bluuebunny/crossref_metadata_2025_split huggingface dataset:
A small unsteady perturbation on the steady hydromagnetic boundary-layer flow past a semi-infinite plate
Authors: Das U. N. 
Published: November 2008

AbstractThis paper is concerned with the unsteady hydromagnetic boundary-layer flow past a semi-infinite flat plate when the oncoming free stream is perturbed by an arbitrary function of time and the applied magnetic field is parallel to the plate far away from it. Following Lighthill, the two-dimensional boundary-layer equations are separated into those representing steady and unsteady parts of the flow and they have been solved in sequence. For the unsteady part of the motion two types of solutions are obtained, one for large times and the other for small times. Also the quasi-steady solution is obtained in terms of the steady solution. The skin friction and the tangential magnetic field at the plate are calculated.
Regular greatest common divisor of two polynomial matrices
Authors: Barnett S. 
Published: November 2008

AbstractLet T(λ) and V(λ) be two polynomial matrices having dimensions l x l and m x l respectively, with T(λ) regular and of degree n and V(λ) of degree at most n – 1. It has recently been shown that a necessary and sufficient condition for T and V to be relatively right prime is that a certain nlm x nl matrix R(T, V) have full rank. It is shown here that if T and V have a greatest common right divisor D(λ), then provided D is regular, its degree k is equal to n – (1/l) rank R. Furthermore, if R˜. denotes the matrix of the first (n – k) lm rows of R, then it is shown that the last (n – k) l columns of R˜ are linearly independent and that the coefficient matrices of D can be obtained by expressing the remaining columns of R˜ in terms of this basis.
Fatou–Zygmund sets
Authors: Ross Kenneth A. 
Published: November 2008

1. Let G be a compact Abelian group with character group X. Let be an increasing sequence of finite symmetric subsets of X, and consider a symmetric subset P of . For any Hermitian complex-valued function u on P, we write snu for the real-valued trigonometric polynomial . Edwards, Hewitt and Ross(4) investigated the following property for a non-void measurable subset W of G satisfying W ⊂ (int W)−:The validity of this implication was shown to be independent of the choice of . Accordingly, if (*) holds, P is called an FZ(W)-set. If P is an FZ(W)-set for all W, then P is termed a full FZ-set or full Fatou-Zygmund set. In this paper, we characterize the full FZ-sets as FZ(G)-sets satisfying a certain algebraic condition. In particular, we show that if G is connected, then a symmetric subset of X is an FZ(G)-set if and only if it is a full FZ-set. Some of the techniques are adaptations of those of Mme Déchamps-Gondim(1), (2). The class of full FZ-sets is not always closed under the operation of finite unions; this contrasts with the situation for Sidon sets and for FZ(G)-sets.
Difference-covers that are not k-sum-covers. II
Authors: Connolly D. M. , Williamson J. H. 
Published: November 2008

AbstractWe examine the possibility of establishing the existence of a compact subset E of ℝ such that E–E contains a non-degenerate interval and the semigroup generated by E has measure zero. We show that the existence of such an E is equivalent to the existence of a sequence of difference-covers that are not k-sum-covers for each k∈ℕ, and, further, is equivalent to the existence of an asymmetric maximal Raikov system.
Characterizing pure loss GI/G/1 queues with renewal output
Authors: Daley D. J. 
Published: November 2008

SummaryIn a pure loss GI/G/1 queueing system, necessary and sufficient conditions are given for the output to be a renewal process. These conditions involve dependence between the service distribution and the renewal function of the arrival process: for example, if pr {service time < ξ} = 0 for some ξ > 0, then it is sufficient for the renewal function to be that of a quasi-Poisson process with index ξ.
Characterizations of certain multivariate distributions
Authors: Wang Y. H. 
Published: November 2008

LetX1,X2, …,Xn, ben(n≥ 2) independent observations on a one-dimensional random variableXwith distribution functionF. Letbe the sample mean andbe the sample variance. In 1925, Fisher (2) showed that if the distribution functionFis normal thenandS2are stochastically independent. This property was used to derive the student'st-distribution which has played a very important role in statistics. In 1936, Geary(3) proved that the independence ofandS2is a sufficient condition forFto be a normal distribution under the assumption thatFhas moments of all order. Later, Lukacs (14) proved this result assuming only the existence of the second moment ofF.The assumption of the existence of moments ofFwas subsequently dropped in the proofs given by Kawata and Sakamoto (7) and by Zinger (27). Thus the independence ofandS2is a characterizing property of the normal distribution.
Waves on a shearing current: a uniformly valid asymptotic solution
Authors: McKee W. D. 
Published: November 2008

