bluuebunny/crossref_metadata_2025 huggingface dataset:
Determination of the semi-nice dimensions
Authors: Wall C. T. C.
Published: November 2008

As the culmination of a notable sequence of papers, Mather [6] gave a necessary and sufficient condition that stable maps were dense in C∞(N, P): it is that the dimensions n and p satisfy the condition n <σ(n, p), where σ(n, p) is the codimension (in a sufficiently large jet space) of the set of jets in Jr(n, p) whose classification (for ℋ-equivalence) ‘involves moduli’.
A note on annihilator Banach algebras
Authors: Giotopoulos S.
Published: November 2008

The purpose of this note is to present simple proofs of the basic results concerning semi-simple annihilator Banach algebras as well as new results (for terminology notation and the standard approach see [2]).
Limit theorems for random compact sets in Banach space
Authors: Puri Madan L. , Ralescu Dan A.
Published: November 2008

The concept of random set, though vaguely known for a long time (possibly since Buffon's needle problem), did not develop until Robbins [25, 26] provided for the first time a solid mathematical formulation of this concept and investigated relationships between random sets and geometric probabilities. Later on (in a different context) this concept gave rise to a more general concept of set-valued function in topology, and applications were also found in several areas such as economics (see, for example, Aumann[3] and Debreu[10]) and control theory (see, for example, Hermes [13]), among others. Recently in two independent formulations, D. G. Kendall [17] and Matheron[21] provided a comprehensive mathematical theory of this concept influenced by the geometric probability point of view. Actually, much of the research in this area falls under the heading of stochastic geometry (see, for example, M. G. Kendall and P. A. P. Moran [18]). The D. G. Kendall and Matheron theories have been compared and ‘reconciled’ by Ripley [24]. In the past few years random sets have been investigated as extensions of random variables and random vectors, and in this framework the problems of deriving limit theorems have received a great deal of attention. This approach is benefiting greatly from probability results in Banach spaces.
On ( h(n)) summability methods
Authors: Kuttner B. , Sukla I. L.
Published: November 2008

In 1967 Segal introduced the Dirichlet convolution (, h(n)), generalizing a method of Ingham developed in studies on the Prime Number Theorem. In this paper we establish necessary and sufficient conditions on the sequence h(n) in order that the convolution method (, h(n)) be conservative. Further conditions are established for the method to be absolutely conservative.
On the facial structure of the unit balls in a GL-space and its dual
Authors: Edwards C. M. , Rüttimann G. T.
Published: November 2008

In the early sixties Effros[9] and Prosser[14] studied, in independent work, the duality of the faces of the positive cones in a von Neumann algebra and its predual space. In an implicit way, this work was generalized to certain ordered Banach spaces in papers of Alfsen and Shultz [3] in the seventies, the duality being given in terms of faces of the base of the cone in a base norm space and the faces of the positive cone of the dual space. The present paper is concerned with the facial structure of the unit balls in an ordered Banach space and its dual as well as the duality that reigns between these structures. Specifically, the main results concern the sets of norm-exposed and norm-semi-exposed faces of the unit ball V1 in a GL-space or complete base norm space V and the sets of weak*-exposed and weak*-semi-exposed faces of the unit ball in its dual space V* which forms a unital GM-space or a complete order unit space.
Random variables with unsymmetrical linear regressions
Authors: Kingman J. F. C.
Published: November 2008

In § 33 of [2], Professor Williams asks whether there are L1 random variables† X, Y, Z (not identically zero) such that
On the non-realizability of certain 3-manifolds by Dehn surgery
Authors: Boyer Steven
Published: November 2008

We construct examples of compact 3-manifolds which have finite cyclic first homology groups but which are not realizable by Dehn surgery on a knot in a homotopy 3-sphere. A necessary condition for a 3-manifold M to be the result of such a surgery is that π1( M) be normally generated by a single element (corresponding to a meridian of the knot), that is π1(M) should have weight 1. As we do not expect this to hold in general for the free product of non-trivial groups we are naturally led to consider connected sums. For instance, if G denotes the binary icosahedral group, it is known that ℤ* G has weight greater than 1 (see [2]). Thus, if H is the Poincaré sphere and M is any 3-manifold with first homology ℤ, M # H is not the result of surgery on a knot in a homotopy 3-sphere. Unfortunately this purely group-theoretic approach is too difficult in general owing to the intractability of the weight 1 condition (see § 9 of [4]). Thus we adopt a strategy involving an interplay between group theory and geometry. Our method is based on the following:
Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups
Authors: Lau Anthony To-Ming
Published: November 2008

Let G be a topological semigroup, i.e. G is a semigroup with a Hausdorff topology such that the map (a, b) → a.b from G × G into G is continuous when G × G has the product topology. Let C(G) denote the space of complex-valued bounded continuous functions on G with the supremum norm. Let LUC (G) denote the space of bounded left uniformly continuous complex-valued functions on G i.e. all f ε C(G) such that the map a → laf of G into C(G) is continuous when C(G) has a norm topology, where (laf )(x) = f (ax) (a, x ε G). Then LUC (G) is a closed subalgebra of C(G) invariant under translations. Furthermore, if m ε LUC (G)*, f ε LUC (G), then the function

is also in LUC (G). Hence we may define a product

for n, m ε LUC(G)*. LUC (G)* with this product is a Banach algebra. Furthermore, ʘ is precisely the restriction of the Arens product defined on the second conjugate algebra l∞(G)* = l1(G)** to LUC (G)*. We refer the reader to [1] and [10] for more details.
Norm form equations. III: positive characteristic
Authors: Mason R. C.
Published: November 2008

