bluuebunny/crossref_metadata_2025_split huggingface dataset:
Rarefied gas flow between parallel plates
Authors: Williams M. M. R. 
Published: November 2008

AbstractThe flow of a rarefied gas between parallel plates has been studied via the linearized Boltzmann transport equation. Using a general boundary condition, which includes an arbitrary ratio of specular to diffuse reflection from the wall, we have derived an integral equation for the mass flow velocity. The integral equation is solved by using a replication property of the kernel and application of the method of Muskelishvili.The total volumetric flow rate is obtained and a slip boundary condition is deduced for use with the hydrodynamic equations.Certain aspects of the eigenvalue spectrum associated with the Boltzmann equation are discussed.
On the Rayleigh assumption in scattering by a periodic surface. II
Authors: Millar R. F. 
Published: November 2008

AbstractThe Rayleigh assumption, which concerns the domain of validity of a representation for the field scattered by a periodic surface under time-harmonic plane-wave excitation, is re-examined. The analysis employs a technique developed to locate singularities of solutions to the Helmholtz equation. When applied to the surface profile v = b cos κu (-∞ < u < ∞) considered originally by Lord Rayleigh, it is found that the Rayleigh assumption is valid if 0 ≤ κb < 0·448 and is not valid if κb > 0·448; this is more precise than an earlier result. It is shown how these findings may be reconciled with the work of others who have suggested, or concluded, that the Rayleigh assumption is never valid.
Arcs with increasing chords
Authors: Larman D. G. , McMullen P. 
Published: November 2008

Let f:[0, 1]→R2 be a Jordan arc, and for t, u ∈ [0, 1] let d(t, u) = d(f(t), f(u)) denote the Euclidean length of the chord between f(t) and f(u), and l(t, u) = l(f(t), f(u)) the corresponding arc-length, when this is defined. We say that f has the increasing chord property if d(t2, t3) ≤ d(t1, t4) whenever 0 ≤ t1 ≤ t2 ≤ t3 ≤ t4 ≤ 1. In connexion with a problem in complex analysis, K. Binmore has asked (private communication, see (1)) whether there exists an absolute constant K such that.
A note on orthogonality and permutability of subnormal subgroups
Authors: Lennox John C. 
Published: November 2008

Let H and K be groups with derived sub groups H´ and K´. Following (5) we say that H and K are orthogonal, and write H ⊥ K, if and only if the tensor product H/H´ ®K/K´ is trivial. If H and K are sub groups of a group we say that H and K permute if and only if HK = KH. We recall finally that the subgroup H of the group G is said to be subnormal in G, written H sn G, if and only if there exists a finite chain of subgroupsconnecting H to G.
The use of Riemann problems in solving a class of transcendental equations
Authors: Burniston E. E. , Siewert C. E. 
Published: November 2008

AbstractA method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.
Polynomial approximations to the solution of the heat equation
Authors: Scraton R. E. 
Published: November 2008

AbstractAn approximation is found to the solution of the partial differential equationin the region −1 ≤ x ≤ 1, t > 0, where u satisfies a general linear boundary condition on x = ± 1. This approximation is a polynomial in x, and is an exact solution of a perturbed form of the differential equation. By choosing the perturbation appropriately, this approach is mathematically equivalent to some recent methods for solving the differential equation in the form of a Chebyshev series. Better approximations to the required solution (and particularly to the eigenvalues) are obtained by choosing the perturbation to satisfy a least squares criterion.
The vorticity equation as an angular momentum equation
Authors: Chatwin P. C. 
Published: November 2008

In a Newtonian fluid, in which the body forces are conservative, in which the pressure is a function only of density and in which the kinematic viscosity v is uniform, the vorticity ω satisfies the equationwhere u is the velocity field, so that ω = ▿ × u. This equation is normally derived by taking the curl of the Navier–Stokes equations. However, the vorticity has many interpretations in terms of the angular velocity of elements of fluid and it is natural to expect that (1) can be derived by equating the rate of change of the angular momentum of a small material volume element about its centre of mass with the moment of the forces acting on the element. Such a derivation is presented here in the hope that it may be of pedagogic interest.
The effect of a semi-contaminated free surface on mass transport
Authors: Porter D. , Dore B. D. 
Published: November 2008

