bluuebunny/crossref_metadata_2025_split huggingface dataset:
The effects of strong suction on laminar boundary layers
Authors: Buckmaster J. 
Published: November 2008

AbstractThe title problem is investigated with the view of clarifying the nature of the separation in an adverse pressure gradient when the suction υ0 is very strong. A linear model is investigated, but it is argued that this must contain many of the essential features of the exact (non-linear) problem. With a free-stream U = 1 − x the similarity solution u = (1 − x)f(y) is appropriate when (υ0x − y) ≫ 1, x = O(1), 1−x = O(1). There is an O(1) layer centred on y = υ0x in which more complex x-dependence first appears and then, when (y − υ0x) ≫ 1, the solution assumes its final asymptotic behaviour. The y = υ0x layer is non-uniform in x and exhibits a marked change in behaviour when (1 − x;) = O(l/υ0). The solution in this narrow rectangle is singular like (1 − x)−2 at the trailing edge. It is these singular terms that induce separation and reversed flow in an exponentially small neighbourhood of the trailing-edge.
An iterative method to calculate the phases of Coulomb functions
Authors: Martins P. De A. P. 
Published: November 2008

AbstractThe differential equationdefining the function of the amplitude sL is integrated by an iterative procedure. An expression for the phaseis obtained in terms of integrals of ωL and its derivatives. The method is applied to the numerical calculation of Coulomb functions and the accuracy of the results is discussed. Recurrence relations are used to obtain øL, L ≽ 1.
Comments on the classical theory of magnetic monopoles
Authors: Miller D. T. 
Published: November 2008

AbstractThe classical theory of electromagnetism with both electric and magnetic charges is discussed. Following Gamblin(l) we proceed from an action principle and investigate the resulting particle equations. A consistent theory in which electrically and magnetically charged particles interact amongst themselves and with each other, without any constraints, is shown to be possible, in contrast to the conclusions of Gamblin. The introduction of constraints is considered.
An elastostatic circle theorem
Authors: Aderogba K. 
Published: November 2008

AbstractAn isotropic infinite plane containing a circular inhomogeneity is subjected to an arbitrary loading condition. Assuming that the unperturbed elastic field is known, it is proved that the disturbed Papkovich potentials are expressible in terms of the potentials for the homogeneous plane. This knowledge can save considerable labour in the actual construction of the elastic field for the composite plane. The results are applied to some particular problems which include that of an arc displacement discontinuity in the composite plane. This example has as yet not been solved explicity by other methods and reveals that the displacement field at the cavity surface is independent of the elastic constants.
Collapsing K × I
Authors: Webster Dallas E. 
Published: November 2008

Zeeman(5) once bravely made the following conjecture:Conjecture. Suppose K is a contractible 2-complex and I is the unit interval [0, 1]. Then K × I collapses.This conjecture is interesting since it trivially implies the Poincaré conjecture. For if C is a homotopy 3-cell, then it has a contractible 2-dimensional spine, so that C × I would be a collapsible 4-manifold. But then C × I would be a 4-cell, with C = C × 0 in its 3-sphere boundary, and the PL Schoenfliess theorem shows that C is a 3-cell.
On the exterior problems of acoustics
Authors: Ursell F. 
Published: November 2008

AbstractThe method of integral equations is the most familiar method of proving existence theorems for the Helmholtz equation of acoustics. The wave potentials are expressed as surface distributions of wave sources (for the Neumann problem) or wave dipoles (for the Dirichlet problem). By a wave source is meant the free-space wave source. The source and dipole strengths for the exterior potentials are found to be solutions of Fredholm integral equations of the second kind which are, however, singular at a certain discrete set of frequencies corresponding to eigensolutions of the interior problems. The existence of exterior solutions at the expected frequencies can still be shown, but the proof involves a detailed and complicated study of the interior solutions. It is physically evident that this difficulty arises from the method of solution and not from the nature of the problem.
Oscillations of retarded differential equations
Authors: Sficas Y. G. , Staikos V. A. 
Published: November 2008

