bluuebunny/crossref_metadata_2025_split huggingface dataset:
Boundary layers in micropolar liquids
Authors: Willson A. J. 
Published: November 2008

AbstractConsideration is given to the steady flow of a micropolar liquid near a rigid boundary. It is shown that while micro-inertia itself is not important, nevertheless, some properties of the microstructure do play a vital rôle in determining the structure of the boundary layer. The Kármán—Polhausen method is used to provide an estimate of the shear stress at the boundary, and detailed calculations are given for flow near stagnation. The important significance of the standard length of the micropolar liquid is demonstrated for this flow, as for other flows in this medium.
The Rikitake two-disc dynamo system
Authors: Cook A. E. , Roberts P. H. 
Published: November 2008

AbstractIt is shown that the solution of the Rikitake two-discdynamo system may be described by an orbiting point which, for sufficiently large time, lies arbitrarily close to a limit surface of bounded area. Reversal of the field currents of the dynamo coils are shown to occur in the juxtaposed regions of the two sheets of the limit surface. The two singular points of the system are shown, by Liapounov's direct method, to be unstable foci. An asymptotic theory is developed for the case of small difference in dynamo velocities; the theory is applied to cases of small dissipation in which orbits tend to become nearly periodic with a single oscillation between reversals.
Convergence of weighted sums of independent random variables
Authors: Rohatgi V. K. 
Published: November 2008

1. Introduction. Let {Xk: k ≥ 1} be a sequence of independent, but not necessarily identically distributed, random variables. Suppose that the random variables Xn are uniformly bounded by a random variable X in the sense that(1) P(|Xn| ≥x) ≤ P(|X| ≥ x)for all x > 0. Write qn(x) = P(|Xn| ≥ x) and q(x) = P(|X| ≥ x).
On hearing the shape of a drum: an extension to higher dimensions
Authors: Waechter R. T. 
Published: November 2008

The inverse eigenvalue problem for vibrating membranes (4), may also be examined in three or more dimensions. Let us suppose that λn are the eigen values of the problemwhere Ω is a closed convex region or body in En and S is the bounding surface of Ω. The basic problem is to determine the precise shape of Ω on being given the spectrum of eigenvalues λn. In analogy with the membrane problem, it is clear that the trace function may be constructed in identical fashion; thuswhere G(r, r', t) is the Green's function of the diffusion equationand satisfies the Dirichiet condition G(r, r', t) = 0, r∈S, and the initial condition G(r, r', t) → δ(r–r') as t → 0.
An open mapping theorem
Authors: Ng Kung-Fu 
Published: November 2008

Let (E, τ) be a complete, semi-metrizable topological vector space. Let p be a pseudo-norm (not to be confused with a semi-norm, cf. (8), p. 18) inducing the topology τ. For each positive real number r, letLet f be a continuous linear function from E into a topological vector space F. The open mapping theorem of Banach may be stated as follows: If f is nearly open, that is, if the closure of each f(Vr) is a neighbourhood of O in F then whenever β > α > O; in particular, each f(Vr) is a neighbourhood of O. We note that f, identifying with its graph, is a closed linear subspace of the product space E × F. In this paper, we shall employ techniques developed by Kelley (6) and Baker (1) to extend the theorem to the case where f is taken to be a closed cone in E × F. The generalized theorem throws some light onto the duality theory of ordered spaces. In particular, the theorem of Andô–Ellis is generalized to (not assumed, a priori to be complete) normed vector spaces.
On the structure of non-Euclidean crystallographic groups
Authors: Singerman David 
Published: November 2008

Let denote the group of transformations of the upper-half complex plane U onto itself of the formIf, on U, we introduce the Riemannian metric ds = |dz| y−1 (z = x + iy), then U becomes a model of the hyperbolic plane and its group of isometries. The set of elements of type I, the orientation-preserving isometries form a subgroup of index two in , which we denote by .
Module invariants and root numbers for quaternion fields of degree 41r
Authors: Fröhlich A. 
Published: November 2008

