bluuebunny/crossref_metadata_2025 huggingface dataset:
A simple proof of the Mazur-Orlicz summability theorem
Authors: Fridy J. A.
Published: November 2008

In 1933(1), Mazur and Orlicz stated that, if a conservative (i.e. convergence preserving) matrix sums a bounded nonconvergent sequence, then it must sum an unbounded sequence. Their proof of this result (2) was one of the early applications of functional analysis to summability theory, and it is based on rather deep topological properties of F K-spaces. In (3) Zeller obtained a proof of this important theorem as a consequence of his study of the summability of slowly oscillating sequences. The purpose of this note is to give a simple direct proof of this theorem using only the well-known Silverman-Töplitz conditions for regularity. In order to reduce the details of the argument, we state and prove the result for regular matrices rather than conservative matrices.
Topological properties of real simple germs, curves, and the nice dimensions n > p
Authors: Damon James
Published: November 2008

Infinitesimally stable germs play an important role both as germs from which global C∞-stable mappings are constructed and as germs representing versal unfoldings of (C∞ or holomorphic) germs. Because of the presence of moduli, the C∞ (or analytic) classification of these germs is insufficient and the topological classification of these germs must be understood as well. Here we consider the classification of such germs in the region where no moduli occur. This region is important for several reasons. Most importantly, it contains the infinitesimally stable germs occurring in the nice dimensions. These are the dimensions in which globally infinitesimally stable mappings are dense among the proper C∞-mappings. In (4), it was proved that the topological and C∞-classifications agree for infinitesimally stable germs f: n, 0 → p, 0 in the nice dimensions, n ≤ p. This was then used in (5) to characterize those topologically stable germs which are C∞-stable.
Comparison theorems for conic bundles
Authors: Newstead P. E.
Published: November 2008

In (10), M. S. Narasimhan and S. Ramanan proved a theorem to the effect that a certain conic bundle associated with a non-singular quadratic complex does not come from a vector bundle ((10), proposition 8·1); a similar topological result was proved in (12). In the course of attempting to extend these results to the singular case, I found that I wanted to use some results on conic bundles which were not readily available in the literature. The object of this note is to give proofs of these results; the work on quadratic complexes is still in progress and the first part will appear shortly (13). A further application will appear in (14).
Solitary wave solutions for a model of the two-way propagation of water waves in a channel
Authors: Toland J. F.
Published: November 2008

Bona and Smith (6) have suggested that the coupled system of equations

has the same formal justification as other Boussinesq-type models for the two-way propagation of one-dimensional water waves of small but finite amplitude in a channel with a flat bottom. The variables u and η represent the velocity and elevation of the free surface, respectively. Using the energy invariant

they show that for a restricted, but nevertheless physically relevant, class of initial data, the system (1·1) has solutions which exist for all time, and that in such circumstances the wave height is bounded solely in terms of the initial data.
Incompleteness of (nq + n - q - 2, n)-arcs in finite projective planes of even order
Authors: Wilson B. J.
Published: November 2008

1. It was shown by Barlotti (1) that the number k of points on a (k, n)-arc of a finite projective piane of order q

and that if q ≢ 0 (mod n) then for n ≥ 3

.
Sifting short intervals
Authors: Friedlander John B.
Published: November 2008

Let φ (X) denote a function satisfying limx→∞, φ(X) = ∞. Let ℬ be a sequence of positive integers and let T(X) = T(X, ℬ, φ) be the set of real numbers y, 1 ≤ y ≤ X, such that the interval (y, y + φ(y)] contains no member of ℬ.
On equimultiplicity
Authors: Herrmann M. , Orbanz U.
Published: November 2008

This note consists of some investigations about the condition ht(A) = l(A) where A is an ideal in a local ring and l(A) is the analytic spread of A (9).

