bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some consequences of bond alternation in long polyenes
Authors: Salem L. 
Published: November 2008

ABSTRACTThe effect of a twofold bond alternation on the bond ordersandand on the π-electron contributionto the diamagnetic susceptibility of a cyclic even hydrocarbon polyeneis investigated. Power series expansions and asymptotic expressions are given forand χπin terms of the parametert2(0 ≤t2< 1) which characterizes the amount of bond alternation. It is found that bond alternation reduces both bond order and χπstrongly, the effect being more drastic the greater the bond alternation (t2→0).
Self reciprocal properties of certain functions
Authors: Rao V. V. L. N. 
Published: November 2008

The object of this note is to study the properties of some functions self reciprocal in the Hankel transform. I denote a function f(x) as Rμ, if it is self reciprocal for Hankel transforms of order μ so that it is given bywhere Jμ(x) is a Bessel function of order μ. If μ = ½, f(x) is denoted by Rs while f(x) is written as Rc when μ = − ½.
On covering a regular polygon with a triangle
Authors: Eggleston H. G. 
Published: November 2008

In this note we consider a particular type of covering problem. Let T be given a plane set and Tθ be the set obtained from T by a rotation about some point in the plane through an angle θ in the clockwise sense. If a set K is such that for every θ there is a translation which transforms Tθ into a subset of K then we say that K is a rotation cover of T. The problem considered here is to determine for fixed n, l the triangle of least area which is a rotation cover for an n-sided regular polygon of side length l. In each case the solution is an equilateral triangle the altitude of which is given byThis solution is unique.
A Matrix Factorization Problem in the Theory of Random Variables Defined on a Finite Markov Chain
Authors: Miller H. D. 
Published: November 2008

SummaryLet {kr} (r = 0, 1, 2, …; 1 ≤ kr ≤ h) be a positively regular, finite Markov chain with transition matrix P = (pjk). For each possible transition j → k let gjk(x)(− ∞ ≤ x ≤ ∞) be a given distribution function. The sequence of random variables {ξr} is defined where ξr has the distribution gjk(x) if the rth transition takes the chain from state j to state k. It is supposed that each distribution gjk(x) admits a two-sided Laplace-Stieltjes transform in a real t-interval surrounding t = 0. Let P(t) denote the matrix {Pjkmjk(t)}. It is shown, using probability arguments, that I − sP(t) admits a Wiener-Hopf type of factorization in two ways for suitable values of s where the plus-factors are non-singular, bounded and have regular elements in a right half of the complex t-plane and the minus-factors have similar properties in an overlapping left half-plane (Theorem 1).
Planetary equations in terms of vectorial elements
Authors: Allan R. R. , Ward G. N. 
Published: November 2008

AbstractThe planetary equations for natural elements, which do not depend upon the choice of a particular frame of reference, are derived by using the theory of Poisson brackets. These natural elements include vectorial elements which lead to the introduction of vector and dyadic Poisson brackets. The use of vectorial elements can also lead to redundancy in the set of elements; this idea is extended to show that as many redundant elements as desired can be used and that the evaluation of the derivatives of the disturbing function can be simplified thereby.
Distributions of the direction and collinearity factors in discriminant analysis
Authors: Kshirsagar A. M. 
Published: November 2008

AbstractExact tests devised by Bartlett and Williams for the adequacy of a single discriminant function in the case of several groups are applicable to a wide range of problems in multivariate analysis. The appropriate likelihood criterion is factorized into direction and collinearity factors; and the exact distribution of these factors under the conditions of only one non-zero canonical correlation was first given by Bartlett in the general case of any numbers of dependent and independent variables, making use of geometrical arguments.In this paper the factors are expressed directly in terms of the matrices occurring in the multivariate analysis of variance table; and the results are derived by an analytical method making use of matrix transformations and rectangular coordinates.
The formulation of quantum mechanics in terms of phase space functions
Authors: Fairlie D. B. 
Published: November 2008