1. The results. Let l be an odd prime, r ≥ 1, and letbe the quaternion group of order 4lr, as given by generators and relations. Throughout N is a tamely ramified normal number field with Galois group Gal (N/Q) = H (a ‘quaternion field’), and its ring of integers. We are interested in the structure of as a module over the integral group ring ZH. Deriving, first, certain classgroup invariants for locally free ZH-modules, we shall then determine those for the module in terms of the arithmetic invariants of N/Q. When 1 ≡ – 1 (mod 4), this yields again a Galois module interpretation of Artin root numbers quite analogous to that in (2). On the other hand for l ≡ 1 (mode 4), we shall get a weak ‘normal integral basis theorem’. The original impetus for this work came from computations of J. Queyrut, who – in different language – obtained these results in the case l = 3, r = 1 (cf. (7)). The tools, we are using, come from the general theory developed in recent years with such concrete applications in mind, and it is perhaps of interest to see how the various ‘strands’, on root numbers (cf. (3), (4)), on locally free modules (cf. (5)), and on Galois module structure (cf. (6)) are here pulled together. For technical reasons, we shall impose on N the slight further restriction, that l be non-ramified, although our results would remain true without this. Both the statements and the proofs of the theorem depend on ideas contained in (5) and (6). The reader who is prepared to take them for granted should, however, be able to read the present paper independently of those papers.
The Stokes phenomenon and generalized contiguous transformations of some generalized hypergeometric functions
Authors: Heading J. 
Published: November 2008

AbstractPrevious investigations by the author into the Stokes phenomenon pertaining to solutions of the differential equation dnu/dzn = (–1)nzmu are extended in order to find when different equations have the same set of Stokes multipliers, with perhaps a series of zeros being additionally allowed. The reason for periodic cycles to exist (with n fixed and m varying), with the same Stokes multipliers regained after a complete cycle, is traced to certain transformation properties of the equations. Within the first cycle (with n fixed and m varying) further remarkable identities exist between the Stokes multipliers, and this also is traced to special transformations between the equations. Relations are found toexist when values of m are chosen so that the highest common factors of the two integers n and n/(n + m) are identical. Finally, a transformation of the independent variable is deduced whereby the set of Stokes multipliers for an equation of order n is identical (apart from the additional zeros) to that for an equation of lower order. A hierarchy of equations is thrown up, whereby certain basic equations are transformed to yield more advanced equations of higher order and different m.
Dynamic elastic moduli of a suspension of imperfectly bonded spheres
Authors: Mal A. K. , Bose S. K. 
Published: November 2008

AbstractAn isotropic elastic material containing a random distribution of identical spherical particles of another elastic material is considered. The bonding between the spheres and the matrix is imperfect, so that slip may occur at interfaces when stress is applied to the medium. The shear stresses at the interface is assumed to be proportional to the amount of slip. The velocity and attenuation of the average harmonic elastic waves propagating through such a medium are calculated. The results are valid to the lowest order in frequency for wave lengths long compared with the radius of the sphere. The dynamic elastic moduli are obtained from these results and are compared with available results for welded contact. The variations in thePandSwave velocities for propagation across earthquake faults is discussed.
A generalized inverse for arbitrary operators between Hilbert spaces
Authors: Erdelyi I. 
Published: November 2008

AbstractA function analytic approach to the generalized inversion problem, for arbitrary operators between Hilbert spaces, is investigated in the present paper.The generalized inverse is defined as the inverse of the largest invertible restriction of the given operator and it is extended by zero to the orthogonal complement of the range of the invertible restriction. This domain-dense operator satisfies, on some restricted manifolds, the defining properties of the generalized inverse in some special cases, and it provides the least extremal solution of possibly inconsistent linear equations.
Operators on the generalized entire sequences
Authors: Maddox I. J. 
Published: November 2008

Let p = (pk) and q = (qk) be any sequences of strictly positive numbers. Denote by c0(p) the set of all complex sequences x = (xk) such that . The Köthe–Toeplitz dual of c0(p) was determined in Theorem 6(4). In the case in which p∈l∞ (the space of all bounded sequences), c0(p) becomes a locally convex FK space under the paranorm where M = max (1, sup pk). It has been recently proved by Lascarides(3) that the following three properties are equivalent:(a) p∈c0(i.e.pk → 0),(b) c0(p) is perfect (in the sense of Köthe-Toeplitz duality),(c) c0(p) has the Schur property (i.e. weak and strong sequential convergence are equivalent).
Some remarks on a paper by Vizing on critical graphs
Authors: Fiorini Stanley 
Published: November 2008

