bluuebunny/crossref_metadata_2025_split huggingface dataset:
A class of methods for tabular interpolation
Authors: Larkin F. M. 
Published: November 2008

AbstractA generalization of the Neville–Aitken method is described which allows the construction of interpolating functions, other than polynomials, by means of simple recurrence relations. In particular, simple constructions are given for rational functions and trigonometric series which interpolate prescribed function values at non-equispaced positions of the independent variable.Restrictions imposed by requiring the interpolating functions to be invariant under linear transformations of the coordinates are discussed, and application of the technique to the problem of inverse interpolation is also considered.
An expansion theorem applicable to problems of wave propagation in an elastic half-space containing a cavity
Authors: Gregory R. D. 
Published: November 2008

AbstractThis paper is principally concerned with the two-dimensional time harmonic vibrations of an elastic half-space y ≥ 0, containing a submerged cavity in the form of an infinite circular cylinder. Two sequences of line source potentials are obtained which are singular along the axis of the cylinder, satisfy the free surface conditions on y = 0, and represent outgoing waves at infinity. (The radiation condition.) It is proved that any solution of the governing equations which satisfies the free surface conditions and consists of outgoing waves at infinity is expansible as a sum of these fundamental source potentials, with coefficients to be determined from the boundary conditions on the cylinder only.The requirement of outgoing waves is carefully discussed and it is shown that the conditions taken give rise to, and are satisfied by, potential fields which would be regarded intuitively as representing outgoing waves.
On the coefficient problem for univalent polynomials
Authors: Ławrynowicz Julian 
Published: November 2008

This paper is concerned with estimates of the coefficients Cn for normalized polynomials, inverse to univalent functions in the unit disc, i.e. univalent polynomials of the formconsidered in the largest domain D such that 0 ∈ D and |pn(w)| < 1 for w ∈ D; this domain will be denoted by . Polynomials of the type (1) have been introduced by Charzyński in (1), where it was proved among other results that the domain is simply connected.
The arithmetic of certain semigroups of positive operators
Authors: Lamperti John 
Published: November 2008

Some time ago, S. Bochner gave an interesting analysis of certain positive operators which are associated with the ultraspherical polynomials (1,2). Let {Pn(x)} denote these polynomials, which are orthogonal on [ − 1, 1 ] with respect to the measureand which are normalized by settigng Pn(1) = 1. (The fixed parameter γ will not be explicitly shown.) A sequence t = {tn} of real numbers is said to be ‘positive definite’, which we will indicate by writing , provided thatHere the coefficients an are real, and the prime on the summation sign means that only a finite number of terms are different from 0. This condition can be rephrased by considering the set of linear operators on the space of real polynomials which have diagonal matrices with respect to the basis {Pn(x)}, and noting that
Influence du tenseur de conductivité électrique sur l'écoulement dans un générateur à électrodes finies
Authors: Dragoş Lazar 
Published: November 2008

AbstractThe paper studies the influence of the electrical conductivity tensor upon the motion of a fluid in a MHD generator, under the conditions shown in our preceding work. The problem is also formulated in terms of the theory of distributions and the system of equations which determines the functions Ψ = ψ + y and φ = ϕ + ϕe depends on two parameters λ and v (= ωτ). Due to the Hall current, the problem is no longer asymmetrical in the variable y, as in the first case, it therefore has to be separated into an asymmetric and a symmetric problem. Developing a method of successive approximations as against two parameters, it can be shown that the exact solution of the problem may be obtained.
The distributions of certain factors occurring in discriminant analysis
Authors: Radcliffe J. 
Published: November 2008

AbstractSignificance tests for several hypothetical discriminant functions have been developed by Williams (7,8) and considered further by the author (6). The test criteria consist of the factors in certain factorizations of the residual likelihood criterion, when the effect of the hypothetical discriminant functions has been eliminated. The independence and distributions of the factors can be seen by geometrical considerations, to be a consequence of the manner in which the factors are constructed in the sample space. In the case of a single hypothetical discriminant function Kshirsagar (5) has produced analytic proofs, by means of matrix transformations, of the independence and distributions of the factors. In this paper we shall give analytic proofs of the independence and distributions of the factors, given in sections 4 and 5 of the authors' paper (6), by extending Kshirsagar's proof to the case of several hypothetical discriminant functions.
The Dirac spinor in six dimensions
Authors: Lord E. A. 
Published: November 2008