AbstractA relationship between the Hamiltonian of a system and its distribution function in phase space is sought which will guarantee that the average energy is the weighted mean of the Hamiltonian over phase space. This relationship is shown to imply the existence of a wave function satisfying the Schrödinger equation, and dictates the possible forms of time-dependence of the distribution function.
The stability of Couette flow of certain anisotropic fluids
Authors: Leslie F. M. 
Published: November 2008

AbstractThe stability of the flow between concentric, rotating cylinders is discussed when the gap is small and the cylinders are rotating in the same direction for a class of anisotropic fluids in which the fluid has a preferred direction. An important conclusion of the analysis is that a steady-state solution of the equations has previously been considered unstable on false grounds.
Short surface waves in the presence of a finite dock. I
Authors: Holford R. L. 
Published: November 2008

AbstractA long thin plate of finite width (a finite dock) extends over part of the otherwise free surface of a semi-infinite body of water under gravity and is given a forced heaving motion of small amplitude about this position. The solution of the boundary-value problem for the velocity potential of the resulting forced (two-dimensional) surface-wave motion may be reduced to that of an integral equation of the second kind for the value of the potential on the dock by means of an appropriate Green's function. There is an infinite number of choices for such a Green's function, and we show below how to construct one for which the kernel of the corresponding integral equation tends to zero with the ratio wavelength/dock-width. The integral equation may then be solved by iteration to calculate the short-wave asymptotics of the original wave-making problem.
On matrix methods for the solution of partial differential equations
Authors: Wadsworth M. , Wragg A. 
Published: November 2008

Bickley and McNamee (1) describe techniques for obtaining the solution of finite difference equations, arising from partial differential equations, making extensive use of matrix methods. In all cases solutions are obtained by solving algebraic equations as distinct from differential equations. For example, in order to solvethe second space derivative is replaced by finite differences and the time derivative is replaced either by substituting the backward finite difference form or by using the Laplace transformation.
Boundary problems for additive processes defined on a finite Markov chain
Authors: Keilson J. , Wishart D. M. G. 
Published: November 2008

In a previous paper (3), to which this is a sequel, a central limit theorem was presented for the homogeneous additive processes defined on a finite Markov chain, a class of processes treated extensively by Miller (4). A typical homogeneous process {R(t), X(t)} takes its values in the spaceand is described by a vector distribution F(x, t) with componentsand an increment matrix distribution B(x) governing the transitions. The present paper treats the motion of the process in the same space when its homogeneity is modified by the presence of a set of boundary states in x. Such bounded processes have many applications to the theory of queues, dams, and inventories. Indeed, this paper and its predecessor were motivated initially by a desire to discuss queuing systems with many servers and many service phases. We will treat both absorbing boundaries and associated passage time densities, and reflecting boundaries. For the latter our main objective is an asymptotic discussion of the tails of the ergodic distribution.
Diffraction at high frequencies by a circular disc
Authors: Jones D. S. 
Published: November 2008

AbstractIt is shown how to convert the integral equation for the pressure distribution on a circular disc in an axisymmetric sound wave into a singular integral equation of the first kind. This singular integral equation has a simple kernel and can be transformed easily into an integral equation of the second kind which is especially useful at high frequencies. Although a direct iteration on this last integral equation fails, an indirect method is devised which ensures that each iterate is of lower order than the preceding at high frequencies. The form of the general term in the iteration is given together with the first terms of its asymptotic behaviour. It is relatively simple to estimate the error caused by stopping at any particular iterate.Detailed calculations are made for a plane wave striking the disc at normal incidence.
A spatially homogeneous gravitational field
Authors: Joseph V. 
Published: November 2008

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.
A periodicity theorem in homological algebra
Authors: Adams J. F. 
Published: November 2008

Introduction. In (1–3,6) it is shown that homological algebra can be applied to stable homotopy-theory. In this application, we deal with A -modules, where A is the mod p Steenrod algebra. To obtain a concrete geometrical result by this method usually involves work of two distinct sorts. To illustrate this, we consider the spectral sequence of (1,2):Here each group Extss, t which occurs in the E2 term can be effectively computed; the process is purely algebraic. However, no such effective method is given for computing the differentials dr in the spectral sequence, or for determining the group extensions by which is built up from the E∞ term; these are topological problems.
A hypergeometric transformation associated with the Appell function F4
Authors: Srivastava H. M. 
Published: November 2008

