bluuebunny/crossref_metadata_2025_split huggingface dataset:
Wald's identity and absorption probabilities for two-dimensional random walks
Authors: Barnett V. D. 
Published: November 2008

SummarySuppose a particle executes a random walk on a two-dimensional square lattice, starting at the origin. The position of the particle after n steps of the walk is Xn = (Xl, n, X2n), whereand we will assume that the Yi are independent bivariate discrete random variables with common moment generating function (m.g.f.)where a, b, c and d are non-negative. We assume further that (i) pi, j is non-zero for some finite positive and negative i, and some finite positive and negative j (− a ≤ i ≤ b, − c ≤ jd), such values of i and j including – a, b and – c, d, respectively, whenever a, b, c or d is finite, and (ii) the double series defining Φ(α, β) is convergent at least in some finite region D, of the real (α, β) plane, which includes the origin.
Magneto-thermo-elastic plane waves
Authors: Purushothama C. M. 
Published: November 2008

AbstractThe combined effects of uniform thermal and magnetic fields on the propagation of plane waves in a homogeneous, initially unstressed, electrically conducting elastic medium have been investigated.When the magnetic field is parallel to the direction of wave propagation, the compression wave is purely thermo-elastic and the shear wave is purely magneto-elastic in nature. For a transverse magnetic field, the shear waves remain elastic whereas the compression wave assumes magneto-thermo-elastic character due to the coupling of all the three fields—mechanical, magnetic and thermal. In the general case, the waves polarized in the plane of the direction of wave propagation and the magnetic field are not only coupled but are also influenced by the thermal field, once again exhibiting the coupling of the three fields. The shear wave polarized transverse to the plane retains its magneto-elastic character.Notation.Hi = primary magnetic field components,ht = induced magnetic field components,To = initial thermal field,θ = induced thermal field,C = compression wave velocity.S = shear wave velocity,ui = displacement components,cv = specific heat at constant volume,k = thermal conductivity,η = magnetic diffusivity,μe = magnetic permeability,λ, μ = Lamé's constants,β = ratio of coefficient of volume expansion to isothermal compressibility.
Rotating fluid masses in general relativity. II
Authors: Boyer R. H. 
Published: November 2008

AbstractWe describe some properties of a stationary, isolated, axially symmetric, rotating body of perfect fluid, according to general relativity. We first specialize to the case of constant specific entropy and constant angular velocity. The latter condition is equivalent to rigidity in the Born sense; both conditions are consequences of a simple variational principle. The hydrodynamic equations can then be integrated completely. Analogous first integrals are given also for the case of differential rotation. No use is made of the full field equations.
General study of a heat transmission problem of a channel-gas flow with Neumann-type thermal boundary conditions
Authors: Tyagi V. P. 
Published: November 2008

AbstractIn this paper a fundamental problem of thermal transport in a channel-gas flow has been studied. The most general solution in terms of integral formulae has been obtained when the duct is bounded by an arbitrary closed contour, the prescribed normal temperature gradient at the wall varies arbitrarily along the periphery, and the specified additional heat generation varies in an arbitrary manner from point to point in a cross-section. The power series solution is also discussed, and is given in a separate section. One of the objects of the present study is to look forward to the qualitative as well as quantitative effects of viscous dissipation and work of compression. Several results and all the graphs of Tao ((13)) have also been corrected.
The attenuation of a Rayleigh wave in a half-space by a surface impedance
Authors: Gregory R. D. 
Published: November 2008

AbstractA time harmonic Rayleigh wave, propagating in an elastic half-space y ≥ 0, is incident on a certain impedance boundary condition on y = 0, x > 0. The resulting field consists of a reflected surface wave, scattered body waves, and a transmitted surface wave appropriate to the new boundary conditions. The elastic potentials are found exactly by Fourier transform and the Wiener-Hopf technique in the case of a slightly dissipative medium. The ψ potential is found to have a logarithmic singularity at (0,0), but the φ potential though singular is bounded there. Analytic forms are given for the amplitudes of the reflected and transmitted surface waves, and for the scattered field. The reflexion coefficient is found to have a simple form for small impedances. A uniqueness theorem, based on energy considerations, is proved.
Applications of the theory of the general hodograph equation
Authors: Mackie A. G. 
Published: November 2008