This paper aims to provide a complete resolution of the general norm form equation over function fields of positive characteristic. In a previous paper [4] we studied norm forms in the simpler case of zero characteristic; that study forms the starting point for the present investigations. Diophantine problems over function fields of positive characteristic were first investigated by Armitage in 1968 [1], who clamied to have established an analogue of the Thue–Siegel–Roth–Uchiyama theorem for such fields. This claim was refuted by Osgood in 1975 [6], who also derived a correct analogue of Thue's approximation theorem. in 1983 a different attack was made on Diophantine problems over function fields, the principal weapon being a bound [2] for the heights of the solutions of the unit equation
On Bohr almost periodicity
Authors: Milnes Paul
Published: November 2008

The first examples of Bohr almost periodic functions that are not almost periodic were given by T. -S. Wu. Later, the present author showed that Bohr almost periodic functions could be distal (and not almost periodic) and even merely minimal. Here it is proved that all Bohr almost periodic functions are minimal. The proof yields an unusual feature about the orbit of a Bohr almost periodic function, one which does not characterize Bohr almost periodic functions, but can be used to show that a Bohr almost periodic function f that is point distal must be distal or, if f is almost automorphic, it must be almost periodic. Some pathologies of Bohr almost periodic functions are discussed.
Improving certain simple eigenvalue bounds
Authors: Hyydö Seppo , Merikoski Jorma Kaarlo , Virtanen Ari
Published: November 2008

Throughout this paper we let A = (aij) be a non-zero n × n matrix-we study real matrices only–with row sums R1,…Rn and eigenvalues λ1,…,λn, ordered λ1≥…≥λn if they are real. We denote E = (1,…,1)T and su A = ΣiΣjaij = ETAE. If A is symmetric, a simple property of the Rayleigh quotient is that

satisfies

and
Rational homotopy equivalences of Lie type
Authors: Papadima Stefan
Published: November 2008

Consider K⊂G, a proper pair of equal rank compact connected Lie groups. It is known (see [6], proof of theorem 1·1) that the group of self-homotopy equivalences of the rationalization of G/K is (anti)isomorphic, in a natural way, to the group of graded algebra automorphisms of H*(G/K; ℚ). On one side of the matter there is the fact that AutH*(G/K; ℚ) almost gives the integral picture of the group of homotopy classes of the self-homotopy equivalences of G/K, that is, up to a finite ambiguity and up to grading automorphisms of H*(G/K; ℚ) (i.e. those acting on H2i as λi.id, for some non-zero λ∈ℚ): see also [6]. On the other side there is the classical description by Borel[2] of H*(G/K; ℚ) in terms of invariants of Weyl groups, which gives hope for a satisfactory understanding of AutH*(G/K; ℚ).
An evaluation of the Jones polynomial of a parallel link
Authors: Sakuma Makoto
Published: November 2008

The Jones polynomial VL(t) of a link L in S3 contains certain information on the homology of the 2-fold branched covering D(L) of S3 branched along L. The following formulae are proved by Jones[3] and Lickorish and Millett[6] respectively:
On a conjecture on Riemann summability (R, k)
Authors: Kwee B.
Published: November 2008

The series is said to be summable (R, k) to s, where k is a positive integer, if

converges for all values of h in some neighbourhood of the origin and if its sum tends to s as h → 0.
On the Euler characteristic mod 2 of real projective varieties
Authors: Szafraniec Zbigniew
Published: November 2008

Let f1, …, fs: ℝn+1→ℝ be homogeneous polynomials, and let

The Euler characteristic χ(X) is an important topological and geometric invariant of X.
Estimates for a multilinear form on the sphere
Authors: Drury S. W.
Published: November 2008

The object of this paper is to make Lp estimates for the n-linear form

defined on n-tuples of functions (ø1, …, øn) on the sphere Sn−1 inℝn.
An almost everywhere central limit theorem
Authors: Brosamler Gunnar A.
Published: November 2008

The purpose of this paper is the proof of an almost everywhere version of the classical central limit theorem (CLT). As is well known, the latter states that for IID random variables Y1, Y2, … on a probability space (Ω, , P) with we have weak convergence of the distributions of to the standard normal distribution on ℝ. We recall that weak convergence of finite measures μn on a metric space S to a finite measure μ on S is defined to mean that

for all bounded, continuous real functions on S. Equivalently, one may require the validity of (1·1) only for bounded, uniformly continuous real functions, or even for all bounded measurable real functions which are μ-a.e. continuous.
The spectrum of a one-dimensional pseudo-differential operator
Authors: Wong M. W.
Published: November 2008

We describe the spectrum of a self-adjoint pseudo-differential operator on L2 (– ∞, ∞). We show that the essential spectrum coincides with the interval ([1, ∞) and give a lower bound for the lowest eigenvalue in (– ∞, 1). A sufficient condition for the existence of an eigenvalue in (– ∞, 1) is also given.
Elliptic curves with good reduction away from 2: II
Authors: Pinch R. G. E.
Published: November 2008

