bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the method of matched asymptotic expansions
Authors: Fraenkel L. E. 
Published: November 2008

AbstractThe prescription for forming composite series, and a modified form of that procedure, are used systematically and extensively to derive uniform asymptotic approximations to various given functions which cannot be approximated uniformly by expansions of classical (Poincaré) type. The formal method of matched expansions is then applied to a boundary-value problem for an ordinary differential equation with a turning point. It is proved with the help of the uniform approximations found earlier that in this problem a restricted form of the asymptotic matching principle is valid, even when it is applied to truncated inner and outer expansions which do not overlap to the order of the terms being matched.
A new generating function for Jacobi polynomials
Authors: Saxena R. K. 
Published: November 2008

In an earner paper ((6), p. 209) the author has given a generating function for the Jacobi polynomials defined by ((5), p. 254)In the present note we obtain another generating function for these polynomials. The results given earlier by Manocha and Sharma ((4), p. 432) in these proceedings and Brafman in (2) follow as a particular case of our result.
Multiple scattering of plane harmonic elastic waves in an infinite solid by an arbitrary configuration of obstacles
Authors: Barratt P. J. 
Published: November 2008

AbstractThe multiple scattering of plane harmonic P and S waves in an infinite elastic solid by arbitrary configurations of obstacles is considered. Integral equations relating the far-field multiple scattering amplitudes to the corresponding single scattering functions are obtained and asymptotic solutions are found by an iterative procedure. The scattering of a plane harmonic P wave by two identical rigid spheres is investigated.
Compressible flows with circular sector hodographs
Authors: McLaughlin Maureen D. , Pack D. C. 
Published: November 2008

AbstractThe general solution of Chaplygin's equation for the motion of an inviscid compressible fluid is obtained for ‘simple wedge flows’. Some particular examples are given and a discrepancy in earlier Russian papers explained. After a discussion of the properties of the velocity potential and the expression for the physical coordinates in terms of the hodograph variables, a general theorem on sonic jets is proved, namely, that the physical changes due to the presence of solid boundaries in the flow are completed within a finite distance in those directions in which the flow becomes finally a sonic jet.
Dimensionally dependent identities
Authors: Lovelock David 
Published: November 2008

AbstractIn the general theory of relativity a number of apparently unrelated identities peculiar to a 4-dimensional space are frequently used. However, the proofs usually presented appear to have no common ideas and, furthermore, it is not clear at what stage the dimensionality restriction plays a significant role. In this note a technique is presented which explicitly exhibits the dimensionality dependence and thereby enables the above identities to be generalized forn-dimensional spaces. It is also shown that the above identities are all special cases of a more general identity valid forn= 4.
On the remainder in the two-dimensional central limit theorem
Authors: Dunnage J. E. A. 
Published: November 2008

Our object here is to refine the theorem proved in (3), and we use the notation of that paper. Let Z1, Z2, …, Zn, where Zr = (Xr, Yr), be independent random variables in two dimensions with zero first-order moments and finite third-order moments; and et the covariance matrix of Zr beWe writeLet (x, y) be the distribution function of the sum and let (x, y) be the normal distribution function having the same first- and second-order moments as (x, y).
Difference-covers that are not k-sum-covers. I
Authors: Jackson T. H. , Williamson J. H. , Woodall D. R. 
Published: November 2008

AbstractVarious constructions are described for sets F = F(q, k, l) of residues modulo q such that F–F contains all residues while (k)F = F + F + … + F (k summands) omits l consecutive residues, in the cases k = 2, 3, 4 and 5. Let Q(k, l) denote the set of moduli q for which such a set F(q, k, l) exists. The following results are proved: q∈Q (2, 1) if and only if q ≥ 6; q∈Q(2,l) if q ≥ 4l + 2; 29, 31 and 33∈Q(3, 1) and if q∈Q(3, 1) if q ≥ 35; 24l + 21∈Q(3, l) if q ≥ 44l + 41. Upper bounds are also obtained for the least elements in Q(4, l) and Q(5, l).
A decomposition identity for a class of Riemannian invariants
Authors: Pavelle Richard 
Published: November 2008

AbstractAn identity of fundamental interest in General Relativity is the breakup or ‘decomposition’ of the scalar curvature density into an ordinary divergence in addition to a term constructed solely from the metric tensor and its first derivative. It is proven that this identity is the most elementary example of an identity satisfied by all members of a particularly important class of Riemannian invariants. For a subset of these invariants, the decomposition identity undergoes a simplification that connects this material with some problems of current research interest.
On Blasius's equation governing flow in the boundary layer on a flat plate
Authors: Richardson S. 
Published: November 2008

