bluuebunny/crossref_metadata_2025 huggingface dataset:
On the motion of a liquid in a spheroidal cavity of a precessing rigid body. II
Authors: Roberts P. H. , Stewartson K.
Published: November 2008

It is supposed that a viscous incompressible fluid is contained in an oblate spheroidal cavity (major axes a, eccentricity e) in a rigid body, and that, up to time t = 0, both fluid and container rotate together with angular velocity ω about the minor axis LB of the spheroid, which is fixed in space. At t = 0, the axis of rotation is moved impulsively, and is given a motion of precession (angular velocity Ω) about an axis LS fixed in space, which makes an angle α with LB. It is required to find the ultimate state of motion of the fluid relative to the container. In a previous paper (Stewartson and Roberts (4)), this problem was solved for arbitrary α under the assumptions that

where v is the kinematic viscosity. In the present paper, it is shown how the problem may be solved for arbitrary e (including zero) under the assumptions that
Unified theory for the solutions of the unsteady thermal boundary-layer equation
Authors: Sarma G. N.
Published: November 2008

The unsteady two-dimensional thermal boundary-layer equation linearized as by Lighthill is studied. Two different problems are considered mainly, one in Part I and the other in Part II. Part I deals with the solution when the temperature of the main stream is constant and that of the wall is unsteady and Part II when the temperature of the main stream is constant and the heat transfer from the wall is unsteady. Unified methods are developed from which the results for the stagnation flow and the flow along a flat plate, etc., can be derived as special cases. The results of the unsteady velocity boundary-layer equations analysed by Sarma are used and solutions are obtained in two cases, first, when the main stream is in steady motion and the wall is in an arbitrary motion and secondly when the main stream is in unsteady motion and the wall is at rest. The flat plate problem is considered in detail; the results agree with those given by Lighthill and Moore.
Two weak Poincaré theorems
Authors: Doylea P. H.
Published: November 2008

Theorem 1. Let M3be a compact 3-manifold and let M3 = E3 ∪ R be a standard decomposition where R is a subcomplex in a triangulation of M3((2)). If M3is a homology 3-sphere while R contains no arc that is wild in M3then M3 = S3
A boundary-layer theory for plates with initial stress
Authors: Laws N.
Published: November 2008

A theory is presented for small deformations of a plate which is initially stressed, the state of initial stress not necessarily being obtained by elastic deformation from some other unstressed state. The method used is an asymptotic integration of the full three-dimensional equations. The usual Kirchhoff boundary conditions for stretching and bending are deduced from the analysis.
On the consistency and relative strength of regular summability methods
Authors: Copping J.
Published: November 2008

Statement of results. Let A and B be two matrix summability methods, and S a given set of sequences. We shall say that B is S-stronger than A if B sums every sequence which belongs to S and is summed by A. If each of A, B is S-stronger than the other, A and B will be called S-equivalent. If B is S-stronger than A, but A is not S-stronger than B, we say that B is strictly S-stronger than A.
Evaluation of an integral containing Bessel functions
Authors: Miller G. F.
Published: November 2008

The integral, involving the functions Jn+½ and J−n−½(x) where n is a positive integer, arises in a problem in electrical network theory and represents a measure of the overall error in the diagonal Padé approximant to the function e−s. A method of evaluation based on Euler's transformation of series is described, values of the integral are tabulated to five decimal places for n = 1(1)10(5)40, and the asymptotic behaviour for large n is determined.
The transverse flexure of uniformly loaded curvilinear and rectilinear polygonal plates
Authors: Bassali W. A. , Barsoum F. R.
Published: November 2008

Complex variable methods are applied to derive exact solutions in closed forms for the small deflexions of uniformly loaded thin isotropic plates bounded by regular curvilinear polygonal contours havingnsides. The supported boundary is either clamped or has equal boundary cross-couples. For rectilinear edges the latter conditions agree with those for a simply supported boundary. The plates taken in thez-plane are conformally mapped on the unit circle in the ζ-plane by the general mapping function
Transverse surface waves in magneto-elasticity
Authors: Purushothama C. M.
Published: November 2008

It has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.
Applications of the theory of the general hodograph equation
Authors: Mackie A. G.
Published: November 2008

For a gas with a general equation of state the stream function for the flow past a flat plate is determined when the plate is held at an angle ½π–α to the stream. At infinity the Mach number M1 = 1 and free streamlines, on which M1 = 1, extend from the edges of the plate to infinity downstream. The method of solution requires the determination of the correct singularity corresponding to the free stream and the subsequent satisfying of the boundary conditions. The drag coefficient is determined in the form of a contour integral and the computational problems in evaluating the drag are discussed. The integral is evaluated for small values of α for a gas with an equation of state as given by Tomotika and Tamada(6).
Still another way to calculate representations of the three-dimensional pure rotation group
Authors: Albert R. H.
Published: November 2008

An explicit formula is derived for exp (iβJz) as a finite sum of irreducible tensor components. With this formula, a technique is developed to obtain the matrix elements of exp (iβJy).
Asymmetric inequalities for non-homogeneous ternary quadratic forms
Authors: Dumir Vishwa Chander
Published: November 2008

