bluuebunny/crossref_metadata_2025 huggingface dataset:
A resolution of the Euler operator II
Authors: Shakiban Chehrzad
Published: November 2008

An exact sequence resolving the Euler operator of the calculus of variations for partial differential polynomials in several dependent and independent variables is described. This resolution provides a solution to the ‘Inverse problem of the calculus of variations’ for systems of polynomial partial equations.

That problem consists of characterizing those systems of partial differential equations which arise as the Euler-Lagrange equations of some variational principle. It can be embedded in the more general problem of finding a resolution of the Euler operator. In (3), hereafter referred to as I, a solution of this problem was given for the case of one independent and one dependent variable. Here we generalize this resolution to several independent and dependent variables simultaneously. The methods employed are similar in spirit to the algebraic techniques associated with the Gelfand-Dikii transform in I, although are considerably complicated by the appearance of several variables. In particular, a simple algebraic proof of the local exactness of a complex considered by Takens(5), Vinogradov(6), Anderson and Duchamp(1), and others appears as part of the resolution considered here.
Isometries of non-commutative Lp-spaces
Authors: Yeadon F. J.
Published: November 2008

The spaces Lp(, φ) for 1 ≤ p ≤ ∞, where φ is a faithful semifinite normal trace on a von Neumann algebra , are defined in (10),(2),(14). The problem of determining the general form of an isometry of one such space into another has been studied in (i), (6), (9), (12), (5). Our main result, Theorem 2, is a characterization of such isometries for 1 ≤ p ≤ ∞, ≠ 2. The method of proof is based on that of (7), where isometries between Lp function spaces are characterized. The main step in the proof is Theorem 1, which gives the conditions under which equality holds in Clarkson's inequality.
A new chain complex for the homology of the Steenrod algebra
Authors: Singer William M.
Published: November 2008

Let A be the Steenrod algebra over the field F2. For any graded A-module M we construct here a small chain complex of A-modules EM. This complex computes the homology of the Steenrod algebra with coefficients in M, in the sense that:

The complexes F2 ⊗AEM are comparable in size but slightly larger than those that arise from the Λ-algebra(4). We are motivated to introduce them because they can be used to prove an embedding theorem for the homology of the Steenrod algebra. In fact, we construct a functor K on the category of graded. A-modules, and using the complexes EM, prove that there is a natural, one-one map:
A criterion for the (e, c)-summability of Fourier series
Authors: Siddiqi Jamil A.
Published: November 2008

1. A series with partial sums {An} is said to be summable (e, c) (c > 0) if

exists, where it is to be understood that An+k = 0 when n+k < 0. The (e, c)-sum-mability method which is a regular method of summation was introduced by Hardy and Littlewood (3) (cf. also (5)) as an auxiliary method to prove the Tauberian theorem for Borel summability, viz, if Σan is summable (B) to A and an = 0(n−½), then it converges to A.
Osculating hyperplanes and a quartic combinant of the nonsingular model of the Kummer and Weddle surfaces
Authors: Dye R. H.
Published: November 2008

The nonsingular model of Kummer's surface, or its birational equivalent the Weddle surface, is an octavic surface F in [5], projective space of dimension 5 (11), ((10), p. 53), ((1), pp. 218, 219). F is the base variety of a net N of quadrics with a common self-polar simplex S, and has on it 32 lines. These form a single orbit under the group G, of order 32, consisting of the harmonic homologies fixing S.
Inverse scattering problem for transparent obstacles
Authors: Petkov Vesselin
Published: November 2008

Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. Set

We wish to study the filtered scattering amplitude, related to the transmission problem

Here w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C∞(K¯), called the index of refraction, has the property α(x) > 0 for x ∈ K¯.
The join of several subnormal subgroups
Authors: Williams J. P.
Published: November 2008

In (2) Lennox and Stonehewer proved:
Let G be a group with subnormal subgroups H and K, and let J = 〈H, K〉. Suppose that J/J′ has finite rank. Then

(i) given positive integers a and b, there exists c such that γc(J) ≤ γa(H). γb(K) and

(ii) J is subnormal in G.
General position properties of ANR's
Authors: Mitchell W. J. R.
Published: November 2008

This paper investigates the ‘general position’ properties which ANR's may possess. The most important of these is the disjoint discs property of Cannon (5), which plays a vital role in recent striking characterizations of manifolds (5, 9, 12, 18, 19, 22). Also considered are the property Δ of Borsuk(2) (which ensures an abundance of dimension-preserving maps), and the vanishing of local homology groups up to a given dimension (cf. (9)). Our main results give relations between these properties, and clarify their behaviour under the stabilization operation of taking cartesian product with the real line. In the last section these results are applied to give partial solutions to questions about homogeneous ANR's.
Infinitely many disk knots with the same exterior
Authors: Plotnick Steven P.
Published: November 2008

This paper addresses the question of how well the exterior of a knot determines the knot. It is well known that for a knotted sphere pair (Sn+2, Sn),n≥ 2, a given exterior corresponds to at most two distinct knots (1), (4), (10); examples of distinct knots with the same exterior are given in (2), (6). For a knotted ball pair (Bn+2, Bn),n≥ 2, the situation may be more complicated. In fact, given an arbitrary positive integerN, Hitt-Sumners (7), (8) constructedNdistinct ball pairs with the same exterior,n≥ 4.
The parametric blowing-up of two-dimensional local domains
Authors: Schenzel Peter
Published: November 2008