AbstractThe original approach of Blasius to the solution of the differential equation now associated with his name was to develop the unknown function as a power series. Unfortunately, this series has a limited radius of convergence, so that such a representation is not valid over the whole range of interest. It is shown here that, if we work instead with a particular inverse function, this can be expanded as a power series which converges for all relevant values of the independent variable. Moreover, the number associated with the solution which is of principal physical interest can be expressed in terms of the asymptotic properties of the coefficients of this series. Exploiting this relationship, we find upper and lower bounds for this number in terms of the zeros of two particular families of polynomials.
The asymptotic analysis of canonical problems in high-frequency scattering theory
Authors: Boyd W. G. C. 
Published: November 2008

AbstractThe asymptotic treatment of high-frequency scalar wave problems has in the past been rather unsatisfactory. Typically, the integral representations which arose were evaluated by stationary phase, or as a series of residues. The justification of these methods was usually heuristic and formal. In this paper, a method is advanced which, it is claimed, may be applied to any one-parameter separation of variables problem. The method assumes an integral representation whose contour of integration is the real axis. It is then only necessary to deform this contour in the neighbour-hood of the real axis to derive rigorous asymptotic expansions of the field in both the illumination and shadow. The method is applied to the particular example of scattering by a plane boundary in a general stratified medium with monotonically increasing refractive index.
A note on a centrality property of finitely generated soluble groups
Authors: Lennox J. C. 
Published: November 2008

We recall from (3) that a group G is (centrally) eremitic if there exists a positive integer e such that, whenever an element of G has some power in a centralizer, it has its eth power. The eccentricity of an eremitic group G is the least such positive integer e.In ((4), Theorem A) we proved that if A is a torsion free Abelian normal subgroup of a finitely generated group G with G/A nilpotent, then G has a subgroup of finite index with eccentricity 1. In this note we use a much simpler method to prove a stronger result.
Osculatory properties of a certain curve in [n]
Authors: Edge W. L. 
Published: November 2008

1. When, as will be presumed henceforward, no two of a0, a1, …, an are equal the n + 1 equationsare linearly independent; x0, x1, …, xn are homogeneous coordinates in [n] projective space of n dimensions—and the simplex of reference S is self-polar for all the quadrics.
The nuclearity of operators generated by Hölder continuous kernels
Authors: Cochran James Alan 
Published: November 2008

Introduction. The space Cp is the class of operators on a Hilbert space for which the norm ∥K∥p = [trace (KK*)P/2]/p is finite. Equivalently, a compact operator is in Cp ifwhere the μn are the so-called ‘singular values’ of K (characteristic values of the non-negative compact operator [K] ≡ (KK*)½). The case p = 2 gives the familiar class of Hilbert–Schmidt operators, while C1 is the collection of trace-class or nuclear operators considered by Schatten(12), Lidskii(11), and Gohberg and Krein(7), among others.
Lifting convergent sequences with networks
Authors: Webb J. H. 
Published: November 2008

Definition (Moukoko Priso(2)). A locally convex spaceE[T] is said to have a strict absorbent network of type Σ if there exists in E a familyof absolutely convex absorbent sets such that(1) if {nk} is a sequence of positive integers andfor each k, then the seriesconverges in E[T](2) for each sequence {nk} there is a sequence {λk} of positive real numbers such that, ifand 0 ≤ μk ≤ λkfor each k, then(i) converges in E[T], and(ii) for each p.
On the short cylindrical waves due to a body heaving on water. I
Authors: Rhodes-Robinson P. F. 
Published: November 2008

AbstractIn this paper we obtain the short-wave asymptotic value of the force coefficient for a heaving body partially immersed in the free surface of water which has finite constant depth. The body is required to intersect the free surface normally and have a vertical axis of symmetry. The motion of the water is thus axisymmetric with short outgoing cylindrical waves at a distance, and these must be calculated. For this we use a non-rigorous argument. The potential problem discussed is analogous to the two-dimensional problem afready investigated involving a heaving surface cylinder. Numerical values are obtained in the case of a half-immersed sphere in conclusion.
Extending embeddings of Rn−1 in Rn
Authors: Smith Anthony 
Published: November 2008