In this paper we are dealing with the oscillatory and asymptotic behaviour of the nth order, (n> 1), retarded differential equationwheregis differentiable on the half-line (t0,∞) with (I)g(t) ≤ tfor everyt ≥ t0(II)g'(t)≥ 0 for everyt≥t0(III)= ∞.
The static two body problem
Authors: Zum Hagen H. Müller 
Published: November 2008

AbstractThe problem of whether there exist static solutions of Einstein's equations for two extended bodies surrounded by vacuum is investigated. Equilibrium conditions for the general static situation are derived and their physical meaning discussed. Special cases of the problem are solved by using these equilibrium conditions. In one of these cases, the essential assumptions are that the space time is axisymmetric and that the matter of which the two bodies are composed consists of perfect fluid. Solu tions are also obtained in which these restrictions are weakened.
A characterization of M-Summands
Authors: Evans Richard 
Published: November 2008

In the structure theory of Banach spaces as developed in (1), an important role is played by subspaces which are the ranges of projections having norm properties akin to those of the classical Banach spaces. A linear projection e on a Banach space V is called an M-projection ifand an L-projection if, insteadA closed subspace J of V is called an M-Summand if it is the range of an M-projection and an M-Ideal if J0 is the range of an L-projection in V′. Every M-Summand is an M-Ideal but the reverse is false.
A note on the percolation probabilities of pairs of closely similar lattices
Authors: Sykes M. F. , Rehr J. J. , Glen Maureen 
Published: November 2008

AbstractThe percolation probabilities of the face-centred cubic and close-packed hexagonal lattices are found not to be identical; the identity of their critical percolation probabilities remains an open question. Other pairs of closely similar lattices are discussed.
Intrinsically characterized acceleration waves in heat-conducting elastic materials
Authors: Chadwick P. , Currie P. K. 
Published: November 2008

AbstractThis paper is concerned with a particular class of acceleration waves in heat-conducting elastic materials, namely those waves for which the acceleration amplitude is a proper vector of both the isothermal and isentropic acoustical tensors. Acceleration waves with this characteristic property are found to fall naturally into two distinct sub-classes, and close parallels are shown to exist between the members of the sub-classes and waves for which the acceleration amplitude is either longitudinal or transverse to the direction of propagation. Particular attention is given here to waves of the quasi-longitudinal type, the quasi-transverse variety having been studied in some detail elsewhere.
Series solution of the biharmonic equation in the rectangular domain with some applications to mechanics
Authors: Vaughan H. 
Published: November 2008

SummaryA double series solution of the biharmonic equation is derived in the rectangular domain. The solution utilizes the finite double Fourier sine transform and the analysis shows how the transform may be evaluated for quite arbitrary boundary conditions, the solution then being found from the corresponding inversion formula.The method is applied to some classical boundary value problems which have been investigated by other means by earlier workers. It is felt that some of the series solutions given here are more amenable to computation than some of the earlier methods.In some of the problems considered, notably the elastostatics of the rectangular plate and the bending of clamped plates, the method reduces to solving an infinite set of linear equations. In such cases, a finite leading matrix of the coefficients has to be considered. In the examples considered, this technique produced results which converged to known solutions obtained by other methods. However, the mathematical criteria which permit the infinite system to be curtailed, have not been established.
A commutant property of symmetric ternary algebras
Authors: Sullivan W. G. , Joseph A. 
Published: November 2008

AbstractA commutant property of ternary algebras, defined as linear subspaces of ℬ(ℋ) (bounded operators on some Hubert space ℋ) closed under three-fold multiplication, is demonstrated through the recovery of an operator from its non- orthogonal restrictions.
Thermostatics of an elastic Cosserat plate containing a circular hole
Authors: Gürgöze İ. T. 
Published: November 2008

AbstractIn this paper, the general theory of a Cosserat surface given by Green, Naghdi and Wainwright(1), has been applied to the problem of a thermo-elastic Cosserat plate containing a circular hole of radius a. We assume that the major surfaces of the plate and the boundary of the hole are thermally insulated and that a uniform temperature gradient τ exists at infinity. In the limiting case, when h/a → 0, where h is the thickness of the plate, the thermal stresses at the circular hole reduce to those obtained by Florence and Goodier (4), by means of the classical plate theory. Results for the other limiting case h/a → ∞ are also given.
Analytical considerations of barrier transmission
Authors: Heading J. 
Published: November 2008