A well-known theorem of Minkowski on the product of two linear forms states that if

are two linear forms with real coefficients and determinant Δ = |αδ − βγ| ≠ 0, then given any real numbers c1, c2 we can find integers x, y such that
On the convex kernel of a compact set
Authors: Larman D. G.
Published: November 2008

Suppose that E is a compact subset of a topological linear space ℒ. Then the convex kernel K, of E, is such that a point k belongs to K if every point of E can be seen, via E, from k. Valentine (l) has asked for conditions on E which ensure that the convex kernel K, of E, consists of exactly one point, and in this note we give such a condition. If A, B, C are three subsets of E, we use (A, B, C) to denote the set of those points of E, which can be seen, via E, from a triad of points a, b, c, with a ∈ A, b ∈ B, c ∈ C. We shall say that E has the property if, whenever A is a line segment and B, C are points of E which are not collinear with any point of A, the set (A, B, C) has linear dimension of at most one, and degenerates to a single point whenever A is a point.
Generalized Neumann expansions involving hypergeometric functions
Authors: Srivastava H. M.
Published: November 2008

1. Making use of the familiar abbreviation

let us adopt a contracted notation for the generalized hypergeometric function AFB[x] and write

where (a) denotes the sequence of parameters
The linear theory of an elastic Cosserat plate
Authors: Green A. E. , Naghdi P. M.
Published: November 2008

Some features of the linear theory of an elastic Cosserat plate are discussed and special attention is given to a bending theory which corresponds to the bending of a transversely isotropic three-dimensional plate. A useful representation for the solution of the system of differential equations characterizing the bending of an elastic Cosserat plate is deduced and the results are applied to the problem of an infinite Cosserat plate with a circular hole, the plate being in a state of uniform bending at infinity.
A theorem on perfect Singer difference sets
Authors: Yates D. L.
Published: November 2008

This theorem proves the equivalence of two conjectures on perfect Singer difference sets, one of which is concerned with the actual computation of the set, and the other being of interest in the theory of multipliers and fixed sets.
A theorem about hyperspaces
Authors: Hursch J. L.
Published: November 2008

Recently Isbell(4) and Ward (6) have given examples of pairs of uniformities inducing the same topology on the hyperspace of subsets of a uniform space. Smith (5) has shown that, if two uniformities induce the same topology on the hyperspace, they must be equal in proximity. The author, in (2), has introduced a relation, ‘height’, between uniformities which is in a sense dual to proximity. It is the purpose of this paper to show that, if two uniformities are equal in proximity and height, then they induce the same topology on the hyperspace. Although Ward's uniformities are not equal in height, an example of two distinct uniformities equal in proximity and height is given in (3). In fact, a slight modification of that example will give an example of a countably infinite number of distinct uniformities, all of which are equal in proximity and height.
On the structure ofk-chromatic graphs
Authors: Dirac G. A.
Published: November 2008

It is shown that fork≥ 5 in everyk-chromatic graph there is a set ofkdistinct verticesV1, …,Vkwith the property that fori, j= 1, …,kandi≠jthe graph contains the union of a set of 4 paths connectingViandVjno two of which have any edge or any vertex besidesViandVjin common andk− 1 paths connectingViandVjno two of which have any edge in common.
Note on diffraction by a disc
Authors: Heins A. E. , Jones D. S.
Published: November 2008

A simple formula is derived for the connexion between the scattered fields due to a sound-soft, a sound-hard and a perfectly conducting circular disc respectively.
Ein neuer Beweis eines Satzes von Magnus
Authors: Stammbach U.
Published: November 2008

The author provides a new and very simple proof of the following theorem of Magnus (2):

Theorem. Let the group G have both a presentation with n + r generators and r relations also a presentation with n generators. Then G is the free group on n generators.
The β- and γ-duality of sequence spaces
Authors: Garling D. J. H.
Published: November 2008

AK-space (E, τ) is a linear spaceEof sequences with a locally convex topology τ for which the inclusion map: (E, τ) → (ω, product topology) is continuous. In (2) topological properties ofK-spaces were determined directly from properties of the spaceEand the topology τ. It is, however, very natural to consider duality properties ofK-spaces and the purpose of this paper is to determine some of these properties.
A new formula for Jacobi polynomials
Authors: Sharma B. L.
Published: November 2008

The main aim of the present paper is to give a new generating function for a product of n-Jacobi polynomials. The result established in this paper is the extension of my formula (4).
Some integrals involving Gauss's hypergeometric function and Meijer's G-function
Authors: Bajpai S. D.
Published: November 2008

The object of this paper is to evaluate some integrals involving the product of Gauss's hypergeometric function and Meijer's G-function by expressing the G-function as a Mellin–Barnes type integral and interchanging the order of integrations. The integrals are important because on specializing the parameters they lead to many results for MacRobert's E-function, Bessel, Legendre, Whittaker functions and other related functions. In what follows δ is a positive integer and Δ(δ, α) represents the set of parameters
A theorem of Hardy, Littlewood and Pólya and some related results for infinite vectors
Authors: Perfect Hazel
Published: November 2008