AbstractIn papers (7, 8), Vizing studied graphs which are critical with respect to edge colourings. In particular, he obtained bounds on the number of edges and on the circuit length of such graphs in terms of its maximum valency. The object of this paper is to improve these bounds by obtaining others which also take into account the order of the graph.
Sufficient conditions for regularity, recurrence and ergodicity of Markov processes
Authors: Tweedie Richard L. 
Published: November 2008

AbstractTwo sets of conditions are found on the Q-matrix of an irreducible Markov process on a countably infinite state space which ensure that Q is regular; the first set also implies that the Markov process is ergodic, the second that it is recurrent. If the process is not irreducible, the conditions still imply regularity, and then either non-dissipativity or ‘ultimate recurrence’ (reducible analogues of ergodicity and recurrence) of the process. Conditions sufficient for ergodicity or recurrence of the process in the non-regular and regular case are also given. The results parallel (and use) results for discrete time Markov chains, and the known discrete time recurrence condition is extended to the reducible case. The conditions are illustrated by a competition process example.
Derangements and Laguerre polynomials
Authors: Even S. , Gillis J. 
Published: November 2008

AbstractGiven a set consisting of n1, objects of type 1, n2 of type 2, …, nk of type k, we denote by the number of possible derangements of the set i.e. permutations in which no object occupies a site originally occupied by an object of the same type. A formula is found for in terms of Laguerre polynomials, and some of its implications are considered.
The generation of surface waves over a sloping beach by an oscillating line source
Authors: Morris Clare A. N. 
Published: November 2008

AbstractA line source whose strength varies sinusoidally with time and also with the co-ordinate measured along its length is situated parallel to the shoreline of a beach of angle ¼π0. Both long-and short-wave solutions are found. It is shown that for certain positions of the source, long waves are not radiated to infinity, while in the short-wave regime, the solutions take the form of edge-waves, with resonances occurring at certain wavenumbers. Computations of the free-surface contours are presented for a range of wavenumbers.
An empirical form of the square root law and the central limit theorem
Authors: Freedman David 
Published: November 2008

Consider a long, finite sequence xl, x2, …, xN of repeated measurements on the same physical quantity. The usual model is that the data consists of observed values on a sequence X1, X2, …, XN of independent and identically distributed random variables. It is customary to require that the Xi have a finite mean and variance: µ = E(Xi) is the ‘true value’ of the quantity being measured; andmeasures the variability in the measuring process.
Some points in βN
Authors: Kunen Kenneth 
Published: November 2008

AbstractAssuming either the continuum hypothesis or Martin's axiom, we show that in the space βN – N, there are: (a) points which are not P-points, but which are also not limit points of any countable set, and (b) a countable set of points dense in itself such that each of the points is not a limit point of any countable discrete set. Our method is to construct such points in the Stone space of a measure algebra, and then embed that Stone space into βN – N. We also, by a similar use of measures, establish the independence of the existence of selective ultrafilters by showing that there are none in the random real model.
On the Banach–Saks property
Authors: Partington J. R. 
Published: November 2008

A Banach space X is said to have the Banach–Saks property (BS) if every bounded sequence (xn) in X has a subsequence (), which is (C, 1) convergent in norm to a point x in X; that is,Kakutani (7) showed that all uniformly convex spaces are (BS); moreover, all (BS) spaces are reflexive. It is further known that both these implicationsare strict: see, for example, Baernstein (1) and Diestel (4).
The left Hilbert algebra associated to a semi-direct product
Authors: Rousseau R. 
Published: November 2008

AbstractLet A and G be locally compact groups and α a continuous action of G on A, and let denote the semi-direct product of A and G. Then we prove that the left Hilbert algebra of continuous functions with compact support, has the same achieved left Hilbert algebra, as the crossed product of K(A)" by the associated action α̃ of G on . As a consequence we obtain that the canonical weight on is the dual weight of the canonical weight on K(A)".
On the Lp convergence of sums of independent random variables
Authors: Hall Peter 
Published: November 2008