Let (A, M) be a local Noetherian integral domain of dimension two and X = Spec A. For an ideal IA the graded ring RA(I) = noIn denotes the Rees algebra of A with respect to I. The projective scheme Y = Proj RA(I) is called the blowing-up of X (resp. A) along I. Then there exists a proper mapping : YX. The preimage Z = 1(V(I)) is called the exceptional fibre. Note that induces an isomorphism
The centre of the second dual of a commutative semigroup algebra
Authors: Parsons D. J.
Published: November 2008

IfSis an infinite, discrete, commutative semigroup then the semigroup algebral1(S) is a commutative Banach algebra. Its dual isl∞(S), which is isometrically iso-morphic to C(βS), the space of continuous functions on the Stone-Čech compactification of S. This fact enables us to identify the second dual ofl1(S) withM(βS), the space of bounded regular Borel measures on βS. Endowed with the Arens product the second dual is also a Banach algebra, so it is natural to ask whether a product may be defined inM(βS) without reference tol1(S). In §4 this is shown to be possible even when S is a non-discrete semitopological semigroup, provided that the operation in S may be extended to make βSinto a left-topological semigroup in the manner of, for example, [2] where further references may be found. (Note, however, that the construction there is of a right-topological semigroup.) Having done this we may use results on βSto provide information about the measure algebra.
An extremal function for contractions of graphs
Authors: Thomason Andrew
Published: November 2008

The function c(p) is defined for positive integers p ≥ 4 by

where > denotes contraction. Random graph examples show

In 1968 Mader showed that c(p) ≤ 8(p − 2) [log2 (p − 2)] and more recently Kostochka showed that p√(log p) is the correct order for c(p). We present a simple argument showing c(p) ≤ 2.68p √(log2p)(l + ο(l)).
Inequalities related to Hardy's and Heinig's
Authors: Cochran James A. , Lee Cheng-Shyong
Published: November 2008

In a 1975 paper [8], Heinig established the following three inequalities:

where A = p/(p + s − λ) with p, s, λ real numbers satisfying p + s > λ,p > 0;

where B = p/(2p + sp − λ −1) with p, s, λ real numbers satisfying 2p +sp > λ, + 1, p > 0;

where is a sequence of nonnegative real numbers,

and C = p[l + l/(p + s−λ)] with p, s, λ real numbers satisfying s > 0, p ≥ 1, and p +s > λ 0.
Note on almost complex structures on products of lens spaces
Authors: Kobayashi Teiichi
Published: November 2008

The purpose of this note is to count almost complex structures on products of some lens spaces.
Conjugacy classes of double covers of monomial groups
Authors: Humphreys John F.
Published: November 2008

LetGbe a finite group,Snbe the symmetric group onnsymbols andAnbe the corresponding alternating group. The conjugacy classes of the wreath productGSn(or monomial group as it is sometimes known) and the conjugacy classes ofGAnhave been described by Kerber (see [2] and [3]). The groupSnhas a double covernso that the faithful complex representations of this double cover may be regarded as protective representations ofSn. In Section 2, a particular double cover forGSnis constructed, the faithful complex representations of this group being the subject of a joint article with Peter Hoffman[1]. In the present paper, our task is to determine whether a conjugacy class ofGSncorresponds to one or to two conjugacy classes in the double cover ofGSn(and similarly forGAn). The main results, Theorems 1 and 2, are stated precisely in Section 2 and proved in Sections 3 and 4 respectively. The case whenG= 1 provides classical results of Schur ([5], Satz IV). WhenGis a cyclic group, Read [4] has determined the conjugacy classes, not just for our particular double cover, but for all possible double covers ofGSn.
Uniform ε-independence and the convergence in distribution of randomly indexed sequences
Authors: dorea C. C. Y. , david H. T. , werner N. M.
Published: November 2008

A notion of ‘uniform ε-independence’ (u.ε.i.) is proposed for a sequence {Xn} successively indexed by random indices {τk}. The u.∊.i. property yields results other than those in the previous random indexing literature. Complementing the u.∊.i. property by suitable ‘approximation’ one recovers these previous results.
Isomorphisms of H*-algebras
Authors: Mira Jose Antonio Cuenca , Palacios Angel Rodriguez
Published: November 2008

H*-algebras were introduced and studied by Ambrose [1] in the associative case, and the theory has been extended to such particular classes of non-associative algebras as Lie [18, 19], Jordan[20, 21, 7], alternative [11] and non-commutative Jordan [6] algebras. In all these cases the core of the matter is showing that every H*-algebra (in the given class) with zero annihilator is the closure of the orthogonal sum of its minimal closed ideals (each of which is a topologically simple H*-algebra), and then listing all the topologically simple H*-algebras in the class. In fact every nonassociative H*-algebra with zero annihilator is the closure of the orthogonal sum of its minimal closed ideals [6, theorem 2·7], so the problem of the classification of topologically simple non-associative H*-algebras becomes interesting. In relation with this problem the question arises whether, once an algebra A has been structured as a topologically simple H*-algebra, every H*-algebra structure on A is (up to a positive multiple of the inner product) totally isomorphic to the given one (see [3] and [11, section 4]). As a consequence of the results in this paper we give a general affirmative answer to this question.
The transfer and Whitehead's conjecture
Authors: Kuhn Nicholas J. , Priddy Stewart B.
Published: November 2008