We recall that a square matrix (finite or infinite) with non-negative elements and with each row-sum and column-sum equal to 1 is called doubly-stochastic (d.s.). If each row-sum and column-sum of a non-negative square matrix is less than or equal to 1, the matrix is called doubly-substochastic (d.s.s.).
High-frequency diffraction of the radiation from a nearby source
Authors: Jones D. S.
Published: November 2008

An approximate formula is found for the field produced on the boundary of an obstacle in an inhomogeneous medium by a source which is close to the boundary. Both harmonic and aperiodic waves are discussed.
Generation of an axisymmetrical acoustic pulse by a deformable sphere
Authors: Tupholme G. E.
Published: November 2008

In this paper we consider sound pulses generated in the fluid outside an impermeable sphere by axisymmetrical time-dependent deformations of the sphere. Following an account of some analytic techniques applicable to this class of problems, a detailed study is made of the case in which the movement of the spherical boundary is confined to a cap of angle α (0 < α < π). In this case a rather complicated pattern of wavefronts develops consisting of a direct (spherical) wavefront, diffracted wave-fronts and a toroidal wavefront having as its centre circle the edge of the cap. Approximations to the velocity potential near the various wavefronts are obtained and some numerical results are given.
A general theory of unsteady boundary-layer flows
Authors: Sarma G. N.
Published: November 2008

The unsteady two-dimensional boundary-layer flows are investigated, using the equations linearized as by Lighthill. It is assumed, unlike separable forms and power functions taken by Sarma, that the perturbations which cause the unsteadiness in the flow are arbitrary functions of the distance along the flow and the time. In addition to the Reynolds number, it is explicitly assumed that the flow for large times is defined by a set of parameters like

ξ = φ/U0, U0(x) and φ (x are functions associated with the main stream in steady flow, λ(x, t) represents a perturbation, t time and x is the distance along the surface. This particular assumption is essentially an idea that is suggested by the work of Sarma. In solving the equations a number of free constants and arbitrary functions are used, which will be specified according to the given physical situation. For large times series solutions are assumed in terms of the above parameters and ultimately sets of differential equations are obtained in a single variable. Thus the theory makes the problem ready for computational work. For small times using the steady state solutions given in this paper, we proceed along the same lines as given in the work of Sarma. The velocity as well as thermal boundary layers are analysed in this paper.
Kruskal's theorem for matroids
Authors: Welsh D. J. A.
Published: November 2008

Kruskal's theorem for obtaining a minimal (maximal) spanning tree of a graph is shown to be a special case of a more general theorem for matroid spaces in which each element of the matroid has an associated weight. Since any finite subset of a vector space can be regarded as a matroid space this theorem gives an easy method of selecting a linearly independent set of vectors of minimal (maximal) weight.
Uniqueness theorems for analytic functions of one and of several complex variables
Authors: Rubel L. A. , Taylor B. A.
Published: November 2008

1. Suppose thatfis a function analytic on a regionGin complexn-spaceCn, and thatf(m)(w(m)) = 0 for eachm= (m1,m2,…,mn),mi= 0, 1, 2,…, where
Some further results on the birth-and-death process and its integral
Authors: Puri Prem S.
Published: November 2008

In a simple homogeneous birth-and-death process with λ and μ as the constant birth and death rates respectively, letX(t) denote the population size at timet,Z(t) the number of deaths andN(t) the number of events (births and deaths combined) occurring during (0,t). Also let. The results obtained include the following:

(a) An explicit formula for the characteristic quasi-probability generating function of the joint distribution ofX(t),Y(t) andZ(t).

(b) LetX(0) = 1. It is shown that, ift→ ∞ while λ ≤ μ,N(t) ↑Na.s., whereNtakes only positive odd integral values. If λ > μ, thenP[N(t) ↑ ∞] = 1 − μ/λ. Given thatN(t)∞, the limiting distribution ofN(t) is similar to that ofN. It was reported earlier (Puri (11)), that the limiting distribution ofY(t) is a weighted average of certain chi-square distributions. It is now found that these weights are nothing but the probabilitiesP[N= 2k+ 1] (k= 0, 1,…).

(c) Let λ = μ, andMXω),MYωandMZωbe defined as in (36), then as

where the c.f. of (X*;Y*;Z*) is given by (38).

(d) Exact expressions for the p.d.f. ofY(t) are derived for the cases (i) λ = 0, μ > 0, (ii) λ > 0, μ = 0. For the case (iii) λ gt; 0, μ > 0, since the complete expression is complicated, only the procedure of derivation is indicated.

(e) Finally, it is shown that the regressions ofY(t) and ofZ(t) onX(t) are linear forX(t) ≥ 1.
Bezout rings and their subrings
Authors: Cohn P. M.
Published: November 2008

The importance of principal ideal domains (PIDs), both in algebra itself and elsewhere in mathematics is undisputed. By contrast, Bezout rings, ‡ although they represent a natural generalization of PIDs, play a much smaller role and are far less well known. It is true that many of the properties of PIDs are shared by Bezout rings, but the practical value of this observation is questioned by many on the grounds that most of the Bezout rings occuring naturally are in fact PIDs. However, there are several fairly natural methods of constructing Bezout rings from other rings, leading to wide classes of Bezout rings which are not PIDs, and it is the object of this paper to discuss some of these methods.
Plane separation
Authors: Doyle P. H.
Published: November 2008