AbstractLet {Xnj, 1 ≤ j ≤ kn} be independent random variables with zero means and satisfying . Let p ≥ 1. We prove thatif and only if, for all ε > 0,and we use this result to obtain necessary and sufficient conditions for the Lp convergence of sums of non-negative, independent random variables.
On the existence theory for irrotational water waves
Authors: Keady G. , Norbury J. 
Published: November 2008

AbstractThis paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the velocity potential by ø, the period in ø of the waves by 2L, and the maximum angle of inclination between the tangent to the surface and the horizontal by θm.Krasovskii (12) established that, at each fixed Q and L, there exist wave solutions for each value of θm strictly between zero and ⅙π. We establish that, at each fixed Q and L, there exist wave solutions for each value of qc strictly between c and zero. Here qc is the flow speed at the crest, andwhere g is the acceleration due to gravity. Krasovskii's set of solutions is included in the set that we obtain.
Injective modules for group algebras of locally finite groups
Authors: Musson I. M. 
Published: November 2008

Two recent results relate the existence of injective modules for group algebras which are ‘small’ in some sense to the structure of the group.(1) The trivial kG-module is injective if and only if G is a locally finite group with no elements of order p = char k (9).(2) If (G) is a countable group, then every irreducible kG-module is injective if and only if G is a locally finite p′ group which is abelian-by-finite (9) and (11)
Instability theorems for certain fifth-order differential equations
Authors: Ezeilo J. O. C. 
Published: November 2008

1. Consider the constant-coefficient fifth-order differential equation:It is known from the general theory that the trivial solution of (1·1) is unstable if, and only if, the associated (auxiliary) equation:has at least one root with a positive real part. The existence of such a root naturally depends on (though not always all of) the coefficients a1, a2,…, a5. For example, ifit is clear from a consideration of the fact that the sum of the roots of (1·2) equals ( – a1) that at least one root of (1·2) has a positive real part for arbitrary values of a2,…, a5. A similar consideration, combined with the fact that the product of the roots of (1·2) equals ( – a5) will show that at least one root of (1·2) has a positive real part iffor arbitrary a2, a3 and a4. The condition a1 = 0 here in (1·4) is however superfluous whenfor then X(0) = a5 < 0 and X(R) > 0 if R > 0 is sufficiently large thus showing that there is a positive real root of (1·2) subject to (1·5) and for arbitrary a1, a2, a3 and a4.
Boundaries for polydisc algebras in infinite dimensions
Authors: Globevnik J. 
Published: November 2008

AbstractLet AB be the algebra of all bounded continuous functions on the closed unit ball B of c0, analytic on the open unit ball, with sup norm, and let AU be the sub-algebra of AB of those functions which are uniformly continuous on B. Call a set S ⊂ B a boundary of AB (AU) iffor every f ∈ AB (f ∈AU, respectively). In the paper we study the boundaries of AB and AU. We give a complete description of the boundaries of AU and present some necessary and some sufficient conditions for a set to be a boundary of AB. We also give some examples of boundaries.
Special functions, infinite divisibility and transcendental equations
Authors: Ismail Mourad E. H. , May C. Ping 
Published: November 2008

AbstractWe establish integral representations for quotients of Tricomi ψ functions and of several quotients of modified Bessel functions and of linear combinations of them. These integral representations are used to prove the complete monotonicity of the functions considered and to prove the infinite divisibility of a three parameter probability distribution. Limiting cases of this distribution are the hitting time distributions considered recently by Kent and Wendel. We also derive explicit formulas for the Kent–Wendel probability density functions.
On bundle completion of parallelizable manifolds
Authors: Dodson C. T. J. , Sulley L. J. 
Published: November 2008

AbstractIn (5), Schmidt devised a procedure for completing a space-time M by adjoining a boundary ∂M called the b-boundary. Bosshard(1) and Johnson(4) have shown that certain Friedmann and Schwarzschild space-times have non-Hausdorff b-completions.In (2), (3), the first author considered a modification of the b-completion which gives a Hausdorff completion in the Friedmann case. The modification used a parallelization of the space-time and can be given in terms of the linear connexion determined by the parallelization. We show that the completion obtained is the Cauchy completion in a particular Riemannian metric on the manifold and so is always Hausdorff.
Ergodic theorems for semifinite von Neumann algebras: II
Authors: Yeadon F. J. 
Published: November 2008