AbstractThe success of approximate methods in the calculation of transmission coefficients of waves penetrating potential barriers rests, not so much on any satisfactory approximation theory, but on a comparison with a particular barrier, namely the parabolic barrier. The paucity of exact analytical solutions of barrier problems has prevented an explicit detailed analysis of the errors involved, but two recently devised barriers with analytical solutions are investigated here, in order to compare the exact values of the transmission coefficients (both as to their mathematical structure and numerically) with their approximate forms. An estimate is also made of the effect of neglecting poles existing in the complex propagation plane.
A new physical characterization of stationary and static space-times
Authors: Müller zum Hagen H. 
Published: November 2008

AbstractA space time is stationary if and only if it admits a congruence of time-like curves such that the distance between any two curves is time independent. The distance between two curves A and B, which are not necessarily infinitesimally close to each other, is defined as half the trip-time of a photon, which travels from A to B and back to A.
High frequency diffraction by a circular disc
Authors: Williams W. E. 
Published: November 2008

AbstractThe problem considered is that of transforming the integral equations obtained by Jones (2, 3), for diffraction by a circular disc so that they can be solved by iteration for any general incident field. A method of achieving this transformation is presented for the case of axi-symmetric incident fields. The generalization of the method to non-axi-symmetric problems is also examined.
On the superposition of gravitational waves
Authors: Griffiths J. B. 
Published: November 2008

AbstractThe nature of the non-linear interaction between two gravitational waves in the general theory of relativity is considered. A new exact solution of the vacuum field equations describing this case is given. It describes two gravitational waves with both transverse and longitudinal components, propagating in opposite directions along ‘shearing’ and ‘twisting’ geodesic congruences with zero contraction
A two turning-point problem in fluid mechanics
Authors: McKee W. D. 
Published: November 2008

AbstractA uniformly valid asymptotic solution is found for waves refracted by a shearing current or by bottom topography in the case where two straight caustics are present. The ratio of the amplitude of the reflected wave to that of the incident wave increases monotonically from 1/√2, when the caustics are close together, to unity when they are widely separated. A slight modification of the theory gives an expression for the frequencies of waves trapped between two caustics.
Proof of a conjecture about the distribution of divisors of integers in residue classes
Authors: Erdös P. , Hall R. R. 
Published: November 2008

Let k be a positive integer and F(x, k) denote the number of integers n < x which have a divisor in every residue class prime to k. Erdös (1) proved that for every fixed ε > 0, we have F(x, k) ˜ x whenand conjectured the following result, which we prove in this paper.
Invariant properties of wave propagation in n-dimensional space
Authors: Heading John 
Published: November 2008

AbstractThe paper continues earlier work on the generalization in n-dimensional space of the differential equations governing the propagation of electromagnetic waves in inhomogeneous anisotropic ionospheric plasma. Here there are investigated certain properties of the equations and their solutions that are independent of the dimension n of the space in which propagation takes place. The isotropic case is discussed, together with a special anisotropic model for which the various planes of circular polarization are geometrically related to each other.
Global stability of genetic systems governed by mutation and selection. II
Authors: Moran P. A. P. 
Published: November 2008

AbstractAn infinite genetic population of haploid particles is considered in which selection is controlled by a single locus at which there are an infinite number of possible alleles. These alleles are arranged in an infinite sequence and mutation occurs only to nearest neighbours. This is the ‘ladder model’ of Ohta and Kimura which was put forward as a possible explanation of the distributions of electromorphs in electrophoretic observations. Following an earlier paper, conditions are obtained on the selection coefficients which ensure that a stationary stable state exists. One such model is solved explicitly. The problem, important in evolutionary theory, of the rate of approach to such stationary states starting from some other state, is also discussed briefly.
The static–geometric analogy in the equations of thin shell structures
Authors: Calladine C. R. 
Published: November 2008

