bluuebunny/crossref_metadata_2025_split huggingface dataset:
The structure of modules over polycyclic groups
Authors: Brown Kenneth A. 
Published: November 2008

AbstractThe structure of modules over polycyclic group rings RG is investigated using the idea of a link P ⇝ Q between prime ideals of RG. The representation theory of RG splits into two parts – the part we discuss is determined by the representation theory of certain Noetherian polynomial identity factor rings of subrings of RG.
On nth roots and infinitely divisible elements in a connected Lie group
Authors: McCrudden M. 
Published: November 2008

For any group G, x ∈ G and n ∈ ℕ (the natural numbers), leti.e. the set of all nth roots of x in G. If G is a Hausdorff topological group, then Rn(x, G) is a closed set in G, but may otherwise be quite complicated. However, as we have observed in (4), if G is a compact Lie group, then Rn(x, G) always has a finite number of connected components, and this result has led us to wonder about the connectedness properties of Rn(x, G) for other Lie groups G. Here is the result.
Edgeworth expansion of the distribution of Stein's statistic
Authors: Hall Peter 
Published: November 2008

AbstractWe derive a two-term Edgeworth expansion for the distribution of Stein's double sampling statistic in the case of a non-normal parent population. The first term describes the main effect of skewness, while the second describes the main effect of kurtosis and the secondary effect of skewness. The remainder is shown to be uniformly negligible in comparison with these effects. Explicit conditions are given for the expansion to be valid. These conditions are considerably weaker than those which were imposed in an earlier derivation of the ‘exact’ distribution of Stein's statistic.
On the interaction between Tollmien-Schlichting and Rayleigh-Bénard instabilities in the presence of a longitudinal magnetic field
Authors: Rudraiah N. , Shivaraya E. S. 
Published: November 2008

AbstractThe method used by Gage and Reid(10) to investigate hydrodynamic stability of thermally stratified fluid is extended to hydromagnetic stability to study the effect of aligned magnetic field on the stability of unstable thermal stratification under the assumption of small magnetic Reynolds number. The interaction between the Tollmien–Schlichting–Stuart mechanism of instability due to shear and magnetic field and Rayleigh–Bénard–Thompson mechanism of instability due to thermally unstable stratification and magnetic field is brought out in detail. It is shown that, although Squire's transformation can be used to reduce the three-dimensional problem to an equivalent two-dimensional one, Squire's theorem is not valid. This conclusion follows from the fact that in our analysis the Richardson number Ri ( < 0) will not be greater than the value −0·92 × 10−6. In particular, it is shown that for the values of stratification parameter n ≤ 0·6 the effect of magnetic field for small values of Stuart number N is to augment instability and impose the restriction on the validity of our numerical procedure. However, for η = 0·8 a sharp transition from unstable to stable flow takes place at N = 0·3. A physical explanation for this based on eddies is given.
Semifinite traces on JBW-algebras
Authors: King W. P. C. 
Published: November 2008

A JB-algebra is a real Jordan algebra A which is also a Banach space and whose norm and multiplication satisfy the two following conditions(i) ∥a2∥ = ∥a∥2,(ii) ∥a2 − b2∥ ≤ max{∥a2∥, ∥b2∥},for all elements a and b in A. A JB-algebra which is also a Banach dual space is called a JBW-algebra. The properties of JB-algebras and JBW-algebras can be found in (3), (4), (8) and (15).
Generalized Bianchi identities for horizontal distributions
Authors: Crampin M. 
Published: November 2008

A linear connection on a differentiable manifold M defines a horizontal distribution on the tangent bundle T(M). Horizontal distributions on tangent bundles are of some interest even when they are not generated by connections. Much of linear connection theory generalizes to arbitrary horizontal distributions. In particular, there are generalized versions of Bianchi's two identities for the torsion T and curvature Rwhere C denotes the cyclic sum with respect to X, Y and Z. These identities are derived below by associating with a horizontal distribution a graded derivation of degree 1 in a graded Lie algebra of vertical forms on M. This approach reveals the fundamentally algebraic origin of the Bianchi identities.
Semimartingales and the empirical distribution
Authors: Al-Hussaini Ata N. , Elliott Robert J. 
Published: November 2008