In (7) we proved maximal and pointwise ergodic theorems for transformations a of a von Neumann algebra which are linear positive and norm-reducing for both the operator norm ‖ ‖∞ and the integral norm ‖ ‖1 associated with a normal trace ρ on . Here we introduce a class of Banach spaces of unbounded operators, including the Lp spaces defined in (6), in which the transformations α reduce the norm, and in which the mean ergodic theorem holds; that is the averagesconverge in norm.
Attenuation of elastic waves in a cracked, fluid-saturated solid
Authors: Chatterjee A. K. , Mal A. K. , Knopoff L. , Hudson J. A. 
Published: November 2008

AbstractThe problem of the determination of the overall dynamic elastic moduli of an elastic solid permeated by uniformly distributed penny-shaped cracks is considered. The cracks are assumed to be filled with a viscoelastic material. The orientations of the cracks may be either parallel or perfectly random. The overall velocities as well as the specific attenuation coefficients of plane harmonic compressional and shear waves are calculated for low frequencies and dilute concentration of the cracks.
A quadratic mapping with invariant cubic curve
Authors: Penrose Roger , Smith Cedric A. B. 
Published: November 2008

AbstractIn the projective plane, if H is a harmonic homology (linear transformation with H2 = I), and G a general inversion (quadratic transformation projectively equivalent to an inversion), then under a certain condition there is a pencil of cubics each of which is invariant under G, H separately. These are related to transformations discovered by Mandel, Todd and Lyness. As a near converse, we find that, given a Pascal configuration, there is a quadratic Cremona transformation under which each cubic passing through the vertices of the configuration is invariant. As a by-product, parametric expressions are found for elliptic functions of a fifth of a period.
Cohen–Macaulay properties for balanced big Cohen–Macaulay modules
Authors: Sharp R. Y. 
Published: November 2008

Let A be a (commutative, Noetherian) local ring (with identity) and let a1,…, an be a system of parameters (s.o.p.) for A. A (not necessarily finitely generated) A-module M is said to be a big Cohen–Macaulay.A-module with respect to a1,…, an if a1,…, an is an M-sequence, that is if M ‡ = (a1,…, an) M and, for each i = 1,…, n,One of the main open problems in commutative algebra at the present time is that of establishing the existence of a big Cohen–Macaulay module with respect to a specified s.o.p. in an arbitrary local ring. The work and writings of Hochster, such as (5), show that, if the existence of such modules could be established, then several conjectures in commutative algebra, some of which are quite long-standing, would be settled. Moreover, Hochster has established the existence of such big Cohen–Macaulay modules whenever the local ring A concerned contains a field as a subring, or has dimension not exceeding 2: see ((5), chapters 4, 5) and (4).
Conditions for an affine manifold with torsion to have a Riemann–Cartan structure
Authors: Ni Wei-Tou 
Published: November 2008

AbstractNecessary and sufficient conditions for the local existence of a metric compatible with the affine connection are obtained in terms of the Riemann tensor and its first-order covariant derivatives in a generic affine manifold with torsion. In case these conditions are satisfied, the solutions of the metric are given in terms of integrals and are unique up to a constant scale factor. Some global conditions are also obtained and discussed.
Vector sums of Valentine convex sets
Authors: Eggleston H. G. 
Published: November 2008

SummaryA set X in Euclidean space is Valentine n–convex, or simply n–convex' if it has the following property. If X contains a subset Y consisting of n distinct points then X also contains the points of at least one segment with end points in Y. We show here that the vector sum of two plane compact 3-convex sets is 5-convex (which complements the result of I. D. Calvert(1) that the intersection of two plane compact 3-convex sets is 5-convex) and that the vector sum of a plane connected compact 3-convex set with itself is 4-convex. These results are not true in 4 dimensional space. It is an open question whether or not they are true in 3-dimensional space.