been demonstrated, at least in print.
Forced vertical oscillations in a viscous stratified fluid
Authors: Dore B. D. 
Published: November 2008

AbstractThe linear fluid dynamics is considered when infinite vertical boundaries are set in oscillatory vertical motion. The case of exponential stratification with constant kinematic viscosity is explicitly studied. When the forcing frequency equals the Brunt–Vaisälä frequency for the fluid, the customary boundary layers are absent in the steady-state oscillation, however small be the kinematic viscosity; for a semi-infinite fluid the corresponding horizontal extent of the region influenced by the boundary motion is then of the order of the stratification length. The sign of the phase angle is everywhere dependent on whether the magnitude of the forcing frequency is greater than or less than that of the Brunt–Vaisäla frequency.
Integrals with a large parameter: paths of descent and conformal mapping
Authors: Ursell F. 
Published: November 2008

AbstractThe method of steepest descents is widely used to find the asymptotic expansion of contour integrals of the formwhere N is a large positive parameter, and f(z) and g(z) are analytic functions of z. (For the sake of simplicity it will here be supposed that f(z) and g(z) are regular except at ∞, but our arguments can be extended to include singularities at other points.) In the method of steepest descents the path of integration is deformed into a new equivalent path consisting of the paths of steepest descent through a and b, together with paths of steepest descent through certain saddle points, the relevant saddle points. (Paths of descent, etc., are defined in §1 below.) Watson's Lemma then shows that the complete asymptotic expansion depends on the local behaviour of f(z) and g(z) at the end-points and at the relevant saddle-points. On the other hand to determine which saddle-points are relevant is a global (non-local) problem and requires either the tracing of paths of steepest descent all the way from saddle-points and endpoints to ∞, or some other global process. It has often been noted that in applications of Watson's Lemma the paths of steepest descent can be replaced by a wider class of paths of descent. In this way we are led to global problems like the following: Given 2points z = α and z = β where Nf(a) > Nf(β), can apath of descent be drawn from α to β? If also Ff(α) = Ff(β), can a path of steepest descent be drawn from α to β?
On topological quotient maps preserved by pullbacks or products
Authors: Day B. J. , Kelly G. M. 
Published: November 2008

We are concerned with the category of topological spaces and continuous maps. A surjection f: X → Y in this category is called a quotient map if G is open in Y whenever f−1G is open in X. Our purpose is to answer the following three questions:Question 1. For which continuous surjections f: X → Y is every pullback of f a quotient map?Question 2. For which continuous surjections f: X → Y is f × lz: X × Z → Y × Z a quotient map for every topological space Z? (These include all those f answering to Question 1, since f × lz is the pullback of f by the projection map Y ×Z → Y.)Question 3. For which topological spaces Z is f × 1Z: X × Z → Y × Z a qiptoent map for every quotient map f?
Two results on very strongly homogeneous algebras
Authors: Körner T. W. 
Published: November 2008

AbstractWe show that under quite general circumstances a Banach algebra R need not be closed in its tilda algebra . In answer to a query of Katznelson we show that there is a very strongly homogeneous algebra B ≠ C0(R) on R with R as carrier space such that non-analytic functions operate on B.
A Wiener-Hopf solution to the triple integral equations for the electrified disc in a coplanar gap
Authors: Spence D. A. 
Published: November 2008

AbstractThe axisymmetric potential problem for a plane circular electrode of radius a in a concentric hole of radius b in a coplanar earthed sheet is formulated in terms of triple integral equations for the Hankel transform of the potential, and reduced to a single Fredholm equation by use of the Erdélyi-Kober fractional operators.In the limit of small gap width (b − a)/b, the equation takes the formwhich is solved by applying the Wiener-Hopf technique to the Mellin transform of f(x). This leads to the asymptotic expressionfor the capacity of the disc; for the opposite limit the expressionis derived. Numerical integration of the governing Fredholm equation has been carried out for a range of intermediate values of b/a.
Integer difference covers which are not k-sum covers, for k = 6, 7
Authors: Connolly Dennis 
Published: November 2008

Constructions are given of sets F(k), (k = 6, 7) of residues mod q(k), (for a suitably chosen integer q(k)) such that F(k) – F(k) contains all residues, whilehas a gap of an assigned number of consecutive residues.
On mass transport induced by interfacial oscillations at a single frequency
Authors: Dore B. D. 
Published: November 2008

