bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Interaction of Longitudinally Polarized Vibrations in an Isotropic Dielectric
Authors: Simons S. 
Published: November 2008

ABSTRACTA theoretical treatment is given of the relaxation time for the absorption of longitudinally polarized vibrations in an isotropie medium. Employing standard phonon interaction theory, the relaxation time is obtained in terms of certain integrals, depending parametrically on the ratio of transverse to longitudinal sound velocity. These integrals are evaluated numerically over the range which this ratio takes in practice. The results are applied to a consideration of solid argon, sodium chloride and germanium.
Unsymmetrical flow patterns past a finite wedge profile in a High subsonic stream
Authors: Helliwell J. B. 
Published: November 2008

ABSTRACTThe flow pattern past a thin wedge-like profile set at a small angle of attack in a gas flowing with high subsonic or sonic velocity is discussed within the order of the transonic approximation. In the model considered the flow has a stagnation point at the nose of the wedge and breaks away, with velocity equal to that of sound, from the shoulders. The velocity is subsonic throughout the whole field of flow. The solution of the boundary-value problem for the wedge in a channel is formulated as a pair of dual integral equations. The complete solution is given for the wedge in a free stream and the dimensions of the profile, together with the lift coefficient, are computed as functions of the transonic similarity parameter.
The effects of surface tension and viscosity on the stability of two superposed fluids
Authors: Reid W. H. 
Published: November 2008

ABSTRACTThe effect of surface tension on the stability of two superposed fluids can be described in a universal way by a non-dimensional ‘surface tension number’ S which provides a measure of the relative importance of surface tension and viscosity. When both fluids extend to infinity, the problem can be reduced to the finding of the roots of a quartic equation. The character of these roots is first analysed so as to obtain all possible modes of stability or instability. Two illustrative cases are then considered in further detail: an unstable case for which the density of the lower fluid is zero and a stable case for which the density of the upper fluid is zero, the latter case corresponding to gravity waves. Finally, the variational principle derived by Chandrasekhar for problems of this type is critically discussed and it is shown to be of less usefulness than had been thought, especially in those cases where periodic modes exist.
Some self-reciprocal functions and kernels
Authors: Lakshmikanth V. 
Published: November 2008

The aim of this note is to find out some self-reciprocal functions and kernels for Fourier-Bessel integral transforms. Following Hardy and Titchmarsh(i), we shall denote by Rp the class of functions which satisfy the homogeneous integral equationwhere Jp(x) is a Bessel function of order p ≥ − ½. For particular values of p = ½, − ½, we write Rs and Rc irrespectively.
On homotopy Abelian H-spaces
Authors: Stasheff James 
Published: November 2008

ABSTRACTWe consider H-spaces which are Abelian ‘up to homotopy’ (cf. (9)). We analyse this condition in terms of the homotopy of an associated space called ‘the projective plane’. The analysis is applied to show that ΩCP(3) is homotopy Abelian.
Two problems on convex bodies
Authors: Croft H. T. 
Published: November 2008

We solve two problems on convex bodies stated on p. 38 of S. M. Ulam's book, A collection of mathematical problems (New York, 1960).Problem 1. This problem is due to Mazur. In three-dimensional Euclidean space there is given a convex surface W and a point O in its interior. Consider the set V of all points P defined by the requirement that the length of the interval OP is equal to the area of the plane section of W through O and perpendicular to OP. Is the (centrally symmetric) set V a convex surface?
Applications of Møller's theory on energy and its localization in general relativity
Authors: Florides Petros S. 
Published: November 2008

ABSTRACTMøller's theory on the concept of energy and its localization in general relativity is applied to calculate the energy of the interior and exterior Schwarzschild fields. It is found that the energy is equal to the (Newtonian) gravitational mass of the material system associated with the fields and that all the energy resides wholly in the material system.
Transition Integrals for Si IV and CaII
Authors: Douglas A. S. , Garstang R. H. 
Published: November 2008

AbstractAtomic wave functions calculated using the Hartree—Fock equation and a polarization potential are used to obtain mean square radii of atomic orbitals for the ions Si8+ and Ca+, and transition integrals for the Si IV and Ca II spectra. A table of radial wave functions for Ca+ is given. Our results are compared with those obtained from other wave functions, and in one case with an experimental value, and generally good agreement is obtained.
On magneto-thermo-elastic plane waves
Authors: Paria G. 
Published: November 2008