AbstractThe mass transport velocity field is determined for surface waves which propagate from a region with a clean free surface into a region beneath an inextensible surface film. The waves are assumed to be incident normally on the edge of the film. Determination of this velocity field requires the investigation of a mixed boundary value problem for the bi-harmonic equation, the solution of which is obtained using the Wiener–Hopf technique. Streamlines for the mean motion of the fluid particles are thus obtained. It is found that considerable vertical displacement of fluid is possible due to the presence of the surface film.
A generalized Kerr-Schild solution of Einstein's equations
Authors: Vaidya P. C. 
Published: November 2008

AbstractA very general exact solution of Einstein's equation Rik = σξiξk, is given in terms of the Kerr-Schild metric, gik = ηij + Hξiξk, where ξi is a shearfree geodetic null congruence. The Kerr-Schild solution for Rik = 0 is derived as a particular case.
Integrals with a large parameter and several nearly coincident saddle points; the continuation of uniformly asymptotic expansions
Authors: Martin J. 
Published: November 2008

AbstractIn the contour integralf and g are regular functions of z in a neighbourhood of the contour C and of the complex parameters (α1, α2, …, αp) = α in a domain of . N is a positive parameter and asymptotic expansions are considered as N → + ∞. The method of steepest descents provides an asymptotic expansion for each fixed value of α, but this is non-uniform with respect to α near critical values α0 at which certain saddle points tend to coincidence. A more complicated expansion, involving Airy functions or generalizations thereof, is valid and uniform for α near α0. This expansion is known to be valid in a neighbourhood of α0 which does not depend on N, in contrast to certain other expansions having regions of validity which contract to a point or surface as N → ∞. It is thereby suggested that the actual region of validity has a definite geometrical shape determined by the functions f and g and the contour C, just as steepest descents expansions are valid in regions bounded by Stokes' lines. In this paper, procedures are derived for the determination of such regions, subject to assumptions concerning f, g and C. The validity of the expansion is established in regions so determined.
The numerical solution of systems of stiff ordinary differential equations
Authors: Cash J. R. 
Published: November 2008

AbstractAlgorithms are developed for the numerical solution of systems of first-order ordinary differential equations, the solutions of which have widely different rates of variation. The iterative procedures described use a step length of integration proportional to the rate of change of the required slowly varying solution in a region of integration, where either the transient components of the complete solution have become negligible compared with the chosen working accuracy or in a region where rapidly increasing components of the solution are theoretically possible but are made absent by the initial conditions. Several numerical examples are given to demonstrate the algorithms.
The normal and subnormal structure of general linear groups
Authors: Wilson J. S. 
Published: November 2008

The problem of locating and classifying the normal subgroups of GLn(R), the general linear group of degree n over a commutative ring R with an identity element, has received considerable attention. The solution when R is a field is well known (of. Dieudonné(5), Artin(1)): unless n is equal to two and R has two or three elements, normal subgroups of GLn(R) either lie in the centre of GLn(R) or contain the special linear group SLn(R). However, if R is not a field, then for each ideal I of R the natural map R → R/I induces a homomorphismand, if 0 < I < R, the kernel of θ1 is a non-central normal subgroup of GLn(R) which does not contain SLn(R). The most that may be expected is that each normal subgroup determines an ideal I of R, in such a way that all normal subgroups determining the same ideal I lie between suitably defined greatest and smallest normal subgroups of GLn(R) corresponding to I. For example, write ZI for the inverse image of the centre of GLn(R/I) under the homomorphism θI, and write KI for the intersection of SLn(R) with the kernel of θI. Then KI ≽ ZI, and the results of Klingenberg(7) and Mennicke(9) show that if n ≥ 3, and if R is either a local ring or the ring of rational integers, then any normal subgroup H of GLn(R) satisfiesfor some uniquely determined ideal I. There are many similar theorems. That the above result breaks down for arbitrary rings, even for large n, follows easily from the negative solution to the congruence subgroup problem for certain rings of algebraic integers (see Bass, Milnor and Serre(3)).
Arrivals associated with a class of self-similar problems in elastodynamics
Authors: Willis J. R. , Bedding R. J. 
Published: November 2008