In this paper we continue the study of elliptic curves defined over a quadratic field with good reduction at primes not dividing 2 begun in [9] (referred to as I). We extend the results of I to show that such a curve must have a point of order 2 also defined over when d = −7, −3, −2, −1, 2, 3 or 5 and list all such curves over .
Locally compact topologies on abelian groups
Authors: Morris Sidney A.
Published: November 2008

It is shown that an abelian group admits a non-discrete locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group ofp-adic integers or to an infinite product of non-trivial finite cyclic groups. It is also proved that an abelian group admits a non-totally-disconnected locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group of real numbers. Further, if an abelian group admits one non-totally-disconnected locally compact group topology then it admits a continuum of such topologies, no two of which yield topologically isomorphic topological groups.
Spectra of derived module homomorphisms
Authors: Robinson Alan
Published: November 2008

We introduce a new construction in stable homotopy theory. If F and G are module spectra over a ring spectrum E, there is no well-known spectrum of E-module homomorphisms from F to G. Such a construction would not be homotopy invariant, and therefore would not serve much purpose. We show that, provided the rings and modules have A∞ structures, there is a spectrum RHomE(F, G) of derived module homomorphisms which has very pleasant properties. It is homotopy invariant, exact in each variable, and its homotopy groups form the abutment of a hypercohomology-type spectral sequence.
Poisson convergence and semi-induced properties of random graphs
Authors: Karoński Michał , Ruciński Andrzej
Published: November 2008

Barbour [l] invented an ingenious method of establishing the asymptotic distribution of the number X of specified subgraphs of a random graph. The novelty of his method relies on using the first two moments of X only, despite the traditional method of moments that involves all moments of X (compare [8, 10, 11, 14]). He also adjusted that new method for counting isolated trees of a given size in a random graph. (For further applications of Barbour's method see [4] and [10].) The main goal of this paper is to show how this method can be extended to a general setting that enables us to derive asymptotic distributions of subsets of vertices of a random graph with various properties.
Symmetries of generalized Klein-Gordon (including sine-Gordon) equations in three or more dimensions
Authors: Gordon T. J.
Published: November 2008

Much recent attention has been devoted to those nonlinear partial differential equations admitting higher-order conservation laws (e.g. [2] and references therein) or equivalently admitting higher-order symmetries. In particular the sine-Gordon equation possesses such symmetries [5, 7] where is the two-dimensional d'Alembertian operator. The question posed and solved here is whether such behaviour is possible in higher dimensions. We therefore consider the ‘Generalized Klein–Gordon’ (GKG) equation

in N dimensions where and N ≥ 3.
Some combinatorial results for Weyl groups
Authors: Idowu A. J. , Morris A. O.
Published: November 2008

The aim of this paper is to prove some results involving Weyl groups which are useful in an application to give a combinatorial construction of representations of Weyl groups which generalizes the well-known Young tableau method for symmetric groups. A preliminary version of these applications has been given in [12]. As these results seem to be of independent interest they are gathered together in the present paper.
Elliptic curves with good reduction away from 3
Authors: Pinch R. G. E.
Published: November 2008

In this paper we list the elliptic curves defined over Q(√− 3) with good reduction away from the prime dividing 3. As in [8] and [9] a discriminant estimate is used to show that such a curve must have a subgroup of order 3 defined over Q(√−3).
Balanced big Cohen-Macaulay modules and flat extensions of rings
Authors: Zarzuela Santiago
Published: November 2008

Let A be a (commutative, Noetherian) local ring. The big Cohen-Macaulay conjecture asserts that if a1,…,an is a system of parameters for A there exists an A-module M such that a1,…,an is an M-sequence. Then we say that M is a big Cohen-Macaulay module with respect to a1,…,an. This conjecture implies some important conjectures in commutative algebra and has been established affirmatively by M. Hochster for any ring containing a field as a subring (see [9] for further information).
Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups
Authors: MacLachlan C. , Reid A. W.
Published: November 2008

Arithmetic Fuchsian and Kleinian groups can all be obtained from quaternion algebras (see [2,12]). In a series of papers ([8,9,10,11]), Takeuchi investigated and characterized arithmetic Fuchsian groups among all Fuchsian groups of finite covolume, in terms of the traces of the elements in the group. His methods are readily adaptable to Kleinian groups, and we obtain a similar characterization of arithmetic Kleinian groups in §3. Commensurability classes of Kleinian groups of finite co-volume are discussed in [2] and it is shown there that the arithmetic groups can be characterized as those having dense commensurability subgroup. Here the wide commensurability classes of arithmetic Kleinian groups are shown to be approximately in one-to-one correspondence with the isomorphism classes of the corresponding quaternion algebras (Theorem 2) and it easily follows that there are infinitely many wide commensurability classes of cocompact Kleinian groups, and hence of compact hyperbolic 3-manifolds.
The growth of the number of prime knots
Authors: Ernst C. , Sumners D. W.
Published: November 2008

A fundamental and interesting question in knot theory is:

Question 1. How many prime knots of n crossings are there ?