AbstractThe to method of matched asymptotic expansions is employed to calculate the mass tre sport velocity due to combinations of small amplitude oscillatory waves propagatir, at a single frequency in fluid systems with density and viscosity dis-continuities. Interfacial boundary layers are considered in terms of the curvilinear coordinate system described by Longuet-Higgins(1). The order of magnitude of the mass transport velocity calculated for a general oscillatory disturbance is the same as that calculated for interfacial progressive waves by Dore(2). For standing waves, the time-averaged motion of the fluid particles forms a cellular structure in each fluid layer; the mass transport velocity due to modal interactions is associated with a similar structure.
On isotropic tensors and elastic moduli
Authors: Ogden R. W. 
Published: November 2008

AbstractThe use of even-order isotropic tensors in non-linear elasticity theory is discussed in this paper. A notation is adopted through which these tensors can be represented conveniently so that their interdependence is clearly shown. Information about the number of independent elastic constants required is then readily available for use in an expansion of the stress to various orders in the strain relative to the undistorted configuration of the elastic material in question.For an incompressible isotropic hyperelastic solid, it is shown that each principal component of the distortional part of the stress is expressible as a function only of the corresponding principal component of strain to the fourth order. Under certain conditions, which are not too restrictive, this result can be extended to higher orders.
On the digits of the multiples of an irrational p-adic number
Authors: Mahler Kurt 
Published: November 2008

Let α be an irrational p-adic number, r an arbitrary positive integer. Our aim is to prove that there exists a rational integer X satisfyingsuch that every possible sequence of r digits 0, 1, …, p – 1 occurs infinitely often in the canonical p-adic series for Xα. It is clear that it suffices to prove this result for p-adic integers.
Internal wave motion in a non-homogeneous viscous fluid of variable depth
Authors: Dore B. D. 
Published: November 2008

AbstractA method of solution is given to the problem of internal wave motion in a non-homogeneous viscous fluid of variable depth. The approach is based on the inviscid theory of Keller and Mow(l) and on boundary-layer analysis. For internal progressive waves in uniform depths, it reduces essentially to the theory given by Dore(2). The present results are also applicable to surface waves when the fluid is homogeneous.
On cyclic maps
Authors: Snaith V. P. 
Published: November 2008

Throughout X will denote a connected, finite C.W. complex.Let G be a subgroup of ∑n, the symmetric group, which acts transitively on the Cartesian product, Xn, of the space X. A map f:Xn→X is G-symmetric if it commutes with the action of G. If x0εX is a base point let i:X→Xn denote the inclusion, i(x) = (x,x0, …,x0). In ((6); (7); (11)–(13)) the following problem is posed: if X is an orientable topological n-manifold, what is the set of integers which may be obtained as the degree of(f.i) where f is a G-symmetric map? The degree of(f.i) is called the James number of f. If G = ∑n(G = Zn) a G-symmetric map will be called a symmetric map (a cyclic map). If X = Sn, the n-sphere, this problem has been studied in ((6)–(8), (11)–(13))
The non-existence of standing modes in certain problems of linear elasticity
Authors: Gregory R. D. 
Published: November 2008

AbstractSuppose that an elastic half-space, which contains certain surface defects, inclusions and cavities, is in free, two-dimensional, time-harmonic vibration, with the wave field at infinity ‘outgoing’ in character. It is shown that the elastic potentials representing such a ‘standing mode’ can be expressed in the form of contour integrals, for instanceU(t) being an analytic function of t. By considering the far field of these potentials, it is shown that U(t) is zero on a certain arc in the t-plane and is therefore identically zero. It follows that ø(r) is zero everywhere and this proves the non-existence of such standing modes in these configurations.This uniqueness theorem justifies the solution given by the author (Gregory (2)) for the problem in which time harmonic stresses act on the walls of a cylindrical cavity lying beneath the surface of an elastic half-space. It is also shown that if a Rayleigh surface wave is incident on any system of surface defects, inclusions and cavities, then energy must be transferred from the surface wave to scattered outgoing body waves of both P and S types.
The departure process from a queueing system
Authors: Kelly F. P. 
Published: November 2008

