bluuebunny/crossref_metadata_2025_split huggingface dataset:
FK spaces which include strongly summable sequences
Authors: Maddox I. J. 
Published: November 2008

The following interesting result on strongly summable sequences is due to Kuttner (2).Theorem 1. Let 0 < p < 1. Then given any Toeplitz matrix A there is a sequence summable wp which is not summable A.As usual, for 0 < p < ∞, we denote by wp the space of strongly summable sequences with index p. Thus x = (xk) ∈ wp if and only if there is a number l such thatStrongly summable sequences arise in the theory of Fourier series, see e.g. (8), Chapter X, in Ergodic theory, see e.g. (1), as well as in summability theory.
Recurrences in multidimensional arithmetic sequences
Authors: Hemmer S. , Hemmer P. C. 
Published: November 2008

Let unity and the irrational components ri of a d-dimensional vector r be linearly independent, and consider the integers n for whichwhere {x} denotes the fractional part of x. It is a trivial restriction to assume that ri and φi lie between 0 and 1. This note is concerned with the question: what are the gaps between the successive n?
S.I.P. measures on metrizable groups
Authors: Karanikas C. 
Published: November 2008

Let G be a metrizable non-discrete locally compact group. Let M(G) be the convolution measure algebra of G. We shall denote by Lx and Rx, x β G, the left and the right translation operation on M(G), respectively. A measure μ β M(G) has strongly independent powers or μ is a s.i.p. measure, if, for x β G and n, m β N,whenever n ≠ m or x ≠ e, where e is the identity of G. If a measure μ satisfies (1) for x = e and n + m, we say that μ has independent powers, or μ is an i.p. measure. Notice that the powers μn and μm of μ are convolution powers.
A modular version of Jensen's formula
Authors: Rohrlich David E. 
Published: November 2008

A well-known result of classical function theory, Jensen's formula, expresses the integral around a circle of the log modulus of a meromorphic function in terms of the log modulus of the zeros and poles of that function lying inside the circle. Explicitly, if F is a meromorphic function on the unit disc {ω ε ℂ: |ω| < 1} and F(0) = 1, then, for 0 < r < 1,where ordωF is the order of F at ω. The purpose of this note is to observe that a formula analogous to (1) holds when F is replaced by a modular function for SL2(ℤ) and the integral by a suitable double integral over a fundamental domain. We shall derive this modular variant of Jensen's formula from the usual version by applying the Rankin-Selberg method and the first Kronecker limit formula. The argument admits some extension to Fuchsian groups other than SL2(ℤ), and to modular forms of weight other than zero; this point will be discussed later.
On Wh3 of a Bieberbach group
Authors: Nicas Andrew J. 
Published: November 2008

A closed aspherical manifold is a closed manifold whose universal covering space is contractible. There is the following conjecture concerning the algebraic K-theory of such manifolds:Conjecture. Let Γ be the fundamental group of a closed aspherical manifold. Then Whi(Γ) = 0 for i ≥ 0 where Whi(Γ) is the i-th higher Whitehead group of Γ.
The spectrum (P ⋀ bo) −∞
Authors: Davis Donald M. , Mahowald Mark 
Published: November 2008

There are spectra P−k constructed from stunted real projective spaces as in [1] such that H*(P−k) is the span in ℤ/2[x, x−1] of those xi with i ≥ −k. (All cohomology groups have ℤ/2-coefficients unless specified otherwise.) Using collapsing maps, these form an inverse systemwhich is similar to those of Lin ([15], p. 451). It is a corollary of Lin's work that there is an equivalence of spectrawhere holim is the homotopy inverse limit ([3], ch. 5) and Ŝ–1 the 2-adic completion of a sphere spectrum. One may denote by this holim (P–κ), although one must constantly keep in mind that , but rather
Affine algebras of Gelfand-Kirillov dimension one are PI
Authors: Small L. W. , Stafford J. T. , Warfield R. B. 
Published: November 2008

The aim of this paper is to prove:Theorem.Let R be an affine (finitely generated) algebra over a field k and of Gelfand-Kirillov dimension one. Then R satisfies a polynomial identity. Consequently, if N is the prime radical of R, then N is nilpotent and R/N is a finite module over its Noetherian centre.
Compact multipliers on weighted hypergroup algebras
Authors: Ghahramani F. , Medgalchi A. R. 
Published: November 2008

