bluuebunny/crossref_metadata_2025_split huggingface dataset:
A remark on the proof of dispersion relations in quantum field theory
Authors: Taylor J. G. 
Published: November 2008

In order to complete fully the proof of the fixed momentum-transfer dispersion relations for elastic scattering in quantum field theory given by Bremermann, Oehme and Taylor (1) it is necessary (2) to discuss more fully the analyticity of the absorptive part A(t, γ, Δ) in the mass variable γ. We are using the notation of (1), with 2Δ the momentum transfer and 4t2 the total energy of the initial system. For simplicity of discussion we will only treat the case of the elastic scattering of equal mass particles of mass m, the other cases discussed in (1) can be treated similarly. The crucial point of the proof, as first pointed out in (3), is to prove thatis regular in γ in a strip . It was only proved explicitly in (1) that A(t, γ, Δ) is regular for each t, in a strip , where δ may depend on t. In order to prove the analyticity in S of the integral in equation (1) it is necessary to show that δ(t) may be chosen to be independent of t, at least above some finite value of t (possibly large).
On the solution of certain integral equations by generalized functions
Authors: Miller J. B. 
Published: November 2008

This note is concerned with a method by which generalized solutions can be shown to exist for certain types of integral equationswhere f(x) ∈ L2(0, ∞). The method is briefly this. An extended meaning is given to such equations by using generalized functions of a particular type. Then, if (1) denotes a transformation which has no everywhere-defined inverse in the usual sense, it may be possible to define in the extended sense an inverse transformationso that if f is given, a generalized function g = can be determined as a solution of (1).
Solutions of unsteady boundary-layer equations
Authors: Sarma G. N. 
Published: November 2008

AbstractThe unsteady two-dimensional boundary-layer equations, linearized as by Lighthill are studied. A unified method is developed, from which the results for the stagnation flow, the flow along a flat plate, the flow in a converging canal, etc., can be derived as special cases. Solutions are obtained in two systems, one when the main stream is in unsteady motion and the wall is at rest and the other when the main stream is in steady motion and the wall is in an arbitrary motion. The stagnation flow has been done by Glauert and generalized by Watson. The flow along a flat plate and the flow in a converging canal are considered in detail.
Note on the relations between series equations and integral equations
Authors: Ashour A. A. 
Published: November 2008

Williams ((3)) has transformed certain series equations in Legendre functions to Bessel integral equations; his main result being that ifthenand vice versa. (Here, n is written for Williams's n + m. The coefficients an are related to Williams's An by a factor. There is an extra factor 2 in equation (7) in Williams's paper which appears to be an error.)
An asymptotic bound for the residual area of a packing of discs
Authors: Larman D. G. 
Published: November 2008

Suppose that a sequence of discsarranged in decreasing order of diameters, forms a packing within the unit plane square I2. It has been shown, by Florian(1), that the area ofis at least O(a), where a is the radius of θn. However, Gilbert (2) has produced some empirical results for the Apollonius packing 71 of discs which seem to suggest that for such a packing, the area of the setis at least O(as) for some positive real number s, less than one. As Gilbert remarks, it is difficult to imagine that the Apollonius packing is not the extremal case, and so, that it would seem likely that there exists a positive real number s, less than one, such that for a general packing, the area ofis at least O(as). The purpose of this paper is to establish this result by showing that 0·97 is an allowable value for s.
On ‘translated quasi-Cesàro’ summability
Authors: Kuttner B. 
Published: November 2008

Corresponding to a fixed sequence {μn}, the Hausdorff method of summability (H, μn) is defined by the sequence-to-sequence transformation†where we writeThe quasi-Hausdorff method (H*, μn) is defined by the transformationthus the matrix of the (H*, μn) transformation is the transpose of that of the (H*, μn) transformation. A method introduced by Ramanujan (9), which we will call‡ (S,μn) is given by the transformationThus the elements of row n of the matrix of the (S, μn) transformation are those of the corresponding row of the (H*, μn) transformation moved n places to the left.
The integration of generalized hypergeometric functions
Authors: Srivastava H. M. 
Published: November 2008