In (4) we proved the following: If R is a local ring and P a prime ideal such that R/P is regular then (under some technical assumptions) ht(P) = l(P) is equivalent to the equimultiplicity e(R) = e(RP). Also for a general ideal A (which need not be prime), the condition ht(A) = l(A) can be translated into an equality of certain multiplicities (see Theorem 0).
Tori in the diffeomorphism groups of simply-connected 4-manifolds
Authors: Melvin Paul
Published: November 2008

Let M be a closed simply-connected 4-manifold. All manifolds will be assumed smooth and oriented. The purpose of this paper is to classify up to conjugacy the topological subgroups of Diff(M) isomorphic to the 2-dimensional torus T2 (Theorem 1), and to give an explicit formula for the number of such conjugacy classes (Theorem 2). Such a conjugacy class corresponds uniquely to a weak equivalence class of effective T2-actions on M. Thus the classification problem is trivial unless M supports an effective T2-action. Orlik and Raymond showed that this happens if and only if M is a connected sum of copies of ± ;P2 and S2 × S2 (2), and so this paper is really a study of the different T2-actions on these manifolds.
Random uniform triangles and the alignment problem
Authors: Small Christopher
Published: November 2008

Let n points be drawn independently and uniformly from a compact convex set K. The distribution of the shape of the resulting n–ad is determined and studied in the region corresponding to near alignment. Special attention is given to the case n ≥ 4 and a table provided to help in the assessment of practical data (e.g. megalithic ‘alignments’). The Broadbent factor, representing the effect of stretching the parent distribution, is computed explicitly.
Some orthogonal and complete sets of Bessel functions associated with the vibrating plate
Authors: Higgins J. R.
Published: November 2008

Abstarct

Some orthogonal sets of Bessel functions of real order v are identified using the equation Δ2u = utt of the vibrating plate. Our main concern is with the L2 completeness of such sets, and we prove that the well known ‘clamped edge’ type is complete for v > -1, thus completing a result of E. Dahlberg. We also study a very closely related set and show that it needs an extra (non-Bessel) function for completeness.

Our method for proving the completeness is based on one given by H. Hochstadt in connection with Dini functions. We have found it necessary to reorganize Hoch-stadt's method and correct some errors contained in it.

Certain isolated values of v require special attention and we treat these by subjecting the Dalzell completeness criterion to a continuity argument.
Supercontinuity
Authors: Henle J. M. , Mathias A. R. D.
Published: November 2008

Let K > ω and . It is known that there then exists a non-trivial k-additive 2-valued measure, Vk, on the set [K]k of subsets of k of cardinality K..
Real inversion theorems for generalized Stieltjes transforms. II
Authors: Love E. R. , Byrne Angelina
Published: November 2008

This paper is a continuation of (3), in which we proved extensions, to generalized Stieltjes transforms, of some inversion theorems of Widder(l) for ordinary Stieltjes transforms. The numbering of formulae, lemmas and theorems continues on consecutively from that in (3). The last formula in (3) is numbered (32), and the last lemma or theorem is Theorem 18.
Sifting short intervals II
Authors: Friedlander John B.
Published: November 2008

Let g(y) denote an arbitrary real-valued function satisfying g(y) → ∞ as y → ∞. One expects, and, subject to certain conjectures, Heath-Brown(3) has proved, that for all y in (1, X], apart from a set of measure o(X), the interval (y, y + g(y) log y] contains primes.
Continuation of analytic structure in the maximal ideal space of a uniform algebra
Authors: Shackell John R.
Published: November 2008

Let A be a uniform algebra with maximal ideal space M and Shilov boundary Σ; see (8), (18) or (21) for the basic definitions. If Σ is different from M, there is often analytic structure in M/Σ. However this is not always the case, as is shown by the classical example of Stolzenberg in (16). Hence much of the considerable amount of research on this topic has been devoted to finding conditions which ensure the presence of analytic structure in M/Σ One particularly fruitful line of development has been concerned with one-dimensional analytic structure; in particular we have in mind the classical theorem of Bishop (see (2), chapter 11) and the more recent result of Aupetit and Wermer(2).
Eigen-values of Lipschitz kernels
Authors: Reade J. B.
Published: November 2008

Asymptotic estimates are obtained for the eigen-values of symmetric kernels which satisfy a Lipschitz condition of order α, where 0 < α ≤ 1, on a bounded region. For 0 < α < 1, the eigen-values are shown to be O(1/nα+½) for general kernels, and O(1/nα+1) for positive definite kernels. For α = 1, the eigen-values are shown to be O(1/n+3/2) in general, but only O(1/n2) when the kernel is positive definite. Examples are given to show these estimates are best possible for powers of n.