AbstractLet Mω(X) be a weighted hypergroup algebra, and Lω(X) be the Banach algebra of measures μ ε Mω(X) such that the function x ↦ (1/ω(x))δx* |μ| is norm continuous. We characterize compact multipliers on Lω(X). This extends the characterization of compact multipliers on weighted group algebras and some classes of weighted semigroup algebras.
The convolution metric dg
Authors: Yukich J. E. 
Published: November 2008

SummaryWe introduce and study a new metric on denned bywhere is the space of probability measures on ℝk and where g: ℝk→ is a probability density satisfying certain mild conditions. The metric dg, relatively easy to compute, is shown to have useful and interesting properties not enjoyed by some other metrics on . In particular, letting pn denote the nth empirical measure for P, it is shown that under appropriate conditions satisfies a compact law of the iterated logarithm, converges in probability to the supremum of a Gaussian process, and has a useful stochastic integral representation.
The subnormal structure of general linear groups
Authors: Vaserstein L. N. 
Published: November 2008

Let A be an associative ring with 1. For any natural number n, let GLnA denote the group of invertible n by n matrices over A, and let EnA be the subgroup generated by all elementary matrices ai, j, where aεA and 1 ≤ i ≡ j ≤ n. For any (two-sided) ideal B of A, let GLnB be the kernel of the canonical homomorphism GLnA→GLn(A/B) and Gn(A, B) the inverse image of the centre of GLn(A/B) (when n > 1, the centre consists of scalar matrices over the centre of the ring A/B). Let EnB denote the subgroup of GLnB generated by its elementary matrices, and let En(A, B) be the normal subgroup of EnA generated by EnB (when n > 2, the group GLn(A, B) is generated by matrices of the form ai, jbi, j(−a)i, j with aA, b in B, i ≡ j, see [7]). In particuler,is the centre of GLnA
On Hammersley's minimum problem for a rolling sphere
Authors: Arthurs A. M. , Walsh G. R. 
Published: November 2008

AbstractThe problem posed by Hammersley (1983) of finding the shortest path along which a sphere can roll from one prescribed state to another is formulated by using quaternion calculus of variations and optimal control theory. This leads to a system of coupled nonlinear differential equations with prescribed end conditions. From the resulting expression for the curvature, it is shown that the differential equation of the required path in intrinsic coordinates is the same as the equation of motion of a simple pendulum, giving a solution in terms of elliptic integrals.
Delooping the total Stiefel–Whitney class
Authors: Kozlowski A. 
Published: November 2008

Let FH(X) denote the group of units of the classical cohomology ring H(X) = Πn≥0Hn(X; Z/2) of a CW-complex X. The total Stiefel–Whitney class can be viewed as a group homomorphism where is the reduced real K-theory of X. Both and FH( ) are representable functors, with representing spaces BO and FH, and thus w can be represented by a map w: BO → FH. By the Bott periodicity theorem, BO is an infinite loop space, and by a theorem of G. Segal[9] so is FH. However, it is well known that w is not an infinite loop map; this was first shown in [10]. The purpose of this paper is to prove the following:Theorem 0·1. w: BO → FHis a loop map but not a double loop map.
Representation-theoretic interpretation of a formula of D. E. Littlewood
Authors: Józefiak Tadeusz , Weyman Jerzy 
Published: November 2008

This note is a continuation of our attempts (see [3]) to give a satisfactory representation-theoretic justification of the following formula of D. E. Littlewood:where sI is the Schur symmetric function corresponding to a partition I, |I| is the weight of I, r(I) is the rank of I, and the summation ranges over all self-conjugate partitions (i.e. partitions I such that I = I where I is the partition conjugate to I).
The Stokes constants for a cluster of transition points
Authors: Fröman Nanny , Fröman Per Olof , Lundborg Bengt 
Published: November 2008

AbstractThe connection problems associated with the one-dimensional Schrödinger equation in the presence of a general isolated cluster containing an unspecified number of complex transition points in unspecified positions can be studied by means of the phase-integral method developed by Fröman and Fröman. Any anti-Stokes line, i.e. any line in the complex z-plane on which the solutions behave as travelling waves with constant flow, must asymptotically (i.e. in the limit of large values of |z|) point in one of m +2 possible directions, which divide the region around the cluster into m +2 sectors, where m is the degree of the cluster. The tracing of these waves from an anti-Stokes line, bounding a sector, to an anti-Stokes line constituting the other boundary of the same sector is expressed by means of the Stokes constant for the sector in question. This paper examines the relation between these m + 2 Stokes constants in the general case when the transition points in the cluster may also be close-lying in the sense that it is impossible to treat them individually, when the solutions are traced. Under the assumption that the effective potential in the Schrodinger equation is a regular analytic function in a sufficiently large region containing the cluster, it is shown that the m + 2 Stokes constants are in general constrained by three algebraic relations, which are obtained for arbitrary m. The cases m = 1, 2, 3 and 4 are worked out in detail.
Differentiable positive definite kernels and Lipschitz continuity
Authors: Cochran James A. , Lukas Mark A. 
Published: November 2008