In the usual notation for generalized hypergeometric functions we letwhereand (a) denotes the sequence of parametersThroughout the present paper we shall suppose that there are A of the a parameters, Bof the b parameters, and so on. Thus ((a))m is to be interpreted asand similar interpretations hold for ((b))m, etc.
On stability of parallel flow of an incompressible fluid of variable density and viscosity
Authors: Drazin P. G. 
Published: November 2008

ABSTRACTSome aspects of generation of water waves by wind and of turbulence in a heterogeneous fluid may be described by the theory of hydrodynamic stability. The technical difficulties of these problems of instability have led to obscurities in the literature, some of which are elucidated in this paper. The stability equation for a basic steady parallel horizontal flow under the influence of gravity is derived carefully, the undisturbed fluid having vertical variations of density and viscosity. Methods of solution of the equation for large Reynolds numbers and for long-wave disturbances are described. These methods are applied to simple models of wind blowing over water and of fresh water flowing over salt water.
A property of certain even integral functions
Authors: Monticelli F. 
Published: November 2008

In some problems where sine, cosine or Bessel functions are involved (e.g. (l), p. 35 et seq.), one has to satisfy certain initial conditions so that one obtains relations of the typewhere t is a real parameter such that |t| < 1, and ±αn(n = 1, 2, …) are real simple zeros of an even or odd integral function f(z), being z = x + iy. An's are coefficients to be determined and, of course, ±ω is a real number that is not a zero of f(z).
Gaps and steps for the sequence nθ mod 1
Authors: Slater Noel B. 
Published: November 2008

For a given θ(0 < θ < 1) and r = 0, 1, 2, 3,… there are two related problems on the fractional parts {rθ}, namely:the gap problem: for any φ (0 < φ < 1) to determine the gaps between the successive r for whichthe step problem: for the setrearranged in ascending order, to determine the steps into which the interval [0,1] is thereby partitioned. There are subsidiary problems of the numbers of gaps or steps of the various lengths, and also of the permutation of 1,…, N when (2) is arranged in order.
On the differential equation governing the rear stagnation point in magnetohydrodynamics and Goldstein's ‘backward’ boundary layers
Authors: Leibovich S. 
Published: November 2008

AbstractExistence and uniqueness proofs for a boundary-value problem associated with a magnetohydrodynamic Falkner–Skan equation are presented. Relevant special cases of the problem herein considered include the magnetohydrodynamic rear stagnation point flow, and the non-magnetic ‘backward boundary layers’ of Goldstein(2).
An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle
Authors: McLenaghan R. G. 
Published: November 2008

AbstractThe validity of Huygens' principle in the sense of Hadamard's ‘minor premise’ is investigated for scalar wave equations on curved space-time. A new necessary condition for its validity in empty space-time is derived from Hadamard's necessary and sufficient condition using a covariant Taylor expansion in normal coordinates. A two component spinor calculus is then employed to show that this necessary condition implies that the plane wave space-times and Minkowski space are the only empty space-times on which the scalar wave equation satisfies Huygens' principle.
Determination of phase velocities of a circular helix using the method of internal constraints
Authors: Lincoln J. W. , Nikkhah M. , Volterra E. 
Published: November 2008

AbstractA procedure is described to determine phase velocities of a circular helix. Computations are made for three helix configurations using the method of internal constraints. The results so obtained are compared with the results obtained by using the elementary theory proposed by J. H. Michell, and the extended elementary theory proposed by A. B. Basset.
The combinatorial structure of the Hughes plane
Authors: Room T. G. 
Published: November 2008

AbstractThe main purpose of this paper is to describe the construction of an incidence table for the Hughes plane of order q2. To do this it is necessary first to construct a table of the same pattern for the Galois plane, and this requires the expression in terms of explicit matrices of the Singer cyclic group of the plane as the composition of cyclic groups of orders q2 + q + 1 and q2 − q + 1. The two tables constructed have some combinatorial properties of possible interest.In the Galois plane of order q2 there are two types of polarities, one with q2 + 1 singular points on a conic, and the other with q3 + 1 singular points on the Hermitian analogue of a conic. Correspondingly in the Hughes plane there are polarities with ½(q3 + q + 2) and with ½(q3 + 2q2 − q + 2) singular points.The paper concludes with the complete incidence table for the Hughes plane of order 25, together with the data necessary for its construction.The Hughes plane and some of its properties are described in Hughes(1), Zappa(2), Rosati(3) and Ostrom(4). The property which enables the Hughes plane to be most easily constructed from the corresponding Galois plane, and which will be used in this paper, is to be found in Room (5).
Convex series
Authors: Jameson G. J. O. 
Published: November 2008