Recently in these proceedings (see (5), p. 175) by applying Goldstein's form of Parseval's relation ((4), p. 105) to the operational pairs ((3), p. 284)where R[(b ± c)2] > 0 and ((3), p. 293)where R(½ − λ + μ) > 0, it was proved that ifthenprovided R(½ − λ + μ + ν) > 0 and R[(b ± c)2] > R(a), 0.
Lower bound energy calculations for
Authors: Walmsley Mary , Coulson C. A. 
Published: November 2008

AbstractTwo different calculations are made of lower bounds for the electronic energy of . In the first the method of truncated Hamiltonians due to Bazley and Fox is adapted in such a way that the nuclear charge rather than the energy becomes the eigenvalue. Lower bounds are calculated for the energies of the six lowest σg and six lowest σu states, as well as of the three lowest of both πg and πu symmetries. This approach gives better convergence than when the energy is used as eigenvalue. In the second calculation the method of Temple and Kato is shown to give a satisfactory value for the energy of the ground state, provided that some necessary knowledge of the energy of the first-excited state is available.
The Monte Carlo method in quantum statistical mechanics
Authors: Handscomb D. C. 
Published: November 2008

ABSTRACTThis paper describes, in general terms, a Monte Carlo method for estimating statistical parameters of quantum-mechanical systems. In this method, we construct a Markov chain of transitions between finite sequences of indices, and obtain these parameters in terms of parameters of the limit distribution. This is an extension of the method of Metropolis for classical systems, and may have equally wide application.
Locally flatPLsubmanifolds with codimension two
Authors: Wall C. T. C. 
Published: November 2008

We refer the reader to the IHES notes of Zeeman (14) for basic facts aboutPL(or piecewise-linear) manifolds. IfMmis a locally flatPL-submanifold ofQm+2, our object will be to study the normal structure ofMinQ: one of our main results is:There exists a PL-bundle over M, with fibre a 2-simplex, which is PL-homeomorphic to a neighbourhood of M in Q; moreover, the bundle and homeomorphism are unique up to equivalence. We also make an application to smoothing theory.
A generalization of a boundedness theorem for a certain third-order differential equation
Authors: Ezeilo J. O. C. 
Published: November 2008

1. This paper investigates the boundedness, as t → ∞, of the solutions of the real differential equationwhere α is a constant and φ2, φ3, ψ depend on the arguments shown with φ2, φ′3, ψ continuous.
A direct iteration method of obtaining latent roots and vectors of a symmetric matrix
Authors: Jennings A. 
Published: November 2008

AbstractThis paper describes a method whereby iteration can be carried out simultaneously with two or more trial vectors in order to obtain the latent roots of largest modulus of a symmetric matrix and their corresponding latent vectors. The convergence of any particular vector is automatically accelerated by making use of the current approximations to those vectors subdominant to it, the dominant latent vectors being obtained quite rapidly. The method is particularly suitable where a few of the dominant latent roots and vectors are required of a large symmetric matrix.
Oscillations of a rigid sphere embedded in an infinite elastic solid
Authors: Chadwick P. , Trowbridge E. A. 
Published: November 2008

AbstractA detailed study is made of angular oscillations of small amplitude about a fixed axis of a rigid sphere embedded in an infinite elastic solid. Three modes of vibration of the sphere are considered: steady oscillations arising from the application of a periodic torque; forced oscillations produced by an arbitrary time-dependent torque; and free oscillations excited by an impulsive torque. Due to the transfer of energy to the surrounding material by the radiation of an elastic shear wave, free oscillations of the sphere are damped, the principal parameter affecting the damping being the density contrast between the sphere and its surroundings. Illustrative numerical results, referring to steady and free oscillations of the sphere, are presented in graphical form.
Oscillations of a rigid sphere embedded in an infinite elastic solid
Authors: Chadwick P. , Trowbridge E. A. 
Published: November 2008