Notation and results. The main results of this paper are (a) a new proof of the canonical Schoenflies theorem and (b) a non-compact version of the canonical Schoen-flies theorem.The result (a) is already known(5); the existing proof is based on the proof by Brown of the ordinary Schoenflies theorem, whereas ours is based on that of Mazur and Morse.
Two disc dynamos with viscous friction and time delay
Authors: Cook A. E. 
Published: November 2008

AbstractTwo extensions of the Rikitake model are examined; the first includes viscous friction and the second includes time delay. By use of Liapounov's direct method the viscous system is shown to have an unstable limit cycle associated with two of the three singular points. By numerical integration true ‘reversals of field’ are shown to occur for both the viscous and time delay cases.
Mutual spaces and mutuality
Authors: Amson J. C. 
Published: November 2008

AbstractThe theory of dual spaces and duality is extended from a pair of vector spaces in duality to a list of more than two vector spaces in mutuality. The notions of a canonical bilinear functional and of compatible topologies for a dual pair are extended to those of a canonical multilinear functional and of compatible topologies for a mutual list. Compatible topologies are characterized by means of an extended version of the Mackey–Arens Theorem. Directions for further work are noted.
On Kneser's conjecture for bounded 3-manifolds
Authors: Heil Wolfgang 
Published: November 2008

1. The classical Kneser conjecture states that if M is a closed 3-manifold and π1(M) ≈ A * B, a free product, then there exist 3-manifolds MA, MB such thatand π1(MA) ≈ A, π1(MB) ≈ B. This has been proved by John Stallings(6).
An inequality for the trace of the product of two symmetric matrices
Authors: Theobald C. M. 
Published: November 2008

Let A, B be real symmetric n × n matrices having orthogonal reductionswhere ΛA = diag (λ1(A), …, λn(A)) and ΛB = diag (λ1(B), …, λn(B)) and the sets of latent roots are each in descending order. (Thus we may say that the latent vectors of A, B are ordered with respect to respectively.) Let the multiplicities of the roots and in order of occurrence be respectively and , so that
One-transversal families
Authors: Rado Richard 
Published: November 2008

Let I be a set andbe a family of sets Aν labelled by the elements of I. Throughout, parentheses ( ) denote families and curly brackets {} denote sets. A transversal, or system of distinct representatives, of F is, by definition, a family (xν: ν ∈ I) of objects xν, for ν ∈ I, such that †Thus the family ({1, 2,} {1, 2}) has exactly two transversals, namely (1,2) and (2, 1). Let TF denote the set of all transversals of F. Much work has been done on the question of characterizing those F for which TF ≠ Ø. We are here going to characterize those F for which TF has exactly one element. In contrast to the more familiar case TF ≠ Ø, our argument is effective irrespective of the cardinalities of I and Aν.
Spectral asymmetry and Riemannian geometry. III
Authors: Atiyah M. F. , Patodi V. K. , Singer I. M. 
Published: November 2008

In Parts I and II of this paper ((4), (5)) we studied the ‘spectral asymmetry’ of certain elliptic self-adjoint operators arising in Riemannian geometry. More precisely, for any elliptic self-adjoint operator A on a compact manifold we definedwhere λ runs over the eigenvalues of A. For the particular operators of interest in Riemannian geometry we showed that ηA(s) had an analytic continuation to the whole complex s-plane, with simple poles, and that s = 0 was not a pole. The real number ηA(0), which is a measure of ‘spectral asymmetry’, was studied in detail particularly in relation to representations of the fundamental group.
Magnetohydrodynamic flow past sources in the presence of a wall
Authors: Chee-Seng Lim 
Published: November 2008

AbstractAn incompressible magnetohydrodynamic flow, bounded below by a semi-infinite solid wall insulator with a plane surface, is weakly perturbed by two-dimensional (i.e. cylindrical) sources immersed within the fluid. Certain results of Chee-Seng(1) are employed to establish an exact analytic solution for arbitrary source functions. Both direct emission and reflected disturbance fields are hyperliptic, i.e. partly hyperbolic and partly elliptic. The reflected hyperbolic mode is propagated as a Riemann invariant of a modified incident field and its Hilbert transform. This propagation occurs along reflected characteristics whose (acute) inclination with the interface is generally unequal to that of the incident characteristics, but which are, instead, parallel to those non-incident characteristic rays emanating away from the interface.
A note on Smale's formulation of electrical network theory
Authors: Arrowsmith D. K. , Smith R. 
Published: November 2008