ABSTRACTThe solutions of the equationobtained by the author in (3) are applied to determine the Kirchhoff-Helmholtz flow past a wedge in which the free stream Mach number has any value from 0 to 1 inclusive. For small wedge angles the results are developed further and expressions are found for the drag coefficient and for the asymptotic shape of the free streamlines far downstream. While general formulae are obtained for an arbitrary functionk(σ) more detailed results are given for the particular function k(σ) which corresponds to the case of a polytropic gas.
A new proof of the Routh-Hurwitz stability criterion using the second method of Liapunov
Authors: Parks P. C. 
Published: November 2008

ABSTRACTThe second method of Liapunov is a useful technique for investigating the stability of linear and non-linear ordinary differential equations. It is well known that the second method of Liapunov, when applied to linear differential equations with real constant coefficients, gives rise to sets of necessary and sufficient stability conditions which are alternatives to the well-known Routh-Hurwitz conditions. In this paper a direct proof of the Routh-Hurwitz conditions themselves is given using Liapunov's second method. The new proof is ‘elementary’ in that it depends on the fundamental concept of stability associated with Liapunov's second method, and not on theorems in the complex integral calculus which are required in the usual proofs. A useful by-product of this new proof is a method of determining the coefficients of a linear differential equation with real constant coefficients in terms of its Hurwitz determinants.
A note on lemmas of Green and Kondo
Authors: Morris A. O. 
Published: November 2008

Let R be the field of rational numbers, {x} = {x1, z2, …}, {y} = {y1, y2, …} be two countably infinite sets of variables and t an indeterminate. Let (λ) = (λ1, λ2, …, λm) be a partition of n. Then Littlewood (5) has shown thatcan be expressed in the formwhere Qλ(x, t) and Qλ(y, t) denote certain symmetric functions on the sets {x} and {y} respectively. In additionwhere is the partition of n conjugate to (λ). In fact, Littlewood (5) showed thatwhere the summation is over all terms obtained by permutations of the variables xi (i = 1, 2, …) and.
Flow due to a point source of momentum in a viscous fluid contained in a sphere
Authors: Ranger K. B. 
Published: November 2008

AbstractIt is argued that the zero Reynolds limit of the steady incompressible axially symmetric viscous fluid motion interior to a sphere due to a Landau source at the centre is a Stokes flow. The first three terms of the perturbation expansion are determined and the order of magnitude of the general term not derivable from the Landau source is established. Comparison of the convection terms with the diffusion terms for each order of the Reynolds number demonstrates self consistency at each stage of the expansion.
Topological degree of non-compact mappings
Authors: Taylor J. G. 
Published: November 2008

AbstractWe extend the notion of topological degree to a suitable class of continuous mappings of a locally convex Hausdorff topological vector space into itself which are not completely continuous. This extension and the resulting existence theorems for non-linear equations are further extended to product spaces. Our extension is developed with application to quantum field theory in mind; this application is made elsewhere.
Stability of an elastico-viscous liquid film flowing down an inclined plane
Authors: Gupta A. S. , Rai Lajpat 
Published: November 2008

AbstractAn analysis is made of the stability of a layer of an elastico-viscous liquid flowing down an inclined plane in the presence of two-dimensional disturbances. The modified Orr-Sommerfeld equation is solved by a regular perturbation technique for disturbances of large wavelengths. It is shown that in the absence of surface tension, the layer is more unstable as compared with that for an ordinary viscous liquid if Q1 > Q2, Q1 and Q2 being stress relaxation and strain retardation parameters respectively.
Reflected and diffracted fields within a medium formed by a circular cylinder and two planes
Authors: Maulik Tapendra Nath 
Published: November 2008

AbstractGreen's function for SH-line source inside a wedge shaped medium with its apex removed by a circular cylindrical surface has been obtained. Exact location of the image sources facilitates the determination of the reflexion and diffraction at the circular and also at the plane boundary of the multiple phases clearly. The scattered field from the corner is indicated. The connexion of this solution with that of complete wedge has been shown with suitable contour integrations.
The average number of real zeros of a random trigonometric polynomial
Authors: Das Minaketan 
Published: November 2008