1. Introduction. Let A be a subset of a Hausdorff topological linear space. By a convex series of elements of A we mean a series of the form where an∈A and λn ≥ 0 for each n, and . We say that A is:(i) CS-closed if it contains the sum of every convergent convex series of its elements;(ii) CS-compact if every convex series of its elements converges to a point of A (this bold terminology is chosen because sets satisfying this condition turn out to have properties analogous to those of compact sets).
Corner regions in the asymptotic solution of ε∇2u = ∂u/∂y with reference to MHD duct flow
Authors: Cook L. Pamela , Ludford G. S. S. , Walker J. S. 
Published: November 2008

AbstractIn the asymptotic solution of the title equation for simple boundary data on the rectangle 0 ≤ x ≤ l, 0 ≤ y ≤ 1 the bottom corners are not passive, as has previously been supposed, but in fact generate the parabolic side layers at x = o, l. The top corners, though passive, lead to unconventional elliptic quarter-plane problems. Implications for the MHD duct problem are indicated.
On a quantum mechanical model for a maser I
Authors: Hasler Martin 
Published: November 2008

AbstractThe model is closely connected with a model by Lamb and Scully (10). Atoms described as two-level systems, initially in an incoherent superposition of the two levels, interact successively during a time T with an electromagnetic field of which only one mode is taken into consideration. In the limit as infinitely many atoms have interacted, it is shown that the field either approaches a thermal distribution or is excited to arbitrarily high Photon numbers according to whether or not the lower level of the atoms is initially more probable than the upper level. It is also shown that in any case the correlations between pure Photon number states converge to 0. If the atoms are initially in the upper level it is proved that the Photon number grows roughly as the square root of the number of atoms that have interacted. Throughout the discussion number-theoretical properties of T play a disturbing role. The last mentioned result in fact depends on a sharp (but arbitrary) value for T and is therefore disqualified for physical interpretation.
The associated graded ring of an integral group ring
Authors: Passi Inder Bir S. , Vermani Lekh Raj 
Published: November 2008

Let G be an Abelian group, the symmetric algebra of G and the associated graded ring of the integral group ring ZG, where (AG denotes the augmentation ideal of ZG). Then there is a natural epimorphism (4)which is given on the nth component byIn general θ is not an isomorphism. In fact Bachmann and Grünenfelder(1) have shown that for finite Abelian G, θ is an isomorphism if and only if G is cyclic. Thus it is of interest to investigate ker θn for finite Abelian groups. In view of proposition 3.25 of (3) it is enough to consider finite Abelian p-groups.
On the generation of short internal waves by cylinders oscillating at the surface separating two infinite liquids
Authors: Gorgui M. A. , Kassem S. E. 
Published: November 2008

AbstractThis paper is an investigation of the short-wave asymptotic motion due to a cylinder heaving at the surface separating two infinite liquids. The cylinder is assumed to have a smooth cross-section of an arbitrary shape that intersects the surface of separation at right angles. A non-rigorous argument is used to get the asymptotic expansion of the velocity potentials of the motion in the two liquids in the far field. The asymptotic evaluation of the coefficients describing wave-making, virtual-mass and damping are also obtained in terms of the limit potentials of the motions in the two liquids.
Cushions, cigars and diamonds: an area-perimeter problem for symmetric ovals
Authors: Croft H. T. 
Published: November 2008

P. R. Scott (1) has asked which two-dimensional closed convex set E, centro-symmetric in the origin O, and containing no other Cartesian lattice-point in its interior, maximizes the ratio A/P, where A, P are the area, perimeter of E; he conjectured that the answer is the ‘rounded square’ (‘cushion’ in what follows), described below. We shall prove this, indeed in a more general setting, by seeking to maximizewhere κ is a parameter (0 < κ < 2); the set of admissible E is those E centro-symmetric in 0 that do not contain in their interior certain fixed lattice-points. There are two problems, the unrestricted one , where there is no given upper bound on A (it will become apparent that this problem only has a finite answer when κ ≥ 1) and the restricted one , when one is given a bound B and we must have A ≤ B. Special interest attaches to the case B = 4, both because of Minkowski's theorem: any E symmetric in O and containing no other lattice-point has area at most 4; and because it turns out that it is a ‘natural’ condition: the algebraic expressions simplify to a remarkable extent. Hence in what follows, the ‘restricted case ’ shall mean A ≤ 4.
A continuum model of many-body interactions in a perfect crystal
Authors: Parry G. P. 
Published: November 2008