AbstractIn this paper, which is a continuation of (1), we study steady (i.e. time-harmonic) and transient rectilinear oscillations of small amplitude of a rigid sphere embedded in an infinite elastic solid. Two types of transient motions are considered, forced oscillations in which the sphere is subject to a prescribed time-dependent force, and free oscillations in which the sphere is set in motion by an impulsive force. For each mode of vibration of the sphere the character of the solution is determined by two parameters, the density contrast between the sphere and its surroundings and a parameter related to the Poisson's ratio of the elastic solid. Numerical results referring to transient rectilinear oscillations are presented in graphical form.
Infinite sets of identities for classical polynomials and Bessel functions
Authors: Abdelkader Mostafa A. 
Published: November 2008

AbstractAn identity for a rational function is used, in conjunction with generating functions for a certain class of polynomials, to derive infinite sets of identities for these polynomials. Identities are given for the polynomials of Legendre, Gegenbauer, Hermite, Tchebycheff and L. Carlitz. A novel type of classification for these polynomials is indicated. Next, infinite sequences of identities for various Bessel functions and for power functions are derived. New identities for trigonometric functions are also given, as well as brief miscellanea on: functions resembling Dirac's delta function, integral transforms and a functional equation.
Absolute summability of infinite series on a scale of Abel type summability methods
Authors: Mishra Babban Prasad 
Published: November 2008

Suppose that λ > − 1 and thatIt is easy to show thatWith Borwein(1), we say that the sequence {sn} is summable Aλ to s, and write sn → s(Aλ), if the seriesis convergent for all x in the open interval (0, 1)and tends to a finite limit s as x → 1 in (0, 1). The A0 method is the ordinary Abel method.
On the linear exponential family
Authors: Wani J. K. 
Published: November 2008

In this paper we give a characterization theorem for a subclass of the exponential family whose probability density function is given bywhere a(x) ≥ 0, f(ω) = ∫a(x) exp (ωx) dx and ωx is to be interpreted as a scalar product. The random variable X may be an s-vector. In that case ω will also be an s-vector. For obvious reasons we will call (1) as the linear exponential family. It is easy to verify that the moment generating function (m.g.f.) of (1) is given by
The expansion of water-wave potentials at great distances
Authors: Ursell F. 
Published: November 2008

AbstractThe wave function φ(x, y) satisfies the equationin the infinite regionand satisfies the boundary condition Kφ + φy = 0 on the two line segments (y = 0, −∞ < x < −R) and (y = 0, R < x < ∞). We are not concerned with the properties of φ(x, y) inside the circle r = R. It is shown that outside the circle r = R the wave function φ(x, y) can be written as the sum of a wave source, a wave dipole, regular waves and wave-free potentials. (These basic functions are defined in section 2.) The proof makes use of analytic continuation into the image region (r > R, y ≤ 0) cut along the negative y-axis.Two methods are given for this step. The first method uses Schwarz's symmetry principle to define the auxiliary wave function Φ = Kφ + φy throughout r > R, and φ can then be found by solving differential equations in the y or x direction. The second method uses Green's theorem. Applications in the theory of water waves are suggested.
Generalization of Hölder's and Minkowski's inequalities
Authors: Daykin D. E. , Eliezer C. J. 
Published: November 2008

In a recent paper (1) the authors considered some generalizations of Cauchy's inequality. The method of approach was by the construction of certain convex functions (where by a convex function we mean a function f(x) satisfyingfor every pair of unequal values x1 and x2). For example, it was shown that if (a), (b) are the sets of non-negative real numbers a1, …,an; bl, …, bn, the functionwhich had been used earlier by Callebaut(2), is a convex function with minimum at x = 0, except if the sets (a) and (b) are proportional, in which case the function is a constant. This function takes the value (σab)2 when x = 0 and (σa2) (Σb2) when x = 1, and the property of convexity gives Cauchy's inequality.
Steady longitudinal motion of an insulating cylinder in a conducting fluid
Authors: Waechter R. T. 
Published: November 2008

