bluuebunny/crossref_metadata_2025 huggingface dataset:
Two limit theorems for ergodically regenerated stochastic processes
Authors: Kupka Joseph
Published: November 2008

There is a subtle difference between the recurrent event of Feller and the regenerative phenomenon of Kingman: The former regenerates an entire ambient process, whereas the latter regenerates only itself. This paper generalizes Feller's definition to a discrete regenerative phenomenon E in association with an arbitrary discrete-time stochastic process X. Two limit theorems of a general character are proved for the process X when it is regenerated by an ergodic phenomenon E. The first implies that X becomes strictly stationary at a uniform rate which is determined solely by the asymptotic behaviour of E. The second is essentially a mixing convergence theorem which implies the asymptotic independence of regenerating and regenerated events. Applications include (1) the outright independence of the regenerating events and the regenerated events which occur ‘at the end of time’, and (2) the identification of the transient features of X with the null sets of the stationary limiting probability. Numerous open questions are posed.
Countable lattice-ordered groups
Authors: Glass A. M. W.
Published: November 2008

A lattice-ordered group is a group and a lattice such that the group operation distributes through the lattice operations (i.e. f(g ∨ h)k = fgk ∨ fhk and dually). Lattice-ordered groups are torsion-free groups and distributive lattices. They further satisfy f ∧ g = (f−1 ∨ g−1)−1 and f ∨ g = (f−1 ∧ g−1)−1. Since the lattice is distributive, each lattice-ordered group word can be written in the form ∨A ∧B ωαβ where A and B are finite and each ωαβ is a group word in {xi: i ∈ I}. Unfortunately, even for free lattice-ordered groups, this form is not unique. We will use the prefix l- for maps between lattice-ordered groups that preserve both the group and lattice operations, and e for the identity element. A presentation (xi;rj(x) = e)i∈I, j∈J is the quotient of the free lattice-ordered group F on {xi: i∈I} by the l-ideal (convex normal sublattice subgroup) generated by its subset {rj(x): j ∈ J}. {xi: i ∈ I} is called a generating set and {ri(x):j∈J} a defining set of relations. If I and J are finite we have a finitely presented lattice-ordered group. If we can effectively enumerate all lattice-ordered group words r1(x), r2(x),… in xi; i∈I}. If I is finite and J (for this enumeration) is a recursively enumerable set, we say that we have a recursively presented lattice-ordered group. Throughout Z denotes the group of integers and ℝ the real line.

Our purpose in this paper is to prove the natural analogues of three theorems from combinatorial group theory (5), chapter IV, theorems 4·9, 3·1 and 3·5-in particular, theorem C is a natural analogue of an unpublished theorem of Philip Hall (4).
On conjectures of Moore and Serre in the case of torsion-free suspensions
Authors: Selick Paul
Published: November 2008

Let p be a prime. A space X is said to have a homotopy exponent at p if multiplication by pr annihilates the p-torsion of πn(X) for some non-negative integer r independent of n. X is said to have totally finite rational homotopy if ⊕n πn (X) ⊗ ℚ is a finite vector space. Moore has conjectured that these properties are related for finite simply connected CW complexes.

Moore's Conjecture. A space having the homotopy type of a finite simply connected CW complex has a homotopy exponent at p if and only if it has totally finite rational homotopy.

For convenience I will divide the conjecture into its two implications so that I can refer to each separately.
Torsion in semicomplete nilpotent groups
Authors: Fournelle Thomas A.
Published: November 2008

Let Aut G and Inn G denote the group of all automorphisms of the group G and the subgroup of all inner automorphisms of G, respectively. A group G is said to be complete if it has trivial centre and Aut G = Inn G. Examples of such groups abound and they have been the object of study for many years. Following Heineken (8) we call a group G semicomplete if Aut G = Inn G.
Ribbon fibred knots, cobordism of surface diffeomorphisms, and pseudo-Anosov diffeomorphisms
Authors: Bonahon F.
Published: November 2008

For a long time, the main activity in knot theory, we would even say the only one for the problems related to knot cobordism, has been focused onto the development and the analysis of various algebraic invariants. The present paper intends to illustrate some geometric techniques, and to advertise a recent theorem of Casson and Gordon (8) which provides a necessary condition for a fibred classical knot to be ribbon (see definition below) in terms of a cobordism property of its monodromy. We want to show how this last result, combined with some previous work of ours on the cobordism of surface diffeomorphisms (4) (see also (10)) and Thurston's theory of pseudo-Anosov diffeomorphisms (28), (12), can effectively be used to show that a knot is not ribbon.
Whitehead groups of certain hyperbolic manifolds
Authors: Nicas A. J. , Stark C. W.
Published: November 2008

An aspherical manifold is a connected manifold whose universal cover is contractible. It has been conjectured that the Whitehead groups Whj (π1 M) (including the projective class group, the original Whitehead group of π1M, and the higher Whitehead groups of [9]) vanish for any compact aspherical manifold M. The present paper considers this conjecture for twelve hyperbolic 3-manifolds constructed from regular hyperbolic polyhedra. Hyperbolic manifolds are of special interest in this regard since so much is known about their topology and geometry and very little is known about the algebraic K-theory of hyperbolic manifolds whose fundamental groups are not generalized free products.
Extreme points of unbounded, closed and convex sets in Banach spaces
Authors: Polyrakis Ioannis A.
Published: November 2008