AbstractReade[11] has shown that positive definite kernels K(x, t) which satisfy a Lipschitz condition of order α on a bounded region have eigenvalues which are asymptotically O(1/n1+α). In this paper we extend this result to positive definite kernels whose symmetric derivative Krr(x, t) = ∂2rK(x, t)/∂xτ ∂tτ is in Lipα and establish λn(K) = O(1/n2r+1+α). If ∂Krr/∂t is in Lipα, the anticipated asymptotic estimate is also derived.The proofs use a well-known result of Chang [2], recently rederived by Ha [5], and estimates based upon finite rank approximations to the kernels in question. In these latter estimates we employ the familiar piecewise linear ‘hat’ basis functions of approximation theory.
Best approximation in L(X, Y)
Authors: Deeb W. , Khalil R. 
Published: November 2008

AbstractLet X, Y be Banach spaces and G a closed subspace of Y. Let L(X, Y) be the space of bounded linear operators from X into Y. In this paper we investigate when L(X, G) is proximal in L(X, Y). Further, we discuss the related problem of proximinality of L∞(T, G) in L∞(T, Y). We improve results obtained by Light and Cheney in this direction.
Improvement of the generalized quantal Bohr–Sommerfeld quantization condition
Authors: Lundborg Bengt , Fröman Per Olof 
Published: November 2008

AbstractThe quantal quartic oscillator, characterized by two real and two complex conjugate transition points (simple zeros), is studied by means of the phase-integral method developed by Fröman and Fröman, and various quantization conditions are obtained. The main results, obtained in §3·3 and §4, are summarized below.A correction to the generalized Bohr–Sommerfeld quantization condition, due to the complex conjugate transition points, is obtained from estimates of the. F-matrix for a path passing above the complex conjugate transition points. This quantization condition is closely related to the quantization condition for a double-oscillator. The correction is shown to be rigorously valid when the distance between the real transition points is large compared to the distance between the complex conjugate ones, which may lie at an unspecified distance from each other.At sufficiently large distances from the cluster of four transition points the solutions of the Schrödinger equation can be characterized by the Stokes constants between anti-Stokes lines emerging from the cluster in six directions towards infinity. There are initially six non-trivial such Stokes constants in the problem under consideration, but, from the results in previous papers by N. Fröman and the present authors, these Stokes constants are linked by a number of algebraic relations, so that one or two Stokes constants suffice to describe the solutions far away from the cluster of transition points. The quantization condition is expressed in terms of these Stokes constants. Approximate values of the relevant Stokes constants are given in the three limiting cases when all four transition points coalesce (and the first-order phase-integral approximation is used), when the distance between the real transition points is sufficiently large (extreme double-oscillator), and in the Bohr-Sommerfeld limit.
Explicit formulae for polygonally generated shape-densities in the basic tile
Authors: Le Hui-Lin 
Published: November 2008

AbstractKendall and Le [4] gave an exact algorithm for the computation of a polygonally generated (auxiliary) shape-density m̃(x, y) which we used to obtain ‘exact’ numerical densities for given (x, y). Here I derive an explicit formula for m̃(x, y), for an arbitrary convex plane polygon K, valid when the shape-point (x, y) lies in what will be called the ‘(upper) basic tile’ of the associated singular tessellation. In most circumstances this is all that is needed for the statistical analysis of collinearities.
Fourier restriction theorems for degenerate curves
Authors: Drury S. W. , Marshall B. P. 
Published: November 2008

Fourier restriction theorems contain estimates of the formwhere σ is a measure on a smooth manifold M in ∝n. This paper is a continuation of [5], which considered this problem for certain degenerate curves in ∝n. Here estimates are obtained for all curves with degeneracies of finite order. References to previous work on this problem may be found in [5].
Equidimensional immersions of locally compact groups
Authors: Hofmann K. H. , Wu T. S. , Yang J. S. 
Published: November 2008