Theorem. A simple closed curve J in the plane E2separates E2.
A note on Riesz means
Authors: Das G.
Published: November 2008

1. For the familiar definition of (R, λn, κ), (R*, λn, κ) and (N, p) means and their notations, see, for example (3). If {fn} is any arbitrary sequence, we adopt the convention throughout that f−1 = 0. A method of absolute summability |A| is said to be ineffective if it is absolutely regular and sums only absolutely convergent sequences. The main object of this note is to prove absolute analogues of Kuttner's results in (3). And for this we need to prove a theorem (Theorem 1) on ineffectiveness for |N, p| method.
The flow of a micropolar liquid layer down an inclined plane
Authors: Willson A. J.
Published: November 2008

Consideration is given to the flow of a micropolar liquid down an inclined plane. The steady state is analysed and Yih's technique is employed in an investigation of the stability of this flow with respect to long waves. Detailed calculations are given for thin films and it is shown that the micropolar properties of the liquid play an important role in the stability criterion.
Rotation of a reinforced circular cylindrical tube
Authors: Chaudhry H. R. , Chawla A. N.
Published: November 2008

The theory of large elastic deformation of reinforced elastic materials is applied to discuss the rotation of a circular tube of incompressible elastic material, reinforced with inextensible cords lying along helical paths.
A probabilistic proof of a formula for Jacobi polynomials by L. Carlitz
Authors: Milch Paul R.
Published: November 2008

Letbe the Jacobi polynomial as defined by Szegö in (7) (see equation (4) below.) Carlitz in (2) presented among others the following formula

Although, as Carlitz claims, this formula may be derived directly from the definition of Jacobi polynomials, a probabilistic proof such as presented below may shed some new light on formula (1), as well as suggest probabilistic proofs for other similar formulas of Jacobi polynomials, e.g. those given by Manocha and Sharma in (4) and (5) and by Manocha in (3). In addition, it is quite possible that this method of proof will result in the derivation of some new formulas for Jacobi polynomials.
The particular integral in plate problems
Authors: Sayer F. P.
Published: November 2008

In the course of this paper series expressions are obtained for the displacement vector so that the stresses take prescribed values on the bounding surfaces z = ±h of the plate. Since no conditions are satisfied on the curved surface that forms the bounding edge of the plate these expressions or particular integrals cannot, in general, be solutions to three-dimensional plate problems. They are, however, complementary to the work of Green in (1).
Properties of certain measures on a topological group
Authors: Drury S. W.
Published: November 2008

We denote by M(G) the space of bounded regular borel measures on a non-discrete locally compact Abelian topological group G. Under the convolution product and norm of total mass M(G) becomes a complex commutative banach algebra. We denote by Φ the space of m.l.f.s (multiplicative linear functionals) on M(G) and by σ the subset of Φ consisting of functionals symmetric in the sense that

where * denotes the usual involution on M(G). These matters are discussed more fully in Williamson (1).
Surface instability of a dielectric fluid in an electric field
Authors: Michael D. H.
Published: November 2008

This paper is a sequel to a recent paper (1) in which the author discussed gravity waves on a horizontal layer of conducting fluid with a normal electrostatic field at the free surface. In this work results are given for waves in an incompressible dielectric fluid, in a similar configuration. Treating the dielectric as an inviscid fluid the stability of the system is first described in terms of the changes in potential energy in a small static displacement. The result so obtained is then confirmed by a normal mode analysis in which a dispersion relation is obtained for the inviscid model. The paper gives finally a discussion of the results for a viscous dielectric fluid, the main point of which is that, as in (1), in the transition from stable to unstable disturbances viscosity plays no part, and that the stability characteristics are the same as those for an inviscid dielectric fluid.
Continuous and Köthe–Toeplitz duals of certain sequence spaces
Authors: Maddox I. J.
Published: November 2008

If (X, g) is a paranormed space, with paranorm g (see (2)), then we denote by X* the continuous dual of X, i.e. the set of all continuous linear functionals on X. If E is a set of complex sequences x = (xk) then E† will denote the generalized Köthe–Toeplitz dual of E
Integral representations for solutions of Heun's equation
Authors: Sleeman B. D.
Published: November 2008

In 1914 Whittaker(12) conjectured that the Heun differential equation is the simplest equation of Fuchsian type whose solution cannot be represented by a contour integral; instead the nearest approach to such a solution is to find a homogeneous integral equation satisfied by a solution of the differential equation. In this paper we reconsider Whittaker's conjecture and show that in fact solutions of Heun's equation can be represented in terms of contour integrals, similar to those of Barnes for the hypergeometric equation. The integrands of these integrals are of a rather complicated nature and cannot be said to involve known or simpler functions although they do provide expressions for the analytic continuation of Heun functions analogous to those for the hypergeometric functions.
A note on the space-time frame of Eddington
Authors: Klotz A. H.
Published: November 2008

It is shown that Eddington's Fundamental Theory admits only four basic operators. The symmetry properties and the reality conditions of the E-frame of reference are formulated in an abstract way.
A counter-example to the three balls problem
Authors: Lickorish W. B. R. , Rourke C. P.
Published: November 2008