In this paper we examine the existence of extreme points in unbounded, closed and convex subsets K of a Banach space X.
The number of small-amplitude limit cycles of Liénard equations
Authors: Blows T. R. , Lloyd N. G.
Published: November 2008

We consider second order differential equations of Liénard type:

Such equations have been very widely studied and arise frequently in applications. There is an extensive literature relating to the existence and uniqueness of periodic solutions: the paper of Staude[6] is a comprehensive survey. Our interest is in the number of periodic solutions of such equations.
Holomorphic and abstract inducing
Authors: Hannabuss K. C.
Published: November 2008

A method of constructing projective representations of separable locally compact groups in reproducing kernel Hilbert spaces is presented, based on the generalized inducing process of Rieffel and Fell. Examples show that the method can be used to construct some well-known holomorphically induced representations. Some representations on cohomology spaces are also described.
a-convexity
Authors: Pinch R. G. E.
Published: November 2008

For a ε R, we define a subset V of Rn to be a-convex if x, y ε V implies

Clearly V is (1 — a)-convex iff it is a-convex: V is convex iff it is a-convex for all a ε [0, 1], and any set is 1-convex. We define the a-convex hull of V to be the intersection of all a-convex subsets of Rn containing V. Put D = 0,1} and D(a) the a-convex hull of D in R1. If V is a-convex and x, y ε V, then V must contain the points of the line through x, y given by {tx + (1 — t) y: t ε D(a)} and so in this paper we concentrate on the study of D(a).
The generalized Penrose-Ward transform
Authors: Eastwood Michael G.
Published: November 2008

The Penrose transform is an integral geometric method of interpreting elements of various analytic cohomology groups on open subsets of complex projective 3-space as solutions of linear differential equations on the Grassmannian of 2-planes in 4-space. The motivation for such a transform comes from interpreting this Grassmannian as the complexification of the conformal compactification of Minkowski space, the differential equations being the massless field equations of various helicities. This transform is a cornerstone of twistor theory [22, 24, 30], but the methods generalize considerably as will be explained in this article. Closely related is the Ward correspondence[28], a non-linear version of a special case of the Penrose transform. It also admits a rather more general treatment. The object of this article is to explain the general case and the natural connection between the Penrose and Ward approaches.
Strong laws for randomly indexed U-statistics
Authors: Horváth Lajos
Published: November 2008

A strong approximation for randomly indexed U-statistics is derived. The special case when the indices are stopping times based upon the jackknife estimator of the variance is discussed.
Holomorphic maps of discs into balls of lp-spaces
Authors: Globevnik Josip
Published: November 2008

Let 1 ≤ p < ∞, let be the open unit ball of lp and let Δ be the open unit disc in ℂ. We prove that there is a holomorphic map such that F(Δ) is dense in and such that whenever .
Inequivalent, bordant group actions on a surface
Authors: Livingston Charles
Published: November 2008

An action of a group, G, on a surface, F, consists of a homomorphism

ø: G → Homeo (F).

We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with ø(g) orientation-preserving for all g ε G. In addition we will consider only effective (ø is injective) free actions. Free means that ø(g) is fixed-point-free for all g ε G, g ≠ 1. This paper addresses the classification of such actions.
Generalized adjunction and applications
Authors: Ionescu Paltin
Published: November 2008

The linear system |K + C| ‘adjoint’ to a curve C on a projective surface was studied by the classical Italian geometers. The adjoint system to a hyperplane section H of smooth projective surface was investigated systematically, in modern terms, by Sommese [22] and Van de Ven [26]. The map associated to the linear system |K + (r−1)H|, where H is a hyperplane section of a smooth variety of arbitrary dimension r, was used to classify submanifolds of ℙn with ‘small invariants’ (e.g. degree, sectional genus, etc.); see [10]. On the other hand, Sommese [23, 24, 25] studied adjoint systems to a smooth ample divisor H on a smooth threefold X and obtained, as applications, many interesting results about the pair (X, H). As noticed independently by several authors (see e.g. [17], [4], [11]) the appearance of Mori's deep contribution [20] (see also [21]) put the subject of adjunction in a new perspective. Accordingly, the present paper–which relies heavily on Mori's results and on the contraction theorem due to Kawamata-Shokurov (see [14])–contains a systematical study of various adjoint systems to an ample (possibly non-effective) divisor on a manifold of arbitrary dimension. More precisely, the main result (which is contained in Section 1) gives the precise description of polarized pairs (X, H), where X is a complex projective mani–fold of dimension r and H an ample divisor on it (not necessarily effective), such that Kx + iH is not semiample (respectively ample) for 1 ≤ i = r + 1, r, r − 1, r − 2 (respectively i = r + 1, r, r − 1).
Lindelöf locales and realcompactness
Authors: Madden J. , Vermeer J.
Published: November 2008

We show that a locale possesses the localic analogue of the property of realcompactness if and only if it is regular Lindelöf. Thus, the localic version of the Hewitt real-compactification, originally defined by G.Reynolds using σ-frames, is the regular Lindelöf reflection. An immediate consequence is that a space is realcompact if and only if it is the point space of a regular Lindelöf local (3·2). We point out a nice analogy between a theorem of Reynolds and Stone's classical representation theorem for boolean algebras. Finally, we show that the quasi-F cover of a compact Hausdorff space is the Stone–čech compactifications of the smallest dense Lindelöf sublocale.
A lower bound for the spectrum of a one-dimensional pseudo-differential operator
Authors: Wong M. W.
Published: November 2008