In this paper we present a proof of G. W. Whitehead's conjecture about symmetric products of the sphere spectrumS.Our methods are based on the transfer, the Steinberg module, and the structure of the Hecke algebra. Our results are valid for all primes and extend those of the first author forp= 2 [7]. As originally stated, the conjecture asserts that

is zero onp-primary components in positive degrees [11]. By considering the quotientsL(k)= Σ-kSPpkS/SPk-1-S, this is seen to be equivalent to the exactness of

on homotopy groups, where ∂kis the connecting map and ε is the inclusion of the bottom cell. Here and throughout all spaces and spectra are localized atp.
A law of the iterated logarithm for weakly exchangeable arrays
Authors: Scott D. J. , Huggins R. M.
Published: November 2008

In Eagleson and Weber [2] a central limit theorem for weakly exchangeable arrays is given as a consequence of a reverse martingale central limit theorem. As noted in their remarks, a direct application of this is a central limit theorem for the classical U-statistics. Here we give a corollary to the functional law of the iterated logarithm of Scott and Huggins [4] and use this to obtain laws of the iterated logarithm for weakly exchangeable arrays and hence for U-statistics under a finite (2 + δ)th moment condition.
Note on desuspending the Adams map
Authors: Cohen F. R. , Neisendorfer J. A.
Published: November 2008

Let p denote a fixed prime and let Pn(pr) denote the cofibre of the degree pr map on Sn–1. We consider π*P3(pr) and show that the map q in the cofibre sequence

induces a split epimorphism on the p-primary component of π2pS3 if p > 2. That analogous maps q: Pn(pr) →Sn, n ≥ 4, induce split epimorphisms on the p-primary component of πn+2p-3Sn, p > 2, is shown in work of J. F. Adams [1]. It is the purpose of this note to document the above computation in the case n = 3 for the use of others.
Inequalities related to those of Hardy and of Cochran and Lee
Authors: Love E. R.
Published: November 2008

One of the inequalities recently found by Cochran and Lee([1], theorem 1) is the following.

If γ and p are real numbers with p > 0, and f(t) is measurable and non-negative on (0, ∞), then
Complex convexity and the geometry of Banach spaces
Authors: Dilworth S. J.
Published: November 2008

The notion of PL-convexity was introduced in [4]. In the present article several results are proved which related PL-convexity to various aspects of the geometry of Banach spaces. The first section introduces the moduli of comples convexity and makes a comparison with the more familiar modulus of uniform convexity. It is shown that unconditional convergence of implies convergence of . In the next section the moduli and are shown to be related. The method of proof gives rise to a theorem about strict c-convexity of Lp(X) and a result on the representability in Lp(X).
Eigenvalues of positive integral operators with certain entire kernels
Authors: Little G.
Published: November 2008

Suppose that (an) (n ≥ 0) is a square-summable sequence of strictly positive real numbers; then the integral operator T on L2(− 1,1) given by

is compact and positive and, therefore, its eigenvalues can be arranged into a sequence λ0 ≥ λ1 ≥ λ2 ≥ … of non-negative real numbers which decreases to 0.
Packing regularity of sets in n-space
Authors: Raymond Xavier Saint , Tricot Claude
Published: November 2008

The notion of packing measure, introduced in [12], [13] and [10], has been used by comparison with Hausdorif measure to study the regularity and rectifiability of sets in the plane [11]. Since a few technical mistakes can be found in [10], lemma 5·11 and [11], lemma 3·2, we wish in this paper to give the corresponding exact proofs, together with a natural development of this theory in higher dimensions.
Metric Diophantine approximation with two restricted variables I. Two square-free integers, or integers in arithmetic progressions
Authors: Harman Glyn
Published: November 2008

In this paper, together with [7] and [8], we shall be concerned with estimating the number of solutions of the inequality

for almost all α (in the sense of Lebesgue measure on Iℝ), where, and bothmandnare restricted to sets of number-theoretic interest. Our aim is to prove results analogous to the following theorem (an improvement given in [2] of an earlier result of Khintchine [10]) and its quantitative developments (for example, see [11, 12,6]):

Let ψ(n) be a non-increasing positive function of a positive integer variable n. Then the inequality (1·1) has infinitely many, or only finitely many, solutions in integers to, n(n > 0) for almost all real α, according to whether the sum

diverges, or converges, respectively.
A topological criterion for group decompositions
Authors: Hebda J. , Moylan P.
Published: November 2008

Given a connected Lie group G and a closed connected subgroup H of G we prove a necessary and sufficient condition that G decomposes into the Cartesian product of H with G/H is that a similar decomposition holds for the maximal compact subgroups of G and H. Our criterion is applied to the three series of groups for which G/H is SO0(p, q)/SO0(p, q − 1), SU(q + 1, q + 1)/S[U(q + 1, q) × U(1)], and SU(q + 1, q + 1)/SL(n, ℂ) ⋊ H(n) (p, q ≥ 1), and we list the values of p and q for which G ≅ H × G/H in each of the three cases. We describe certain decompositions for some of the groups. We show the usefulness of our criterion in obtaining characterization of the space of differentiable vectors for a unitary induced group representation, and, finally, we show by example of SU(2, 2), how the asymptotic properties of certain function spaces for induced group representations are readily obtained using our results. Our results should be of interest to those working in de Sitter and conformal field theories.
Sprays, universality and stability
Authors: Riego L. Del , Dodson C. T. J.
Published: November 2008