Over time, knot theorists have answered this question for n ≤ 13 by the method of exhaustion: one writes down a list of all possible knots of n crossings, and then works hard to eliminate duplications from the list [12]. A perhaps easier question is the following:
Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients
Authors: Borwein David
Published: November 2008

The paper is concerned with properties of the Dirichlet series where {λn} is a strictly increasing unbounded sequence of real numbers with λ1 > 0. One of the main Tauberian results proved is that if a1 ≥ 0, an > 0 for n = 2, 3, …, a(x) ≤ ∞ for all x ≥ 0, An:= a1 + a2 + … + an → ∞, an λn = o((λn+1-λn)An), an λn sn > − H(λn+1 − λn) An and then A new summability method Dλ, a based on the Dirichlet series a(x) is defined and its relationship to the weighted mean method Ma investigated.
The Hilbert transform of Schwartz distributions. II
Authors: Chaudhry M. Aslam , Pandey J. N.
Published: November 2008

Let D(R) be the Schwartz space of C∞ functions with compact support on R and let H(D) be the space of all C∞ functions defined on R for which every element is the Hilbert transform of an element in D(R), i.e.

where the integral is defined in the Cauchy principal-value sense. Introducing an appropriate topology in H(D), Pandey [3] defined the Hilbert transform Hf of f ∈ (D(R))′ as an element of (H(D))′ by the relation

and then with an appropriate interpretation he proved that

.

In this paper we give an intrinsic description of the space H(D) and its topology, thereby providing a solution to an open problem posed by Pandey ([4], p. 90).
Degrees bounding minimal degrees
Authors: Chong C. T. , Downey R. G.
Published: November 2008

A set is called n-generic if it is Cohen generic for n-quantifier arithmetic. A (Turing) degree is n-generic if it contains an n-generic set. Our interest in this paper is the relationship between n-generic (indeed 1-generic) degrees and minimal degrees, i.e. degrees which are non-recursive and which bound no degrees intermediate between them and the recursive degree. It is known that n-generic degrees and minimal degrees have a complex relationship since Cohen forcing and Sacks forcing are mutually incompatible. The goal of this paper is to show.
Limit laws for the averages of exponential random variables
Authors: Horváth Lajos
Published: November 2008

Let {Xi. i ≥1} be a sequence of independent exponential random variables with mean 1. Setting S(n) = X1 +…+ Xn, S(0) = 0, we define

where f is a real-valued, measurable function satisfying

.
Residually finite groups of finite rank
Authors: Lubotzky Alexander , Mann Avinoam
Published: November 2008

The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters’, show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird. Thus it seems reasonable to impose the type of condition that enables us to apply the theory of finite groups. Two such conditions are local finiteness and residual finiteness, and here we are interested in the latter. Specifically, we consider residually finite groups of finite rank, where a group is said to have rank r, if all finitely generated subgroups of it can be generated by r elements. Recall that a group is said to be virtually of some property, if it has a subgroup of finite index with this property. We prove the following result:

Theorem 1. A residually finite group of finite rank is virtually locally soluble.
The Markov branching process with density-independent catastrophes. III. The supercritical case
Authors: Pakes Anthony G.
Published: November 2008

This paper continues the study initiated in [9] of the Markov branching process (MBP) with a density-independent catastrophe component. The population size process (Xt) was investigated in the subcritical and critical cases in [11], and the present paper is concerned with a parallel investigation of the supercritical case. We refer the reader to [11] for definitions and notation, and we will not repeat them here.
Infinite coverings of ideals by cosets with applications to regular sequences and balanced big Cohen–Macaulay modules
Authors: Duncan Andrew J.
Published: November 2008

This paper is devoted to the study of unions of ideals in commutative rings. The starting point is the prime avoidance lemma and an accompanying but diverse body of results on coverings of ideals by unions of ideals, which is described in Section 1. In Sections 4 and 5 these known facts, about finite and infinite unions, are combined and generalized, two distinct but overlapping cases emerging. All that is proved in Sections 4 and 5 turns on the crucial Lemma 2·1 in Section 2, which shows that a cover of an arbitrary ideal by cosets can be lifted to a cover of the entire ring. In Section 3 we introduce and define α-sieves, which provide a concise framework for the expression of applications. In Sections 6 to 9 various applications of Sections 4 and 5 are investigated.
A theoretical framework for proper homotopy theory
Authors: Ayala R. , Quintero A. , Dominguez E.
Published: November 2008

Following the techniques of ordinary homotopy theory, a theoretical treatment of proper homotopy theory, including the known proper homotopy groups, is provided within Baues's theory of cofibration categories.
On the orders of ideal classes in prime cyclotomic fields
Authors: Thaine Francisco
Published: November 2008

In this article we exhibit a method complementary to the method presented in [4], that allows us, at least in some important cases, to obtain exact expressions for the orders of ideal classes of cyclotomic fields in terms of properties of the units of the field. We consider only the particular case in which the classes belong to the p-Sylow subgroup (A)p of the ideal class group of a real p-cyclotomic field, but it appears that the results can be generalized.
Remarks on quantic nuclei
Authors: Sun Shu-Hao
Published: November 2008

Quantales were first introduced by Mulvey[3] in order to provide a possible setting for constructive foundations for quantum mechanics, as well as a non-commutative analogue of the maximal spectrum of a C*-algebra. Quantales have since been studied by several authors: see [1, 3, 4, 5].
The asymptotic behaviour of bounded semigroups in a Banach algebra
Authors: Bercovici Hari
Published: November 2008