AbstractLet a1, a2,… be a sequence of mutually independent, normally distributed, random variables with mathematical expectation zero and variance unity; let b1, b2,… be a set of positive constants. In this work, we obtain the average number of zeros in the interval (0, 2π) of trigonometric polynomials of the formfor large n. The case when bk = kσ (σ > − 3/2;) is studied in detail. Here the required average is (2σ + 1/2σ + 3)½.2n + o(n) for σ ≥ − ½ and of order n3/2; + σ in the remaining cases.
On the invariance of the essential spectrum of an arbitrary operator. III
Authors: Schechter Martin 
Published: November 2008

The spectrum of the hydrogen energy operator(Δ is the Laplacian and r is the distance from the origin) consists of the non-negative real axis and a sequence of negative eigenvalues of finite multiplicities converging to O. In the present study we are interested in finding sufficient conditions on a potential q(x) such that the spectrum of the operatorin En has a ‘hydrogen-like’ spectrum, i.e. a spectrum consisting of(a) the non-negative real axis,(b) at most a denumerable set of negative eigenvalues of finite multiplicities having zero as its only possible limit point.
Note on the representation of integers as sums of certain powers
Authors: Thanigasalam K. 
Published: November 2008

In the paper entitled ‘Asymptotic formula in a generalized Waring's problem’, I established an asymptotic formula for the number of representations of a large natural number N in the formwhere x1, x2, …, x7 and k are natural numbers with k ≥ 4 (see (2) Theorem 2).
The self-similar problem of the expanding elliptical crack in an anisotropic solid
Authors: Burridge R. , Willis J. R. 
Published: November 2008

AbstractThe title problem is solved by a semi-inverse method involving plane wave expansions. Expressions are given for stress singularities near the crack edge and for the radiation patterns produced by the crack. The case of an elliptical crack in an isotropic medium expanding under shear is examined in detail. Finally, some generalizations are discussed. Solutions are outlined for when the centre of the crack is allowed to move and for a self-similar phase transformation problem, in which a phase change takes place in an expanding ellipsoidal region.
(LF)-spaces with absolute bases
Authors: Bennett G. , Cooper J. B. 
Published: November 2008

Suppose E is a locally convex space over a field K which can be the real line or the complex plane. Then a basis for E is a sequence (xk) of elements of E such that, if x ∈ E, x can be expressed uniquely aswhere ξk ∈K for each k. If this representation converges absolutely, i.e. iffor every continuous seminorm p on E, then (xk) is called an absolute basis for E. If the mappings x → ξk from E into K are continuous for each k, then (xk) is a Schauder basis for E. The purpose of this paper is to prove some results for (LF)-spaces with bases and to use them to extend some theorems due to Pietsch. We recall that an (F)-space is a complete metrizable locally convex space and an (LF)-space the inductive limit of a strictly increasing sequence of (F)-spaces (En, τn) such that τn+1|En = τn for all n.
On critical pairs of product sets in a certain matrix group
Authors: McCrudden M. 
Published: November 2008

1. Introduction. If G is a locally compact Hausdorff topological group, and μ is (left) Haar measure on G, then we denote by ℬ(G) the class of all Borel subsets of G having finite measure, and by VG the set {μ(E): E ∊ ℬ(G)} of real numbers. The product set function of G, ΦG: VG × VG → VG, is defined (see (4) and (5)) byand, for each u, v ∈ VG, we call a pair (E, F) of Borel subsets of G a critical (u, v)-pair, if μ(E) = u, μ(F) = v, and μ*(EF) = ΦG(u, v). We denote the class of all critical (u, v)-pairs by and we write ℰG for .
Summability methods which include the Riesz typical means. II
Authors: Russell B. C. 
Published: November 2008

By making use of a convergence-factor theorem of Bosanquet(3), Cooke((4), Theorem I) gave conditions for a regular sequence-to-sequence summability matrix B to be at least as strong as Cesàro summability (C, κ) (κ > 0), namely:Theorem C. Let κ > 0. In order that the T-matrix B = (bρμ) shall satisfy B ⊇ (C, κ) it is necessary and sufficient thatIf 0 < κ ≤ 1 then (2) alone is necessary and sufficient.
General relativity from gauge invariance
Authors: Lord Eric A. 
Published: November 2008