In a 1928 paper [1], Hardy and Littlewood published the following inequality which is valid for all non-negative measurable functions ƒ and g on ( − ∞, ∞):

where 1 < p, q < ∞, 0 < λ < 1, l/p + 1/q + λ = 2 and Cλp, q depends only on λ, p, q; ‖ƒ‖p and ‖g‖q are the Lp and Lq norms of ƒ and g respectively. See also p. 288 of the monograph [2] by Hardy, Littlewood and Pólya for a discussion of this inequality and related matters.
The Markov branching process with density-independent catastrophes I. Behaviour of extinction probabilities
Authors: Pakes Anthony G.
Published: November 2008

Let (Xt: t ≥ 0) be the Markov branching process (MBP) with a density independent catastrophe component. It is denned to be the Feller process on the non-negative integers having the generator

Here {pj} is the offspring distribution which satisfies p1 = 0 and p0 < 1, ρ is the per capita birth rate, κ is the rate of occurrence of catastrophe events, {δj: j ≥ 0} is the decrement distribution and . Thus Xt can be interpreted as the size of a population in which individuals reproduce according to the rules of a MBP – see Athreya and Ney[1], chap, III – and where there is an external and independent Poisson process of catastrophe events, κ per unit time, and if j < i each such event reduces the population size by j with probability δj. Usually we assume that δ0 = 0 on the basis that a catastrophe always reduces the population size. Let f(s) = Σpjsj and assume that . This ensures that the MBP obtained by setting κ = 0 is regular ([1], p. 105) and hence (Xt) is the unique Markov process corresponding to the above generator when κ > 0.
Some groups which classify knots
Authors: Zimmermann B.
Published: November 2008

Groups associated to a knot in S3 which classify the knot have been constructed by Conway and Gordon [4], Simon [12] and Whitten[16]; see also [1] and [19] for certain special classes of knots. In this note we show that for a knot K in S3 of the groups π1(S3/K)/〈malb〉 classify the knot; here m resp. l denote a meridian resp. longitude of the knot and 〈〉 denotes normal closure. This is based on Thurston's orbifold geometrization theorem [13–15] and the following result (see also [8, 19]):

Theorem 1. Let O1 and O2 be good closed irreducible 3-orbifolds which possess a decomposition into geometric pieces (along Euclidean 2-suborbifolds, see [2, 15]) and have infinite (orbifold-) fundamental group. Then O1 and O2 are diffeomorphic (as orbifolds) if and only if π1 O1 and π1 02 are isomorphic.
Idealizations of maximal Buchsbaum modules over a Buchsbaum ring
Authors: Yamagishi Kikumichi
Published: November 2008

Throughout this paper A denotes a Noetherian local ring with maximal ideal m and M denotes a finitely generated A-module. Moreover stands for the ith local cohomology functor with respect to m (cf. [10]). We refer to [15] for unexplained terminolog.
The reduction of a pair of singular integral equations
Authors: Porter D.
Published: November 2008

A method is derived for converting a pair of coupled singular integral equations of a certain form into a single equation of the same (Cauchy-separable) type. Reduction methods for systems of singular integral equations are generally directed towards the construction of equivalent Fredholm equations. Preservation of the singular nature of the kernel in the reduction process permits the powerful techniques associated with Cauchy kernels to be used in seeking closed solutions of the original pair.

The example given, derived previously from a problem in wave diffraction theory, illustrates many aspects of the method.
Existentially closed central extensions of locally finite p-groups
Authors: Leinen Felix , Phillips Richard E.
Published: November 2008

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we let

where ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.
Envelopes and characteristics
Authors: Bruce J. W.
Published: November 2008

Envelopes of hypersurfaces arise in many different geometric situations. For example, the canal surfaces associated with a space curve can be obtained as the envelope of spheres of a fixed radius centred on that curve. (Other examples can be found in [11], chapter II and [4], chapter 5). In what follows we shall be entirely concerned with the local structure of such envelopes. So essentially we have a smooth map germ with 0 a regular value of the restriction of F to . For near 0 we have a smooth hypersurface near , where . The envelope of this family of hypersurfaces is obtained by eliminating t from the equations . Moreover, it can be identified with the discriminant of F viewed as an unfolding, by the x variables, of the function germ . This observation, together with standard results on versal unfoldings of functions, allows one to determine the local structure of many ‘generic’ geometric envelopes. See [2] for details.
A prime strongly positive amphicheiral knot which is not slice
Authors: Flapan Erica
Published: November 2008

We begin by giving several definitions. A knot K in S3 is said to be amphicheiral if there is an orientation-reversing diffeomorphism h of S3 which leaves K setwise invariant. Suppose, in addition, that K is given an orientation. Then K is said to be positive amphicheiral if h preserves the orientation of K. If, in addition, the diffeomorphism h is an involution then K is strongly positive amphicheiral. Finally, we say a knot is slice if it bounds a smooth disc in B4. In this note we shall give a smooth example of a prime strongly positive amphicheiral knot which is not slice.
Two notes on ideal-transforms
Authors: Katz Daniel , Ratliff Louis J.
Published: November 2008

The first note gives two new characterization of the ideal-transform T(I) of a finitely generated regular ideal I in a large class of rings. Specifically, if b is a regular element in I, then there exists a regular element c ∈ I and a multiplicatively closed set S of regular elements in R such that T(I) = T((b, c)R) = Rb ∩ Rc = Rb ∩ Rs, so T(I) is the ideal-transform of an ideal generated by two elements, and every ring of the form Rb ∩ Rs is an ideal-transform. The second theorem shows that if T(I) is integrally closed, then it is a Krull ring. As an application of these results we strengthen some known results concerning when certain ideal-transforms of the Rees ring R(R, I) are finite or integral extension rings of R(R, I).
Torsion classes in the cohomology of congruence subgroups
Authors: Arlettaz Dominique
Published: November 2008