Let T be an operator on a complex Banach space such that sup {‖Tn‖: n ≥ 0} < ∞; such operators are said to be power-bounded. For such an operator one defines the peripheral spectrum to be the set

where σ(T) denotes the spectrum of T, and T is the unit circle in ℂ. Esterle proved in [3] that limnn→∞ ‖Tn−Tn+1‖ = 0 provided that ‖T‖ ≤ 1 and σ{T} = {1}. Later Katznelson and Tzafriri [6] proved the same result for power-bounded operators such that σΓ(T) = {1}, and in fact they proved a more general result. More precisely, let be an absolutely convergent Taylor series, i.e. , and assume that f is of spectral synthesis for σΓ(T) (in particular f|σΓ(T) ≡ 0). Then limn→∞ ‖f(T) Tn‖ = 0. Katznelson and Tzafriri prove an analogous result, in which T is replaced by a commuting k-tuple (T1, T2, …, Tk) of contractions. In this case they consider functions of the form f(T1, T2, …, Tk), where f is either an absolutely convergent Taylor series if k is odd, or an element of a smaller algebra if k is even. The result of Katznelson and Tzafriri was further extended in the case of a single contraction T by Esterle, Strouse and Zouakia[4], who consider functions f(T) where f is allowed to be in a more general function algebra. For instance, if T acts on a Hilbert space, they allow f to be an element of the disk algebra.
Tensor products which do not preserve operator algebras
Authors: Blecher David P.
Published: November 2008

Of late the link between operator algebras and certain tensor products has been reiterated [5]. We prove here that the projective and Haagerup tensor products of two infinite-dimensional C*-algebras is not even topologically isomorphic to an algebra of operators on a Hilbert space. Estimates are given for the distance of the tensor product from such an algebra. Nonetheless with respect to a natural multiplication the Haagerup tensor product of two algebras of Hilbert space operators is completely isometrically isomorphic to an algebra of operators on some B(ℋ).
On groups associated to a knot
Authors: Zimmermann B.
Published: November 2008

LetKbe a knot in the 3-sphereS3; letmbe a meridian and1a longitude ofK. In [1] we gave a detailed study of the ‘π-orbifold group’O(K): π1(S3\K)/〈m2〉 of the knot, where 〈m2〉 is the subgroup normally generated by the square of the meridian. In particular, we found out to what extent the π-orbifold group classifies knots (and links) and determines the symmetry group of a knot. In the present paper, we consider the groupsGn(K): = π1(S3\K)/〈ln〉. Our main results are the following.
Lindelöf locales and ℕ-compactness
Authors: Paseka J.
Published: November 2008

In the theory of locales (pointless topologies) some lattice-theoretical properties of certain classes of locales (Lindelöf, paracompact locales) behave ‘better’ than in the case of topological spaces. In this context we show that a locale is localic ‘ℕ-compact’ if and only if it is 0-dimensional Lindelöf. This is an analogue of the theorem of Madden and Vermeer [9] that a locale possesses the localic version of real compactness if and only if it is Tychonoff Lindelöf. As a consequence, we offer a localic analogue of ℕ-compactification, which is exactly the 0-dimensional Lindelöf reflection.
The number of infinite substructures
Authors: Macpherson Dugald , Mekler Alan H. , Shelah Saharon
Published: November 2008

Given a relational structure M and a cardinal λ < |M|, let øλ denote the number of isomorphism types of substructures of M of size λ. It is shown that if μ < λ are cardinals, and |M| is sufficiently larger than λ, then øμ ≤ øλ. A description is also given for structures with few substructures of given infinite cardinality.
Points of egress in problems of Hamiltonian dynamics
Authors: Amick C. J. , Toland J. F.
Published: November 2008

First we consider an elementary though delicate question about the trajectory in ℝn of a particle in a conservative field of force whose dynamics are governed by the equation

Here the potential function V is supposed to have Lipschitz continuous first derivative at every point of ℝn. This is a natural assumption which ensures that the initial-value problem is well-posed. We suppose also that there is a closed convex set C with non-empty interior C° such that V ≥ 0 in C and V = 0 on the boundary ∂C of C. It is noteworthy that we make no assumptions about the degeneracy (or otherwise) of V on ∂C (i.e. whether ∇V = 0 on ∂C, or not); thus ∂C is a Lipschitz boundary because of its convexity but not necessarily any smoother in general. We remark also that there are no convexity assumptions about V and nothing is known about the behaviour of V outside C.
The Lindelöf Tychonoff Theorem and choice principles
Authors: Schlitt G.
Published: November 2008

It is an important result in frame theory that the coproduct of a family of regular Lindelöf frames is Lindelöf [3]. We show that this ‘Lindelöf Tychonoff Theorem’ or ‘LTT’ is independent of ZF and indeed lies close in logical strength to the Axiom of Countable Choice, quite unlike the case with the usual (frame) Tychonoff Theorem. Along the way we construct the regular Lindelöf coreflection and obtain a simple proof of the LTT as a corollary.
Characteristic classes invariant under stable fibre homotopy type
Authors: Astey L. , Gitler S. , Micha E. , Pastor G.
Published: November 2008

In a letter dated 19 November 1988, addressed to Samuel Gitler, with copies to the three other authors of [2], J. F. Adams formulated the problem studied and solved in the present paper. In his letter, Adams provided the key ingredient for its solution and proved a first result. (See (1·2) and the second paragraph of the proof of (1·1)) We therefore wish to express our debt of gratitude to the late Professor Adams for his essential contribution, without which this paper could not have been written.
Cofiniteness and vanishing of local cohomology modules
Authors: Huneke Craig , Koh Jee
Published: November 2008