AbstractThe spinor representations of the rotation group in a six-dimensional space with indefinite metric are shown to be four-component spinors, which become the usual Dirac spinors when the formalism is restricted to a four-dimensional subspace. Eriksson's work on the five-dimensional Lorentz group is found to result from a restriction of the six-dimensional treatment to a five-dimensional subspace, and the algebraic significance of Eriksson's work is thereby clarified.
On product sets in a unimodular group
Authors: McCrudden M. 
Published: November 2008

Let G be a locally compact Hausdorff topological group, with µ the left Haar measure on G, and µ* the corresponding inner measure. If R denotes the real numbers, ℬ(G) denotes the Borel† subsets of G of finite measure, and VG = {µ(E):E∈ℬ(G)}, then, following Macbeath(4), we define ΦG: VG × VG→ R bywhere AB denotes the product set of A and B in G.
Subalgebras of modular annihilator algebras
Authors: Barnes B. A. 
Published: November 2008

Throughout this paper we deal only with complex and semi-simple algebras. Let B be such an algebra. We denote the socle of B as SB. B is a modular annihilator algebra if B/SB is a radical algebra, i.e. if every element of B is quasi-regular modulo the socle of B; see (1) or (12). Now assume that B is a modular annihilator algebra and a Banach algebra. Then any semi-simple closed subalgebra of B is a modular annihilator algebra by ((4), Cor. to Theorem 4·2,). It is not true, however, that any semi-simple subalgebra A of B is a modular annihilator algebra, even when A is a Banach algebra in some norm. We give a simple example to illustrate this. Let A be the algebra of all complex functions f, continuous on the closed unit disk D in the complex plane, analytic in the interior of D, and such that f(0) = 0. A is a Banach algebra in the usual sup norm over D. Now consider the norm on A defined byLet B be the completion of A in this norm. A has an involution * defined by and also ‖ff*‖ = ‖f‖2 for all f ∈ A. Therefore B is a B*-algebra. It is not difficult to verify that the only non-zero multiplicative linear functionals on A which are continuous with respect to the norm ‖·‖, are the point evaluations at 1/n, n = 1, 2 …. It follows that every non-zero multiplicative linear functional on B is an extension of one of these point evaluations to B. Thus B can be identified with the algebra of all complex sequences which converge to zero.
Exact solutions for transverse electromagnetic wave propagation in a cylindrically stratified axially magnetized plasma
Authors: Westcott B. S. 
Published: November 2008

AbstractThe equations describing transverse propagation of electromagnetic waves in a cylindrically stratified plasma, in which a static magnetic field is imposed parallel to the axis of cylindrical symmetry, are examined. A systematic method developed previously for isotropic media, Heading (3), Westcott (6) is adapted to yield generalized proffles relating to the plasma properties. These proffles are capable of producing exact solutions for the field distribution in terms of standard transcendental functions. Previously known proffles appear as special cases of the analysis.
Extremum principles for electrostatic and magnetostatic problems
Authors: Arthurs A. M. , Robinson P. D. 
Published: November 2008

AbstractComplementary variational principles are derived for a class of electrostatic and magnetostatic problems using the pairs of adjoint operators (grad, – div) and (curl, curl). This theory unifies the principles of Dirichlet and Thomson in electrostatics and of Schrader in magnetostatics. The results are illustrated by deriving upper and lower bounds for the capacity of a surface, and it is shown how such bounds can be systematically improved by Ritz procedures.
On the Dirichiet product of Cesàro-summable series
Authors: Jukes K. A. 
Published: November 2008