ABSTRACTThe propagation of plane waves in a thermo-elastic body placed in a magnetic field has been investigated. It is shown that the problem can be reduced to one of pure thermo-elasticity, provided that the longitudinal elastic wave velocity is suitably increased in the case of infinite electrical conductivity. For finite electrical conductivity and low frequency, however, the thermo-elastic coupling factor is to be increased.
On space-times with bounded empty regions
Authors: Marder L. 
Published: November 2008

AbstractIf two empty regions of space-time are entirely separated by matter, little information of the nature of one region can be gained by knowledge of the other. Examples of a hollow Schwarzschild sphere and a hollow static torus are considered. In the first of these, it is shown that the size of the flat interior is not at all limited by the smallness of the Schwarzschild mass constant, the outer spherical boundary, or the condition that the sphere be constructed only of matter of positive density with positive stress-energy scalar.
Fundamental figures, in four and six dimensions, over GF(2)
Authors: Edge W. L. 
Published: November 2008

Introduction. This paper falls into three parts.In §§ 1–5 it is explained how, when the base field of the geometry is GF(2), there are figures of n + 2 interlocking polygons in [n], every two polygons sharing a vertex. When n is even these ½(n + 1) (n + 2) vertices lie in an [n − 1], and two of them are conjugate in a certain null polarity when, and only when, they do not belong to the same polygon.
Application of the Laplace transform method to wave motions involving strong discontinuities
Authors: Chadwick P. , Powdrill B. 
Published: November 2008

AbstractFormulae are obtained for the Laplace transforms of the first and second partial derivatives of a function of time and position which, together with its first partial derivatives, is discontinuous on a moving surface. These formulae are then used in a discussion of the application of the Laplace transform method to the solution of mixed initial and boundary-value problems in linear thermoelasticity. Particular attention is given to thermoelastic disturbances involving plane shock waves, and it is pointed out that no properly posed formulation of problems of this type has yet been found.
Non-linear interactions, causality and the R-matrix
Authors: Power E. A. , Saavedra I. 
Published: November 2008

AbstractThe problem of causality in non-relativistic scattering where a bounded region of non-linear interaction occurs is re-examined in the context of a paper by Ebel. In the model considered it is shown that the acausal behaviour cannot be accounted for in the straightforward manner that is possible for an energy-dependent but linear potential which gives rise to a similar R-matrix.
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

AbstractIt 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 thatwhere 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

AbstractThe 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.
A boundary-layer theory for plates with initial stress
Authors: Laws N. 
Published: November 2008

AbstractA 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.
Evaluation of an integral containing Bessel functions
Authors: Miller G. F. 
Published: November 2008

AbstractThe 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

AbstractComplex 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

AbstractIt 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

ABSTRACTFor 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).
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 ifare 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
The linear theory of an elastic Cosserat plate
Authors: Green A. E. , Naghdi P. M. 
Published: November 2008

AbstractSome 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.
On the structure ofk-chromatic graphs
Authors: Dirac G. A. 
Published: November 2008

AbstractIt 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.
Generation of an axisymmetrical acoustic pulse by a deformable sphere
Authors: Tupholme G. E. 
Published: November 2008

AbstractIn 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

AbstractThe 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 likeξ = 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

AbstractKruskal'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.
Some further results on the birth-and-death process and its integral
Authors: Puri Prem S. 
Published: November 2008

AbstractIn 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 aswhere 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.
The flow of a micropolar liquid layer down an inclined plane
Authors: Willson A. J. 
Published: November 2008

AbstractConsideration 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.
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 formulaAlthough, 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.
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 thatwhere * denotes the usual involution on M(G). These matters are discussed more fully in Williamson (1).
Integral representations for solutions of Heun's equation
Authors: Sleeman B. D. 
Published: November 2008

AbstractIn 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.
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 asvalid for all α
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 asandrespectively, 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 variablesfor which we suppose , the tail probability will be called an extreme tail probability if the normal approximationis poor, when is asymptotically normal and n is large. This paper concerns the specialization of (1.1) in whichwith 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

AbstractAn 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

AbstractThe 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.