Let R be a noetherian local ring with maximal ideal m and residue field k. If M is a finitely generated R-module then the local cohomology modules are known to be Artinian. Grothendieck [3], exposé 13, 1·2 made the following conjecture:

If I is an ideal of R and M is a finitely generated R-module, then HomR (R/I, ) is finitely generated.
Cube-full numbers in short intervals
Authors: Shiu P.
Published: November 2008

An innovation by D. R. Heath-Brown on square-full numbers in short intervals is applied to establish an asymptotic formula for the number of cube-full numbers in the interval
Pointwise bounded approximation by polynomials
Authors: O'Farrell Anthony G. , Perez-Gonzalez Fernando
Published: November 2008

For a bounded open set U ⊂ ℂ, we denote by H∞(U) the collection of all bounded analytic functions on U. We let X denote bdy (U), the boundary of U, Y denote the polynomial hull of U (the complement of the unbounded component of ℂ / X), and U* denote mt (Y), the interior of Y. We denote the sup norm of a function f: A → ℂ by ∥f∥A:

We denote the space of all analytic polynomials by ℂ[z], and we denote the open unit disc by D and the unit circle by S1.
Invariance principles for logarithmic averages
Authors: Csörgő Miklós , Horváth Lajos
Published: November 2008

We obtain weak and strong Gaussian approximations for logarithmic averages of indicators of normalized partial sums. The proofs are based on invariance principles for integrals of an Ornstein–Uhlenbeck process and on strong approximations of normalized partial sums by Orstein–Uhlenbeck processes.
On the instability of a class of generalized strong curvature singularities
Authors: Kondracki Witold , Królak Andrzej , Rudnicki Wiesław
Published: November 2008

Cosmic censorship hypothesis [1] is a major unsolved problem in classical general relativity. According to this hypothesis singularities occurring in generic space-times should not be naked. This means that there should not be singularities to the future of a regular initial surface that are visible to observers at infinity A mathematically precise statement of the hypothesis is that a space-time should be future asymptotically predictable from a partial Cauchy surface ([2] p. 310).
Remarks on structurally stable proper foliations
Authors: Brunella Marco
Published: November 2008

Let M be a closed manifold of dimension 3 and let Fol(M) be the space of codimension one C∞-foliations on M. A foliation ∈ Fol(M) is said to be Cr- structurally stable if there exists a neighbourhood V of in Fol(M) in the (Epstein) Cr-topology such that every foliation is topologically conjugate to , through a homeomorphism near to the identity. Some background on the problem of structural stability of foliations can be found in [8]. In this paper we shall be concerned with proper foliations, i.e. foliations all of whose leaves are proper.
Odd perfect numbers
Authors: Heath-Brown D. R.
Published: November 2008

It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10300 (see Brent[1]). Moreover it has been proved by Hagis[4]and Chein[2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in priniciple be obtained solely by calculation, in view of the result of Pomerance[6] who showed that if N is an odd perfect number with at most k prime factors, then

Pomerance's work was preceded by a theorem of Dickson[3]showing that there can be only a finite number of such N. Clearly however the above bound is vastly too large to be of any practical use. The principal object of the present paper is to sharpen the estimate (1). Indeed we shall handle odd ‘multiply perfect’ numbers in general, as did Kanold[5], who extended Dickson's work, and Pomerance. Our result is the following.
On satellite knots
Authors: Kouno Masaharu , Motegi Kimihiko
Published: November 2008

Throughout this paper we work in the smooth category and assume that all knots are oriented and consider two knots K1 and K2 to be equivalent if and only if there is an orientation preserving homeomorphism h:S3→S3 which carries K1 onto K2 so that their orientations match. We write K1 ≅ K2 if K1 and K2 are equivalent and – K denotes the knot obtained from K by inverting its orientation.
Diophantine approximation in Kleinian groups
Authors: Stratmann Bernd
Published: November 2008

The δ-homogeneity of the Patterson measure is used for a closer study of the limit sets of Kleinian groups. A combination of the properties of this measure with concepts of diophantine approximations is shown to lead to a more detailed understanding of these limit sets. In particular, it is seen to how great an extent the studies of these sets, in terms of Hausdorff measure or Hausdorff dimension, are limited in a natural way.
A family of 2(p − 1)-sparse cohomology theories and some actions on
Authors: Brunetti Maurizio
Published: November 2008

Let p be an odd prime, and h*( − ) a multiplicative mod p cohomology theory with a complex orientation satisfying the 2(p − 1)-sparseness condition. A formula concerning the formal group law for such h*( − ) is used to investigate the structure of h*(BG), G being a finite group whose p-Sylow subgroups are cyclic.
Non-simple geodesics in hyperbolic 3-manifolds
Authors: Jones Kerry N. , Reid Alan W.
Published: November 2008

Chinburg and Reid have recently constructed examples of hyperbolic 3-manifolds in which every closed geodesic is simple. These examples are constructed in a highly non-generic way and it is of interest to understand in the general case the geometry of and structure of the set of closed geodesics in hyperbolic 3-manifolds. For hyperbolic 3-manifolds which contain immersed totally geodesic surfaces there are always non-simple closed geodesics. Here we construct examples of manifolds with non-simple closed geodesics and no totally geodesic surfaces.
H1 boundedness of oscillatory singular integrals with degenerate phase functions
Authors: Pan Yibiao
Published: November 2008