Segal(1) in his paper ‘Summability by Dirichlet convolutions’ makes direct use (in the proofs of Theorems 4 and 6) of a result on the Dirichlet product of two series which may be stated as follows: is (C, k)-summable to the sum α (k≥0) and is (C, l)-summable to the sum β, (l ≥ 0), then the Dirichlet productis (C, k + l + 1)-summable to the sum αβ.’
On the construction of G-spaces and applications to homogeneous spaces
Authors: Gottlieb Daniel Henry 
Published: November 2008

In (3), the author defined the notion of a G-space. A G-space is a weaker notion than that of an H-space. The main purpose of this paper is to present various means of constructing G-spaces. As an application of some of the techniques of (3) and of this paper (though not an application of the concept of G-space) we shall prove the following theorem:Theorem. Let G be a connected compact Lie group and let H be a connected subgroup of maximal rank. Then H3(G/H; Z) = 0. In fact, the Hurewicz homomorphism is trivial for odd dimensions.
The period equation for primes p congruent to 1 (mod 5)
Authors: Rajwade A. R. 
Published: November 2008

Let p = 1 + 5n be a rational prime congruent to 1 (mod 5). Let ζ = e2πi/p and let g be a primitive root mod p. Let the non-zero residues g, g2, …, gp-1 (mod) p be divided into five classes , ℬ, , , ℰ, where gν ∈ , ℬ, , , ℰ according as ν ≡ 0, 1, 2, 3, 4 (mod 5). Letbe the 5-nomial periods. Then it is well known (see (3)) that they are the roots of a monic polynomial with integral coefficients. Our object is to determine these coefficients in terms of the quantities A, B, C, D, E, Y, Z considered in a previous paper (2), p. 65. A large number of relations connecting these quantities have been obtained in the above-mentioned paper and we shall use these relations to simplify the coefficients and get them in a reasonably compact and symmetrical form.
The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers
Authors: Temperley D. J. , Todd L. 
Published: November 2008

AbstractLaminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.
The combinatorial structure of the Hughes plane. II
Authors: Room T. G. 
Published: November 2008

AbstractIn the first part of this paper, tests were described for determining which points of any line in a Galois plane II of order q2 are to be transferred to the conjugate line in order to transmute II into the corresponding Hughes plane Ω. In this part of the paper the tests are refined to provide, in relation to some fixed point in the central subplane δ0 of Ω (i) a simple geometrical condition of transfer for a certain set of ½q(q2−1) points of II and (ii) a simple aglebraic condition for the remaining points of II – δ0. These tests eliminate from the computation (for a given value of q) the necessity of calculating the third coordinates of ½q2 (q2−1) points in order to determine which are not-squares.
Coupled fields in inhomogeneous warm plasmas with static pressure gradients. I
Authors: Burman R. 
Published: November 2008

Abstract.This paper deals with small amplitude waves in inhomogeneous warm electron plasmas. The waves are coupled electromagnetic and electron-acoustic waves, and are described by Maxwell's equations together with single-fluid hydrodynamical equations. Here, previous work is generalized by including the effect of a static pressure gradient. Coupled wave equations are obtained and specialized to the case of a planar stratified plasma. Then, as a preliminary to a treatment of wave coupling, the behaviour of the solutions of the uncoupled wave equations in a coupling region is investigated. The static pressure gradient complicates the behaviour of the uncoupled field components; singularities occur at two points which coalesce as the static pressure gradient is allowed to tend to zero.
Cayley maps and symmetrical maps
Authors: Biggs Norman 
Published: November 2008

AbstractIn this paper we shall show how combinatorial methods can be applied to the study of maps on orientable surfaces. Our main concern is with maps which possess a certain kind of symmetry, called vertex-transitivity. We show how an extension of the well-known method of Cayley can be used to construct such maps, and we give conditions which suffice for the automorphism groups of these maps to have non trivial vertex-stabilizers. Finally, we investigate the special case when the skeleton of the map is a complete graph; a classical theorem of Frobenius then implies that all vertex-transitive maps are given by our extension of Cayley's construction.
Inclusion relations for Riesz typical means
Authors: Jakimovski A. , Tzimbalario J. 
Published: November 2008