AbstractA uniformly valid asymptotic solution for waves on a shearing current is presented. This solution is more general than the previous WKB solutions because it is valid at and near a caustic. Far from the caustic line, the solution reduces to the WKB solution. It predicts that an incident wave will be reflected from a straight caustic with the same amplitude and a ½π phase shift.
Diffraction of impulsive elastic waves by a fluid cylinder
Authors: Jha Ramanand 
Published: November 2008

AbstractIn this paper, the problem of diffraction of an impulsivePwave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).
Rate of growth and convergence factors for power methods of limitation
Authors: Ziv Abraham 
Published: November 2008

Let , where pk are complex numbers, have 0 < ρ ≤ ∞ for radius of convergence and assume that P(x) ≠ 0 for α ≤ x < ρ (α < ρ is some real constant). Assuming that is convergent for all (x ∈ [0, ρ), we define the P-limit of the sequence s = {sk} byThis, so called, power method of limitation (see (3), Definition 9 and (1) Definition 6) will be denoted by P. The best known power methods are Abel's (P(x) = 1/(1 – x), α = 0, ρ = 1) and Borel's (P(x) = ex, α = 0, ρ = ∞). By Cp we denote the set of all sequences, P-limitable to a finite limit and by the set of all sequences, P-limitable to zero.
Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid axially symmetric conical die
Authors: Robinson A. R. , Thompson J. C. 
Published: November 2008

AbstractA solution which is exact within the framework of the classical theory of elasticity is obtained for the title problem assuming that the half space is homogeneous and isotropic, and that the die indents at a constant rate. If the shape of the die and the elastic medium are specified, the rate of indentation uniquely determines the outward speed of the edge of the expanding contact zone. The magnitude of this speed, relative to the speeds of the dilatational, rotational and Rayleigh waves in the elastic medium, determines which of four possible characteristic transient stress states will occur. Each of the four ranges of contact speed is solved by the method of rotational superposition of self-similar potentials which is briefly described in the Appendix.
On the coefficients and means of functions omitting values
Authors: Hayman W. K. , Weitsman A. 
Published: November 2008

Letbe regular in U = {|z| < 1}. Suppose that the values of f(z) all lie in a domain D in the w-plane. If certain geometrical restrictions are made on D we can deduce growth conditions on the maximum modulusthe meansand the coefficients αn. Good bounds for M(r, f) have been obtained under various conditions on D.
A unified approach to the solution of four crack problems in plane elastostatics
Authors: Stallybrass M. P. 
Published: November 2008

AbstractFour crack problems are considered in classical two-dimensional elastostatics. Each problem is equivalent to a mixed boundary-value problem for a quarter-plane. A governing functional relation of the Wiener–Hopf type is obtained for each problem by the application of various Mellin transforms. It is shown that values for the stress intensity factor, and the crack energy, in corresponding ‘interior’ arid ‘exterior’ problems are identical for certain distributions of crack pressure.
Small solutions of the congruence
Authors: Williams Kenneth S. 
Published: November 2008

Throughout this paper a0, a1, a2, l1, l2 denote fixed integers with l1 ≥ 2, l2 ≥ 2. We let l = max(l1, l2) and let P be the set of primes Mordell (4) has shown that for any sufficiently large prime p the congruenceis soluble. Thus there are at most a finite number of such p for which (1·1) is insoluble. If there is at least one prime p ∈ P for which (1·1) is insoluble, we let p0 denote the largest of such p, so that (1·1) is soluble for all p ∈ P with p > p0 but not for p = p0. Otherwise (1·1) is soluble for p ∈ P and we let p0 = 1. From the work of Mordell (4) we haveFor p ∈ P with p > p0 (1·1) is thus always soluble and any such solution (x1, x2) can be taken to satisfyChalk(2) has posed the problem of estimating a ‘small’ solution of (1·1), at least for p sufficiently large; that is a solution for which p in the inequality (1·3) can be replaced by something less than p. Smith(5) has shown that for p sufficiently large there is always a solution satisfying 1 ≤ xi ≪ p¾log p (i = 1, 2). It is the purpose of this paper to prove the following sharper and more precise result.
The application of a new source potential to the problem of the transmission of water waves over a shelf of arbitrary profile
Authors: Evans D. V. 
Published: November 2008