AbstractThe ‘static-geometric analogy’ in thin shell structures is a formal correspondence between equilibrium equations on the one hand and geometric compatibility equations on the other. It is well known as a fact, but no satisfactory explanation of its basis has been given. The paper gives an explanation for the analogy, within the framework of shallow-shell theory. The explanation is facilitated by two innovations: (i) separation of the shell surface conceptually into separate stretching (S) and bending (B) surfaces; (ii) use of change of Gaussian curvature as a prime variable. Various limitations of the analogy are pointed out, and a scheme for numerical calculation which embodies the most useful features of the analogy is outlined.
A buckling model for the set of umbilic catastrophes
Authors: Thompson J. M. T. , Gaspar Z. 
Published: November 2008

AbstractZeeman has drawn attention to the sequences in which catastrophes, or modes of instability, can be linked, and it is a common observation that sequences of catastrophes of low order are always found in the environment of catastrophes of higher order. In this paper, a simple buckling model is presented that generates in an elegant manner a complete sequence of the umbilic catastrophes as represented by the semi-symmetric branching points. The scan of a single fundamental parameter of this model is shown to trace a route through all regimes of the umbilic bracelet, giving in turn the hyperbolic, symbolic, elliptic, parabolic and hyperbolic umbilic catastrophes.
Two inequalities for the complete symmetric functions
Authors: Baston V. J. 
Published: November 2008

In (l) Hunter proved that the complete symmetric functions of even order are positive definite by obtaining the inequalitywhere ht denotes the complete symmetric function of order t. In this note we show that the inequality can be strengthened, which, in turn, enables theorem 2 of (l) to be sharpened. We also obtain a special case of an inequality conjectured by McLeod(2).
A non-uniform rate of convergence in a local limit theorem
Authors: Basu Sujit K. 
Published: November 2008

AbstractLet {Xn} be a sequence of iid random variables. If the common charac-teristic function is absolutely integrable in mth power for some integer m ≥ 1, then Zn = n−½(X1 + … + Xn) has a pdf fn for all n ≥ m. Here we give a necessary and sufficient condition for sup as
n. → ∞, where φ (x) is the standard normal pdf and M(x) is a non-decreasing function of x ≥ 0 such that M(0) > 0 and M(x)/xδ is non-increasing for 0 < δ ≤ 1.
On triangle contractive operators in Hilbert spaces
Authors: Ang Dang Dinh , Hoa Le Hoan 
Published: November 2008

AbstractLet H be a finite dimensional real or complex Hilbert space. We denote by Λ(x, y, z) the area of the triangle with vertices x, y, z ∈ H. A map f: H → H is triangle contractive TC if 0 < α < 1 and for each x, y, z ∈ H eitherorandandWe prove that if f is TC either there is a fixed point w = f(w) or a fixed line L = ⊃ f(L) We characterize the f which are TC and continuous but have no fixed point.
Closed braids which are not prime knots
Authors: Morton H. R. 
Published: November 2008

An element B ∈ Bn, the braid group on n strings, which can be written asin terms of the standard generators of Bn is called a split braid. It is easy to see that the resulting closed braid is the connected sum of the closed braids Ĉ and on k + 1 and n − k strings respectively (figure 1).
Bifurcations at a spherical hole in an infinite elastoplastic medium
Authors: Bassani J. L. , Durban D. , Hutchinson J. W. 
Published: November 2008

AbstractThe bifurcation problem of an infinite elastoplastic medium surrounding a spherical cavity and subjected to uniform radial tension or compression at infinity is studied. The material is assumed to be incompressible, and its behaviour is modelled by both hypoelastic (flow theory) and hyperelastic (deformation theory) constitutive relations. No bifurcation was found with the flow theory. Surface bifurcation modes were discovered with the deformation theory in both tension and compression. An independent study is also presented of surface bifurcations of a semi-infinite elastoplastic material under equi-biaxial stress. The critical strain for the half-space coincides with the strain at the spherical cavity at the lowest bifurcation.
An example in the theory of solubl groups
Authors: Hawkes T. O. 
Published: November 2008