AbstractNecessary and sufficient conditions for sequence-to-sequence or sequence-to-function summability method to include (R, λ, α), when 1 < α ≤ 2, are given. Also, for suitably restricted sequences λ, necessary and sufficient conditions for a series-to-sequence or series-to-function summability method to include (R, λ, α) for 1 < α ≤ 2 are given. These results are obtained by showing that a certain sequence {δj} (j ≥ 0) is a Schauder-basis in Rλα(N) for each α, 1 < α ≤ 2.
The instability of a vortex sheet on a subsonic stream under acoustic radiation
Authors: Jones D. S. , Morgan J. P. 
Published: November 2008

AbstractThis paper is concerned with the linear theory of the transmission of sound through a vortex sheet separating two fluids in relative motion, but with the same density and sound speed. For harmonic excitation asolution is determined, with particular attention to transition regions where large effects might be expected, and it is found that Helmholtz instability plays no role in this solution. However, this harmonic field does not lead to a solution of the initial value problem which satisfies causality. When causality is complied with an additional field must be superimposed which gives waves growing exponentially in space in the harmonic case and a singularity, which is more severe than has been previously encountered, in the time-dependent problem. The consequent effects of this instability are discussed.
Kolmogorov's differential equations for non-stationary, countable state Markov processes with uniformly continuous transition probabilities
Authors: Goodman Gerald S. , Johansen S. 
Published: November 2008

1. SummaryWe shall consider a non-stationary Markov chain on a countable state space E. The transition probabilities {P(s, t), 0 ≤ s ≤ t <t0 ≤ ∞} are assumed to be continuous in (s, t) uniformly in the state i ε E.
On the three-body problem
Authors: Lekner J. 
Published: November 2008

AbstractWe consider the ground state of a system of three interacting particles of equal mass. An integro-differential equation is obtained for the optimum pair function f in the product wavefunction Ψ(123) = f(12)f(13)f(23). The solution for harmonic forces reproduces the known exact ground state. Approximate analytic solutions are obtained for inverse-square forces, and for a general force law in the semiclassical limit.
A characterization of the circle and its applications to Hermitian operators
Authors: Bollobás Béla 
Published: November 2008

Let X be a complex normed space and let T be a Hermitian linear operator on X (i.e. the numerical range of T is real). It was proved by Bonsall (see (4); Theorem 10.13) that thenfor every u ∈ X. This inequality was improved by the author (3) toInequality (1) is closely related (see (3)) to some inequalities of Hadamard (6) and Kolmogorov (7) about the successive derivatives of functions in L∞(−∞, ∞). It was also shown in (3) (and was, in fact, shown already in (7)) that the constant 2 is best possible in (1). However, as we shall see, inequality (1) can be sharpened considerably if T attains its norm on u, i.e. if ‖Tu‖ = ‖T‖‖u‖.
Simultaneous approximation of two additive forms
Authors: Liu Ming-Chit 
Published: November 2008

1. Introduction. In 1948, H. Heibronn (6) improved Vinogradov's result (11) and obtained that for any ε > 0 there exists some positive constant C(ε) which depends on ε only such that, for any real number θ and any integer N ≥ 1, there is an integer x satisfyingHere ∥t∥ means the distance from t to the nearest integer.
Martin's axiom and Hausdorif measures
Authors: Ostaszewski A. J. 
Published: November 2008

AbstractA theorem of Besicovitch, namely that, assuming the continuum hypothesis, there exists in any uncountable complete separable metric space a set of cardinality the continuum all of whose Hausdorif h-measures are zero, is here deduced by appeal to Martin's Axiom. It is also shown that for measures λ of Hausdorff type the union of fewer than 2ℵ0 sets of λ-measure zero is also of λ-measure zero; furthermore, the union of fewer than 2ℵ0 λ-measurable sets is λ-measurable.
On continuous functions with graphs of σ-finite linear measure
Authors: Foran James 
Published: November 2008

