bluuebunny/crossref_metadata_2025_split huggingface dataset:
Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc
Authors: Jones D. S. 
Published: November 2008

AbstractA method already developed for the diffraction of scalar waves by a circular disc is generalized so as to be applicable to the diffraction of an electromagnetic wave. The generalization leads, in a straightforward manner, to an asymptotic development of the current density on the disc at high frequencies. The principal complication which arises is in solving three simultaneous linear equations for three constants which occur in the method of solution. Detailed calculations are given for a normally incident plane wave.
Two-dimensional elastic inclusion problems
Authors: List R. D. , Silberstein J. P. O. 
Published: November 2008

AbstractA system of equations is derived for determining the elastic fields in an inclusion and its surrounding finite matrix when the inclusion suffers a physical change and, if not constrained by the matrix, would undergo a deformation . A method for obtaining the exact solution of these equations, when the matrix and inclusion have the same elastic constants, is described and the particular problem of the square inclusion in an infinite matrix solved.
Collapsing three-dimensional convex polyhedra
Authors: Chillingworth D. R. J. 
Published: November 2008

If L is a subcomplex of a simplicial complex K, we say that L is obtained from K by an elementary simplical collapse if K − L consists of a simplex σ of some dimension d together with one ‘free’ face of σ, i.e. a face τ of dimension d − 1 which is a face of no other simplex of K except σ. Such a collapse is said to take place through σ from τ. If L can be obtained from K by a finite sequence of elementary simplicial collapses we say that K simplicially collapses (s-collapses) onto L, denoted by K ↘ LIf K is regarded as being embedded in some Euclidean space we shall for convenience of notation fail to distinguish between K and its underlying polyhedron.
Magneto-elastic coupling effects on the propagation of harmonic waves in an electrically conducting elastic plate
Authors: Purushotham C. M. 
Published: November 2008

AbstractThe influence of a uniform external magnetic field on the propagation of harmonic waves in a perfectly conducting elastic plate extending to infinity in vacuum, with its plane boundaries free of mechanical tractions, has been studied. With the plane of the field and the direction of wave propagation being normal to the plate, it is found that the effects of electromagnetic radiation into the adjoining free space cannot be neglected in the case of waves polarized in the plane. When the field is aligned with the direction of propagation, the maximum influence appears to be on long flexural waves, whereas if the field is normal to the plate then the effect is very much pronounced on long plate waves, and the flexural waves propagate almost with Alfvén velocity.
Relations between arithmetical functions
Authors: Evelyn C. J. A. 
Published: November 2008

In a recent note(1) I proved that if μ(n) denotes the usual Möbius function, N denotes a fixed positive integer and ifthenwhere T runs through all natural numbers ≤ x which are not divisible by an Nth power. In the present paper I shall establish some further relations of this character and, in particular, I shall prove that ifwherethenThus, in some respects, L(x) appears more regular than M(x), the sum over L(x/T) being multiplicative, whereas M(x1/N) is not.
Démonstration du théorème sur la suite spectrale des fibrés au sens de Kan
Authors: Lusztig Gheorghe , Moscovici Henri 
Published: November 2008

AbstractWe give a relatively simple proof of the theorem on the spectral sequence of a fibre-space in the sense of Kan. The method consists in the reduction to locally trivial fibre-spaces by minimal fibrings and in the use of a very simple acyclic model theory (without degeneracies).
On the general correspondence between field theories and the theories of direct interparticle action
Authors: Narlikar J. V. 
Published: November 2008

AbstractIt is well known that classical electrodynamics can be described both as a field theory and as a theory of direct interparticle action. In the present paper it is shown that, provided certain general conditions are satisfied, fields of arbitrary spin have their counterparts in ‘direct particle fields’. This correspondence between the two formalisms is established in the Riemannian space-time used for general relativity.
Existence theorems for H-space inverses
Authors: Sibson Robin 
Published: November 2008