The estimates for general kernels are known. In 1931, Hille and Tamarkin used infinite determinants to obtain weaker estimates in the case 0 < α < 1, but the same estimates as ours for α = 1. In 1937, Smithies sharpened the estimates for 0 < α < 1 to the ones we give by a variant of the method used by Weyl in 1912 for smooth kernels. Cochran obtained the same estimates in 1972 using Fredholm determinants. Our proof uses Weyl's method in its original form for 0 < α < 1, and in Smithies' variant for α = 1, so in all cases simplifies previous proofs.

The estimates for positive definite kernels are, as far as we know, new. The proofs use the method of our recent paper on smooth positive definite kernels.
Absolutely divergent series and classes of Banach spaces
Authors: Ruckle William H.
Published: November 2008

A normed space E is said to be series immersed in a Banach space X if for every absolutely divergent series nxn in E there is a continuous linear mapping T from E into X such that nTxn diverges absolutely. The theorem of Dvoretzky and Rogers(1) implies that a normed space E is series immersed in a finite dimensional space if and only if E itself is finite dimensional. In (4) and (9) it was shown that E is series immersed in lp 1 p < if and only if E is isomorphic to a subspace of Lp() for some measure . In particular, E is isomorphic to an inner product space if and only if it is series immersed in a Hilbert space. The property of series immersion was further studied in the papers (7) and (8). The main results in these two papers are conditions on X under which E series immersed in X would imply E locally immersed in X, a condition slightly stronger (formally) than E finitely representable in X.
Some properties of maximal measures on compact convex sets
Authors: Batty C. J. K.
Published: November 2008

Let be a maximal measure on a compact convex set K, K* be the state space of the space of all continuous functions f: KK ℝ which are affine in the first variable, 1 be the -algebra on K generated by the Baire sets and the compact extremal subsets of K, and = {BeK1}. Then

(i) For any fixed continuous function g:K ℝ and -almost all x in K, there is a closed face of K containing x on which g is constant.

(ii) The image of under the map :KK* defined by f, (x) = f(x, x) is the unique maximal measure on K* representing its barycentre

(iii) induces a measure on (eK) satisfying certain regularity conditions.
Central limit theorems for a class of symmetric statistics
Authors: Weber N. C.
Published: November 2008

Motivated by problems in the analysis of spatial data, central limit theorems are developed for U-statistics whose kernels depend on the size of the observed sample. These theorems are then applied to obtain results for the interpoint distance statistic and the large angle statistic.
Minimum growth of harmonic functions and thinness of a set
Authors: Wu Jang-Mei G.
Published: November 2008

In [3], Barth, Brannan and Hayman proved that if u(z) is any non-constant harmonic function in ℝ2, ø(r) is a positive increasing function of r for r ≥ 1 and

then there exists a path going from a finite point to ∞, such that u(z) > ø(|z|) on Γ. Moreover, they showed by example that the integral condition above cannot be relaxed.
Composite matrix inverses and generalized Gershgorin sets
Authors: Nwokah O. D. I.
Published: November 2008

In computational matrix algebra, Gershgorin's Theorem [8] and Ostrowski's Theorem[14] play key roles in establishing regularity conditions for complexn×nmatrices. As a result of this importance as well as possible applications in other areas, several extensions of these results have been made (Kotelyanski[9], Ky Fan [5], Brauer[2], Nwokah[10]), for point set matrices. More recently, further extensions have been made to include regularity conditions for composite matrices (matrices partitioned into blocks) (Brenner [3], Van der Sluis[16], Feingold and Varga[6], Cook [4]). Cook's result was motivated by engineering applications but is rather restrictive since, like Feingold and Varga, it requires that the matrices under consideration be diagonally dominant. In this paper, the diagonal dominance condition is replaced by a more general condition (theH-matrix condition). Estimates for the diagonal blocks of block-partitioned matrix are then obtained. The results on inclusion regions for eigenvalues unifiex the previous results of Feingolg and Varga [6], kotelyanski [9], Brauer [2], and generalizes the earlier results of Nwokah [10], from point matrices to block-partitioned matrices. In a sense, these results complement those of brenner [3] Van der Sluis [16], but like those of Cook [4], have a more immediate direct application to control engineering in the area of computer-aided design of composite feedback control systems (Nwokah [12]), which will be briefly reviewed towards the end of the paper.
Strongly plus-amphicheiral knots are algebraically slice
Authors: Long D. D.
Published: November 2008