AbstractProcesses related to the empirical distribution are shown to converge to a time changed Brownian motion. In particular, the time change of the Brownian motion differs from the time change obtained by using the distribution function: this gives rise to two different representations of a related Brownian bridge.
Fourier restriction theorems for curves with affine and Euclidean arclengths
Authors: Drury S. W. , Marshall B. P. 
Published: November 2008

Let M be a smooth manifold in . One may ask whether , the restriction of the Fourier transform of f to M makes sense for every f in . Since, for does not make sense pointwise, it is natural to introduce a measure σ on M and ask for an inequalityfor every f in (say) the Schwartz class. Results of this kind are called restriction theorems. An excellent survey article on this subject is to be found in Tomas[13].
A tabular method for correcting skewness
Authors: Hall Peter 
Published: November 2008

AbstractWe propose a smooth correction for skewness in an asymptotically normal statistic. Unlike the case of approximation by Edgeworth expansion, our correction applies uniformly in all values of the level. The correction is based on a ' comparison statistic', and, in the case of the Studentized mean, it enables removal of all effects of skewness up to terms of order.
The dual J* of the James space has cotype 2 and the Gordon-Lewis property
Authors: Pisier Gilles 
Published: November 2008

AbstractWe prove the result in the title. More generally we consider the Banach space υp, of all sequences (xn) of scalars such thatwhere the supremum runs over all increasing sequences n1 ≤ n2 ≤ …. We show that is of cotype 2 if p ≽ 2 and of cotype p′, where 1/p′ + 1/p = 1, if p ≤ 2. Similar results are obtained for the analogous function spaces.
Corrigendum
Authors: Kleidman Peter B. , Wilson Robert A. 
Published: November 2008

Volume 102 (1987), 17–23‘The maximal subgroups of Fi22’We reported on some computer calculations which we used to complete the enumeration of the maximal subgroups of the sporadic simple group Fi22 and of its automorphism group Fi22:2. Unfortunately there was an error in these calculations. We have therefore repeated all the calculations, incorporating much more thorough checking routines.
Multiplicative functions at consecutive integers. II
Authors: Hildebrand Adolf 
Published: November 2008

The global behaviour of multiplicative arithmetic functions has been extensively studied and is now well understood for a large class of multiplicative functions. In particular, Halász [5] completely determined the asymptotic behaviour of the meansfor multiplicative functions g satisfying |g| ≤ 1, and gave necessary and sufficient conditions for the existence of the ‘mean value’
A reduction theory of second order meromorphic differential equations, I
Authors: Jurkat W. B. , Zwiesler H. J. 
Published: November 2008

In this article we investigate the meromorphic differential equation X′(z) = A(z) X(z), often abbreviated by [A], where A(z) is a matrix (all matrices we consider have dimensions 2 × 2) meromorphic at infinity, i.e. holomorphic in a punctured neighbourhood of infinity with at most a pole there. Moreover, X(z) denotes a fundamental solution matrix. Given a matrix T(z) which together with its inverse is meromorphic at infinity (a meromorphic transformation), then the function Y(z) = T−1(z) X(z) solves the differential equation [B] with B = T−1AT − T−1T [1,5]. This introduces an equivalence relation among meromorphic differential equations and leads to the question of finding a simple representative for each equivalence class, which, for example, is of importance for further function-theoretic examinations of the solutions. The first major achievement in this direction is marked by Birkhoff's reduction which shows that it is always possible to obtain an equivalent equation [B] where B(z) is holomorphic in ℂ ¬ {0} (throughout this article A ¬ B denotes the difference of these sets) with at most a singularity of the first kind at 0 [1, 2, 5, 6]. We call this the standard form. The question of how many further simplifications can be made will be answered in the framework of our reduction theory. For this purpose we introduce the notion of a normalized standard equation [A] (NSE) which is defined by the following conditions:(i) , where r ∈ ℕ and Ak are constant matrices, (notation: )(ii) A(z) has trace tr for some c ∈ ℂ,(iii) Ar−1 has different eigenvalues,(iv) the eigenvalues of A−1 are either incongruent modulo 1 or equal,(v) if A−1 = μI, then Ar−1 is diagonal,(vi) Ar−1 and A−1 are triangular in opposite ways,(vii) a12(z) is monic (leading coefficient equals 1) unless a12 ≡ 0; furthermore a21(z) is monic in case that a12 ≡ 0 but a21 ≢ 0.
On complete d-sequences and the defining ideals of Rees algebras
Authors: Huckaba Sam 
Published: November 2008