For any prime number p, let Γn, p denote the congruence subgroup of SLn(ℤ) of level p, i.e. the kernel of the surjective homomorphism fp: SLn(ℤ) → SLn(p) induced by the reduction mod p (Fp is the field with p elements). We define

using upper left inclusions Γn, p ↪ Γn+1, p. Recall that the groups Γn, p are homology stable with M-coefficients, for instance if M = ℚ, ℤ[1/p], or ℤ/q with q prime and q ╪ p: Hi(Γn, p; M) ≅ Hi(Γp; M) for n ≥ 2i + 5 from [7] (but the homology stability fails if M = ℤ or ℤ/p).
The Jacobson radical of a band ring
Authors: Munn W. D.
Published: November 2008

A band is a semigroup in which every element is idempotent. In this note we give an explicit description of the Jacobson radical of the semigroup ring of a band over a ring with unity. It is shown, further, that this radical is nil if and only if the Jacobson radical of the coefficient ring is nil. For the particular case of a normal band (see below for the definition) the Jacobson radical of the band ring is nilpotent if and only if the Jacobson radical of the coefficient ring is nilpotent; but this result does not extend to arbitrary bands.
Perturbation of functions by the paths of a Lévy process
Authors: Evans Steven N.
Published: November 2008

In a recent paper Mountford [4] showed, using an ingenious probabilistic argument, that if X is a real-valued stable process with index α < 1 and f: [0, ∞) → ℝ is a non-constant continuous function, then

where we use the notation |A| for the Lebesgue measure of a Lebesgue measurable set A ⊂ ℝ. The argument in [4] appears to make strong use of the strict scaling properties of X and the ‘intermediate value’ property of f.
The Alexander module of a knotted theta-curve
Authors: Litherland Rick
Published: November 2008

Let K be a knotted theta-curve with exterior X, and let ∂_X be one of the two pieces into which ∂X is divided by the meridians of the edges of K. Let X be the universal abelian cover of X. Then is a module over the group ring of H1(X); i.e. over . We call this the Alexander module of K, and denote it by A(K). This, rather than H1(X), seems to be the analogue of the Alexander module of a classical knot; it is a torsion module of deficiency 0. Moreover, it is not an invariant of X alone.
Almost f-algebras and d-algebras
Authors: Bernau S. J. , Huijsmans C. B.
Published: November 2008

In this paper we study the classes of almost f-algebras and d-algebras. Apart from a survey of known properties we present some ‘new’ properties of almost f-algebras and d-algebras and we consider their connection with f-algebras. To be more precise, we show, among other things, in an elementary intrinsic manner, that every Archimedean almost f-algebra is commutative. This result is a considerable improvement upon the fact that every Archimedean f-algebra is commutative. Furthermore, we give a description of the set of nilpotent elements in both an Archimedean d-algebra and an Archimedean almost f-algebra.
Representing types in Orlicz and Lorentz sequence spaces
Authors: Bastero Jesús , Raynaud Yves
Published: November 2008

The aim of this paper is to give a representation for the types in some stable Banach sequence spaces, namely in the Orlicz, Lorentz and dual of Lorentz sequence spaces. We also find a characterization for the Lorentz sequence spaces whose class of weakly-null types is locally compact for the topology of uniform convergence on bounded subsets.
Factorization and unbounded approximate identities in Banach algebras
Authors: Dixon P. G.
Published: November 2008

Cohen's Factorization Theorem says, in its basic form, that if A is a Banach algebra with a bounded left approximate identity, then every element x ∈ A may be written as a product x = ay for some a, y ∈ A. Such is the beauty and importance of this result that much interest attaches to the question of whether the hypothesis of a bounded left approximate identity can be weakened, or whether a converse result exists. This paper contributes to the study of that question.
Function spectra
Authors: Elmendorf A. D.
Published: November 2008

Boardman's stable category (see [5]) is a closed category ([4], VII·7), and in the best of all possible worlds, the category of spectra underlying the stable category would be closed as well; this would make life considerably easier for those doing calculations in stable homotopy theory. Unfortunately none of the categories of spectra introduced to date are closed; only S, the category introduced in [2], is even symmetric monoidal. The problem with making S closed is that it comes equipped with an augmentation to I, the category of universes and linear isometries (called Un in [2]), which preserves the symmetric monoidal structure. Since I is not closed, this makes it difficult to see how S might be closed.
Minimal atlases on 3-manifolds
Authors: Gómez-Larrañaga J. C. , González-Acuña F. , Hoste Jim
Published: November 2008

In this paper we investigate the minimal number of charts (spaces homeomorphic to open subsets of ℝ3) needed to cover a closed 3-manifold M3. We prove that this number is two if the Bockstein βω1(M3)∈H2(M3;ℤ) of the first Stiefel-Whitney class of M3 is zero and three if it is not. We state several properties equivalent to βω1(M3) = 0, for example the condition of being covered by two orientable subspaces, and the condition that all torsion elements of H1(M3;ℤ) be represented by orientation-preserving loops. We also show that the non-orientable 3-manifolds which can be covered with two charts are precisely those manifolds which can be described as sewn-up r-link exteriors. These are manifolds obtained by removing from S3 the interiors of two disjoint handlebodies of genus r and then identifying the two boundary components by a homeomorphism.
Essentially unbounded chains in compact sets
Authors: Fremlin D. H. , Kunen K.
Published: November 2008

We discuss the possible cofinalities of ⊆ *-chains in ℕ which are ⊆ *-unbounded in their topological closures.