We define an unbased H-space to be a pair (A, m) where A is a space andis a map such that the maps La: x → m(a, x), Ra: x → m(x, a) are homotopy equivalences for all a ∈ A. This is the same as James's definition of an H'-space in (3); we follow his notation as far as possible. (A, m) is homotopy-associative if the maps m(m × 1) and m(l × m) are homotopic. A left (right) a-inverse (a ∈ A) is a map w: A → A such that the composition m(w × 1) d (w(1 × w) d) is homotopic to ka, the constant map to a. d denotes the diagonal map a → (a, a).
On the Brunn-Minkowski coefficient of a locally compact unimodular group
Authors: McCrudden M. 
Published: November 2008

Let G be a locally compact topological group, and let μ be the left Haar measure on G, with μ the corresponding outer measure. If R' denotes the non-negative extended real numbers, B (G) the Borel subsets of G, and V = {μ(C):C ∈ B(G)}, then we can define ΦG: V × V → R' bywhere AB denotes the product set of A and B in G. Then clearlyso that a knowledge of ΦG will give us some idea of how the outer measure of the product set AB compares with the measures of the sets A and B.
The boundary layer on a paraboloid of revolution
Authors: Miller D. R. 
Published: November 2008

AbstractAn analytical study is made of the boundary-layer approximation for the steady laminar flow of a viscous incompressible fluid past a paraboloid of revolution. The functional form of the vorticity distribution is found and shown to involve exponential decay with distance from the surface of the body, and inequalities are established concerning the displacement thickness.The exact results are compared with various linearizations. The Oseen linearization (12) turns out to be incorrect except in the limit of vanishing Reynolds number; this result is connected with the infinite drag of any paraboloid of non-zero thickness. An alternate linearization, related to a method of Burgers (3) and allowing for the displacement effect of the body and of its boundary layer, is shown to give the correct functional form for these quantities. Numerical results are included which bear out these conclusions.
Continuous data dependence for the equations of classical elastodynamics
Authors: Knops R. J. , Payne L. E. 
Published: November 2008

Consider a linear elastic solid occupying a bounded regular three-dimensional region B with smooth surface ∂B. The components of displacement ui referred to cartesian axes xi are then well known to satisfy the system of governing equationsin which t denotes the time variable, x = (x1, x2, x3) denotes the position vector, ρ(x) is the non-homogeneous density, assumed positive,. i(x, t) are the Cartesian components of body force per unit mass, and cijkl(x) are the non-homogeneous elasticities, which apart from certain smoothness conditions stated later, are assumed to possess the symmetryThroughout this paper, all suffixes range over the values 1, 2, 3 and the usual converition of summing over repeated indices is adopted. Except where it is in the interest of clarity we avoid explicit mention of the dependence of functions on their arguments.
On some applications of a theorem of Browder–Levine–Livesay
Authors: Swarup G. A. , Varadarajan K. 
Published: November 2008

The main result proved in this paper can be stated as follows:Theorem. Let Mnbe a closed l-connected topological manifold of dimension n ≥ 5. Then M × R carries a differentiable (respectively aPL) structure if and only if M × S1carries a differentiable (respectively aPL) structure.
The equality of the moduli of certain ratios occurring in the connexion formulae of solutions of some transcendental differential equations
Authors: Heading J. 
Published: November 2008

AbstractThe differential equations governing the propagation of waves of electric and magnetic types in a plane stratified isotropic plasma are suitably generalized, and we investigate the possibility of models for which the moduli of the reflexion coefficients are identical for the two modes. First, the models are examined without the necessity of finding general solutions, and, secondly, by using the circuit relations for the hypergeometric functions occurring in the explicit solutions.
On the series solution to the laminar boundary layer with stationary origin on a continuous, moving porous surface
Authors: Samuel T. D. M. A. , Hall I. M. 
Published: November 2008

AbstractThe similarity solution for a laminar boundary layer on a continuous, moving, porous surface is obtained using a series of exponential terms. The convergence of this series which was previously used by Ackroyd (1) is investigated by a technique due to Weyl (4) and it is summed by a novel technique.
Exact and approximate methods for the investigation of the propagation of waves through a system of barriers
Authors: Heading J. 
Published: November 2008