AbstractIf R is a Noetherian local ring and I = (x1, …, xn)R is an ideal of R then the Rees algebra R[It] can be represented as a homomorphic image of the polynomial ring R[Z1, …, Zn]. The kernel is a homogeneous ideal, and the smallest of the degree bounds among all generating sets, called the relation type of I, is independent of the representation. We derive formulae connecting the relation type of I with the reduction number of I when the analytic spread of I exceeds height(I) by one. In the process we define complete d-sequences with respect to I and use them to help achieve our results. In addition some results on the behaviour of the relation type modulo an element are proved, and examples where the relation type is explicitly computed are presented.
On ideals and sublattices in linear lattices and F-lattices
Authors: Abramovich Y. A. , Lipecki Z. 
Published: November 2008

The main aim of this paper is to study the role of the assumptions in the followingTheorem 0. Every ideal I of codimension 1 in an F-lattice X is closed†.For X a Banach lattice this result appears in [11], ii.5·3, corollary 3. The proof carries over to the case where X is an. F-lattice, i.e. a topological linear lattice the topology of which is metrizable and complete, with the help of a result due to Klee ([10], theorem v.5·5; see also [3], theorem 16·6). We first note that the assumption of metric completeness is essential (Example 2). We then extend Theorem 0 to the case of ideals of finite codimension (Theorem 1), and show that non-closed ideals exist whenever X is infinite-dimensional (Corollary 2). Our main result commenting on Theorem 0 is, however, the existence of dense sublattices of arbitrary codimension between 1 and in every infinite-dimensional F-lattice (Theorem 6).
Some strong limit-2 and Dirichiet criteria for fourth order differential expressions
Authors: Race David 
Published: November 2008

AbstractConditions are given on the real coefficients p, q and r and the weight w, for the fourth order formally symmetric differential expressionto have the properties of being strong limit-2 and Dirichlet at ∞, when considered in the weighted Hilbert space, . These extend existing results due to both W. N. Everitt and V. Krishna Kumar and cover an expression which is important in the study of certain orthogonal polynomials.
Some recent developments concerning asymptotic distributions of pontograms
Authors: Eastwood Vera R. 
Published: November 2008

The data analytical problem of testing whether an empirical set of n given points in the plane could be considered to contain too many straight line configurations in a situation where the generating mechanism of the n points is unknown, was recently reintroduced to the literature by D. G. Kendall and W. S. Kendall[7]. Taking the Land's end data problem (cf. also Broadbent [1] and further references given there) as the anchor point and motivation for their discussion, D. G. and W. S. Kendall developed a new testing device, called the pontogram. The pontogram is a one- parameter stochastic process defined pointwise bywhere N denotes a Poisson process in [0, 1] with N(0) = 0 and unknown intensity parameter μ > 0 and where R = N(1) gives the number of Poisson events in the entire [0, 1] section.
Hopf algebras and regular isotopy invariants for link diagrams
Authors: Hennings M. A. 
Published: November 2008

In this paper, we shall consider the following method for obtaining regular isotopy invariants of link diagrams. Given any link diagramL, equip it with a Morse functionh, so that the diagram consists entirely of crossings, maxima, minima and vertical arcs. Introduce 2-valent graphical vertices to separate the various segments of the diagram. Given a finite index setI, a state σ forLhis an assignation of one element ofIto each graphical vertex. Each segment of the diagram now has a weightassociated with it, given in terms of tensor coordinates indexed by the setIby the picturesand, for any state σ, [Li|σ] denotes the product of the various weights. We then define 〈Lh〉 to be the sum of [Lh|σ] over all possible states σ,
On Waring's problem for cubes
Authors: Brüdern Jörg 
Published: November 2008