An important class of systems of second order differential equations can be represented as sprays on a manifoldMwith tangent bundleTM↠M; that is, as certain sections of the second tangent bundleTTM↠TM. We consider here quadratic sprays; they correspond to symmetric linear connections onTM↠Mand hence to principal connections on the frame bundleLM↠M. Such connections overMconstitute a system of connections, on which there is a universal connection and through which individual connections can be studied geometrically. Correspondingly, we obtain a universal spray-like field for the system of connections and each spray onMarises as a pullback of this ‘universal spray’. The Frölicher-Nijenhuis bracket determines for each spray (or connection) a Lie subalgebra of the Lie algebra of vector fields onMand this subalgebra consists precisely of those morphisms ofTTMoverTMwhich preserve the horizontal and vertical distributions; there is a universal version of this result. Each spray induces also a Riemannian structure onLM; it isometrically embeds this manifold as a section of the space of principal connections and gives a corresponding representation ofTMas a section of the space of sprays. Such embeddings allow the formulation of global criteria for properties of sprays, in a natural context. For example, ifLMis incomplete in a spray-metric then it is incomplete also in the spray-metric induced by a nearby spray, because that spray induces a nearby embedding. For Riemannian manifolds, completeness ofLMis equivalent to completeness ofMso in the above sense we can say that geodesic incompleteness is stable; it is known to be Whitney stable.
On Waring's problem for cubes and biquadrates. II
Authors: Brüdern Jörg
Published: November 2008

In discussing the consequences of a conditional estimate for the sixth moment of cubic Weyl sums, Hooley [4] established asymptotic formulae for the number ν(n) of representations of n as the sum of a square and five cubes, and for ν(n), defined similarly with six cubes and two biquadrates. The condition here is the truth of the Riemann Hypothesis for a certain Hasse–Weil L-function. Recently Vaughan [8] has shown unconditionally , a lower bound of the size suggested by the conditional asymptotic formula. In the corresponding problem for ν(n) the author [1] was able to deduce ν(n) > 0, as a by-product of the result that almost all numbers can be expressed as the sum of three cubes and one biquadrate. As promised in the first paper of this series we return to the problem of bounding ν(n) from below.
The automorphism group of random graphs with a given number of edges
Authors: Łuczak Tomasz
Published: November 2008

An automorphism σ(G) of a graph G is a permutation of the set of its vertices which preserves adjacency. Under the operation of composition the automorphisms of G form a group Aut(G). The graph G is called asymmetric if Aut(G) is trivial, and symmetric otherwise.
Generating families for images of Lagrangian submanifolds and open swallowtails
Authors: Janeczko Stanisław
Published: November 2008

In this paper we study the symplectic relations appearing as the generalized cotangent bundle liftings of smooth stable mappings. Using this class of symplectic relations the classification theorem for generic (pre) images of lagrangian submanifolds is proved. The normal forms for the respective classified puilbacks and pushforwards are provided and the connections between the singularity types of symplectic relation, mapped lagrangian submanifold and singular image, are established. The notion of special symplectic triplet is introduced and the generic local models of such triplets are studied. We show that the open swallowtails are canonically represented as pushforwards of the appropriate regular lagrangian submanifolds. Using the SL2(ℝ) invariant symplectic structure of the space of binary forms of n appropriate dimension we derive the generating families for the open swallowtails and the respective generating functions for its regular resolutions.
Wave source potentials for two superposed fluids, each of finite depth
Authors: Kassem S. E.
Published: November 2008

Problems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line sources are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.
Asymptotic distributions of pontograms
Authors: Csörgő Miklós , Horváth Lajos
Published: November 2008

Let{N(x), x ≥ 0} be a Poisson process with intensity parameter λ > 0, and introduce

When looking for the changepoint in the Land's End data, Kendall and Kendall [7] proved for all 0 < ε1 < 1 − ε2 < 1 that

where {V(s), − ∞ < s < ∞} is an Ornstein–Uhlenbeck process with covariance function exp (−|t − s|). D. G. Kendall has posed the problem of replacing ε1 and ε2 by zero or by sequences εi(n) → 0 (n → ∞) (i = 1, 2), in (1·1). In this paper we study the latter problem and also its L2 version. The proofs will be based on the following weighted approximation of Zn.
The 2-variable polynomial of cable knots
Authors: Morton H. R. , Short H. B.
Published: November 2008

The 2-variable polynomial PK of a satellite K is shown not to satisfy any formula, relating it to the polynomial of its companion and of the pattern, which is at all similar to the formulae for Alexander polynomials. Examples are given of various pairs of knots which can be distinguished by calculating P for 2-strand cables about them even though the knots themselves share the same P. Properties of a given knot such as braid index and amphicheirality, which may not be apparent from the knot's polynomial P, are shown in certain cases to be detectable from the polynomial of a 2-cable about the knot.
Riesz products, Hausdorff dimension and normal numbers
Authors: Brown Gavin , Moran William , Pearce Charles E. M.
Published: November 2008

We say a real number x is normal to base r if the sequence is uniformly distributed modulo [0, 1]. Pollington[10] has proved the following result concerning the normality of numbers.
Homology and cohomology of locally supersoluble groups
Authors: Robinson Derek J. S.
Published: November 2008