In this paper comparisons are made between the class of continuous functions of generalized bounded variation and the class of continuous functions with graphs having σ-finite length i.e. linear measure. An investigationof the differentiability and approximate differentiability of such functions discloses the fact that the latter class is considerably more extensivethan the former one. The following definitions will be needed:(1) A function f is said to be of bounded variation (VB) on a set E ifwhere the supremum is taken over all sequences {[ai, bi]} of non-overlapping intervals with endpoints in E.
On the Uryson type of stochastic integral equations
Authors: Hardiman S. T. , Tsokos Chris P. 
Published: November 2008

AbstractAn investigation of the random or stochastic integral equations of the formandis presented, where ω ∈ Ω, the supporting set of the probability measure space (Ω, A, P). The existence and uniqueness of a random solution, a second-order stochastic process, of the equations is considered. Several theorems utilizing fixed point theorems and successive stochastic approximations give sufficient conditions for the existence of a random solution.
Exact analysis of simply supported rhombic plates under uniform pressure
Authors: Rajaiah K. , Rao Akella Kameswara 
Published: November 2008

AbstractThe simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.
The distribution of current on a cylindrical antenna
Authors: Harvey C. C. 
Published: November 2008

AbstractThe iterative solution of Hallen's integral equation for the current distribution on a lossless dipole transmitting antenna is studied from first principles, and a general solution in terms of an expansion function is derived. In this new solution even the zero-order approximation gives a reasonable representation of both the quadrature and the in-phase current distributions. The choice of an expansion function is discussed. At each stage the approximations which must be made in order to obtain earlier iterative solutions are clearly described. Three low order solutions are derived in detail: the zero-order solution using both a constant expansion parameter and a simple expansion function, and the rst-order solution using a constant expansion parameter. The results are compared and special attention is paid to the very short antenna, although the results are good for lengths up to and including the half-wave dipole. The results are presented in such a way that the first-order admittance of any given antenna may be readily calculated.
The transmission of surface waves through a gap in a vertical barrier
Authors: Porter D. 
Published: November 2008

AbstractThe two-dimensional configuration is considered of a fixed, semi-infinite, vertical barrier extending downwards from a fluid surface and having, at some depth, a gap of arbitrary width. A train of surface waves, incident on the barrier, is partly transmitted and partly reflected. The velocity potential of the resulting fluid motion is determined by a reduction procedure and also by an integral equation formulation. It is shown that the two methods lead to the same Riemann–Hilbert problem. Transmission and reflexion coefficients are calculated for several values of the ratio gap width/mean gap depth.
Some special operators and new classes of locally convex spaces
Authors: Chilana Ajit Kaur 
Published: November 2008

AbstractWe consider some special operators on a locally convex Hausdorff space to itself, which have neat spectral theories and prove some perturbation results. This leads us to define and study a few special classes of locally convex spaces in which various subsets of the algebra of continuous linear operators either coincide or are closely related with each other. These are then compared to the classes of barrelled, infrabarrelled and DF-spaces and examples are given to distinguish them from one another.
On a summability theorem of Berg, Crawford and Whitley
Authors: Garling D. J. H. , Wilansky A. 
Published: November 2008

We recall that a matrix A is said to sum a sequence x if Axε c, the space of all convergent sequences, and that A is conservative if it sums every convergent sequence. If A is conservative, A defines a continuous linear operator on c. Berg (2), Crawford (3)and Whitley (9) have proved the following theorem:Theorem 1. A conservative matrix sums no bounded divergent sequence if and only if,considered as an operator on c, it is range closed and has finite-dimensional null-spac
A singularity in an oceanic boundary layer
Authors: Creegan Aileen , Dyke P. P. G. , Johnson J. A. 
Published: November 2008

AbstractA β-plane ocean is considered, and dissipative processes are modelled by using a coefficient of lateral friction. Attention is focused on the singularity which occurs if the angle that the western boundary makes with the north approaches ½π. The dimensions of the singular region are found using boundary layer techniques, and the solution for the transport stream function valid within it is obtained in closed form.