A classical conjecture in the additive theory of numbers is that all sufficiently large natural numbers may be written as the sum of four positive cubes of integers. This is known as the Four Cubes Problem, and since the pioneering work of Hardy and Littlewood one expects a much more precise quantitative form of the conjecture to hold. Let v(n) be the number of representations of n in the proposed manner. Then the expected formula takes the shapewhere (n) is the singular series associated with four cubes as familiar in the Hardy–Littlewood theory.
Word problems related to derivatives of the displacement map
Authors: Devlin J. 
Published: November 2008

In [6], we considered the equationwhere z ∈ ℂ and the pi are real-valued functions; abstract word-problem concepts and techniques were applied to the local problem of the bifurcation of periodic solutions out of the solution Z ≡ 0. This paper is a sequel to [6]; we present an extension of certain concepts given in that paper, and give a global version of some of our word-problem results.
ℤ2-equivariant hierarchies of irreducible 3-manifolds containing two-sided projective planes
Authors: Kalliongis John 
Published: November 2008

AbstractFor a compact irreducible 3-manifold containing 2-sided projective planes and admitting a ℤ2-action, we consider the problem of when there exists a ℤ2-equivariant hierarchy. We show that a ℤ2-equivariant hierarchy always exists if either every irreducible summand of the orientable double cover has infinite first homology or every 2-sided projective plane is boundary parallel.
A centred norm inequality for singular integral operators
Authors: Bass Richard F. 
Published: November 2008

AbstractLet K be a standard singular integral kernel on ℝ satisfying the usual Hölder continuity condition of order δ, and define (where c is chosen so that the integral of w is 1), the mean of g with respect to the measure w(x) dx, and ‖·‖p the Lp norm with respect to w(x) dx. Although the inequality is not true in general, the centred norm inequality does hold for 1 < p < ∞ if α < δ.
On the existence of minimal Seifert manifolds
Authors: Silver Daniel S. 
Published: November 2008

AbstractFor n ≥ 3, an n-knot K has a minimal Seifert manifold if and only if its group is isomorphic to an HNN-extension with finitely presented base. In this case, any Seifert manifold for K can be converted to a minimal Seifert manifold for K by some finite sequence of ambient 0- and 1-surgeries.
The Gehring–Hayman inequality for quasihyperbolic geodesics
Authors: Heinonen Juha , Rohde Steffen 
Published: November 2008

The quasihyperbolic metric in a proper subdomain D of Rn is defined bywhere the infimum is taken over all rectifiable arcs γ in D joining x and y. There always exists an arc, called a quasihyperbolic geodesic in D, for which the infimum above is attained. We refer to [3], [4], [16], and [17] for the motivation and basic properties of the quasihyperbolic metric.
Optimal choice between parametric and non-parametric bootstrap estimates
Authors: Lee Stephen Man Sing 
Published: November 2008

AbstractA parametric bootstrap estimate (PB) may be more accurate than its non-parametric version (NB) if the parametric model upon which it is based is, at least approximately, correct. Construction of an optimal estimator based on both PB and NB is pursued with the aim of minimizing the mean squared error. Our approach is to pick an empirical estimate of the optimal tuning parameter ε∈[0, 1] which minimizes the mean square error of εNB+(1−ε) PB. The resulting hybrid estimator is shown to be more reliable than either PB or NB uniformly over a rich class of distributions. Theoretical asymptotic results show that the asymptotic error of this hybrid estimator is quite close in distribution to the smaller of the errors of PB and NB. All these errors typically have the same convergence rate of order. A particular example is also presented to illustrate the fact that this hybrid estimate can indeed be strictly better than either of the pure bootstrap estimates in terms of minimizing mean squared error. Two simulation studies were conducted to verify the theoretical results and demonstrate the good practical performance of the hybrid method.
Locally compact groups whose conjugation representations satisfy a Kazhdan type property or have countable support
Authors: Kaniuth Eberhard , Markfort Annette 
Published: November 2008

For a locally compact group G with left Haar measure and modular function δ the conjugation representation γG of G on L2(G) is defined byf ∈ L2(G), x, y ∈ G. γG has been investigated recently (see [19, 20, 21, 24, 32, 35]). For semi-simple Lie groups, a related representation has been studied in [25]. γG is of interest not least because of its connection to questions on inner invariant means on L∞(G). In what follows suppγG denotes the support of γG in the dual space Ĝ, that is the closed subset of all equivalence classes of irreducible representations which are weakly contained in γG. The purpose of this paper is to establish relations between properties such as a variant of Kazhdan's property and discreteness or countability of supp γG and the structure of G.
Renewal theory in a random environment
Authors: Baxter Laurence A. , Li Linxiong 
Published: November 2008