AbstractTheoretical and numerical calculations of the mechanical properties of single crystals usually presuppose pairwise interactions between the atoms of the lattice. It follows from this assumption that the Cauchy relations hold in respect of the Green measure of strain. Here we account for many-body interactions between the atoms of the lattice. The main result is that a continuum model of n-body interactions must possess completely symmetric (n − 1)th order Green strain moduli. Existing strain energy functions, used to model crystal elasticity, are thereby given some physical significance.
On fibre spaces and nilpotency. II
Authors: James I. M. 
Published: November 2008

1. Introduction. Let X be a space and let E be a fibre space over E. A fibre-preserving map f: E → E determines, for each point x ∈ X, a map fx: Ex → Ex of the fibre over x. In a previous note (3) the situation was considered where fx is null-homotopic, for all x. In the present note we turn our attention to the situation where fx is homotopic to the identity on Ex, for all x ∈ X. If X admits a numerable categorical covering (as when X is an ANR) then such a fibre-preserving map f is a fibre homotopy equivalence, by the well-known theorem of Dold(1). Then the set Φ1(E) of fibre homotopy classes of such maps forms a normal subgroup of the group Φ*(E) of fibre homotopy classes of fibre homotopy equivalences. The purpose of this note is to proveTheorem 1.1. Let X be a paracompact space of finite category. Let E be a fibre bundle over X of which the fibres are compact and path-connected ANR's. Then the Φ*(E)-growp Φ1(E) is Φ*(E)-nilpotent of class ≤ cat X.
Hadamard–Landau inequalities in uniformly convex spaces
Authors: Partington J. R. 
Published: November 2008

The inequalityfor fεLp(− ∞, ∞)or Lp(0, ∞) (1≤p ≤ ∞), and its extensionfor T an Hermitian or dissipative linear operator, in general unbounded, on a Banach space X, for xεX, have been considered by many authors. In particular, forms of inequality (1) have been given by Hadamard(7), Landau(15), and Hardy and Little-wood(8),(9). The second inequality has been discussed by Kallman and Rota(11), Bollobás (2) and Kato (12), and numerous further references may be found in the recent papers of Kwong and Zettl(i4) and Bollobás and Partington(3).
Lacunary theorems for Cesàro means
Authors: Kuttner B. , Maddox I. J. 
Published: November 2008

Suppose that (ni) = (n1, n2,…) and (mi) are infinite sequences of positive integers with ni < mi < ni+1. It is well-known and easily proved that, if a series σak is (C, 1) summable to s and has lacunae (ni, mi) such that ak = 0 (ni < k < mi) withthen where
Non-oscillation and asymptotic properties for a class of forced second-order nonlinear equations
Authors: Erbe Lynn H. , Rao V. Sree Hari , Rao K. V. V. Seshagiri 
Published: November 2008

Consider the second order nonlinear equationwhere, r, p, f ε C ([a, + ∞), R), R = (–∞, +∞) with r > 0 and λ > 0 is the quotient of odd integers. One of the prototypes of this class of equations is the generalized Thomas-Fermi of Emden-Fowler equation
A note on trigonometric sums in several variables
Authors: Odoni R. W. K. 
Published: November 2008

In [3, 4] we showed how the use of a random-walk analogue can be made to yield non-trivial information about the behaviour of certain trigonometric sums in one variable. Our aim here is to show how our method can be adapted to yield similar results for a broad class of trigonometric sums in several variables. Letbe a polynomial in v independent variables with integral coefficients. We choose integers n ≥ 0, d ≥ 1 and p ≥ 2 with p prime, and assume that f(x) has total degree ≤ d + 1. We shall consider the problem of obtaining non-trivial upper bounds for the absolute value of sums of the typewhere P = {1, 2, …, p} and f is non-constant.
The packing measure of rectifiable subsets of the plane
Authors: Taylor S. James , Tricot Claude 
Published: November 2008