1. The problem. Throughout this paper, the power set ℕ of the set ℕ of natural numbers will be given its usual compact metrizable topology corresponding to the product topology of {0,1}N. We say that a ⊆ * b if a/b is finite.
Special values of the hypergeometric series
Authors: Joyce G. S. , Zucker I. J.
Published: November 2008

Recently, several authors [1, 3, 9] have investigated the algebraic and transcendental values of the hypergeometric series

for rational parameters a, b, c and algebraic arguments z. This work has led to some interesting new identities such as

and

where Γ(x) denotes the gamma function.
Homomorphisms of two-dimensional linear groups over Laurent polynomial rings and Gaussian domains
Authors: Chen Yu
Published: November 2008

Let GL2(R) be the general linear group of 2 × 2 invertible matrices in M2(R) over a commutative ring R with 1 and SL2(R) be the special linear group consisting of 2 × 2 matrices over R with determinant 1. In this paper we determine the homomorphisms from GL2 and SL2, as well as their projective groups, over Laurent polynomial rings to those groups over Gaussian domains, i.e. unique factorization domains (cf. Theorems 1, 2, 3 below). We also consider more generally the homomorphisms of non-projective groups over commutative rings containing a field which are generated by their units (cf. Theorems 4 and 5). So far the homomorphisms of two-dimensional linear groups over commutative rings have only been studied in some specific cases. Landin and Reiner[7] obtained the automorphisms of GL2(R), where R is a Euclidean domain generated by its units. When R is a type of generalized Euclidean domain with a degree function and with units of R and 0 forming a field, Cohn[3] described the automorphisms of GL2(R). Later, Cohn[4] applied his methods to the case of certain rings of quadratic integers. Dull[6] has considered the automorphisms of GL2(R) and SL2(R), along with their projective groups, provided that R is a GE-ring and 2 is a unit in R. McDonald [9] examined the automorphisms of GL2(R) when R has a large unit group. The most recent work of which we are aware is that of Li and Ren[8] where the automorphisms of E2(R) and GE2(R) were determined for any commutative ring R in which 2, 3 and 5 are units.
Tauberian theorems for general power series methods
Authors: Kiesel R. , Stadtmüller U.
Published: November 2008

Let us assume throughout that (pn) denotes a sequence of reals which satisfies

For real sequences (sn) with increments an = sn – sn−1 for n ≥ 0,(where s−1 = 0), we consider the power seriesmethod of summability (P), where we say

The power series methods (P) containthe so-called (Jp)-methods (R = 1)and the Borel-type methods (Bp)(R = ∞). We consider only regular (P)-methods, i.e. sn → s implies sn → s(P). By theorem 5 in [5], p.49, we have regularity if and only if

Here we are interested in the converse conclusion, namely sn → s(P) implies sn → s, which can only be validiffurther conditions, so-called Tauberian conditions are satisfied by (sn). These so-called Tauberian theorems for power series methods have a long history; see e.g. the books [5, 14, 23], and they found new attentionrecently in the papers [6, 18, 19, 20] and [8, 9, 10, 11, 12]. The latter papers contain certain o- Tauberian theorems for all power series methods in question and O-Tauberian theorems, if the weight sequence (pn) can be interpolated by alogarithmico-exponential function g(·)(see e.g. [4]), i.e.
A cohomological characterization of amenable actions
Authors: Anantharaman-Delaroche C.
Published: November 2008

We give a new characterization of amenability for dynamical systems, in cohomological terms, which generalizes the classical characterization of amenable locally compact groups stated by Johnson.
Asymptotic distributions of weighted pontograms under contiguous alternatives
Authors: Szyszkowicz Barbara
Published: November 2008

Let {N(x), x ≥ 0} be a non-homogeneous, also called non-stationary, Poisson process with density function λ(x), x ≥ 0. We consider the problem of testing the null hypothesis of λ(x) having a constant value against the alternative that λ(x) is a function of x.
Reduction modulo pn of p-adic subanalytic sets
Authors: Veys Willem
Published: November 2008

Let ℚp and ℤp respectively denote the p-adic numbers and the p-adic integers for a fixed prime number p. For any subset Y of and n ∈ ℕ we denote by Nn(Y) the cardinality of the image of Y under the natural map . (Thus we have Nn(Y)≤ pnr.)
Hausdorff measures, Hölder continuous maps and self-similar fractals
Authors: Martin Miguel-Angel , Mattila Pertti
Published: November 2008

Let f: A → ℝn be Hölder continuous with exponent α, 0 < α ≼ 1, where A ⊂ ℝm has finite m-dimensional Lebesgue measure. Then, as is easy to see and well-known, the s-dimensional Hausdorif measure HS(fA) is finite for s = m/α. Many fractal-type sets fA also have positive Hs measure. This is so for example if m = 1 and f is a natural parametrization of the Koch snow flake curve in ℝ2. Then s = log 4/log 3 and α = log 3/log 4. In this paper we study the question of what s-dimensional sets in can intersect some image fA in a set of positive Hs measure where A ⊂ ℝm and f: A → ℝn is (m/s)-Hölder continuous. In Theorem 3·3 we give a general density result for such Holder surfacesfA which implies for example that Hs(E fA) = 0 for any totally disconnected self-similar set. E in this situation. In Theorem 32 we shall first show that such fA has positive s-dimensional lower density H8 almost everywhere.
Cohomology with coefficients in symmetric cat-groups. An extension of Eilenberg–MacLane's classification theorem
Authors: Bullejos M. , Carrasco P. , Cegarra A. M.
Published: November 2008