We work throughout in the p.l. category (see (8)) consisting of polyhedra and p.l. (piecewise linear) maps. We are concerned with the following problem which is of importance in the theory of p.l. transversality.
A new interpretation of the NUT metric in general relativity
Authors: Bonnor W. B.
Published: November 2008

The NUT metric is interpreted as the field of (a) a mass around the origin of coordinates, and (b) a semi-infinite massless source of angular momentum.
Impossibility of class one electromagnetic fields
Authors: Pandey S. N. , Kansal I. D.
Published: November 2008

In a recent paper (1) it has been established that a spherically symmetric space-time of class one cannot describe an electromagnetic distribution of energy. In this investigation the inconsistency of class one conditions with Rainich algebraic conditions was shown in case of spherical symmetry. In the present paper it is shown that the result is true for space-time of class one, in general.
Certain fractional q-integrals and q-derivatives
Authors: Agarwal R. P.
Published: November 2008

In a recent paper Al-Salam(1) has denned a fractional q-integral operator by the basic integral

(1) Where α ≠ 0, −1, −2, …. Using the series definition of the basic integrals, (1·1) is written as

valid for all α
Dirichlet series with independent and identically distributed coefficients
Authors: Clarke L. E.
Published: November 2008

Let be a Dirichlet series. Then it is known that if is divergent, the abscissa of convergence σ1 is given by

and that if is divergent, the abscissa of absolute convergence σ2 is given by
A generalized Euler–Lagrange equation
Authors: Arthurs A. M.
Published: November 2008

A generalized Euler–Lagrange equation is presented. It provides a unified approach to boundary value problems in potential theory, diffusion, magnetostatics, and integral equations.
Addendum to ‘A hypergeometric transformation associated with the Appell function F4’
Authors: Srivastava H. M.
Published: November 2008

The hypergeometric transformation formulae (6) and the one that follows on p. 766 in my paper (1) should be read as

and

respectively, where 2F1[a,b; c; z] denotes Gauss's hypergeometric function, and ((2), p. 211)

with, as usual,

the conditions of convergence for the double series being
Approximations to extreme tail probabilities for sampling without replacement
Authors: Stone M.
Published: November 2008

Introduction and summary: In the distribution of the sum of n random variables

for which we suppose , the tail probability will be called an extreme tail probability if the normal approximation

is poor, when is asymptotically normal and n is large. This paper concerns the specialization of (1.1) in which

with a random permutation of nλ ones and n − nλ zeros, that is, in which T is the total for a simple random sample from the population with sampling fraction λ. In this case, we will always write T as Tλ. For brevity, we may write {c1,…, cn} for .
On the seiche motion in a curved lake
Authors: Johns B. , Hamzah A. M. O.
Published: November 2008

An account is given of the seiche motion in a curved lake. It is shown that the periods of the first two modes of oscillation are effectively unchanged in comparison with those for a straight lake having a length equal to that of the median line along the curved lake. Near to the nodal positions, the surface elevation is uniform across the lake. In the neighbourhood of the anti-nodes, which includes the ends of the lake, the wave amplitude is shown to be a maximum at the outside of the bend.
Compressible flows with circular sector hodographs. II. Réthy flows
Authors: McLaughlin Maureen D. , Pack D. C.
Published: November 2008

The general solution of the Chaplygin equation for ‘simple wedge flows’ is used for the particular case of Réthy flows. The drag coefficient is evaluated and comparisons made with the results obtained from the approximate hodograph equations of Tricomi and of Tomotika and Tamada. A distinction is made between subsonic and transonic régimes and the limitations on the lengths and pressure differences permissible in the various ranges are discussed.
On integral operators with kernels involving Bessel functions (Correction and Addendum)
Authors: Okikiolu G. O.
Published: November 2008

1. Introduction. The purpose of this paper is to correct a number of points in an earlier paper (1) of the same title, and to prove a number of new results which supplement those given in that paper. The notation and definitions of this paper are those of (1).
Integrals involving classical polynomials
Authors: Dhawan G. K.
Published: November 2008

1. Introduction. In a recent paper the author (2) has derived a number of integrals with the help of results ((5), p. 343)

where α, β, α′, β′ are parameters such that

and

whereK has the same meaning as above.
A small unsteady perturbation on the steady hydromagnetic boundary-layer flow past a semi-infinite plate
Authors: Das U. N.
Published: November 2008

This paper is concerned with the unsteady hydromagnetic boundary-layer flow past a semi-infinite flat plate when the oncoming free stream is perturbed by an arbitrary function of time and the applied magnetic field is parallel to the plate far away from it. Following Lighthill, the two-dimensional boundary-layer equations are separated into those representing steady and unsteady parts of the flow and they have been solved in sequence. For the unsteady part of the motion two types of solutions are obtained, one for large times and the other for small times. Also the quasi-steady solution is obtained in terms of the steady solution. The skin friction and the tangential magnetic field at the plate are calculated.
Collapsing K × I to vertical segments
Authors: Wright Perrin
Published: November 2008