In this paper we study the uniform boundedness of oscillatory singular integral operators with degenerate phase functions on the Hardy space H1. The H1 boundedness was previously known when the phase function is nondegenerate. Here we obtain a sufficient condition for H1 boundedness which allows the phase function vanishing to infinite order.
S-integral points on elliptic curves
Authors: Smart N. P.
Published: November 2008

In this paper I give an algorithm to find all ‘small’ S-integral points on an elliptic curve. I would like to thank N. Stephens for suggesting I consider such equations and the Wingate Foundation for supporting me whilst carrying out the research. As is usual c1, c2, …, will denote positive real constants which are effectively computable.
Rigidity of superconformal minimal surfaces lying fully in odd-dimensional unit spheres
Authors: Sakaki Makoto
Published: November 2008

LetSndenote then-dimensional unit sphere. Recently, Bolton, Pedit and Woodward [1,3] have begun to study a class of minimal surfaces inSn, which are called superconformal. In this paper we will discuss the rigidity of superconformal minimal surfaces lying fully inS2m−1among all superconformal minimal surfaces lying fully in odd-dimensional unit spheres.
Numbers badly approximate by fractions with prime denominator
Authors: Harman Glyn
Published: November 2008

We write ‖x‖ to denote the least distance from x to an integer, and write p for a prime variable. Duffin and Schaeffer [l] showed that for almost all real α the inequality

has infinitely many solutions if and only if

diverges. Thus f(x) = (x log log (10x))−1 is a suitable choice to obtain infinitely many solutions for almost all α. It has been shown [2] that for all real irrational α there are infinitely many solutions to (1) with f(p) = p−/13. We will show elsewhere that the exponent can be increased to 7/22. A very strong result on primes in arithmetic progressions (far stronger than anything within reach at the present time) would lead to an improvement on this result. On the other hand, it is very easy to find irrational a such that no convergent to its continued fraction expansion has prime denominator (for example (45– √10)/186 does not even have a square-free denominator in its continued fraction expansion, since the denominators are alternately divisible by 4 and 9).
Farrell cohomology and centralizets of elementary abelian p-subgroups
Authors: Lee Chun-Nip
Published: November 2008

Let Γ be a discrete group. Γ is said to have finite virtual cohomological dimension (vcd) if there exists a finite index torsion-free subgroup Γ′ of G such that Γ′ has finite cohomological dimension over ℤ. Examples of such groups include finite groups, fundamental group of a finite graph of finite groups, arithmetic groups, mapping class groups and outer automorphism groups of free groups. One of the fundamental problems in topology is to understand the cohomology of these finite vcd-groups.
Continuity of functions operating on characteristic functions
Authors: Norvidas Saulius
Published: November 2008

For a locally compact abelian group G let P0(G) denote the set of all characteristic functions on G (i.e., continuous positive definite functions φ with φ(0) = 1). A complex-valued function f is said to operate on P0(G) if f(φ(·)) ∈ P0(G) whenever φ ∈ P0(G). The natural domain for functions operating on P0(G) is the set D(G) = {z ∈ C: z = φ(g), g ∈ G, φ ∈ P0(G)}. It is known that every function operating on P0(G) is continuous on the interior of D(G) for each infinite group G. On the other hand, functions discontinuous on D(G) operate on P0(G) for any discrete G. We show that, for any non-discrete group G, every function operating on P0(G) is continuous on D(G). Together with some earlier results, this statement allows us to obtain a constructive description of operating functions on the whole set D(G).
Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings
Authors: Wu Yinghwa
Published: November 2008

Throughout, (R, m) will denote a d-dimensional CohenMacaulay (CM for short) local ring having an infinite residue field and I an m-primary ideal in R. Recall that an ideal J I is said to be a reduction of I if Ir+1 = JIr for some r 0, and a reduction J of I is called a minimal reduction of I if J is generated by a system of parameters. The concepts of reduction and minimal reduction were first introduced by Northcott and Rees12. If J is a reduction of I, define the reduction number of I with respect to J, denoted by rj(I), to be min {r 0 Ir+1 = JIr}. The reduction number of I is defined as r(I) = min {rj(I)J is a minimal reduction of I}. The reduction number r(I) is said to be independent if r(I) = rj(I) for every minimal reduction J of I.
Isomorphisms and multipliers on second dual algebras of Banach algebras
Authors: Ghahramani Fereidoun , Lau Anthony To-Ming
Published: November 2008

Suppose that A is a Banach algebra and let A be the second dual algebra of A equipped with the first Arens product 3. In this paper we characterize compact and weakly compact multipliers of A, when A possesses a bounded approximate identity and is a two sided ideal in A. We use this to study the isomorphisms between second duals of various classes of Banach algebras satisfying the above properties.
Clifford monoid presentations
Authors: Silva Pedro V.
Published: November 2008

Some decidability results for presentations in the variety of Clifford monoids are obtained. These results are applied in the solution of theE-unitary problem for presentations in the variety of inverse monoids.
Invariant functions on matrices
Authors: Donkin Stephen
Published: November 2008

The ring of symmetric polynomials in n variables may be interpreted as a ring of characters of the general linear group GL(n) (see e.g. [4], §3·5). We consider here a generalization of symmetric function theory in which we deal with trace functions on several matrices over ℂ An important feature of the ‘single matrix variable’ (or classical) case is the characteristic isomorphism (see [5], chapter I, §7) ch: R = between the graded ring R, whose component Rd in degree d is the character group of the symmetric group of degree d, and the ring of symmetric functions Λ in infinitely many variables (obtained from symmetric functions in n variables by taking the graded inverse limit with respect to n).
Cobordism of theta curves in S3
Authors: Taniyama Kouki
Published: November 2008