In this paper we use Takeuchy–Ulbrich's cohomology of complexes of categories with abelian group structure to introduce a cohomology theory for simplicial sets, or topological spaces, with coefficients in symmetric cat-groups . This cohomology is the usual one when abelian groups are taken as coefficients, and the main topological significance of this cohomology is the fact that it is equivalent to the reduced cohomology theory defined by a Ω-spectrum, {}, canonically associated to . We use the spaces to prove that symmetric cat-groups model all homotopy type of spaces X with Πi(X) = 0 for all i ╪ n, n + 1 and n ≥ 3, and then we extend Eilenberg–MacLane's classification theorem to those spaces: .
Locating the radical of a triangular operator algebra
Authors: Mastrangelo Laura , Muhly Paul S. , Solel Baruch
Published: November 2008

Our primary objective is to give necessary and sufficient conditions for a triangular subalgebra of a groupoid C-algebra to be semisimple, i.e. to have vanishing Jacobson radical. If, in addition, the subalgebra is the analytic subalgebra determined by a real-valued cocycle on the groupoid, then we can give an explicit description of the radical in terms of the cocycle. As a consequence of this analysis, we are able to determine when certain analytic crossed products are semisimple.
Spaces of operators between Fréchet spaces
Authors: Bonet José , Lindström Mikael
Published: November 2008

Motivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson–Nissenzweig theorem to Fréchet spaces, we investigate pairs of Fréchet spaces (E,F) such that every continuous linear map fromEintoFis Montel, i.e. it maps bounded subsets ofEinto relatively compact subsets ofF. As a consequence of our results we characterize pairs of Köthe echelon spaces (E,F) such that the space of Montel operators fromEintoFis complemented in the space of all continuous linear maps fromEintoF.
Maximal inequalities of Kahane–Khintchine's type in Orlicz spaces
Authors: Peškir Goran
Published: November 2008

Several maximal inequalities of Kahane–Khintchine's type in certain Orlicz spaces are proved. The method relies upon Lévy's inequality and the technique established in [14] which is obtained by Haagerup–Young–Stechkin's best possible constants in the classical Khintchine inequalities. Moreover by using Donsker's invariance principle it is shown that the numerical constant in the inequality deduced by the method presented is nearly optimal: If is a Bernoulli sequence, and ‖ · ‖ψ denotes the Orlicz norm induced by the function then the following inequality is satisfied:

for all a1,…, an and all n ≥ 1, and the best possible numerical constant which can take the place of lies in the interval ]. Sharp estimates of this type are also deduced for some other maximal inequalities in Orlicz spaces discovered in this paper.
An O-Tauberian theorem and a high indices theorem for power series methods of summability
Authors: Borwein David , Kratz Werner
Published: November 2008

We improve known Tauberian results concerning the power series method of summability Jp based on the sequence {pn} by removing the condition that pn be asymptotically logarithmico-exponential. We also prove an entirely new Tauberian result for rapidly decreasing pn.
Period-multiplying cascades for diffeomorphisms of the disc
Authors: Gambaudo Jean-Marc , Guaschi John , Hall Toby
Published: November 2008

It is a well-known result in one-dimensional dynamics that if a continuous map of the interval has positive topological entropy, then it has a periodic orbit of period 2i for each integer i ≥ 0 [15] (see also [12]). In fact, one can say rather more: such a map has a sequence of periodic orbits (P)i ≥ 0 with per (Pi) = 2i which form a period-doubling cascade (that is, whose points are ordered and permuted in the way which would occur had the orbits been created in a sequence of period-doubling bifurcations starting from a single fixed point). This result reflects the central role played by period-doubling in transitions to positive entropy in a one-dimensional setting. In this paper we prove an analogous result for positive-entropy orientation-preserving diffeomorphisms of the disc. Using the notion [9] of a two-dimensional cascade, we shall show that such diffeomorphisms always have infinitely many ‘zero-entropy’ cascades of periodic orbits (including a period-doubling cascade, though this need not begin from a fixed point).
Examples in non-commutative projective geometry
Authors: Stafford J. T. , Zhang J. J.
Published: November 2008

Let A = k ⊕ ⊕n ≥ 1An connected graded, Noetherian algebra over a fixed, central field k (formal definitions will be given in Section 1 but, for the most part, are standard). If A were commutative, then the natural way to study A and its representations would be to pass to the associated projective variety and use the power of projective algebraic geometry. It has become clear over the last few years that the same basic idea is powerful for non-commutative algebras; see, for example, [ATV1, 2], [AV], [Sm], [SS] or [TV] for some of the more significant applications. This suggests that it would be profitable to develop a general theory of ‘non-commutative projective geometry’ and the foundations for such a theory have been laid down in the companion paper [AZ]. The results proved there raise a number of questions and the aim of this paper is to provide negative answers to several of these.
A note on minors of uncountable graphs
Authors: Komjáth Péter
Published: November 2008

If λ > ω then there are 2λ graphs of cardinal λ none of them being a minor of another.
The convergence of polynomial expansions of positive harmonic functions
Authors: Armitage D. H.
Published: November 2008