In this paper we shall consider contractible 2-dimensional cell complexes K with one 0-cell v, one l-cell a, and one 2-cell D, where the boundary of D is attached to a by a word in a and a−1. In order for such a complex K to be contractible, the attaching word in a and a−1 must have total degree ± 1. The simplest example occurs when the attaching word is a; in this case K is a 2-cell, and is of no interest since K is collapsible. If any other word of degree ± 1 is used, the resulting K is contractible but not collapsible.
A note on the homotopy type of PL2
Authors: Scott G. P.
Published: November 2008

Let O2 denote the group of isometrics of the plane R2 fixing the origin and let PL2 denote the space of piecewise-linear (PL) homeomorphisms of R2 fixing the origin. Akiba has proved that PL2 is homotopy equivalent to O2(1). The purpose of this note is to point out that this result can be proved by the methods of the author in (4). A complete proof of this result using these methods appeared in the author's Ph.D. thesis(5).
On the differential topology of space-time
Authors: Smith J. Wolfgang
Published: November 2008

It has often been assumed in cosmology theory(1) that there exists an average density of matter in space which is everywhere greater than zero. Under this assumption the space-time M will be foliated by curves each of which represents the life history of a particle. In keeping with the postulates of general relativity theory we shall refer to these curves as geodesics. Letting X denote the space of particles one obtains a projection f: M → X which assigns to every P ∈ M the particle found at P. Conversely, given the projection f:M → X, one can recover the geodesics: they are precisely the fibres f−1(x), x∈X.
Slow viscous flow past a rotating sphere
Authors: Ranger K. B.
Published: November 2008

Keller and Rubinow(l) have considered the force on a spinning sphere which is moving through an incompressible viscous fluid by employing the method of matched asymptotic expansions to describe the asymmetric flow. Childress(2) has investigated the motion of a sphere moving through a rotating fluid and calculated a correction to the drag coefficient. Brenner(3) has also obtained some general results for the drag and couple on an obstacle which is moving through the fluid. The present paper is concerned with a similar problem, namely the axially symmetric flow past a rotating sphere due to a uniform stream of infinity. It is shown that leading terms for the flow consist of a linear superposition of a primary Stokes flow past a non-rotating sphere together with an antisymmetric secondary flow in the azimuthal plane induced by the spinning sphere. For a3n2 > 6Uv, where n is the angular velocity of the sphere, U the speed of the uniform stream, and a the radius of the sphere, there is in the azimuthal plane a region of reversed flow attached to the rear portion of the sphere. The structure of the vortex is described and is shown to be confined to the rear portion of the sphere. A similar phenomenon occurs for a sphere rotating about an axis oblique to the direction of the uniform stream but the analysis will be given in a separate paper.
Groups with every proper quotient finite
Authors: Wilson J. S.
Published: November 2008

1·1. We shall write for the class of groups all of whose non-trivial normal subgroups have finite index. Thus, rather obviously, finite groups, simple groups, and the infinite cyclic and dihedral groups all lie in the class . Other examples of -groups are to be found in a variety of contexts. The main result of Mennicke (8) shows that, for n ≥ 3, the factor group of SL(n, Z) by its centre is a -group, where SL(n, Z) denotes the unimodular group of all n × n invertible matrices with integer coefficients and with determinant 1. In McLain(7), an example is given of an infinite, locally finite, locally soluble -group, whose only non-trivial normal subgroups are the terms of its derived series, and in (4), P. Hall discusses an infinite -group, all of whose proper quotients are finite p-groups. If is a class of groups closed under taking homomorphic images, it is easily seen that the existence of an infinite -group satisfying the maximal condition for normal subgroups implies the existence of an infinite -group in the class , so that certain questions concerning the finiteness of groups satisfying the maximal condition for normal subgroups can be interpreted as questions about -groups.
Regular greatest common divisor of two polynomial matrices
Authors: Barnett S.
Published: November 2008

Let T(λ) and V(λ) be two polynomial matrices having dimensions l x l and m x l respectively, with T(λ) regular and of degree n and V(λ) of degree at most n – 1. It has recently been shown that a necessary and sufficient condition for T and V to be relatively right prime is that a certain nlm x nl matrix R(T, V) have full rank. It is shown here that if T and V have a greatest common right divisor D(λ), then provided D is regular, its degree k is equal to n – (1/l) rank R. Furthermore, if R˜. denotes the matrix of the first (n – k) lm rows of R, then it is shown that the last (n – k) l columns of R˜ are linearly independent and that the coefficient matrices of D can be obtained by expressing the remaining columns of R˜ in terms of this basis.
Equivariant integrality theorems for differentiable manifolds
Authors: Roberts R. S.
Published: November 2008

In differential topology it is often useful to be able to find restrictions on the possible vector bundles over a given manifold. For the non-equivariant case these restrictions usually state that some rational multinomial in the various charac teristic classes is an integral multiple of the fundamental cocyle.
On the non-autonomous van der Pol equation with large parameter
Authors: Lloyd N. G.
Published: November 2008

We consider the equation

.

where ø = λt + μ; the dot denotes differentiation with respect to a real variable t (frequently for convenience called ‘time’); b, λ, k, μ are parameters independent of x, ẋ t and b, λ, μ independent of k.
Infinitely divisible projective representations of the Lie algebras
Authors: Mathon D.
Published: November 2008