AbstractThere is developed the theory of the propagation of waves through a system of potential barriers. Many properties are derived and discussed, mainly by the use of matrix theory arising from the description of each barrier by a transmission matrix. The extent to which certain previously used approximate methods are applicable and valid is also examined. Two distinct kinds of resonant phenomena are discussed – first when there is no incident wave and secondly when there is no reflected wave. This latter case of perfect transmission is investigated in detail, an examination being given of both why and when it occurs and the time taken to establish such exceptional fields within the barriers.
Subgroups of the modular group
Authors: Stothers W. W. 
Published: November 2008

The modular group, Γ, is the group of linear fractional transformations with integral coefficients and determinant 1. The group is generated by the transformationswhich have orders 2 and 3 respectively. The transformationis of infinite order. Abstractly, the group can be viewed as the free product of cyclic groups of order 2 and 3.
Schauder bases and decompositions in locally convex spaces
Authors: Webb J. H. 
Published: November 2008

Let E[τ] be a locally convex Hausdorif topological vector space, with a Schauder basis {xi, x′j wherefor each x ∈ E. The partial summation operator Sn, defined byis a linear operator on E, whose definition extends at once to a linear operator mapping (E′)* into E, where (E′)* is the algebraic dual of E′. The dual of Sn is the operator S′n, mapping E* into E′, defined byand 〈Snx, x′〉 = 〈x, S′nx′〉 for each x ∈ (E′)*. It is easy to see that S′nx′ → x′ with respect to the weak topology σ(E′, E) for each x′ ∈ E′.
Spectral asymmetry and Riemannian Geometry. I
Authors: Atiyah M. F. , Patodi V. K. , Singer I. M. 
Published: November 2008

1. Introduction. The main purpose of this paper is to present a generalization of Hirzebruch's signature theorem for the case of manifolds with boundary. Our result is in the framework of Riemannian geometry and can be viewed as analogous to the Gauss–Bonnet theorem for manifolds with boundary, although there is a very significant difference between the two cases which is, in a sense, the central topic of the paper. To explain this difference let us begin by recalling that the classical Gauss–Bonnet theorem for a surface X with boundary Y asserts that the Euler characteristic E(X) is given by a formula:where K is the Gauss curvature of X and σ is the geodesic curvature of Y in X. In particular if, near the boundary, X is isometric to the product Y x R+, the boundary integral in (1.1) vanishes and the formula is the same as for closed surfaces. Similar remarks hold in higher dimensions. Now if X is a closed oriented Riemannian manifold of dimension 4, there is another formula relating cohomological invariants with curvature in addition to the Gauss–Bonnet formula. This expresses the signature of the quadratic form on H2(X, R) by an integral formulawhere p1 is the differential 4-form representing the first Pontrjagin class and is given in terms of the curvature matrix R by p1 = (2π)−2Tr R2. It is natural to ask if (1.2) continues to hold for manifolds with boundary, provided the metric is a product near the boundary. Simple examples show that this is false, so that in general
The propagation of Rayleigh waves over curved surfaces at high frequency
Authors: Gregory R. D. 
Published: November 2008

AbstractA formal asymptotic theory, valid at high frequencies, is developed for the propagation of time harmonic Rayleigh surface waves over the general smooth free surface Σ of a homogeneous elastic solid. It is shown that on Σ these Rayleigh waves can be described by a system of surface rays, which are shown to be geodesics of Σ. The amplitude of the waves on Σ is shown to vary in such a way that the energy propagated along a strip of surface rays is constant. The waves are also shown to be dispersive and an explicit first-order dispersion formula is derived.
Diffeomorphisms of some smooth metastably connected manifolds
Authors: Hodgson J. P. E. 
Published: November 2008

Let Mm be a closed connected smooth manifold of dimension m, and set Pm = Mm – int Dm where Dm is a disc in M. In (4), Wall has the following exact sequencewhere (M), (resp. (P)) is the Δ-set of diffeomorphisms of M (resp. P) as in(l), and [M/P] is the set of diffeomorphism classes of smooth manifolds obtained by glueing a disc to the boundary of P. In this paper we obtain some results on π0((M)) for particular M, and in the following sense: Using the techniques of (2), we can determine π0((P)), so the main portion of the paper is concerned with a discussion of the kernel of α. There is a map ω: π1((P)) → Γm+1, given by the obstruction to extending h∈π1((P)) to a concordance of the identity of M to itself, and it is clear that if this map is attached at the beginning of the sequence (*) we get exactness. We will obtain (for certain M) an alternative description of the image of α in terms of those homotopy spheres which can appear as the boundaries of thickenings.
Fractional parts of powers of rationals
Authors: Baker A. , Coates J. 
Published: November 2008