Dense immersions occur frequently in Lie group theory. Suppose that exp: g → G denotes the exponential function of a Lie group and a is a Lie subalgebra of g. Then there is a unique Lie group ALie with exponential function exp:a → ALie and an immersion f:ALie→G whose induced morphism L(j) on the Lie algebra level is the inclusion a → g and which has as image an analytic subgroup A of G. The group Ā is a connected Lie group in which A is normal and dense and the corestrictionis a dense immersion. Unless A is closed, in which case f' is an isomorphism of Lie groups, dim a = dim ALie is strictly smaller than dim h = dim H.
Cocovers and tilting modules
Authors: Rickard Jeremy , Schofield Aidan 
Published: November 2008

We recall [5] that a module T for a finite-dimensional algebra Λ is called a tilting module if(i) T has protective dimension one;(ii) (iii) there is a short exact sequence 0 → Λ → T0 → T1 → 0 with T0 and T1 in add (T), the category of direct summands of direct sums of copies of T.
Hitting times for random walks on vertex-transitive graphs
Authors: Aldous David 
Published: November 2008

AbstractFor random walks on finite graphs, we record some equalities, inequalities and limit theorems (as the size of graph tends to infinity) which hold for vertex-transitive graphs but not for general regular graphs. The main result is a sharp condition for asymptotic exponentiality of the hitting time to a single vertex. Another result is a lower bound for the coefficient of variation of hitting times. Proofs exploit the complete monotonicity properties of the associated continuous-time walk.
The mean square of the Dedekind zeta function in quadratic number fields
Authors: Müller Wolfgang 
Published: November 2008

Let K be a quadratic number field with discriminant D. The aim of this paper is to study the mean square of the Dedekind zeta function ζK on the critical line, i.e.It was proved by Chandrasekharan and Narasimhan[1] that (1) is at most of order O(T(log T)2). As they noted at the end of their paper, it ‘would seem likely’ that (1) behaves asymptotically like a2T(log T)2, with some constant a2 depending on K. Applying a general mean value theorem for Dirichlet polynomials, one can actually proveThis may be done in just the same way as this general mean value theorem can be used to prove Ingham's classical result on the fourth power moment of the Riemann zeta function (cf. [3], chapter 5). In 1979 Heath-Brown [2] improved substantially on Ingham's result. Adapting his method to the above situation a much better result than (2) can be obtained. The following Theorem deals with a slightly more general situation. Note that ζK(s) = ζ(s)L(s, XD) where XD is a real primitive Dirichlet character modulo |D|. There is no additional difficulty in allowing x to be complex.
A new method for generating Bonferroni-type inequalities by iteration
Authors: Galambos Janos , Xu Yuan 
Published: November 2008

LetA1,A2,…,Anbe events on a given probability space, and letmnbe the number of thoseAjwhich occur. PutS0=S0,n= 1, andwhere the summation is over all subscripts satisfying 1 ≤i1<i2< … <ik≤n. For convenience in some formulae we adopt the conventionSk, n= 0 ifk>n. By turning to indicator variables one immediately finds thatInequalities of the formwhereck=ck(r, n) anddk=dk(r, n) are constants (not dependent on the eventsAj, 1 ≤j≤n), possibly zero, are called Bonferroni-type inequalities. This same name applies ifP(mn=r) is replaced byP(mn≥r) in the middle. The best known such inequalities are the method of inclusion and exclusionwherej≥ 0 is an arbitrary integer. An extension of (4) to arbitraryr, called Jordan's inequalities (see Takács [16]), is as follows: for 0 ≤r≤nand for any integerj≥ 0,It is observed by Galambos and Mucci[9] that (5) follows from (4), and indeed, one can always generate inequalities of the form (3) for arbitraryrfrom the special caser= 0 if one utilizes onlySr,Sr+1… in the case ofP(mn=r). As a matter of fact, from the instructions of Galambos and Mucci one has that the inequalitieshold for an arbitrary sequenceA1,A2,…,Anof events if, and only if, for an arbitrary sequenceA1,A2,…,An−rof events,where
Some homological properties of complete modules
Authors: Simon Anne-Marie 
Published: November 2008

In this paper A is a commutative noetherian ring, a an ideal of A and the A- modules are given the a-adic topology.It is a general feeling that completeness is a kind of finiteness condition. We make precise that feeling and, after a result concerning the homology of a complex of complete modules which can be used in place of Nakayama's Lemma, we establish analogies between complete modules and finitely generated ones, with respect to flat dimension, injective dimension, Bass numbers and the Koszul complex. This is particularly clear in the local case, where we have also some partial information on the support of a complete module. With respect to dimension however, the analogy fails, as shown by an example.
Homotopy skein modules of orientable 3-manifolds
Authors: Hoste Jim , Przytycki Jósef H. 
Published: November 2008