AbstractThe free field equations for particles with spin are invariant under a group SL(2, c) whose transformations correspond to changes of representation of the twocomponent spinor algebra. The generalization of the equations which extends this invariance to a guage invariance in the Yang–Mills sense necessitates the introduction of auxiliary fields (which are also necessary to maintain Lorentz covariance). These fields can be interpreted as the potentials of a spin-2 field, just as the auxiliary fields for the charge gauge group are the potentials of a spin-l field (electromagnetism); this spin-2 field is then self-interacting. The Bargmann–Wigner formulation of the linear spin-2 field, when modified by the proposed self-interaction, yields a non-linear theory of a spin-2 field which is shown to be identical with Einstein's gravitational theory. With this interpretation the auxiliary fields take on an extra role of Yang–Mills field for the general coordinate transformation group – that is, they are the components of the affine connexion.
Codimension and analytic spread
Authors: Burch Lindsay 
Published: November 2008

In this paper, I shall establish the sufficiency of certain conditions on an ideal A of a local ring Q, and on a set {g1 …,gk} of elements of Q generating a proper ideal G, for the ideals A and G to be analytically disjoint. Hence I shall establish an upper bound for the analytic spread of A.The maximal ideal of Q will be denoted throughout by M, and it will be assumed that the field Q/M is infinite.
Multipliers on some sequence spaces
Authors: Kurtz J. C. 
Published: November 2008

AbstractLet ω be the space of all (complex) sequences. If E, F are subspaces of ω and if A is any (infinite) normal matrix, we setandIf A is the matrix of a sequence–sequence summability transform, Ā and Â shall denote the series–sequence and series–series forms of the transform, respectively. The multiplier spaces M(c(Ā), c(Ā)), M(lp(Â), l1(Â)) and M(lp(Â), c(Ā)) are characterized (1 ≤ p < ∞). Partial results are given for the spaces M(c(Ā), lp(Â)) and M(lp(Â), lp(Â)).
On a theorem of Posner
Authors: Awtar Ram 
Published: November 2008

Posner (1) proved the following result:Theorem. Let R be a prime ring and d a derivation of R such that, for all a∈R, ad(a)–d(a) a∈Z (centre of R). Then, if d is not a zero derivation, R is commutative.The purpose of this note is to give a short proof of this theorem. We state the following known result ((1), Lemma 1).
On the development of a solitary wave moving over an uneven bottom
Authors: Johnson R. S. 
Published: November 2008

AbstractThe numerical and experimental results given in Madsen and Mei(16) are predicted using asymptotic methods and some knowledge of the Korteweg-de Vries (K-dV) equation. This is accomplished by first deriving, using formal asymptotic expansions, the K-dV equation valid over a variable depth. The depth is chosen, in the first instance, to slowly vary on the same scale as the initial (small) amplitude of the motion. The appropriate form of the Kd-V equation is thenwhereH(X,ξ)describes the surface profile andd(σX)is the changing depth. The rest of the paper is devoted to a study of this equation.
Low Reynolds number flow past a porous spherical shell
Authors: Jones I. P. 
Published: November 2008

AbstractThis paper is concerned with the flow of viscous fluids around and through porous bodies. Previous boundary conditions that have been used are discussed and a generalization of a boundary condition adopted by Beavers and Joseph, for plane boundaries, is proposed for curved surfaces. Using this condition the problem of slow viscous flow past a spherical shell is solved and several special limiting cases are considered.
On the eigenvectors of the energy-momentum tensor in the Einstein–Maxwell theory
Authors: Woolley M. L. 
Published: November 2008

AbstractIt is shown that in the four-dimensional, source-free Einstein–Maxwell theory, four distinct orthogonal eigenvectors of the energy-momentum tensor may be obtained formally by the action of four projection operators on an almost arbitrary vector.The extremal field, of the unified theory of Maxwell, Einstein and Rainich, is obtained explicitly in terms of eigenvectors of the energy-momentum tensor and the energy-momentum tensor itself, expressed in terms of eigenvectors, is seen to take on two equivalent forms. From this, a two-parameter group of Lorentz rotations, which leave the tetrad of eigenvectors unchanged, is deduced.
On forced three-dimensional surface waves in a channel in the presence of surface tension
Authors: Rhodes-Robinson P. F. 
Published: November 2008