AbstractA systematic method is given for finding all of the singularities in the stress fields associated with self-similar elastodynamic problems for half-spaces, directly from representations developed in (1). No particular symmetry is assumed, and both two- and three-dimensional problems are discussed for arbitrarily anisotropic half-spaces. Expressions for body wave arrivals are obtained, reproducing results given in (1), and head wave arrivals, not discussed in (1), are found. Arrivals produced by interfacial dislocations and cracks are found by the same method. As an example, an account of the first arrival produced by a penny-shaped crack expanding under shear on an interface is completed, by finding the head wave that precedes the body wave, already found in (1), in a region exterior to a cone in one of the half-spaces.
Moving forcing effects in a two-phase medium
Authors: Chee-Seng Lim 
Published: November 2008

AbstractAn unbounded two-phase medium is transmitting radiation from a group of uniformly moving, two-dimensional forcing effects. The emission process is governed by two matrix differential equations for both interior regions, accompanied by a common set of boundary conditions along the communicating interface. Anticipating possible hyperbolic modes, in co-existence with elliptic modes during the eventual steady state, a radiation condition is initially applied. This radiation condition, together with a particular boundedness criterion, decides the precise number of boundary equations required. An exact solution is established for moving forcing effects having arbitrary spatial distributions. Those aligned along the interface correspond to sheet sources. Superimposed are additional source sheets virtually induced by the action of internal forcing effects, converting their combined incident field into reflection and refraction. A peculiar feature is the invariant propagation along characteristics of certain hyperbolic modes, under the essential presence of elliptic modes, as real Hilbert transforms (in the sense of principal values) of a net interface source density.
On the elasticity of monatomic crystals
Authors: Parry Gareth P. 
Published: November 2008

AbstractThis is an exploration of the mechanical consequences of the symmetry inherent in a monatomic elastic crystal lattice. The investigation is based on a theorem by means of which the square of the right stretch tensor is uniquely decomposed. Generality is assured by the affine equivalence of all monatomic lattices. Response functions appropriate to perfect monatomic crystals are thereby constructed, and some simple deformation paths are considered.
Global stability of genetic systems governed by mutation and selection
Authors: Moran P. A. P. 
Published: November 2008

AbstractThis paper considers the behaviour of infinite haploid genetic populations under the influence of mutation and selection depending on a single locus. Under wide conditions the Perron–Frobenius theory of non-negative matrices and its generalization by Vere-Jones are used to prove that there is a single globally stable state of the population when there is a finite or, under more restrictive conditions, an infinite set of possible alleles.
The Hopf bifurcation theorem in three dimensions
Authors: Swinnerton-Dyer Peter 
Published: November 2008

AbstractThe Hopf bifurcation theorem describes the creation of a limit cycle from an isolated singular point of a system of first-order differential equations depending on a parameter. This paper describes a method for determining explicitly a range of values of the parameter throughout which the Hopf configuration continues to exist; only the three-dimensional case is described in this paper, but the method can be generalized.
On a conjecture of Carter concerning irreducible Specht modules
Authors: James G. D. 
Published: November 2008

We study the question: Which ordinary irreducible representations of the symmetric group remain irreducible modulo a prime p?Let Sλ be the Specht module corresponding to the partition λ of n. The definition of Sλ is ‘independent of the field we are working over’. When the field has characteristic zero, Sλ is irreducible, and gives the ordinary irreducible representation of corresponding to the partition λ. Thus we are interested in the problem of whether or not Sλ is irreducible over a field of characteristic p.
On non-local continuum mechanics
Authors: Green A. E. , Naghdi P. M. 
Published: November 2008