AbstractA random environment is modelled by an arbitrary stochastic process, the future of which is described by a σ-algebra. Renewal processes and alternating renewal processes are defined in this environment by considering the conditional distributions of random variables generated by the processes with respect to the σ-algebra. Generalizations of several of the standard limit theorems of renewal theory are derived.
On the rank of completely 0-simple semigroups
Authors: Ruškuc N. 
Published: November 2008

AbstractConnected completely 0-simple semigroups are defined by a number of equivalent conditions, and a formula for the rank of these semigroups is proved. As a consequence an alternative proof of the result from [11] is given. In the case of a Rees matrix semigroupM0[G, I, Λ, P] the rank is expressed in terms of |I|, |Λ|,Gand a certain subgroup ofGdepending onP. At the end the minimal rank of all semigroupsM0[G, I, Λ, P] is found for a given groupG. Since every completely simple semigroup is connected, every result has a corollary for these semigroups.
Embedded surfaces in four-manifolds, branched covers, and SO(3)-invariants
Authors: Kotschick D. , Matić G. 
Published: November 2008

One of the outstanding problems in four-dimensional topology is to find the minimal genus of an oriented smoothly embedded surface representing a given homology class in a smooth four-manifold. For an arbitrary homology class in an arbitrary smooth manifold not even a conjectural lower bound is known. However, for the classes represented by smooth algebraic curves in (simply connected) algebraic surfaces, it is possible that the genus of the algebraic curve, given by the adjunction formulais the minimal genus. This is usually called the (generalized) Thom conjecture. It is mentioned in Kirby's problem list [11] as Problem 4·36.
Unconditionally converging polynomials on Banach spaces
Authors: Gonz´lez Manuel , Gutiérrez Joaquín M. 
Published: November 2008

In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that and is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.
Some stability properties of c0-saturated spaces
Authors: Leung Denny H. 
Published: November 2008

AbstractA Banach space is c0-saturated if all of its closed infinite-dimensional subspaces contain an isomorph of c0. In this article, we study the stability of this property under the formation of direct sums and tensor products. Some of the results are: (1) a slightly more general version of the fact that c0-sums of c0-saturated spaces are c0-saturated; (2) C(K, E) is c0-saturated if both C(K) and E are; (3) the tensor product is c0-saturated, where JH is the James Hagler space
Homological finiteness conditions for modules over strongly group-graded rings
Authors: Cornick Jonathan , Kropholler Peter H. 
Published: November 2008

Throughout this paper, k denotes a commutative ring. We will develop a theory of homological finiteness conditions for modules over certain graded k-algebras which generalizes known theory for group algebras. The simplest of our results, Theorem A below, generalizes certain results of Aljadeff and Yi on crossed products of polycyclic-by-finite groups (cf. [1, 11]), but also applies to many other crossed products in cases where little was previously known. Before stating the results, we recall definitions of graded and strongly graded rings. Let G be a monoid. Naively, a G-graded k-algebra is a k-algebra R which admits a k-module decomposition,in such a way that Rg Rh ⊆ for all g, h ∈ G. If R is a G-graded k-algebra and X is any subset of G, then we write Rx for the k-submodule of R supported on X; that isNote that if H is a submonoid of G then RH is a subalgebra of R.
Existence of outgoing solutions for perturbations of and applications to the scattering matrix
Authors: Yamamoto Kazuhiro 
Published: November 2008

In this paper we shall prove an existence theorem and give applications of an outgoing solution of the following problem:where L(x, x) is a second order elliptic differential operator with a potential term q(x), is an exterior domain of ℝn (where n 2) with the C2-class boundary , k is an element of the complex plane or of a logarithmic Riemann surface, and B is either a Dirichlet boundary condition or of the form Bu = vj(x) ajk(x) ku + (x)u with the unit outer normal vector v(x) = (vl,, vn) at x.