Let G be a finite soluble group. In (1) Alperin proves that two system normalizers of G contained in the same Carter subgroup C of G are conjugate in C. In recent unpublished work G.A.Chambers of the University of Wisconsin has proved that, if is a saturated formation, the -normalizers of an A-group are pronormal subgruops; hence, in particular, that two -normalizers contained in an -projector E of an A-group are conjugate in E. In this note we describe an example which shows that in Alperin's theorem the class of nilpotent groups cannot in general be replaced by an arbitary saturated formation without some restriction on the class of soluble groups under consideration. we provePROPOSITION. There exists a saturated formationand a group G which has two-normalizers E1and E2contained in an-projector F of G such that E1and E2are not conjugate in F.
On similarity solutions of the differential equation ψzzzz + ψx = 0
Authors: Gill A. E. , Smith R. K. 
Published: November 2008

AbstractSolutions of the partial differential equation ψzzzz + ψx + 0 of the type ψ = x¼nw(y), where y = zx−¼ and n is an integer, are investigated. The equation occurs as a boundary-layer approximation in certain rotating and stratified fluid flows in which the production of vorticity (due, for example, to changes in the Coriolis parameter with latitude in two-dimensional flows on a beta plane, or by the buoyant generation of vorticity in a Boussinesq fluid) is opposed by a diffusive process. The similarity functions w(y) satisfy the fourth order differential equation.These functions have many properties analogous to those of error functions and parabolic cylinder functions. When n is a non-negative integer, there exist polynomial solutions of the latter equation. These have analogies with Hermite polynomials, although they do not form an orthogonal set in any useful sense. The main properties of the similarity functions are listed, including their series expansions, integral representations, asymptotic expansions and recurrence relations. In particular, a pair of independent solutions, Jon(y) and Kon(y), are denned such that Jon(y) and Kon(y) are real for real y and vanish at an exponential rate as y → + ∞. The function Jon(y) also decays exponentially as y → − ∞ if n is negative, and grows algebraically as y → − ∞ if n is positive. Curves of the functions Jon(y) and Kon(y) are given for |n| ≤ 3 and 0 < y < 6, and their more useful properties are listed.
On Morita's p-adic gamma function
Authors: Barsky Daniel 
Published: November 2008

Y. Morita proved that, for each prime number p, one can define a p-adic continuous function Γp(x) from p to p, interpolating the sequencewhere m runs through the integers m prime to p with 1 ≤ m < n. Our aim is to show how this result is related to Dwork's result on the radius of convergence of
Lattice isomorphisms of Lie algebras
Authors: Towers D. A. 
Published: November 2008

Let L, M be Lie algebras over the same field F and let ℒ(L), ℒ(M) denote their lattices of subalgebras. By an L-isomorphism (lattice isomorphism) of L onto M we mean an isomorphism θ: ℒ(L) → ℒ(M); that is, θ a bijective mapping from ℒ(L) onto ℒ(M) such thatandfor all subalgebras A, B of L (where A ∪ B denotes the subalgebra of L generated by A and B). We shall write A* for θ(A), the image of A ∈ ℒ(L) under an L-isomorphism from L onto M = L*. Then we may ask how closely related are L and L*. In particular, are such important concepts as semisimplicity, solvability, nilpotency and ideals preserved by L-isomorphisms?
An intrinsic conformal Lorentz pseudodistance
Authors: Markowitz Michael J 
Published: November 2008

AbstractAn intrinsic pseudodistance dM is associated to the underlying causal structure of a Lorentzian manifold (M, g). An infinitesimal form for dM is defined on the bundle of null vectors over M and is used to prove that, under certain physically reasonable energy conditions, M is conformally hyperbolic, i.e. that dM is a true distance. As a corollary we obtain sufficient conditions for the conformal hyperbolicity of a globally hyperbolic space-time. Some exact solutions of the Einstein field equations are discussed and possible applications to the study of singularities are outlined.
Solitary wave solutions for a model of the two-way propagation of water waves in a channel
Authors: Toland J. F. 
Published: November 2008

Bona and Smith (6) have suggested that the coupled system of equationshas the same formal justification as other Boussinesq-type models for the two-way propagation of one-dimensional water waves of small but finite amplitude in a channel with a flat bottom. The variables u and η represent the velocity and elevation of the free surface, respectively. Using the energy invariantthey show that for a restricted, but nevertheless physically relevant, class of initial data, the system (1·1) has solutions which exist for all time, and that in such circumstances the wave height is bounded solely in terms of the initial data.