Consider a single-server queueing system with a Poisson arrival process at rate λ and positive service requirements independently distributed with common distribution functionB(z) and finite expectationwhere βλ < 1, i.e. anM/G/1 system. When the queue discipline is first come first served, or last come first served without pre-emption, the stationary departure process is Poisson if and only ifG=M(i.e.B(z) = 1 − exp (−z/β)); see (8), (4) and (2). In this paper it is shown that when the queue discipline is last come first served with pre-emption the stationary departure process is Poisson whatever the form ofB(z). The method used is adapted from the approach of Takács (10) and Shanbhag and Tambouratzis (9).
On the static field in general relativity
Authors: Islam Jamal N. 
Published: November 2008

AbstractThe possibility is explored that the general static solution of Einstein's vacuum field equations is given in terms of a single harmonic function, i.e. solution of the flat space Laplace equation. It is shown that coordinate conditions can be chosen such that one of Einstein's equations reduces to Laplace's equation. To examine the extent to which the metric is determined by the resulting harmonic function ø, a power series expansion is considered in which in the first non-trivial order one gets a system of eight equations for six unknowns. This is reduced to a system of three equations for three unknowns. This is some indication that the coordinate conditions are consistent and shows the sense in which, to this order, the metric is determined by ø. This system of three equations is then solved explicitly for a particular choice of ø, thereby giving an approximate non-axisymmetric solution of Einstein's vacuum equations. This solution is asymptotically flat and could represent the approximate gravitational field of a non-axisymmetric bounded rigid body. The form of a class of time-dependent metric related to the general static metric is discussed.
The uniqueness of Atkinson and Reuter's epidemic waves
Authors: Barbour Andrew D. 
Published: November 2008

Atkinson and Reuter(1) consider travelling wave solutions for the deterministic epidemic, with or without removals, spreading along the line. In the case where there are no removals, they reformulate the problem in terms of the solutions X(·) to the integral equationwhich satisfy X(− ∞) = − ∞, X( + ∞) = 0, X(u) < 0 for u ∈ (− ∞, ∞), whereis the left hand tail of the contact distribution, and where ʗ > 0 is the velocity of the wave corresponding to X. They show that no solution is possible unlessconverges for λ > 0 sufficiently small, and that any solution X must satisfyfor some C > 0. They then prove the following existence theorems.
A counterexample to R. Davidson's conjecture on line processes
Authors: Kallenberg Olav 
Published: November 2008

AbstractRollo Davidson conjectured in 1968 that every stationary second order line process in the plane which has a.s. no parallel lines is necessarily a Cox (or doubly stochastic Poisson) process. This conjecture is disproved here. An affirmative answer is further given to the question whether there exists a lattice type point process in the plane which is stationary under arbitrary area preserving affine transformations.
A new approach to subcritical instability and turbulent transitions in a simple dynamo
Authors: Robbins K. A. 
Published: November 2008

AbstractThe onset of turbulence in many systems appears disorganized and unpredictable. However, the present detailed study of a well-known model reveals a series of well-defined transitions from steady motion to highly non-periodic behaviour. The bifurcation structure of this simple model, which describes both a reversing disc dynamo and Benard convection in thin fluid loops, is characteristic of a class of systems with subcritical instabilities. It is found that the bifurcation curve for this instability does not have a stable branch and that non-periodic and linearly stable steady solutions coexist. The boundary between transient and non-periodic behaviour is marked by a non-uniformity in the number of oscillations between reversals. This non-uniformity, not previously observed, is a striking corroboration of the model's relationship to the geodynamo. Other features of reversal in the disc dynamo such as the presence of two time scales in the oscillations are also exhibited by geomagnetic fields. In addition to a geometric description of the transitions, a one-dimensional mapping first constructed by Lorenz for the system beyond marginal stability, is extended to the subcritical regime. This type of mapping, which can be interpreted in terms of invariant surfaces of the system, may be of value in dissecting more general systems with subcritical Hopf bifurcations.
On the weak convergence of U-statistic processes, and of the empirical process
Authors: Loynes R. M. 
Published: November 2008