Let B(r) denote the open ball of radius r centred at the origin 0 of the Euclidean space ℝN, where N ≥ 2. It is well known that if h is harmonic in B(1), then there exist homogeneous harmonic polynomials Hj of degree j in ℝN such that converges absolutely and locally uniformly to h in B(1) (see, e.g. Brelot[1], Appendice). Further, this series is unique and each Hj is the sum of all the monomial terms of degree j in the multiple Taylor series of h centred at 0. We call the polynomial expansion of h.
Equivariant shape theory
Authors: Čerin Zvonko
Published: November 2008

Equivariant shape theory is an improvement of equivariant homotopy theory which could be regarded as an equivariant version of Borsuk's shape theory. The main result in this paper is a description of the equivariant shape category ShG whose objects are equivariant spaces or G-spaces, i.e. topological spaces endowed with an action of a given topological group G, and whose morphisms are equivariant homotopy or G-homotopy classes of families of multi-valued functions which we call equivariant multi-nets or G-multi-nets. Previously equivariant shape theories have been described only under the assumptions that the group G is either finite or compact. We also study classes of G-spaces on which equivariant shape and equivariant homotopy coincide, look for conditions under which a G-map f: X → Y is an equivariant shape equivalence, and give some characterizations of G-spaces with trivial equivariant shape.
McLain groups over arbitrary rings and orderings
Authors: Droste Manfred , Göbel Rüdiger
Published: November 2008

In 1954, McLain [M] applied some well-known arguments of linear algebra on triangular matrices to establish the existence of characteristically simple, locally finitep-groups, now known as McLain groups [Rob, pp. 347–349]. His groups, having a trivial centre, illustrated sharply the difference between finite and locally finitep-groups. The construction of McLain groups depends on the dense linear ordering (ℚ,≤) and a fieldFpofpelements. It was immediately clear that the parametersFp, ℚ of the McLain groupG(Fp, ℚ) could be replaced by other linearly ordered, dense setsSand by other fieldsFwithout doing much harm to the construction. IfFhas characteristic 0, thenG(F, S) is still locally nilpotent but torsion-free. Wilson [W] investigatedG(Fp, S) for other orderings and Roseblade[R] deeply studied the automorphism group AutG(Fp, S) in his dissertation at Cambridge in 1963.
Zeros of linear combinations of orthogonal polynomials
Authors: Peherstorfer Franz
Published: November 2008

Let ψ be a distribution function on [−1,1] from the Szegö-class, which contains in particular all Jacobi weights, and let (pn) be the monic polynomials orthogonal with respect to dψ. Let m(n)∈ℕ, n∈ℕ, be non-decreasing with limn → ∞ (n − m(n)) = ∞, l(n)∈ℕ with 0 ≤ l(n) ≤ m(n), and μj, n ∈ℝ for j = 0, …, m(n), n∈ℕ. It is shown that for each sufficiently large n, has n−l(n) simple zeros in (−1, 1)and l(n) zeros in ℂ\[−1,1] if for n ≥ n0, has m(n) − l(n) zeros in the disc |z| ≤ r < 1, l(n) zeros outside of the disc |z| ≥ R > 1 and where q > 2 max {r, 1/R}. If m(n) is constant for n ≥ n0 then the statement holds even for such polynomials (pn) orthogonal with respect to a distribution dψ satisfying the weak assumption ψ′ > 0 a.e. on [−1, 1]. For linear combinations of polynomials orthogonal on the unit circle corresponding results are derived.
The equality of 3-manifold invariants
Authors: Barrett John W. , Westbury Bruce W.
Published: November 2008

The invariants of 3-manifolds defined by Kuperberg for involutory Hopf algebras and those defined by the authors for spherical Hopf algebras are the same for Hopf algebras on which they are both defined.
Meromorphic extension of the Selberg zeta function for Kleinian groups via thermodynamic formalism
Authors: Rocha André
Published: November 2008

We prove the existence of a piecewise analytic expanding map associated to certain Kleinian groups without parabolics acting in the 3-dimensional hyperbolic space. These groups have a fundamental domain ℛ with the property that the geodesic planes containing each face are part of the tesselation. We use this map together with the methods of thermodynamic formalism to give another proof that the Selberg zeta function for such groups has a meromorphic extension to ℂ.
Multiplicities in graded rings II: integral equivalence and the Buchsbaum–Rim multiplicity
Authors: Kirby D. , Rees D.
Published: November 2008

While this paper is principally a continuation of [5], with as its object the application of sections 6 and 7 of that paper to obtain results related to the Buchsbaum–Rim multiplicity, it also has connections with [8] which are the subject of the first of the four sections. These concern integral equivalence of finitely generated R-modules. where R is an arbitrary noetherian ring. We therefore introduce a finitely generated R-module M and relate to it a short exact sequence (s.e.s.),

where F is a free module generated by m elements u1,…, um, and L is generated by elements yj, (j = 1, …, n), of F. We identify the elements u1, …, um with a set of indeterminates X1, …, Xm, and F with the R-module S1 of elements of degree 1 of the graded ring S = R[X1, …, Xm].
On the geometry of simple germs of co-rank 1 maps from ℝ3 to ℝ3
Authors: Marar W. L. , Tari F.
Published: November 2008