AbstractIn this paper wave-maker theory including the effect of surface tension is determined for three-dimensional motion of water in a semi-infinite rectangular channel with outgoing surface wave modes allowed for at infinity; the motion is generated by a harmonically oscillating vertical plane wave-maker at the end of the channel and the cases of both infinite and finite constant depth are treated. The solution of the boundary-value problem for the velocity potential is more complicated in the presence of surface tension due mainly to the additional effect of the channel walls at which the normal free surface slopes are prescribed—as also is the slope at the wave-maker—to ensure uniqueness. The simpler three-dimensional solution for a semi-infinite region—obtained long ago by Sir Thomas Havelock in the absence of surface tension for the case of infinite depth—is also noted.
Abstract orthogonality and orthocomplementation
Authors: Cattaneo Gianpiero , Manià Alessandro 
Published: November 2008

AbstractThe notion of orthogonality is axiomatically defined on a poset. Various notions of orthocomplementation are distinguished and conditions are given in order to induce an orthocomplementation from an orthogonality and vice versa. Subsequently ⊥-modular ⊥-poset are defined and the set of morphisms between two posets with orthogonality is briefly discussed. Given the notions of additive monoid and of positive semi-ring, an orthogonality relation is introduced on the set of idempotent elements of a positive semi-ring. Finally, the obtained results are applied to the set of idempotent and absorbent endomorphisms of an additive monoid.
On orthogonality of Riesz products
Authors: Brown Gavin , Moran William 
Published: November 2008

A typical Riesz product on the circle is the weak* limitwhere – 1 ≤ rk ≤ 1, øk ∈ R, λT is Haar measure, and the positive integers nk satisfy nk+1/nk ≥ 3. A classical result of Zygmund (11) implies that either µ is absolutely continuous with respect to λT (when ) or µ is purely singular (when ).
Some theorems on strong regularity of Nörlund methods
Authors: Kuttner B. 
Published: November 2008

1. Given a serieswe will throughout write {sn} for the sequence of its partial sums; that is to say,We will write p, q to denote the sequences {pn}, {qn}; we will write throughoutand will take P−1 = p−1 = 0.
Analytical theory of non-linear oscillations
Authors: Obi Chike 
Published: November 2008

In this paper, we improve on the results of two previous papers (8, 9) by establishing a general existence theorem (section 1·3, below) for a class of periodic oscillations of a wide class of non-linear differential equations of the second order in the real domain which are perturbations of the autonomous differential equationwhere g(x) is strictly non-linear. We then, by way of illustrating the power of the theorem, apply it to the problems which Morris (section 2·2 below), Shimuzu (section 2·3 below) and Loud (section 2·5 below) set themselves on the existence of periodic oscillations of certain differential equations which are perturbations of equations of the form (1·1·1).
A diophantine problem on groups. III
Authors: Baker R. C. 
Published: November 2008

AbstractThe following generalization of a theorem of Weyl appeared in part I of this series of papers. Let G be a locally compact Abelian group with dual group ĝ. Let be a sequence in ĝ, not too slowly growing in a certain precise sense. Then, provided ĝ has ‘not too many’ elements of finite order, the sequencesare uniformly distributed on the circle, for almost all x in G.
Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients
Authors: Askey Richard , Gasper George 
Published: November 2008

The answers to many important questions in the harmonic analysis of orthogonal polynomials are known to depend on the determination of when formulas of the typesand their dualshold, where pn(x) and qn(x) are suitably normalized orthogonal polynomials or orthogonal polynomials multiplied by certain functions; e.g. e−pxLn(x).
The localizability of particles in de Sitter space
Authors: Hannabuss K. C. 
Published: November 2008

AbstractMotivated by the Iwasawa decomposition and its geometrical interpretation, two new decompositions of the de Sitter group are obtained. The first is applied to construct the representations of the de Sitter group in a form immediately comparable with those of the Poincaré group. In particular they act on functions over an hyperboloid like the momentum hyperboloid of the Poincaré group, although they require both positive and negative mass shells of that hyperboloid. Using the second decomposition it is shown that the representations of the de Sitter group are localizable in the sense of Mackey and Wightman. Position operators are exhibited.