In this paper we show that the cobordism classes of theta curves in S3 form a group under vertex connected sum. We investigate this group by means of knot cobordism and link cobordism.
On primes not dividing binomial coefficients
Authors: Sander J. W.
Published: November 2008

We prove that

thus dealing with open problems concerning divisors of binomial coefficients.
On positive harmonic functions
Authors: Allen A. C.
Published: November 2008

Any harmonic function which is defined and positive in the half-plane η > 0 may be expressed by

where C is a non-negative number, and G(x) is a bounded non-decreasing function. For a simple proof see Loomis and Widder (2). Let us write

where w(z) is a regular function of z in η > 0, and satisfies the following conditions: (i) w(z) is real and continuous at all points of the open interval (a, b) of the real axis [the interval may be unbounded]; (ii) there exists a simply connected domain Δ, lying in the half-plane η > 0, whose frontier contains the interval (a, b) of the real axis and which is mapped ‘simply’ on the half-plane υ > 0 by the conformal transformation w = w(z).
The relativistically rigid rod
Authors: Hogarth J. E. , McCrea W. H.
Published: November 2008

A relativistically rigid rod is defined as one along which any disturbance travels with the fundamental speed c without dissipation of energy. A necessary consequence of this definition is that the rod should satisfy a certain ‘equation of elasticity’. If this equation is satisfied, it is shown in accordance with relativistic mechanics that a disturbance of any amplitude is propagated along the (unstressed or stressed) rod with speed c and without dissipation. Consequently, the equation provides also a sufficient condition for rigidity in the sense defined.
Automorphism towers of certain almost soluble groups
Authors: Hulse J. A.
Published: November 2008

Automorphism towers were first considered in (19) with the case of finite groups. Recently polycyclic and extremal groups were considered in (7) and (12) respectively. The purpose of this paper is to consider automorphism towers of groups in a class of almost soluble groups which contains all polycyclic and all extremal groups.
Three-manifolds as branched covers
Authors: Lickorish W. B. R.
Published: November 2008

This note describes a new, and possibly more informative, proof of the fact that any closed orientable 3-manifold is a branched cover over the 3-sphere.
On some theorems of Hurwitz and Sheil-Small
Authors: Hall R. R.
Published: November 2008

We recall a theorem of Hurwitz [5]: let f(θ) be real-valued and periodic, f(θ) ≢ 0, and

where an = bn = 0, 0 ≤ n < N. Then f(θ) has at least 2N sign changes in each period. A similar result with a trigonometric polynomial on the right-hand side of (1) had been obtained earlier by Sturm [7].
The “Overshoot Phenomenon” in Superconductivity
Authors: Misener A. D.
Published: November 2008

It is concluded that the “overshoot phenomenon” in superconductivity described by F. B. Silsbee was due to his method of mounting the specimen.
Functional Pearls: Unravelling greedy algorithms
Authors: Bird Richard S.
Published: November 2008

In my previous Functional Pearls article (Bird, 1992), I proved a theorem giving conditions under which an optimization problem could be implemented by a greedy algorithm. A greedy algorithm is one that picks a ‘best’ element at each stage. Here, we return to this theorem and extend it in various ways. We then use the theory to solve an intriguing problem about unravelling sequences into a smallest number of ascending subsequences.
Exploring the conformations of nucleic acids
Authors: Turcotte Marcel , Lapalme Guy , Major François
Published: November 2008

This paper presents an application of functional programming in the field of molecular biology: exploring the conformations of nucleic acids. TheNucleic Acid three-dimensional structure determination problem(NA3D) and a constraint satisfaction algorithm are formally described. Prototyping and experimental development using the Miranda functional programming language, over the last four years, are discussed. A Prolog implementation has been developed to evaluate software engineering and performance criteria between functional and logic programming. A C++ implementation has been developed for distribution purpose and to solve large practical problems. This system, called MC-SYM for ‘Macromolecular Conformation by SYMbolic generation’, is used in more than 50 laboratories, including academic and government research centres and pharmaceutical companies.
Reference counting as a computational interpretation of linear logic
Authors: Chirimar Jawahar , Gunter Carl A. , Riecke Jon G.
Published: November 2008

We develop an operational model for a language based on linear logic. Our semantics is ‘low-level’ enough to express sharing and copying while still being ‘high-level’ enough to abstract away from details of memory layout, and thus can be used to test potential applications of linear logic for analysis of programs. In particular, we demonstrate a precise relationship between type correctness for the linear-logic-based language and the correctness of a reference-counting interpretation of the primitives, and formulate and prove a result describing the possible run-time reference counts of values of linear type.
Problems with different time scales
Authors: Kreiss Heinz-Otto
Published: November 2008

In this section we discuss a very simple problem. Consider the scalar initial value problem

Here ε > 0 is a small constant and a = a1 + ia2, a1, a2 real, is a complex number with |a| = 1. We can write down the solution of (1.1) explicity. It is

where

is the forced solution and

is a solution of the homogeneous equation

yS varies on the time scale ‘1’ while yF varies on the much faster scale 1/ε. We say that yS, yF vary on the slow and fast scale, respectively. We use also the phrase: yS and yF are the slow and the fast part of the solution, respectively.