We consider in this note two problems which arise naturally in Smale's paper (3).First of all we show that it is easy to extend Smale's results on the dynamics of LCR circuits with non-linear elements to circuits containing triode valves. It should be noted that transistors and other n-ports (1) can also be easily accommodated within this theory with suitable differentiability assumptions. We then further extend the theory to include elements whose voltage depends explicitly on time.
Complex potential equations II. An application to general relativity
Authors: Collins C. B. 
Published: November 2008

AbstractThe results of a previous paper are applied to a study of the class of Kerr–Schild metrics in general relativity. These metrics have the formwhere η is the flat (Minkowski) space-time metric, m is an arbitrary real number, and 1 is a null covector. It is already known that for a certain restricted subclass of these metrics, the vacuum Einstein field equations, viz.can be written in the formwhere γ is a complex potential. Using the methods developed in a previous paper, such space-times are characterized by means of a special family of complex surfaces in three-dimensional Euclidean space, and the exact solutions for the metric g are consequently recovered. It is also shown that the field equations for a much wider class of Kerr–Schild metrics can be expressed in terms of a potential formalism, not only in the vacuum case, but also for many electrovacuum solutions.
Azumaya algebras and rings with polynomial identity (Addendum)
Authors: Goldie Alfred 
Published: November 2008

In the paper published in Mathematical Proceedings 79, 393–399, there is a gap in the proof of Theorem 2 which may present a difficulty to the reader. It occurs in the proof of non-degeneracy of the map g in the ring of matrices Zn, where Z is a finite field. Matrices are chosen, the first is diagonal with distinct entries and the others areWhen n is larger than the number of elements in Z, then such an x0 does not exist in Zn. The argument can, however, be sustained in the following way.
On non-unital Jordan–Banach algebras
Authors: Smith R. R. 
Published: November 2008

A unital JB-algebra is a Jordan algebra A with identity together with a complete norm satisfying, for all a, b ∈ A,(i) (a2b) a = a2(ba),(ii) ∥a2∥ = ∥a∥2,(iii) ∥ab∥ ≤ ∥a∥ ∥b∥,(iv) ∥a2 + b2∥ ≥ ∥a2∥, ∥b2∥.(It should be noted that axiom (iii) is a consequence of (ii) and (iv).) Such spaces have been studied by several authors (3, 6, 11), and as a consequence their structure is now quite well understood. Many of the results of these papers, while relying on the existence of an identity for their proofs, can be formulated for algebras which lack this property. C*-algebra theory and operator theory abound in examples of spaces which fail to be unital JB-algebras only in this one respect, and this motivates the study of the general case undertaken in this note.
Dirichlet's theorem on diophantine approximation
Authors: Baker R. C. 
Published: November 2008

Let N take the values 1, 2, … A theorem of Dirichlet asserts that for any (x, y) in the Euclidean plane R2 the inequalityis soluble in integers q1, q2, p with 0 < max (|q1|, |q2|) ≤ N.
Finiteness and decidability: II
Authors: Johnstone P. T. , Linton F. E. J. 
Published: November 2008

It has been known for some time ((6), p. 270; (4), theorem 9·19) that if is a Boolean topos, then the full subcategory Kf of Kuratowski-finite objects in is again a topos. For a non-Boolean topos , however, Kf need not be a topos, as can be seen when is the Sierpinski topos ((1), example 7·1); on the other hand, two other full subcategories of , coinciding with Kf when is Boolean, suggest themselves as candidates for a subtopos of finite objects. Of one of these, the category dKf of decidable K-finite objects in , the Main Theorem of (1) asserts that it is always a (Boolean) topos. The other is the category sKf of -subobjects of K-finite objects. The inclusionsdKf ⊆ Kf ⊆ sKf are clear.are clear.
Augmentation quotients of some nonabelian finite groups
Authors: Losey Gerald , Losey Nora 
Published: November 2008