Mahler (5) proved in 1957 that for any rational a/q, where a, q are relatively prime integers with a > q ≥ 2, and any ε > 0, there exist only finitely many positive integers n such that ∥(a/q)n∥ < e−εn; here ∥x∥ denotes the distance of x from the nearest integer taken positively. In particular there exist only finitely many n such thatand, as Mahler observed, this implies that the number g(k) occurring in Waring's problem is given byfor all but a finite number of values of k. It would plainly be of interest to establish a bound for the exceptional k and this would follow from an upper estimate for the integers n for which (1) holds. But Mahler's work was based on Ridout's generalization of Roth's theorem and, as is well known, the latter result is ineffective.
On colouring random graphs
Authors: Grimmett G. R. , McDiarmid C. J. H. 
Published: November 2008

AbstractLet ωndenote a random graph with vertex set {1, 2, …,n}, such that each edge is present with a prescribed probabilityp, independently of the presence or absence of any other edges. We show that the number of vertices in the largest complete subgraph of ωnis, with probability one,
The self-intersection formula and the ‘formule-clef’
Authors: Lascu A. T. , Mumford D. , Scott D. B. 
Published: November 2008

We shall consider exclusively algebraic non-singular quasi-projective irreducible varieties over an algebraically closed field. If V is such a variety will be the Chow ring of rational equivalence classes of cycles of Vand the group homomorphism defined by any proper morphism φ: V1 → V2. Alsodenotes the ring homomorphism defined by φ.
Periodic solutions of certain nonlinear autonomous wave equations
Authors: Melrose Richard B. , Pemberton Malcolm 
Published: November 2008

The hyperbolic boundary value problemhas, for δ = 0 and each positive integer k, t-periodic solutions of period τk(ε) = 2Φ/(k2 + ε)½. For a reasonably large class of functions, f, and, for each k, certain values of ε, one at least of these solutions persists for small δ
Banach algebras and absolutely summing operators
Authors: Tonge Andrew M. 
Published: November 2008

If R is a Banach algebra and ø ∈ R′, the dual space, then we may define a bounded linear map byWe shall show that for suitable p the requirement that each be p-absolutely summing constrains R to be an operator algebra, or even, in certain cases, a uniform algebra. In this way we are able to give generalizations of results of Varopoulos (12) and Kaijser (4).
A circular disc containing a radial edge crack opened by a constant internal pressure
Authors: Gregory R. D. 
Published: November 2008

AbstractA circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of lengthb(0 <b< 2a). The disc is in equilibrium in a state of generalized plane stress caused by loading the faces of the crack by a constant internal pressure. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form. The principal results are that the stress concentration factorat the crack tip, the total strain energyW, and the openingUat the mouth of the crack, are given exactly bywhereAis a constant whose value correct to 6 significant figures isand,W0,U0are normalising factors defined in section 6.
Closed graph theorems for generalized inductive limit topologies
Authors: Ruess W. 
Published: November 2008

SummaryThe object of this and a subsequent paper is to investigate the locally convex structure of several strict topologies that are generalizations of R. C. Buck's strict topology β on C(S), S locally compact Hausdorff. If the topology τ of a locally convex space (lcs) (X, τ) is any of these strict topologies, then it is localizable on every absorbing disc T in X, i.e. it is the finest locally convex topology on X agreeing with τ on T. Topologies of this kind are said to be (L)-topologies. As our main tools for the analysis of the structure of strict topologies, we deduce in this paper several closed graph theorems for spaces of type (L). In particular, it is shown that every semi-Montel lcs with a fundamental sequence of bounded sets and every Bτ-complete Schwartz space belongs to the class Bτ(L) of all lcs Y with the property that every closed linear map from any (L)-space X into Y is continuous. Further closed graph theorems are established and many of the known closed graph theorems are deduced as special cases of our results. Moreover, the problem of Bτ-completeness of locally convex spaces belonging to Bτ(L) is considered.
Isotone measures on groups
Authors: Moran W. , Williamson J. H. 
Published: November 2008