AbstractA new source potential is constructed in the linearized theory of water waves. It is shown how this source potential may be used to reduce the problem of the reflexion and transmission of waves by a shelf of arbitrary profile to an integral equation. It is further shown that by suitably restricting the shelf profile, the Fred-holm theory is applicable to the integral equation so that in general a solution of the equation and hence of the problem, exists and is unique except possibly for certain discrete values of the parameters of the problem corresponding to trapping modes over the shelf.
High frequency diffraction by a soft circular disc
Authors: Newby J. C. 
Published: November 2008

AbstractInitially a general incident field is considered and the equations are split into Fourier components. Each Fourier component gives rise to an integral equation similar to that obtained when investigating diffraction of a normally incident plane wave. After the oblique wave has been specified an analysis similar to that used for the normal wave leads to a solution of the problem containing an infinite number of constants. It is shown, however, that these constants do not affect the leading terms of the high frequency scattering coefficient.
Dimensionally dependent divergences
Authors: Horndeski Gregory W. 
Published: November 2008

AbstractIt is well known that in an even dimensional Riemannian space there always exists a particular scalar density which is such that its associated Euler–Lagrange tensor vanishes identically. In this note we show that each of these scalar densities can be expressed as the ordinary divergence of a contravariant vector density. Furthermore, there exists an entire class of contravariant vector densities which enjoy this property. These results are discussed with particular reference to the general theory of relativity.
On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. III
Authors: Robinson-Rhodes P. F. 
Published: November 2008

AbstractThis paper concludes the investigation into the short-wave asymptotic motion due to a cylinder heaving on water of finite constant depth, and we now present a rigorous method for an arbitrary smooth cylinder which intersects the free surface normally. The aim is to justify those assumptions made in a previous paper concerning the asymptotic values on the cylinder of the two related auxiliary potentials–only one of which need be considered–which were introduced to enable an evaluation of the descriptive wave-making and virtual-mass coefficients. This is done by constructing an integral equation of the second kind whose kernel is small and deducing the leading term in the iteration solution. The method is an extension of the method for infinite depth which is treated first and it is found that there is a simple relationship between the kernels. The argument depends to some extent on results established in another previous paper–which is generalized herein–on the rigorous method for the special case of a half-immersed circular cylinder.
Semi-automorphisms of Hadamard matrices
Authors: Hall Marshall 
Published: November 2008

A Hadamard matrix Hn is an n by n matrix H = [hij], i, j = 1, …, n in which every entry hij is + 1 or − 1, such thatIt is well known that possible orders are n = 1, 2 and n = 4m. An automorphism α of H is given by a pair P, Q of monomial ± 1 matrices such thatHere P permutes and changes signs of rows, while Q acts similarly on columns.
A multiplicative property of R-sequences and H1-sets
Authors: Rhodes C. P. L. 
Published: November 2008

Let R be a commutative ring which may not contain a multiplicative identity. A set of elements a1,…,ak in R will be called an H1-set (this notation is explained in section 1) if for each relation r1a1 + … +rkak = 0 (ri ∈ R) there exist elements sij ∈ R such thatwhere Xl,…,Xk are indeterminates. Any R-sequence is an H1-set, but there do exist H1-sets which are not R-sequences (see section 1). Throughout this note we consider an H1-set a1,…,ak which we suppose to be partitioned into two non-empty sets bl…, br and cl,…, cs. Our main purpose is to show that the ideals B = Rb1 + … + Rbr and C = Rc1 + … + Rcs satisfy Bm ∩ Cn = BmCn for all positive integers m and n (Corollary 1). This generalizes Lemma 2 of Caruth(2) where the result is proved when a1,…, ak is a permutable R-sequence. Our proof involves more detail than is necessary just for this, and we obtain various other properties of H1-sets. In particular we extend the main results of Corsini(3) concerning the symmetric and Rees algebras of a power of the ideal Ra1 +… + Rak (Corollary 3).
On Killing vectors and invariance transformations of the Einstein–Maxwell equations
Authors: Woolley M. L. 
Published: November 2008