It is usual to define Lebesgue outer measure in ℝ by using economical coverings by a sequence of open intervals. We start by outlining a different definition which gives the same answer for a bounded measurable E ⊂ ℝ. PutThen λ0 defines a pre-measure, but is not an outer measure because it is not countably sub-additive. However it leads to an outer measure by definingand it can be proved directly that λ is just another definition of Lebesgue outer measure. We do not give the details of this proof as it can also be deduced as a corollary of the main results in the present paper.
On a criterion for hyperplane sections
Authors: Bǎdescu Lucian 
Published: November 2008

Throughout this paper we shall fix an algebraically closed field k. Consider the following:Problem. Let (Y, L) be a normal polarized variety over k, i.e. a normal projective variety Y over k together with an ample line bundle L on Y. Then one may ask under which conditions the following statement holds:(*) Every normal projective variety X containing Y as an ample Cartier divisor such that the normal bundle of Y in X is L, is isomorphic to the projective cone over Y.
Path sensitivity of material response at intrinsic eigenstates in classical plasticity
Authors: Hill R. 
Published: November 2008

AbstractCategories of rigid/plastic response are investigated along arbitrary paths of homogeneous deformation. Successive yield surfaces are presumed to be convex and self-similar relative to certain canonical measures of stress and finite strain. After a general analysis attention is focussed on path-sensitive response in configurations where the canonical rate of hardening vanishes. The analysis is subsequently extended to other types of eigenstate, especially those associated with actual or prospective loading devices. The results are illustrated in the context of formability tests on sheet metal.
The isomorphism class of a set of lattices
Authors: Wilson S. M. J. 
Published: November 2008

AbstractLet R be a Dedekind domain with field of quotients K. Let A be a finite-dimensional K-algebra. We consider isomorphism classes and genera in a category whose objects are indexed sets of full R-lattices in some ambient A-module and whose morphisms are the A-homomorphisms of the ambient A-modules which map each lattice into its corresponding lattice. We find conditions under which the stable A-isomorphism class of one particular lattice in an indexed set will determine the stable class of the indexed set within its genus. We apply our methods to show that if L/K is a tame Galois extension of algebraic number fields then the stable isomorphism class of the set of ambiguous ideals in L considered as Galois modules over K is determined by the class of the ring of integers in L together with the inertia subgroups and their standard representations over the respective residue fields of R.
Bicompleteness of the fine quasi-uniformity
Authors: Künzi Hans-Peter A. , Ferrario Nathalie 
Published: November 2008

AbstractA characterization of the topological spaces that possess a bicomplete fine quasi-uniformity is obtained. In particular we show that the fine quasi-uniformity of each sober space, of each first-countableT1-space and of each quasi-pseudo-metrizable space is bicomplete. Moreover we give examples ofT1-spaces that do not admit a bicomplete quasi-uniformity.We obtain several conditions under which the semi-continuous quasi-uniformity of a topological space is bicomplete and observe that the well-monotone covering quasiuniformity of a topological space is bicomplete if and only if the space is quasi-sober.
Stability of periodic solutions near a collision of eigenvalues of opposite signature
Authors: Bridges Thomas J. 
Published: November 2008

AbstractSome general observations about stability of periodic solutions of Hamiltonian systems are presented as well as stability results for the periodic solutions that exist near a collision of pure imaginary eigenvalues. Let I = ∮ p dq be the action functional for a periodic orbit. The stability theory is based on the surprising result that changes in stability are associated with changes in the sign of dI / dw, where w is the frequency of the periodic orbit. A stability index based on dI / dw is defined and rigorously justified using Floquet theory and complete results for the stability (and instability) of periodic solutions near a collision of pure imaginary eigenvalues of opposite signature (the 1: – 1 resonance) are obtained.
Extension of a theorem of J. H. Grace to transcendental entire functions
Authors: Clunie J. , Rahman Q. I. 
Published: November 2008

The following result is due to J. H. Grace (see [4], p. 356, also see [9], §3).Theorem A. if p is a polynomial such that p(–1) = p(1) then the derivative p' has a zero in each of the half-planes {Rez ≤0} and {Rez ≥0}.