1. Summary and introductionIn (5) a weak convergence result for U-statistics was obtained as a special case of a reverse martingale theorem; in (7) Miller and Sen obtained another such result for U-statistics by a direct argument. As they stand these results are not very closely connected, since one is concerned with U-statistics Uk for k ≥ n, while the other deals with Uk for k ≤ n, but if one instead thinks of k as unrestricted and transforms the random functions Xn which enter into one of these results into new functions Yn by setting Yn(t) = tXn(t−1) one finds that the Yn are (aside from variations in interpolated values) just the functions with which the other result is concerned. As the limiting Wiener process W is well-known to have the property that tW(t−1) is another Wiener process it is not too surprising that both results should hold, and part of the purpose of this paper is to provide a general framework within which the relationship between these results will become clear. A second purpose is to illustrate the simplification that the martingale property brings to weak convergence studies; this is shown both in the U-statistic example and in a new proof of the convergence of the empirical process.
On the static field in general relativity: II
Authors: Islam Jamal N. 
Published: November 2008

AbstractSome aspects are considered of the Einstein vacuum field equations for the diagonal form of the general static metric. A power series expansion is considered in which in the first non-trivial order one gets seven equations for four unknowns. This is reduced to a single Poisson equation in which the source is given in terms of a harmonic function and some arbitrary functions of two variables. A similar reduction is carried out in detail for the next non-trivial order. The approximation scheme can be extended to arbitrarily high orders in principle. The connexion of the diagonal form with the Weyl solutions and the merits of the diagonal and non-diagonal forms are briefly discussed. A general solution of one of the field equations is presented.
On the centres of hereditary JBW-subalgebras of a JBW-algebra
Authors: Edwards C. M. 
Published: November 2008

A JB-algebra A is a real Jordan algebra, which is also a Banach space, the norm in which satisfies the conditions thatandfor all elements a and b in A. It follows from (1.1) and (l.2) thatfor all elements a and b in A. When the JB-algebra A possesses an identity element then A is said to be a unital JB-algebra and (1.2) is equivalent to the condition thatfor all elements a and b in A. For the general theory of JB-algebras the reader is referred to (2), (3), (7) and (10).
A geometric approach to two-timing
Authors: Gilbert A. D. 
Published: November 2008

This paper is concerned with a particular method used in the calculation of asymptotic expansions of solutions to problems which contain a small parameter ∈. The physical idea underlying the method is that the parameter introduces new scales (of length and/or time) into the problem, and that the solution should incorporate these (see, for example, Cole (1)). This may be done in various ways: two-timing (two-scaling, multiple-scaling) does it by demanding that the solution is a function of all relevant scales. Consider, for example, a linear oscillator whose frequency is slowly adjusted, governed byand subject to some initial condition. Account of the slowly varying frequency is taken by the dependence of Ω on ∈t, where 0 < ∈ ≪ 1, and we assume that Ω > 1 for all arguments. The rapid oscillatory behaviour anticipated in the solution is customarily described by a phase function Θ(isin;t)/∈, a generalization of Ωt the case that Ω is constant, while slow changes due to frequency variation occur on a scale ∈t.
On the Williams-Bjerknes tumour growth model: II
Authors: Bramson Maury , Griffeath David 
Published: November 2008

AbstractWilliams and Bjerknes introduced in 1972 a stochastic model for the spread of cancer cells. Cells, normal and abnormal (cancerous), are situated on a planar lattice. With each cellular division, one daughter cell stays put, while the other usurps the position of a neighbour; abnormal cells reproduce at a faster rate than normal cells. We are interested in the long-term behaviour of this system. We showed in ‘On the Williams-Bjerknes Tumour Growth Model I’ (1) that, provided it lives forever, the tumour will eventually contain a ball of linearly expanding radius. Here it is shown that the rate of expansion is actually linear, and that the region of infection has an asymptotic shape which is given by some (unknown) norm. To demonstrate that the tumour contains a ball of linearly expanding radius, we applied in (1) certain techniques common to the field of interacting particle systems; in particular we made use of certain auxiliary Markov chains which are imbedded in the dual processes of our model. Here different techniques are applied. We show that the first infection times of different sites are almost subadditive, and we exhibit various regularity properties of the infection times such as bounds on their moments. These properties of the Williams-Bjerknes process allow one to follow the outline prescribed by Richardson in (7), where he showed that such a process does indeed exhibit a linear growth whose shape is prescribed by a norm.
On maximal Euclidean sets avoiding certain distance configurations
Authors: Croft H. T. , Falconer K. J. 
Published: November 2008

Let us say that a set points in a Euclidean space has property (2) if no 2 points X, Y ∈ S have X Y > 1. Then an easy observation is the following:The maximum area (Lebesgue measure) of a plane set S with property(2) is ¼π, attained only when S is (essentially) a disc.