1. LetGbe a group,ZGits integral group ring and Δ = ΔGthe augmentation idealZGBy anaugmentation quotientofGwe mean any one of theZG-moduleswheren, r≥ 1. In recent years there has been a great deal of interest in determining the abelian group structure of the augmentation quotientsQn(G) =Qn,1(G) and(see (1, 2, 7, 8, 9, 12, 13, 14, 15)). Passi(8) has shown that in order to determineQn(G) andPn(G) for finiteGit is sufficient to assume thatGis ap-group. Passi(8, 9) and Singer(13, 14) have obtained information on the structure of these quotients for certain classes of abelianp-groups. However little seems to be known of a quantitative nature for nonabelian groups. In (2) Bachmann and Grünenfelder have proved the following qualitative result: ifGis a finite group then there exist natural numbersn0and π such thatQn(G) ≅Qn+π(G) for alln≥n0; ifGωis the nilpotent residual ofGandG/Gωhas classcthen π divides l.c.m. {1, 2, …,c}. There do not appear to be any examples in the literature of this periodic behaviour forc> 1. One of goals here is to present such examples. These examples will be from the class of finitep-groups in which the lower central series is anNp-series.
Functionals of diffusion processes as stochastic integrals
Authors: Davis M. H. A. 
Published: November 2008

Let be a standard d-dimensional Brownian motion and L a smooth functional on the space C = Cd[0, 1] of continuous functions from [0,1] to Rd, such that Denote Thenis a square integrable martingale which can be represented as a stochastic integral; consequently the random variable has the representationFor Fréchet differentiable functions L, Clark(1) gave the following formula for the integrand e:
Invariants of pencils of binary cubics
Authors: Newstead P. E. 
Published: November 2008

Let U denote the variety of pencils of binary cubics without base point defined over an algebraically closed field k whose characteristic is not equal to 2 or 3. (For full details of the terminology, see § 2.) There is a natural action of SL(2) on U; our main object is to show that U possesses a good quotient for this action in the sense of ((7), Definition 1·5) or ((4), p. 70), and to identify this quotient with the affine line over k. In fact, we proveTheorem 1. There exists a morphism φ: such that (, φ) is a good quotient of U by SL(2). Moreover, all but one of the fibres of φ are orbits; the exceptional fibre consists of two orbits corresponding to pencils with one or two triple points.
Self-maps of BU
Authors: Clarke Francis 
Published: November 2008

One of the results proved by Lance in (7) is the following.Theorem 1. Let ø: BU(p) → BU(sp) be an H-map, where BU(p) denotes the localization of BU with respect to an odd prime p. Let ø*: π2k(BU(p))→ π2k(BU(p)) ≅ (p)) be multiplication by λk thenif n1 ≡ n2 mod(p − 1).
Infinite loop structures on the algebraicK-theory of spaces
Authors: Steiner Richard J. 
Published: November 2008

LetXbe a topological space with base-point. Thealgebraic K-theory AXofXis a space invented by Waldhausen in (15) for use in geometric topology. It can be defined in two ways, which I shall callgeometricandring-theoretic; Steinberger ((12)) has shown them to be equivalent.The geometric method ((15), corollary to lemma 2·1) givesAXas the group-completion of the geometric realization of a permutative category. It follows from the machinery of May ((4), 4) or Segal (11) thatAXis an infinite loop space in a well-defined way ((6)).
Conserved currents of the Klein–Gordon field
Authors: Gordon T. J. 
Published: November 2008

AbstractA method is presented whereby all locally defined conserved currents of the Klein-Gordon field are found. The mathematical background to the method includes a generalization of the Poincaré lemma of the calculus of exterior differential forms. It is found that the only conserved currents are essentially a countably infinite set of functions, bilinear in the field, together with a single current in the case where the mass is zero. The usual energy-momentum tensor is included amongst these functions. The method does not depend on the use of any canonical formulation of the field theory.
The asymmetry of M0(G)
Authors: Brown G. , Karanikas C. , Williamson J. H. 
Published: November 2008

AbstractLet G be a non-discrete locally compact topological group. A construction is given for a self-adjoint measure μ on G that has independent powers, and is, moreover, in the sub-algebra M0(G) of M(G). From this, the asymmetry of M0(G) (and of M(G) itself) is immediate.
On almost-everywhere convergent eigenfunction expansions of the Laplace–Beltrami operator
Authors: Meaney Christopher 
Published: November 2008

AbstractLet M be a compact Riemannian manifold equipped with Laplace–Beltrami operator Δ. We use the Rademacher-Menchoff theorem and the asymptotics of the eigenvalues of Δ to show that if a function belongs to an L2 Sobolev space of positive index then its expansion, in terms of eigenfunctions of Δ, converges almost everywhere on M.