AbstractIt is shown in this paper that the conservation laws of non-local continuum mechanics are equivalent to, and can be derived from, the conservation of energy and the invariance conditions under superposed rigid body motions. Also, the theory of non-local thermoelasticity is reconsidered in the light of recent developments in thermodynamics, taking invariance conditions fully into account.
On the iteration of rational functions
Authors: Garber V. 
Published: November 2008

In the theory of the iteration of a rational function or transcendental entire function R(z) of the complex variable z we study the sequence of natural iterates, {Rn(z):n = 0, 1,…}, of R, whereThe domain of definition of the iterates is , the extended complex plane (if R is rational), and (if R is entire transcendental) with the topology of the chordal metric and euclidean metric respectively. Fatou(5) and Julia(9) developed a global theory of the iteration of a rational function. In (6) Fatou extended the theory of (5) to transcendental entire functions. A central role is played in the theory by the F-set, F(R), of R, R rational or entire, which is defined to be the set of points at which the family of iterates do not form a normal family in the sense of Montel.
Generalized approximate methods for transmission through a barrier governed by a differential equation of order 2n
Authors: Heading John 
Published: November 2008

AbstractThe potential barrier governed by a second-order ordinary differential equation has been studied for decades, both exactly and approximately. These concepts are generalized so as to be applicable to differential equations of arbitrary even order. The barrier is defined, and the approximate solutions both inside and outside are derived. Transmission through this barrier is investigated by deriving connexion formulae through the two transition points of arbitrary odd order. The transmitted solution is linked through the barrier to the incident and reflected solutions in a unique manner, enabling an approximate transmission coefficient to be calculated and its structure to be ascertained. Every concept in the investigation is a suitable generalization of the elementary case, the generalization possible being a product of the approximate processes adopted and how they limit the nature of the generalization. An inspection of the elementary case and its transmission coefficient gives no hint as to the nature of the generalization, the limitations necessarily imposed, and the structure of the final transmission coefficient, since the elementary case has special features not present in the generalization.
Transforms which almost vanish at infinity
Authors: Pigno Louis 
Published: November 2008

Let be the circle group, M() the set of bounded Borel measures on and ℤ the additive group of integers. If μ ∈ M() and n ∈ ℤ, defineA well-known result of Rajchman states thatThe following quantitative generalization of this result has been given in (2) by K. de Leeuw and Y. Katznelson.
The geometric realization of Wall obstructions by nilpotent and simple spaces
Authors: Mislin Guido 
Published: November 2008

Let π denote a finite group. It is well known that every element of the projective class group K0 ℤπ may be realized as Wall obstruction of a finitely dominated complex with fundamental group π (cf. (13)). We will study two subgroups N0ℤπ and Nℤπ of K0ℤπ, which are closely related to the Wall obstruction of nilpotent spaces. If the group π is nilpotent and if S denotes the set of elements x ∈ K0ℤπ which occur as Wall obstructions of nilpotent spaces, thenIt turns out that in many instances one has N0,ℤπ = Nℤπ (cf. Section 3) and one obtains hence new information on S. The main theorem (2·4) provides a systematic way of constructing finitely dominated nilpotent (or even simple) spaces with non-vanishing Wall obstructions.
On conjectures of Mahowald, Segal and Sullivan
Authors: Lin Wen-Hsiung 
Published: November 2008

In this paper we prove some results about the stable homotopy and cohomotopy of spaces related to the infinite real protective space RP∞. These include M. E. Mahowald's conjecture on the limit of stable homotopy of stunted real projective spaces RP2N+m/RP2N−m as N, m → ∞, G. Segal's Burnside ring conjecture forand the stable analogue of a conjecture of D. Sullivan on RP∞.
A generalization of McDiarmid's theorem for mixed Bernoulli percolation
Authors: Hammersley J. M. 
Published: November 2008