Infinitely divisible group representations were first defined by Streater(1) as an important concept closely related to continuous tensor product. Araki(2) analysed the factorizable representations of Lie groups and obtained a generalization of the Levy–Khinchine formula. A similar concept for Lie algebras was defined and studied by Streater in (3). Although the definition is not strictly an infinitesimal analogue of infinitely divisible representations of Lie groups, the results of (3) in the cohomological formulation are very similar to Araki's main theorem. Parthasarathy and Schmidt(4) generalized the concept of infinite divisibifity to the projective representations of locally compact groups and obtained a one-to-one correspondence between infinitely divisible projective representations and 1-co-cycles in the group cohomology with coefficients in a Hubert space. A similar generalization for Lie algebras is studied in the present paper. Infinitely divisible projective representations of Lie algebras are studied by a purely algebraic method, independently of (4) (since not all our projective representations are necessarily integrable). As expected, a one-to-one relation is obtained between the infinitely divisible projective representations and 1-co-cycles in the cohomology on the corresponding enveloping algebra with coefficients in a Hilbert space. The present problem is simpler than the group case since there is no continuity condition on the multiplier in a Lie algebra. A similar algebraic method was used in a discussion of infinitely divisible representations of canonical anticommutation relations (9).
A bivariate Poisson queueing process that is not infinitely divisible
Authors: Daley D. J.
Published: November 2008

We are using the term ‘bivariate Poisson process’ to describe a bivariate point process (N1(.), N2(.)) whose components (or, marginal processes) are Poisson processes. In this we are following Milne (2) who amongst his examples cites the case where N1(.) and N2(.) refer to the input and output processes respectively of the M/G/∈ queueing system. Such a bivariate point process is infinitely divisible. We shall now show that in a stationary M/M/1 queueing system (i.e. Poisson arrivals at rate λ, exponential service at rate µ > λ, single-server) a similar identification of (N1(.), N2(.)) yields a bivariate Poisson process that is not infinitely divisible.
Fatou–Zygmund sets
Authors: Ross Kenneth A.
Published: November 2008

1. Let G be a compact Abelian group with character group X. Let be an increasing sequence of finite symmetric subsets of X, and consider a symmetric subset P of . For any Hermitian complex-valued function u on P, we write snu for the real-valued trigonometric polynomial . Edwards, Hewitt and Ross(4) investigated the following property for a non-void measurable subset W of G satisfying W ⊂ (int W)−:

The validity of this implication was shown to be independent of the choice of . Accordingly, if (*) holds, P is called an FZ(W)-set. If P is an FZ(W)-set for all W, then P is termed a full FZ-set or full Fatou-Zygmund set. In this paper, we characterize the full FZ-sets as FZ(G)-sets satisfying a certain algebraic condition. In particular, we show that if G is connected, then a symmetric subset of X is an FZ(G)-set if and only if it is a full FZ-set. Some of the techniques are adaptations of those of Mme Déchamps-Gondim(1), (2). The class of full FZ-sets is not always closed under the operation of finite unions; this contrasts with the situation for Sidon sets and for FZ(G)-sets.
On simple, weak and strong models of propositional calculi
Authors: Harrop Ronald
Published: November 2008

In this paper we will be concerned primarily with weak, strong and simple models of a propositional calculus, simple models being structures of a certain type in which all provable formulae of the calculus are valid. It is shown that the finite model property defined in terms of simple models holds for all calculi. This leads to a new proof of the fact that there is no general effective method for testing, given a finite structure and a calculus, whether or not the structure is a simple model of the calculus.
An application of a global entropy inequality to mixtures
Authors: Lindsay K. A.
Published: November 2008

In this paper we study a mixture of a viscous fluid and an elastic solid using a global Clausius–Duhem entropy inequality. Results are similar in character to those obtained by previous writers using a more restricted type of entropy inequality. Special attention is given to the case of a mixture of a Newtonian fluid and an elastic solid.
Difference-covers that are not k-sum-covers. II
Authors: Connolly D. M. , Williamson J. H.
Published: November 2008

We examine the possibility of establishing the existence of a compact subset E of ℝ such that E–E contains a non-degenerate interval and the semigroup generated by E has measure zero. We show that the existence of such an E is equivalent to the existence of a sequence of difference-covers that are not k-sum-covers for each k∈ℕ, and, further, is equivalent to the existence of an asymmetric maximal Raikov system.
Characterizing pure loss GI/G/1 queues with renewal output
Authors: Daley D. J.
Published: November 2008

In a pure loss GI/G/1 queueing system, necessary and sufficient conditions are given for the output to be a renewal process. These conditions involve dependence between the service distribution and the renewal function of the arrival process: for example, if pr {service time < ξ} = 0 for some ξ > 0, then it is sufficient for the renewal function to be that of a quasi-Poisson process with index ξ.
k-Stability of homeomorphisms of Euclidean n-space
Authors: Brakes W. R.
Published: November 2008

Kirby and Siebenmann (in (7)) proved the annulus conjecture in dimensions five and above, by proving the stable homeomorphism conjecture in those dimensions, that is, by proving that every orientation-preserving homeomorphism of Rn is stable, if n ≥ 5. Although this result apparently lessens the importance of stable homeomorphisms, the concept of stability should still be of use in settling the fate of the annulus conjecture in dimension 4, or for uncovering a simple (i.e. non-surgical) proof in other dimensions.
Characterizations of certain multivariate distributions
Authors: Wang Y. H.
Published: November 2008