If E and F are ordered spaces, a map T: E → F is positive ifThe map T is bi-positive if f ≥ 0 ⇔ Tf ≥ 0. It is a natural problem to seek information about the positive and bi-positive linear maps between pairs of ordered vector spaces. The present study is an attempt to elucidate one facet of this general problem (see, for example, (2), vol. II, § 16·7·1, p. 278).
Theoretical plasticity of textured aggregates
Authors: Hill R. 
Published: November 2008

AbstractThe plasticity of metal polycrystals with preferred orientations is considered from a phenomenological standpoint. Some new general theorems are proved, in particular the existence of a work-equivalent function of the tensor strain-rate over any yield surface. The status of the classical theory of plastic anisotropy is re-appraised in the light of recent experiments, which are themselves critically reviewed. A new type of yield function is proposed to account for the so-called anomalous behaviour of some materials.
Augmentation quotients of group rings and symmetric powers
Authors: Sandling Robert , Tahara Ken-Ichi 
Published: November 2008

LetGbe a group with the lower central seriesLetwhere Σ runs over all non-negative integersa1,a2,…,ansuch thatandis theaith symmetric power of the abelian groupGi/Gi+1whereLetI(G) be the augmentation ideal ofGin, the group ring ofGover. Define the additive groupQn(G) =In(G) /In+1(G) for anyn≥ 1. Then it is well known thatQ1(G) ≅W1(G) for any groupG. Losey (4,5) proved thatQ2(G) ≅W2(G) for any finitely generated groupG. Furthermore recently Tahara(12) proved thatQ3(G) is a certain precisely defined quotient ofW3(G) for any finite groupG.
Embedding theorems for groups with an integer-valued length function
Authors: Chiswell I. M. 
Published: November 2008

(1) In this paper we are concerned with normalized integer-valued length functions on a group G, that is, mappings l:G→ℤ satisfying three axioms:(A1′)l(1) = 0(A2) l(x) = l(x−1)for all x∈G(A4) d(x, y) > d(x, z) implies that d(x, z) = d(y, z) for all x, y and z in G, where d(x, y) = ½(l(x) + l(y)−l(xy−1)).These axioms were first considered by Lyndon(6), where their significance is discussed. Lyndon's axiom A1, which we shall not use, stated that l(x) = 0 if and only if x = 1. His axiom A 3 was that d(x, y) ≥ 0 for all x and y in G, but it was noted in (2) that this follows from A1′, A2 and A4. In particular, taking x = y, we find that l(x) ≥ 0 for all x in G. The other major axioms used in (6) were:(A0) l(x2) > l(x), provided that x ≠ 1, and (A5) d(x, y) + d(xl, y1) > l(x) = l(y) implies that x = y.
The edge-cracked circular disc under symmetric pin-loading
Authors: Gregory R. D. 
Published: November 2008

A circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of length b(0 < b < 2a). The disc is in equilibrium in a state of generalized plane stress under various loadings, which are motivated by the fact that this geometry is to become a standard test specimen configuration in the fracture testing of materials.The first cases considered are those in which the disc is loaded by either (i) opposing point forces P normal to the crack, or (ii) opposing point couples M, in each case acting at the crack mouth. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form in each case, and the respective stress intensity factors are given exactly bywhere K+(0), K+(i) are constants whose values areK+(0) = 0.966528…,K+(i) = 0.355715…,correct to 6 decimal places.
Rational projective representations of finite groups
Authors: Humphreys J. F. 
Published: November 2008

Let G bea finite group, let C1, …, Cn be the cyclic subgroups of G and let 1i be the identity linear character of Ci (1 ≤ i ≤ n). It is a well-known result of Artin ((l), 39·1) that a character x of a linear representation of G over the rational numbers may be writtenwhere a1, …, an are integers. In this note, we establish an analogue of this result for characters of projective representations over the rational numbers.