AbstractWe define the homotopy skein module of an arbitrary orientable 3-manifold M. This module is similar to the ordinary skein module defined by the second author but is more appropriate when considering oriented links in M up to link homotopy rather than isotopy. We compute the homotopy skein module of M = F × I for any orientable surface F and show that it is free. In the case where M = F × I the homotopy skein module may be given an algebra structure and we show that as an algebra it is isomorphic to the universal enveloping algebra of the Goldman–Wolpert Lie algebra of F. We show, also in this case, that the homotopy skein module is a quantization of the symmetric tensor algebra associated to the Goldman–Wolpert Lie algebra.
Noisy fluctuating clocks for Markov chains
Authors: Kennedy J. E. 
Published: November 2008

AbstractIn this paper we concern ourselves with the Q-matrices of time-substituted Markov chains where the time-substitutions are based on fluctuating clocks with noise. The results of this paper follow on naturally from the analysis in Kennedy and Williams [3], in which the problems of characterization and of calculation of these Q-matrices were addressed. Here, we study the Q-matrices as functions of the variance σ2 of the noise.
Continuity of solutions of Schrödinger equations
Authors: Nakai Mitsuru 
Published: November 2008

We denote by N(x, y) the Newtonian kernel on the d-dimensional Euclidean space (where d ≥ 2) so that N(x, y) = log|x–y|-1 for d = 2 and N(x, y) = |x−y|2−d for d ≥ 3. A signed Radon measure μ on an open subset Ω in d is said to be of Kato class iffor every y in Ω. where |μ| is the total variation measure of μ.
Generalized Eilenberg–Moore spectral sequences for elementary abelian groups and tori
Authors: Greenlees J. P. C. 
Published: November 2008

AbstractIn this note we prove universal coefficient theorems for Borel cohomology and related theories. Whatever other merit this may have the comment of Borel [5] applies ‘ …elle a au moms l'utilité de bien mettre en évidence le rôle fondamental joué dans cette question par la cohomologie des groupes’.Indeed the purpose of the enterprise is to use homological properties of the group cohomology ring H*(BG+) to study properties of G-spaces. Because of the relative simplicity of ordinary cohomology much attention in the proofs and applications is concentrated on change of groups, and on changes in the way the group action is exploited. Nonetheless we are able to adapt the non-equivariant approach of Adams ([1, 2]; see also [3]). Thus the existence of universal coefficient theorems automatically gives Kiinneth theorems as special cases.
Properly algebraic and spectrum-finite ideals in Jordan systems
Authors: Loos Ottmar 
Published: November 2008

The two main results of this paper are:(i) The set of properly algebraic elements of a Jordan system (algebra, triple system or pair) over an uncountable field is an ideal.(ii) For a semiprimitive Banach Jordan system, the socle, the largest properly algebraic ideal, the largest properly spectrum-finite ideal and the largest von Neumann regular ideal all coincide.
Minimal primal ideals in Banach algebras
Authors: Somerset Douglas W. B. 
Published: November 2008

AbstractAn ideal I in a ring R is primal if whenever J1, …, Jn is a finite set of ideals of R with J1 … Jn = {0} then Ji ⊆ I for at least one i ∈ {1, …, n}. If the ring is commutative then is is easily shown that each primal ideal contains a prime ideal. In this paper it is shown that in a separable semi-simple Banach algebra each primal ideal contains a prime ideal, and that the space of minimal prime ideals is compact and extremally disconnected in the hull-kernel topology. An example is given of an inseparable C-algebra with a primal ideal which does not contain a prime ideal.
The weak Banach-Saks property on Lp(μ, E)
Authors: Cembranos Pilar 
Published: November 2008

A Banach space E is said to have the Banach-Saks property (BS) if every bounded sequence (xn) in E has a subsequence (x′n) with norm convergent Cesaro means; that is, there is x in E such thatIf this occurs for every weakly convergent sequence in E it is said that E has the Weak Banach-Saks property (WBS) (also called Banach-Saks-Rosenthal property).
Kähler–Einstein metrics with SU(2) action
Authors: Dancer Andrew S. , Strachan Ian A. B. 
Published: November 2008

The aim of this paper is to analyse Riemannian Kähler–Einstein metrics g in real dimension four admitting an isometric action of SU(2) with generically three-dimensional orbits. The Kähler condition means that there is a complex structure I, with respect to which the metric is hermitian, such that the two-form Ωdefined byis closed. It is well-known that if this condition holds then Ω is in fact covariant constant.