In a recent article [13] a series of vanishing theorems was obtained for the (co)homology of locally nilpotent groups. These results assert that if (co)homology vanishes in low dimensions (0 or 1), then it vanishes in all dimensions, provided that the module satisfies an appropriate finiteness condition.
OnT(6)-groups
Authors: El-Mosalamy Mohamed S. , Pride Stephen J.
Published: November 2008

This paper is concerned with group presentations satisfying the small cancellation conditionT(6). The definition of this condition is given in §1·2, together with some examples. Before giving the definition, however, we describe (in §1·1) some material which, to a certain extent, motivated our paper. In § 1·3 we state our main theorem, which provides new solutions to the word and conjugacy problems forT(6)-groups.
On the Mal'cev quotients of certain hyperbolic link groups
Authors: Humphries S. P. , Long D. D.
Published: November 2008

In the understanding of hyperbolic 3-manifolds, some of the important open questions revolve around the behaviour of a surface upon the passage to a finite covering space; for example one would like to know if it is possible to replace an immersion by an embedding, or a separating surface by a non-separating one.
The maximal C*-norm and the Haagerup norm
Authors: Itoh Takashi
Published: November 2008

The difference between the maximal C*-norm ‖ ‖max and the Haagerup norm ‖ ‖h on the tensor product space of C*-aIgebras is studied. Let A and B be C*-algebras. It is shown that ‖ ‖max is equivalent to ‖ ‖h on A ⊗ B if and only if A or B is finite-dimensional.
An exotic factor ofS3× ℝ
Authors: Jakobsche W. , Repovš D.
Published: November 2008

Cannon'srecognition problem[10] asks for a short list of topological properties that is reasonably easy to check and thatcharacterizestopological manifolds. In dimensions below three the answer has been known for a long time: see [6, 24]. In dimensions above four it is now known, due to the work of J. W. Cannon [11], R. D. Edwards [14] (see also [12] and [18]), and F. S. Quinn [21], that topologicaln-manifolds (n≥ 5) are preciselyENRℤ-homologyn-manifolds with Cannon'sdisjoint disc property(DDP) [11] and with a vanishing Quinn'slocal surgery obstruction[23]. In dimension four there is a resolution theorem of Quinn [22] (with the same obstruction as in dimensions ≥ 5) and a 1-LCC shrinking theorem of M. Bestvina and J. J. Walsh [5]. However, it is still an open problem to find an effective analogue of Cannon's DDP for this dimension, one which would yield a shrinking theorem along the lines of that of Edwards [14]. For more on the history of the recognition problem see the survey [24].
Seminorms related to weak compactness and to Tauberian operators
Authors: Astala Kari , Tylli Hans-Olav
Published: November 2008

Let E and F be Banach spaces. The semigroup Φ+(E,F) of semi-Fredholm operators consists of the bounded linear mappings E→F with closed image and finite-dimensional kernel. By a well known result of Yood we have that T∈Φ+(E,F) if and only if for any bounded set B⊂E the condition TB relatively compact implies that B is relatively compact. Lebow and Schechter[10] gave a quantitative version of the above qualitative characterization, namely the operator T belongs to Φ+(E,F) if and only if there is c ≥ 0 such that

for all bounded B⊂E. Here γ is the well known Hausdorff measure of non-compactness

with BE the closed unit ball of E.
Global properties of supermanifolds and their bodies
Authors: Bryant Peter
Published: November 2008

In supersymmetric field theories, the use of Berezin-like integrals for curved superspace presupposes the existence of a smooth manifold structure on the underlying curved space (the body). The aim of this paper is to address the following question: when does a Rogers supermanifold have a body manifold?

Elementary techniques from the theory of foliations are used to derive some necessary and sufficient conditions. The main result is the necessity of regularity of the soul foliation in the sense of Catenacci, Reina and Teofilatto. Regularity is not sufficient (for example, punctured superspace is regular with non-Hausdorff body). A sufficient condition (albeit highly sensitive to the choice of charts) is the transitivity of the body relation ˜, a property enjoyed by De Witt supermanifolds.

We show that the body of a quotient supermanifold S/Γ is the quotient of the body (under the induced action). Several examples in the text illustrate that this is extremely useful.

New characterizations ρ-supermanifolds and their saturations are given and the saturation construction is extended to all bodied supermanifolds.
Extended generalized hexagons
Authors: Weiss Richard
Published: November 2008

As in [2], we define a geometry Γ = (B2, …, Br; *) to be an ordered sequence of r pairwise disjoint non-empty sets Bi together with a symmetric incidence relation * on their union B = B1 ∪ … ∪ Br such that if F is any maximal set of pairwise incident elements (i.e. a maximal flag), then |F ∩ Bi| = 1 for i = 1,…, r. The number r is called the rank of Γ. The geometry Γ is called connected if the r-partite graph (Γ, *) is connected.
The sum of Rademacher functions and Hausdorff dimension
Authors: Hu Tian-You , Lau Ka-Sing
Published: November 2008

For 0 < α < 1, let for 0 ≤ x < 1, where is the sequence of Rademacher functions. We give a class of fα so that their graphs have Hausdorff dimension 2 − α. The result is closely related to the corresponding unsolved question for the Weierstrass functions.
Fibrewise separation axioms for locales
Authors: Johnstone P. T.
Published: November 2008