LetX1,X2, …,Xn, ben(n≥ 2) independent observations on a one-dimensional random variableXwith distribution functionF. Let

be the sample mean and

be the sample variance. In 1925, Fisher (2) showed that if the distribution functionFis normal thenandS2are stochastically independent. This property was used to derive the student'st-distribution which has played a very important role in statistics. In 1936, Geary(3) proved that the independence ofandS2is a sufficient condition forFto be a normal distribution under the assumption thatFhas moments of all order. Later, Lukacs (14) proved this result assuming only the existence of the second moment ofF.The assumption of the existence of moments ofFwas subsequently dropped in the proofs given by Kawata and Sakamoto (7) and by Zinger (27). Thus the independence ofandS2is a characterizing property of the normal distribution.
The anisotropic harmonic oscillator group
Authors: King G. M.
Published: November 2008

1. The oscillator group. The one-dimensional oscillator group was studied by Streater (7) when he was comparing different methods of calculating representations. It is interesting to generalize this work and consider the group corresponding to the n-dimensional anisotropic oscillator with frequencies ωj In fact, the ideas can be generalized to even larger groups and, in the process of considering their representa tions, several points emerge connected with the harmonic oscillator degeneracies.
Waves on a shearing current: a uniformly valid asymptotic solution
Authors: McKee W. D.
Published: November 2008

A uniformly valid asymptotic solution for waves on a shearing current is presented. This solution is more general than the previous WKB solutions because it is valid at and near a caustic. Far from the caustic line, the solution reduces to the WKB solution. It predicts that an incident wave will be reflected from a straight caustic with the same amplitude and a ½π phase shift.
On stress rates in solid mechanics with application to elasticity theory
Authors: Ogden R. W.
Published: November 2008

The efficacy of making a careful choice of strain measure in problems of solid mechanics was recognized and fully exploited by Hill(1–4). He brought coherence to fundamental stress and strain analysis by the introduction of the idea of conjugate pairs of stress and strain measures, and provided a platform for the further development of constitutive relations for solid materials.
Diffraction of impulsive elastic waves by a fluid cylinder
Authors: Jha Ramanand
Published: November 2008

In this paper, the problem of diffraction of an impulsivePwave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.

The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).
Rate of growth and convergence factors for power methods of limitation
Authors: Ziv Abraham
Published: November 2008

Let , where pk are complex numbers, have 0 < ρ ≤ ∞ for radius of convergence and assume that P(x) ≠ 0 for α ≤ x < ρ (α < ρ is some real constant). Assuming that is convergent for all (x ∈ [0, ρ), we define the P-limit of the sequence s = {sk} by

This, so called, power method of limitation (see (3), Definition 9 and (1) Definition 6) will be denoted by P. The best known power methods are Abel's (P(x) = 1/(1 – x), α = 0, ρ = 1) and Borel's (P(x) = ex, α = 0, ρ = ∞). By Cp we denote the set of all sequences, P-limitable to a finite limit and by the set of all sequences, P-limitable to zero.
Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid axially symmetric conical die
Authors: Robinson A. R. , Thompson J. C.
Published: November 2008

A solution which is exact within the framework of the classical theory of elasticity is obtained for the title problem assuming that the half space is homogeneous and isotropic, and that the die indents at a constant rate. If the shape of the die and the elastic medium are specified, the rate of indentation uniquely determines the outward speed of the edge of the expanding contact zone. The magnitude of this speed, relative to the speeds of the dilatational, rotational and Rayleigh waves in the elastic medium, determines which of four possible characteristic transient stress states will occur. Each of the four ranges of contact speed is solved by the method of rotational superposition of self-similar potentials which is briefly described in the Appendix.
Non-commutative LP-spaces
Authors: Yeadon F. J.
Published: November 2008

1. Introduction. The spaces L1 and L2 of unbounded operators associated with a regular gauge space (von Neumann algebra equipped with a faithful normal semi-finite trace) are defined by Segal(5) definitions 3.3, 3.7. The spaces Lp (1 < p < ∞, p ± 2) are defined by Dixmier(2) as the abstract completions of their bounded parts. Dixmier makes use of the Riesz convexity theorem to prove the Hölder inequality, and the uniform convexity, and hence reflexivity, of LLp (2 < p < ∞).
On the coefficients and means of functions omitting values
Authors: Hayman W. K. , Weitsman A.
Published: November 2008

Let

be regular in U = {|z| < 1}. Suppose that the values of f(z) all lie in a domain D in the w-plane. If certain geometrical restrictions are made on D we can deduce growth conditions on the maximum modulus

the means

and the coefficients αn. Good bounds for M(r, f) have been obtained under various conditions on D.
On application of a certain formula
Authors: Wani J. K.
Published: November 2008

In this paper we first demonstrate how a certain formula, which expresses (n− 1 )th divided difference in the form of a multiple integral, may be used to obtain the density function of a suitable random variable and then apply this to obtain the density of a useful variate.