AbstractIt is shown that, in a simply connected four dimensional Riemannian space, an arbitrary divergence-free vector generates a one-parameter group of point transformations which leaves Maxwell's equations unchanged. This result is used to show that, if the metric tensor of a simply connected vacuum Einstein–Maxwell space-time admits a group of motions which is also an invariance group of the electromagnetic field tensor, then there exists a one-parameter family of metric tensors all of which satisfy the Einstein–Maxwell equations with the invariant electromagnetic field as source.
Cliques in random graphs
Authors: Bollobas B. , Erdös P. 
Published: November 2008

Let 0 < p < 1 be fixed and denote by G a random graph with point set , the set of natural numbers, such that each edge occurs with probability p, independently of all other edges. In other words the random variables eij, 1 ≤ i < j, defined byare independent r.v.'s with P(eij = 1) = p, P(eij = 0) = 1 − p. Denote by Gn the subgraph of G spanned by the points 1, 2, …, n. These random graphs G, Gn will be investigated throughout the note. As in (1), denote by Kr a complete graph with r points and denote by kr(H) the number of Kr's in a graph H. A maximal complete subgraph is called a clique. In (1) one of us estimated the minimum of kr(H) provided H has n points and m edges. In this note we shall look at the random variablesthe number of Kr's in Gn, andthe maximal size of a clique in Gn.
On finite groups containing no element of order six
Authors: Tyrer A. P. 
Published: November 2008

We prove the following theorem:Theorem A. Let G be a finite simple group of order divisible by 3. Suppose(i) G contains no element of order 6;(ii) G has cyclic Sylow 3-subgroups;(iii) G does not involve A4;(iv) Every 3′-simple section of G is a Suzuki group.Then G ≅ SL(2, 2n) for some odd n ≥ 3.
Inequalities associated with the inversion of elastic stress-deformation relations and their implications
Authors: Ogden R. W. 
Published: November 2008

AbstractFor an elastic solid the constitutive law can be written in terms of the deformation gradient α and its conjugate nominal stress s ≡ s(α), and also in terms of the right stretch u and its conjugate stress τ ≡ τ(u). It is shown that for isotropic elastic solids s(α) is invertible, in the local sense, for all u in the domain of u-space where τ(u) is locally invertible, with the exception of certain configurations which correspond to planes in τ-space.In the global sense a given s corresponds to four distinct τ's, and s is invertible to give four distinct α's when the corresponding τ's are uniquely invertible. That there are four branches of the inversion α(s) is of fundamental importance in that it clarifiesthe extent to which non-uniqueness of solution of boundary-value problems can be expected.The implications of these results in respect of the complementary variational principle are discussed, and the controversy surrounding the use of nominal stress in this principle resolved.Consequences of the required restrictions on τ(u) are examined and discussed in relation to inequalities which may be regarded as entailing physically reasonable response. It is intimated that τ(u) is invertible in the domain of elastic response.
Zero divisors and idempotents in group rings
Authors: Linnell P. A. 
Published: November 2008

1. Introduction. Let kG denote the group algebra of a group G over a field k. In this paper we are first concerned with the zero divisor conjecture: that if G is torsion free, then kG is a domain. Recently, K. A. Brown made a remarkable breakthrough when he settled the conjecture for char k = 0 and G abelian by finite (2). In a beautiful paper written shortly afterwards, D. Farkas and R. Snider extended this result to give an affirmative answer to the conjecture for char k = 0 and G polycyclic by finite. Their methods, however, were less successful when k had prime characteristic. We use the techniques of (4) and (7) to prove the following:Theorem A. If G is a torsion free abelian by locally finite by supersoluble group and k is any field, then kG is a domain.
Phase-integral treatment of transmission through an inverted Morse potential
Authors: Lundborg Bengt 
Published: November 2008