In this paper we study the weak versions of the fibrewise separation axioms for locales over a base locale, whose introduction has been made possible by the development, in a previous paper by the author, of the fibrewise notion of closure for sublocales of locales over a base. We establish the implications which hold between these axioms and the traditional separation axioms for locales, and give counter-examples to show that some of these implications are irreversible.
Copies of l∞ in an operator space
Authors: Drewnowski Lech
Published: November 2008

Let X and Y be Banach spaces. Then Kw*(X*, Y) denotes the Banach space of compact and weak*-weakly continuous linear operators from X* into Y, endowed with the usual operator norm. Let us write E⊃l∞ to indicate that a Banach space E contains an isomorphic copy of l∞. The purpose of this note is to prove the following

Theorem. Kw*(X*, Y) ⊃ l∞if and only if either X ⊃ l∞or Y ⊃ l∞.
Entire functions with Julia sets of zero measure
Authors: Stallard Gwyneth M.
Published: November 2008

We extend results of McMullen about the dynamics of entire functions for which the orbits of the critical values stay away from the Julia set. In particular we show that such functions are expanding on their Julia sets which have self-similarity properties. Under suitable further conditions the Julia sets have plane measure zero.
Jones polynomial invariants for knots and satellites
Authors: Morton H. R. , Strickland P.
Published: November 2008

Results of Kirillov and Reshetikhin on constructing invariants of framed links from the quantum group SU(2)q are adapted to give a simple formula relating the invariants for a satellite link to those of the companion and pattern links used in its construction. The special case of parallel links is treated first. It is shown as a consequence that any SU(2)q-invariant of a link L is a linear combination of Jones polynomials of parallels of L, where the combination is determined explicitly from the representation ring of SU(2). As a simple illustration Yamada's relation between the Jones polynomial of the 2-parallel of L and an evaluation of Kauffman's polynomial for sublinks of L is deduced.
SchurQ-functions and cohomology of isotropic Grassmannians
Authors: Józefiak Tadeusz
Published: November 2008

We prove that for homogeneous spaces of isotropic Grassmannians the Borel map sends the basis of a truncated algebra of SchurQ-functions consisting ofQ-functions orP-functions (depending on a case) onto the basis dual to the basis of Schubert cycles.
On the dimension of the non-Cohen–Macaulay locus of local rings admitting dualizing complexes
Authors: Cuong Nguyen Tu
Published: November 2008

In this paper we mainly consider local rings admitting dualizing complexes. It is well-known that if a Noetherian local ring A admits a dualizing complex, then the non-Cohen–Macaulay (abbreviated CM) locus of A is closed in the Zariski topology (cf. [8, 10]). If the dimension of this locus is zero and A is equidimensional, i.e. the punctured spectrum of A is locally CM and dim(A/P) = dim (A) for all minimal prime ideals P ∈ Ass (A), then A is a generalized CM ring and its structure is well-understood (see [2, 12]). For instance, one of the characterizations of generalized CM rings is the conditions that for any parameter ideal q contained in a large power of the maximal ideal m of A, the difference between length and multiplicity

is independent of the choice of q. However, if the dimension of the non-CM locus is larger than zero, little is known about how this dimension is related to the structure of the local ring A. The purpose of this paper is to show that if M is a finitely generated A-module, then there exist systems of parameters x = (x1, …, xd) (where d = dim M) such that the difference

is a polynomial in n1, …, nd for all positive integers n1, …, nd and the degree of IM(n1, …, nd;x) is independent of the choice of x. We shall also give various characterizations of this degree by using the notion of reducing systems of parameters of Auslander and Buchsbaum[l]. In particular, if the module M is equidimensional we shall show that the degree of IM(n1, …, nd;x) is equal to the dimension of the non-CM locus of M.
Quantum stochastic differential equations on *-bialgebras
Authors: Glockner Peter
Published: November 2008

Many examples of quantum independent stationary increment processes are solutions of quantum stochastic differential equations. We give a common characterization of these examples by a quantum stochastic differential equation on an abstract *-bialgebra. Specializing this abstract *-bialgebra and the coefficients of the equation, we obtain the equations for the Unitary Noncommutative Stochastic processes of [12], the Quantum Wiener Process [2], the Azéma martingales [11] and for other examples. The existence and uniqueness of a solution of the general equation is shown. Assuming the boundedness of this solution, we prove that it is a continuous and stationary independent increment process.
Square-full numbers in short intervals
Authors: Heath-Brown D. R.
Published: November 2008

A positive integer n is called square-full if p2|n for every prime factor p of n. Let Q(x) denote the number of square-full integers up to x. It was shown by Bateman and Grosswald [1] that

Bateman and Grosswald also remarked that any improvement in the exponent would imply a ‘quasi-Riemann Hypothesis’ of the type for . Thus (1) is essentially as sharp as one can hope for at present. From (1) it follows that, for the number of square-full integers in a short interval, we have

when and y = o (x½). (It seems more suggestive) to write the interval as (x, x + x½y]) than (x, x + y], since only intervals of length x½ or more can be of relevance here.)
The integral cohomology rings of some p-groups
Authors: Leary I. J.
Published: November 2008

We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested independently by P. H. Kropholler and J. Huebschmann. This construction has also been used by the author to calculate the mod-p cohomology of the same groups and by B. Moselle to obtain partial results concerning the mod-p cohomology of the extra special p-groups [7], [9].
The classifying space of a crossed complex
Authors: Brown Ronald , Higgins Philip J.
Published: November 2008