Let G be an infinite partially directed graph of finite outgoing degree. Thus G consists of an infinite set of vertices, together with a set of edges between certain prescribed pairs of vertices. Each edge may be directed or undirected, and the number of edges from (but not necessarily to) any given vertex is always finite (though possibly unbounded). A path on G from a vertex V1 to a vertex Vn (if such a path exists) is a finite sequence of alternate edges and vertices of the form E12, V2, E23, V3, …, En − 1, n, Vn such that Ei, i + 1 is an edge connecting Vi and Vi + 1 (and in the direction from Vi to Vi + 1 if that edge happens to be directed). In mixed Bernoulli percolation, each vertex Vi carries a random variable di, and each edge Eij carries a random variable dij. All these random variables di and dij are mutually independent, and take only the values 0 or 1; the di take the value 1 with probability p, while the dij take the value 1 with probability p. A path is said to be open if and only if all the random variables carried by all its edges and all its vertices assume the value 1. Let S be a given finite set of vertices, called the source set; and let T be the set of all vertices such that there exists at least one open path from some vertex of S to each vertex of T. (We imagine that fluid, supplied to all the source vertices, can flow along any open path; and thus T is the random set of vertices eventually wetted by the fluid). The percolation probabilityis defined to be the probability that T is an infinite set.
Basic stress analysis of hyperbolic regimes in plastic media
Authors: Hill R. 
Published: November 2008

AbstractNonlinear problems of two-dimensional deformation or stress in solid continua are considered where the in-plane components of stress are self-equilibrated and subject to a scalar constraint. In applications the latter is often a yield condition for plastic media. Such field equations are frequently hyperbolic, with a pair of characteristic curves through any point. The primary aim is to express the integrable differential relations along the curves in their simplest form, by an optimal choice of coordinates and variables. Special cases of this problem are now classical, but the general case has received little attention and the universal canonic structure of the relations has escaped notice.
The projective extensions of a finite group
Authors: Webb P. J. 
Published: November 2008

Let G be a finite group and let g be the augmentation ideal of the integral group ring G. Following Gruenberg(5) we let (g̱) denote the category whose objects are short exact sequences of zG-modules of the form and in which the morphisms are commutative diagramsIn this paper we describe the projective objects in this category. These are the objects which satisfy the usual categorical definition of projectivity, but they may also be characterized as the short exact sequencesin which P is a projective module.
The volume of certain convex sets
Authors: McMullen P. 
Published: November 2008

AbstractLet Ll …, Lr be independent linear subspaces of Ed, with di = dim Li ≥ 1 (i = 1, …, r), and Ed = L1 + … + Lr. For each i, let K¯;i be a convex body in Li with 0 ∈ K¯i, Ki = K¯i + ti(ti ∈ Ed) any translate of K¯i, and define K = con v (K1 ∪ … ∪ Kr), and similarl K¯. Then vol K ≥ vol K¯. Necessary and sufficient conditions for equality are also obtained.
A note on the magnetic scalar potential of an electric current-ring
Authors: Hulme A. 
Published: November 2008

AbstractThis paper considers the problem of expressing the magnetic scalar potential associated with the steady flow of an electric current around a thin circular wire, in terms of ‘local’ toroidal coordinates. This potential is known to be a multi-valued function of position and so cannot be expressed directly in terms of fundamental (i.e. single-valued) solutions of Laplace's equation. It is shown that the potential can however be expressed quite simply, as an infinite series of multi-valued toroidal harmonics and that this series is rapidly convergent in the neighbourhood of the current-ring.
Note on the reflexion of water waves at a wall in the presence of surface tension
Authors: Rhodes-Robinson P. F. 
Published: November 2008

AbstractIn this note we examine the influence of surface tension on surface waves incident against a fixed vertical plane wall. The motion is time harmonic and is determined by making the initial assumption that the free-surface slope at the wall is prescribed. From the unique solution obtained for the velocity potential, the parameter involved in this specification can be determined, for small laboratory-scale waves at least, using some longstanding experimental results on meniscus behaviour at a moving contact line. The effect of surface tension is to produce a motion wherein reflexion from the wall is not complete and there is a local disturbance, in contrast to the classical standing-wave motion in the absence of surface tension.