AbstractA mathematical analogue between a special class of problems in steady magnetohydrodynamics and appropriate problems in the theory of the scattering of sound pulses is established and exploited. Rigorous asymptotic expansions for large Hartmann numberMare obtained for the exact solution of the prototype problem, the circular cylinder. Asymptotic expansions for largeMin the case of a cylinder whose cross-section is an arbitrary closed convex curve are obtained as a straightforward application of the theory of geometrical optics and Keller's geometrical theory of diffraction.
The decay of oscillations of a non-homogeneous fluid within a container
Authors: Dore B. D. 
Published: November 2008

AbstractThe theory of laminar boundary layers is employed to determine the rate of decay of small amplitude oscillations of a non-homogeneous viscous fluid which completely fills a stationary rectangular container. An application of Green's formula is invoked and an expression is obtained in terms of the (general) density and viscosity distributions.
General series involving H-functions
Authors: Jain R. N. 
Published: November 2008

MacRobert (4–7) and Ragab(8) have summed many infinite and finite series of E-functions by expressing the E-functions as Barnes integrals and interchanging the order of summation and integration. Verma (9) has given two general expansions involving E-functions from which, in addition to some new results, all the expansions given by MacRobert and Ragab can be deduced. Proceeding similarly, we have studied general summations involving H-functions. The H-function is the most generalized form of the hypergeometric function. It contains a vast number of well-known analytic functions as special cases and also an important class of symmetrical Fourier kernels of a very general nature. The H-function is defined as (2)where 0 ≤ n ≤ p, 1 ≤ m ≤ q, αj, βj are positive numbers and aj, bj may be complex numbers.
Degrees of greatest common divisors of invariant factors of two regular polynomial matrices
Authors: Barnett S. 
Published: November 2008

AbstractIn a previous paper it was shown that a necessary and sufficient condition for two regular polynomial matrices T and U to have relatively prime determinants is that a certain matrix R be non-singular. This generalization of the resultant of two scalar polynomials is extended to give an expression for the sum of the degrees of the greatest common divisors of all pairs of invariant factors of T and U in terms of the rank of R. Further, if rank R exceeds a given value then specified pairs of factors are relatively prime.
A note on simplex spaces
Authors: Ng Kung-Fu 
Published: November 2008

Let X be a real Banach space which is partially ordered by a closed cone C. Let X* denote the Banach dual space, and letX is called a simplex space (2) if (X*, C*,‖·‖) is an AL-space. We proved in (3) that X is a simplex space if and only if X is an approximate order-unit-normed space and has the Riesz decomposition property. When the given norm on X is an order-unit norm, some representation theorems are obtained by Effros ((2), theorem 4·8) and Sterrmer ((6), theorem 4·3). In this note, we shall study the representation problem for more general simplex spaces. One of our aims is to prove that X is equivalent to C0(ω) if and only if X has the Urysohn property (for definitions, see below).
Derivation of correction terms for general quadrature formulae
Authors: Grant J. A. 
Published: November 2008

AbstractIn this paper, it will be shown how it is possible, using Bernoulli polynomials of the first kind, to derive correction terms for any quadrature approximation in the form of a weighted sum over a finite interval. The terms derived will involve either the difference or the sum of derivatives taken at the ends of the range of integration, and they will be described as being of either Type A or Type B respectively. There will also be some discussion of the uses of such terms.
Weyl ǵroups and finite Chevalley ǵroups
Authors: Carter R. W. 
Published: November 2008

In his fundamental paper (1) Chevalley showed how to associate with each complex simple Lie algebra L and each field K a group G = L(K) which is (in all but four exceptional cases) simple. If K is a finite field GF(q), G is a finite group of orderwhere l is the rank of L, m is the number of positive roots of L and d is a certain integer determined by L and K. The integers m1, m2,…,m1 are determined by L only and satisfy the condition