The aim of this paper is to show one more facet of the role of crossed complexes as generalisations of both groups (or groupoids) and of chain complexes. We do this by defining and establishing the main properties of a classifying space functor B: from the category of crossed complexes to the category of spaces.
Paracompact locales and metric spaces
Authors: Paseka Jan
Published: November 2008

This paper deals with the category of paracompact locales (‘pointless topologies’), defined in the classic paper [6] of Isbell. A full discussion concerning paracompact locales can be found in Dowker and Strauss[2] and in Pultr[10, 11]. We shall provide a description of paracompact Tychonoff locales by means of a system of suitably chosen metric spaces. This answers Pultr's question whether each paracompact Tychonoff locale is a closed sublocale of a (localic) product of metric spaces.
Contraction subgroups and semistable measures on p-adic Lie groups
Authors: Dani S. G. , Shah Riddhi
Published: November 2008

Continuous one-parameter semigroups {μt}t≥0 of probability measures on a locally compact group which are semistable with respect to some automorphism τ of the group, namely such that τ(μt) = μct for all t ≥ 0, for a fixed c ∈ (0, 1), have attracted considerable attention of various researchers in recent years (cf. [3], [5] and other references cited therein). A detailed study of semistable measures on (real) Lie groups is carried out in [5]. In this context it is of interest to study semistable measures on the class of p-adic Lie groups, which is another significant class of locally compact groups.
Examples of 3-knots with no minimal Seifert manifolds
Authors: Silver Daniel S.
Published: November 2008

We work throughout in the smooth category. Homomorphisms of fundamental and homology groups are induced by inclusion. Ann-knot, formn≥ 1, is an embeddedn-sphereK⊂Sn+2. ASeifert manifoldforKis a compact, connected, orientable (n+ 1)-manifoldV⊂Sn+2with boundary ∂V=K. By [9] Seifert manifolds always exist. As in [9] letYdenoteSn+2split alongV; Yis a compact manifold with ∂Y=V0∪V1, whereVt≈V. We say thatVis aminimal Seifert manifoldforKif π1Vt→ π1Yis a monomorphism fort= 0, 1. (Here and throughout basepoint considerations are suppressed.)
On complete curves in moduli space I
Authors: González Díez Gabino , Harvey William J.
Published: November 2008

Letgdenote the moduli space of compact Riemann surfaces of genusg> 3. It is known thatgis a non-complete quasi-projective variety that contains many complete curves. This is because the Satake compactificationgofgis projective and the boundary\has co-dimension 2; thus by intersectingwith hypersurfaces in sufficiently general position one obtains a complete curve ingpassing through any given set of points [8].
Derivations on a Fréchet convolution algebra associated with a weight
Authors: McClure J. P.
Published: November 2008

For certain Fréchet convolution algebras associated with a weight w on the half-line [0, ∞), we are interested in the question of which Radon measures on [0, ∞) determine the derivations on the algebra. For particular weights, we show that the derivations are determined by those measures in the multiplier algebra of the original algebra. However, we also give an example of a weight for which that characterization fails. The results show a connection between the space of derivations and the behaviour for large y of the ratio w(x + y)/w(x) w(y).
Immersions with non-zero normal vector fields
Authors: Li Bang-He , Li Gui-Song
Published: November 2008

Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).
Mean growth of the derivative of certain classes of analytic functions
Authors: Girela Daniel
Published: November 2008

In this paper we study the question of characterizing those positive Borel measures μ on the unit disc Δ for which the differentiation operator D defined by Df = f′ maps the Hardy space Hp continuously into the Bergman space Bp(dμ) of all functions f analytic in Δ which belong to Lp (Δ, dμ).
Local dimension and regular points
Authors: Barlow Martin T. , Taylor S. James
Published: November 2008

The Hausdorff–Besicovitch dimension of a set A ⊆ ℝd, denoted dim (A), relates to the structure of A in the neighbourhood of its thickest point. If A is irregular then one may wish for an index which will describe the size of A in different places. The obvious definition of the local dimension of A near x is

and it is not hard to verify that
The perturbation of relatively open operators with reduced index
Authors: Labuschagne L. E.
Published: November 2008

Let X and Y denote normed spaces and T:D(T) ⊂ X → Y a linear transformation. It is shown that even in the case where both X and Y are incomplete, the quantity remains constant under both small and compact perturbation, provided that T is relatively open, R(T) is closed, and the perturbation is made in the right ‘direction’. If in addition and N(T) is topologically complemented, the topological complementation of the kernel is also preserved under small perturbations made in the right ‘direction’ and arbitrary compact perturbation. Various counter-examples are exhibited proving these results to be best possible.
On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums
Authors: Hall R. R. , Wilson J. C.
Published: November 2008

A number of authors, including Apostol [1], Carlitz [2], Mikolás [5] and Rademacher [9] have obtained linear relations for the Dedekind sums

(the inhomogeneous sum) and the homogeneous sum

Here denotes the periodic extension into ℝ of the Bernoulli polynomial Bm(X) on [0, 1] given by the relation

with the exception that we define
The iteration of entire functions of small growth
Authors: Stallard Gwyneth M.
Published: November 2008