AbstractThe transmission of a quantal particle through a barrier obtained by inverting a Morse potential is studied by means of the ‘symmetric’ phase-integral approximations introduced by N. Fröman and further developed by N. Fröman and P. O. Fröman. The calculations are performed up to the fifth-order approximation. Approximate expressions for important quantities such as transmission and reflexion coefficients, phases of the wave function and also for quantities related to the phenomenon of resonances, which may occur when the wave function is given as a standing wave, are compared to the corresponding exact quantities, and this comparison shows the great accuracy of these phase-integral approximations.
Some remarks on the existence of spacelike hypersurfaces of constant mean curvature
Authors: Goddard A. J. 
Published: November 2008

AbstractBernstein's theorem states that the only complete minimal graphs in R3 are the hyperplanes. We shall produce evidence in favour of some conjectural generalizations of this theorem for the cases of spacelike hypersurfaces of constant mean curvature in Minkowski space and in de Sitter space. The results suggest that the class of asymptotically simple space-times admitting a complete spacelike hypersurface of constant mean curvature may well be considerably smaller than the general class of asymptotically simple space-times.
A new type of convergence
Authors: Maddox I. J. 
Published: November 2008

In his important paper (1), Lorentz defined the space f of almost convergent sequences, using the idea of Banach limits. If x ∈ l∞(R), the space of bounded real sequences, andwhere the inf is taken over all sets n(1), n(2), …, n(r) of natural numbers, then a Banach limit L may be defined as a linear functional on l∞(R) which satisfies
Formulae for high derivatives of composite functions
Authors: Fraenkel L. E. 
Published: November 2008

This note concerns a question of elementary calculus. Given a smooth composite function u = g o f [with values u(x) = g(f(x))], we write explicit formulae for its derivatives, of arbitrary order, in terms of derivatives of f and g. We consider (A) the general case,in which E, F and G are Banach spaces, and U, V are open sets; (B) the finite-dimensional case E = ℝM and F = ℝN, where ℝM denotes real M-dimensional Euclidean space; and (C) the particular case of (B) (due to restricting g to part of an M-dimensional surface in ℝM + 1) in which N = M + 1 and u(x)= g(x, φ (x)), so that φ denotes a real-valued (scalar-valued) function of x = (x1, …, xM).
On interpolation by analytic maps in infinite dimensions
Authors: Globevnik J. 
Published: November 2008

AbstractLet A be the complex Banach algebra of all bounded continuous complex-valued functions on the closed unit ball of a complex Banach space X, analytic on the open unit ball, with sup norm. For a class of spaces X which contains all infinite dimensional complex reflexive spaces we prove the existence of non-compact peak interpolation sets for A. We prove some related interpolation theorems for vector-valued functions and present some applications to the ranges of analytic maps between Banach spaces. We also show that in general peak interpolation sets for A do not exist.
Waves created against a vertical cliff – a uniform asymptotic solution
Authors: Pramanik A. K. 
Published: November 2008

SummaryThe initial-value problem of waves generated by a moving oscillatory surface pressure against a vertical cliff is solved and a uniform asymptotic analysis of the unsteady state is given. The same problem with no cliff is solved by Kaplan, and by Debnath and Rosenblat but their solutions are not uniform.
On the duality between the behaviour of sums of independent random variables and the sums of their squares
Authors: Hall Peter 
Published: November 2008

AbstractLetXnj, 1 ≤j≤kn, be independent, asymptotically negligible random variables for eachn≥ 1. In certain cases there exists a duality between the behaviour of ΣjXnjand. We extend one of the known forms of this duality, and show that, under mild conditions on the truncated moments of theXnj, the convergence ofto 1 in the mean of orderp(p≥ 1) is equivalent to the convergence of ΣjXnjto the standard normal law, together with the convergence of its 2pth absolute moment to that of a standard normal variable. A similar result holds in the case of convergence to a Poisson law.
The probability that a point of a tree is fixed
Authors: Harary Frank , Palmer Edgar M. 
Published: November 2008

AbstractUsing arguments involving combinatorial enumeration and asymptotics we compute the probability that a point of a random tree is fixed. The method is also applied to homeomorphically irreducible trees to illustrate how it works for other species of trees. To the nearest per cent, the limiting probability of a fixed point in a randomtree is 70%, and for homeomorphically irreducible trees it is 20%.