In this paper we investigate the geometry of simple germs of co-rank 1 maps from ℝ3 to ℝ3. Those of co-dimension 1 have already been dealt with by several authors. In [2], V. I. Arnold considered the problem of evolution of galaxies. For a medium of non-interacting particles in ℝ3 with an initial velocity distribution v = v(x) (and a positive density distribution), the initial motion of particles defines a time-dependent map gt: ℝ3 → ℝ3 given by gt(x) = x + tv(x). At some time t singularities occur and the critical values of gi correspond to points of condensation of particles. Arnold assumed the vector field v is a gradient, that is v = ∇S, for some potential S. J. W. Bruce generalized these results in [4] by dropping the assumption on the velocity distribution and studied generic 1-parameter families of map germs F: ℝ3, 0 → ℝ3, 0.
Converses for the Dodds–Fremlin and Kalton–Saab theorems
Authors: Wickstead A. W.
Published: November 2008

The two theorems in the title give conditions on Banach lattices E and F under which a positive operator from E into F, dominated by another positive operator with some property, must also have that property. The Dodds-Fremlin theorem says that this is true for compactness provided both E′ and F have order continuous norms, whilst the Kalton–Saab theorem establishes such a result for Dunford–Pettis operators provided F has an order continuous norm. These results were originally provided, in their full generality, in [3] and [5], respectively, whilst very readable proofs may be found in chapter 5 of [2] or §3·7 of [6].
Symmetries, conservation laws and variational principles for vector field theories†
Authors: Anderson Ian M. , Pohjanpelto Juha
Published: November 2008

The interplay between symmetries, conservation laws, and variational principles is a rich and varied one and extends well beyond the classical Noether's theorem. Recall that Noether's first theorem asserts that to every r dimensional Lie algebra of (generalized) symmetries of a variational problem there are r conserved quantities for the corresponding Euler-Lagrange equations. Noether's second theorem asserts that infinite dimensional symmetry algebras (depending upon arbitrary functions of all the independent variables) lead to differential identities for the Euler-Lagrange equations.
Towards a theory of R-modules modulo a Serre category
Authors: Kirby David
Published: November 2008

This note is a brief excursion into a new theory of modules over a commutative ring R modulo a Serre subcategory S of the category of R-modules, in the sense that the modules of S are regarded as trivial. As a demonstration of the theory we have chosen to extend the primary decomposition theorem for submodules of a Noetherian .R-module from the familiar case of S trivial (i.e. the only R-module of S is the zero module) to the general case.
Weak compactness in constructive spaces
Authors: Vermeulen J. J. C.
Published: November 2008

We introduce a constructively weak variant of compactness for locales as a supplement to weak closure, a notion which has featured in the constructive formulation of some recent results in locale theory.
Harmonic conjugation in L1 on compact abelian groups
Authors: Asmar Nakhl , Watson Saleem , Watson Saleem
Published: November 2008

Let G denote a compact connected abelian group with character group and normalized Haar measure . As a consequence of the duality theorems (11, theorem 2518), is torsion-free and hence can be ordered. That is, there is a sub-semigroup P of such that
Symmetry characterizations of certain distributions, 1
Authors: Baxter Martin , Williams David
Published: November 2008

Certain interesting distributions are characterized by two or more symmetry properties, and it is a challenge to link these properties in an effective way. Dynkin's advice Discuss the simplest case first is always the best, and here we follow it (and avoid technical jargon) by discussing in detail just one concrete example, which concerns a discounted version of the arc-sine law. Theorem 1 B gives the symmetry properties for this case, and Theorem 1 A shows how they may be exploited to obtain an asymptotic result which we find rather surprising. Section 5 points to one of the generalizations which we shall examine in a sequel, and describes the natural formulation of the strange symmetry property which we first meet at (16b). (The sequel will be in many ways very different from this paper, but will share with it the fact that its results are not those which we originally conjectured.) In Sections 6 and 7 we consider some of the bizarre numerical analysis associated with the current problem.
The Cohn localization of the free group ring
Authors: Farber M. , Vogel P.
Published: November 2008

In [1] P. Cohn suggested the construction of a localization of a ring with respect to a class of square matrices. Let us briefly recall the definitions.
On sign-representable matroids
Authors: Oxley James , Whittle Geoff
Published: November 2008

A matroid M will be called sign-representable if, for every basis B of M, there is a (0, 1, −l)-matrix [Ir|y] representing M over ℚ in which the first r columns correspond to the members of B. The class of sign-representable matroids, which is closely related to the important class of regular matroids, is easily seen to be closed under both duality and the taking of minors. This paper proves several characterizations of the class, including a constructive one, and shows that the excluded minors for the class are U2, 5, U3, 5, the Fano matroid and its dual, and the rank-3 whirl.
On Ingham's Tauberian theorem for partitions
Authors: Auluck F. C. , Haselgrove C. B.
Published: November 2008

The object of this paper is to extend the range of validity of Ingham's Tauberian theorem for partitions (2). Ingham's theorem deals with many types of partitions, but it cannot be used in some cases of importance. With a slight modification of Ingham's notation we define

where P(u) is the number of solutions of

in integers ni ≤ 0, and the λi are a given set of numbers, not necessarily integers, such that 0 < λ1 < λ2 <.… If N(u), the number of λi not exceeding u, is given by

where B > 0, β > 0, and as u → ∞

then, according to Ingham's theorem, when u → ∞

where
Some generalizations of two-point expansions
Authors: Macintyre Sheila Scott
Published: November 2008

Abel's series(1)

may be regarded as a generalization of the Taylor expansion

This note generalizes the two-point series of Lidstone and Whittaker (see (9)) in a similar way. Alternatively, the series discussed might be regarded as generalizations of Abel's series.