We show that if a transcendental entire function has order zero and sufficiently small growth or has order ρ < ½ and regular growth then its set of normality has no unbounded components.
Curves of genus 2 with good reduction away from 2 with a rational Weierstrass point
Authors: Merriman J. R. , Smart N. P.
Published: November 2008

All curves of the title are calculated up to an equivalence relation which is coarser than the relation of isogeny between the associated Jacobian varieties.
On random polynomials over finite fields
Authors: Arratia Richard , Barbour A. D. , Tavaré Simon
Published: November 2008

We consider random monic polynomials of degreenover a finite field ofqelements, chosen with allqnpossibilities equally likely, factored into monic irreducible factors. More generally, relaxing the restriction thatqbe a prime power, we consider that multiset construction in which the total number of possibilities of weightnisqn. We establish various approximations for the joint distribution of factors, by giving upper bounds on the total variation distance to simpler discrete distributions. For example, the counts for particular factors are approximately independent and geometrically distributed, and the counts for all factors of sizes 1, 2, …,b, whereb=O(n/logn), are approximated by independent negative binomial random variables. As another example, the joint distribution of the large factors is close to the joint distribution of the large cycles in a random permutation. We show how these discrete approximations imply a Brownian motion functional central limit theorem and a Poisson-Dirichiet limit theorem, together with appropriate error estimates. We also give Poisson approximations, with error bounds, for the distribution of the total number of factors.
Positivity of some basic cosine sums
Authors: Brown Gavin , Wang Kun-Yang , Wilson David C.
Published: November 2008

We show that all partial sums of 1 + σk−α cos kθ are non-negative for α > α0, where 0·308443 < α0 < 0·308444 and α0 is the unique root of the equation
On the signature and Euler characteristic of certain four-manifolds
Authors: Johnson F. E. A. , Kotschick† D.
Published: November 2008

Let M be a smooth closed connected oriented 4-manifold; we shall say that M satisfies Winkelnkemper's inequality when its signature, σ(M), and Euler characteristic, X(M), are related by

This inequality is trivially true for manifolds M with first Betti number b1(M) ≤ 1.
Dyer–Lashof operations in the Hopf ring for complex cobordism
Authors: Turner Paul R.
Published: November 2008

We give a complete description of the additive Dyer-Lashof operations on the Hopf ringwith coefficients in. We re-prove a result of Ravenel and Wilson [9] giving the operations on the elementand give formulae for the operations on the other generators.
Reflections in extended Bianchi groups
Authors: Vulakh L. Ya.
Published: November 2008

Letdbe a positive square-free number. LetOdbe the ring of integers in Q(√ −d). The groupsPSL(2, Od) are called collectively the Bianchi groups. The extended Bianchi groupBdis the maximal discrete extension ofPSL(2,Od) inPSL(2, C). The groupBdacts by linear fractional transformations on the complex plane C. LetRBdbeBdwith the generator θ,, adjoined. (RBdwill be also called an extended Bianchi group (cf. [18])). A group is said to be reflective if it contains a Coxeter subgroup (i.e. a subgroup generated by reflections) of finite index. The groupsRBdand their subgroups have been investigated in [3, 6, 13, 15, 16, 17, 18, 20, 21]. In 1892 Bianchi[3] proved thatPGL(2,Od)⋊{θ} is reflective ifd≤ 19,d╪ 14 or 17. Vinberg [18] proved that if the groupRBdis reflective, then the orders of all elements of the ideal-class group of the field Q(√ −d) should divide 4. Shaiheev [16] proved that there are only finitely many reflective extended Bianchi groups and found all of them ford≤ 30. Similar results are obtained for groupsPGL(2,Od) ⋊ {θ} which, as Shvartsman [17] showed, are reflective only whend= 1, 2, 5, 6, 10, 13, 21, providedd= 1 or 2 (mod 4).
Filtrations for q-Young modules
Authors: Martin Stuart
Published: November 2008

We show that, over suitable rings, q-Young modules for the Hecke algebra of type A have a filtration by q-Specht modules. The multiplicities are also determined.
On transmission problems for wave propagation in two locally perturbed half-spaces
Authors: Zhang Bo
Published: November 2008

In this paper, we consider transmission problems for wave propagation in two inhomogeneous half-spaces with a locally perturbed hyperplane interface. A radiation condition is obtained for the problem in the framework of the spaces B and B*. It is then used, together with the spaces B, B* and the limiting absorption method to prove the existence of the unique solution to the problem.
A note on the diophantine equation (xm − l) / (x − 1) = yn + l
Authors: Maohua Le
Published: November 2008

Let ℤ, ℕ, ℚ denote the sets of integers, positive integers and rational numbers, respectively. Solutions (x, y, m, n) of the equation (1) have been investigated in many papers:

Let ω(m), ρ(m) denote the number of distinct prime factors and the greatest square free factor of m, respectively. In this note we prove the following results.
Cyclotomic Galois module structure and the second Chinburg invariant
Authors: Snaith Victor P.
Published: November 2008

We study the second Chinburg invariant of a Galois extension of number fields. The Chinburg invariant lies in the class-group of the integral group-ring of the Galois group of the extension. A procedure is given whereby to evaluate the invariant in the case of the real cyclotomic case of regular prime power conductor and their subextensions of p-power degree. The invariant is shown to be zero in the latter cases, which yields new examples giving an affirmative answer to a question of Chinburg ([1], p. 358) which has come to be known as ‘Chinburg's Second Conjecture’ ([3], §4·2).