A classical knot in S3 is said to be slice if it is the boundary of a smooth (or PL locally unknotted) disc in B4. The first obstructions to sliceness were introduced in [3] (the Alexander polynomial is of the form f(t). f(t−1)) and [7] (the signature is zero). Levine defined the notion of algebraically slice knot in [5]. This property implies the first two obstructions vanish.
Semigroups of operators and an application to spectral theory
Authors: Ricker W.
Published: November 2008

A problem of fundamental importance in Spectral Theory consists of finding criteria for an operator to be of scalar-type in the sense of N. Dunford [1]. One relatively general approach in determining such criteria is based on the method of integral transforms (see for example [4], [5], [6], [11], [12]). For example, ifXis a Banach space andTis a continuous linear operator onX, then the group {eitT; treal} exists. As noted by several authors (e.g. [4], [6]), this group can then be effectively used for analysing the operatorT.
An exterior problem in elastodynamics
Authors: Jones D. S
Published: November 2008

A modified kernel is devised which avoids the irregular values which plague the natural integral equations for the exterior problems of harmonic elastic waves in a homogeneous isotropic medium.
Unsound ordinals
Authors: Mathias A. R. D.
Published: November 2008

An ordinal is termed unsound if it has subsets An (nεω) such that un-countably many ordinals are realised as order types of sets of the form ∪ {An|nε a} where a ⊆ ω. It is shown that if ω1 is regular and then the least unsound ordinal is exactly but that if ω1 is regular and the least unsound ordinal, assuming one exists, is at least . Arguments due to Kechris and Woodin are presented showing that under the axiom of determinacy there is an unsound ordinal less than ω2. The relation between unsound ordinals and ideals on w is explored. The paper closes with a list of open problems.
Best L∞-approximation of measurable, vector-valued functions
Authors: Al-Rashed Abdallah M. , Darst Richard B.
Published: November 2008

Let (Ω, ,μ) be a probability space, and let be a sub-sigma-algebra of . Let X be a uniformly convex Banach space. Let A =L∞(Ω, , μ X) denote the Banach space of (equivalence classes of) essentially bounded μ-Bochner integrable functions g: Ω.→ X, normed by the function ∥.∥∞ defined for g ∈ A by

(cf. [6] for a discussion of this space). Let B = L∞(Ω, , μ X), and let f ε A. A sufficient condition for g ε B to be a best L∞-approximation to f by elements of B is established herein.
A topos with no geometric morphism to any Boolean one
Authors: Paré Robert
Published: November 2008

In [1], Julian Cole asked whether every topos is definable over a Boolean one. Peter Johnstone partially answered this in [2] (corollary 3·7) by giving an example of a topos admitting no bounded morphism to any Boolean topos. Here we give a simple example where boundedness is unnecessary.
A topological proof of Stallings' theorem on lower central series of groups
Authors: Cochran Tim. D.
Published: November 2008

For a topologist, the fundamental group G of a space is usually the most important non-abelian algebraic object of study. However, under many equivalence relationships G is not invariant, so topologists have been led to examine other algebraic objects. In particular, for questions of concordance the lower central series of G seems to play the crucial role. Recall that the lower central series Gn(n = 1,2,...) of G is defined by G1 = G, Gn = [G, Gn_1] for n > 1, and the lower central sequence of G is the sequence of quotients G/Gn.
Probabilistic proofs of asymptotic formulas for some classical polynomials
Authors: Maejima Makoto , Assche Walter Van
Published: November 2008

Recently Stadje [9] gave asymptotic formulas for some Bessel functions by using a probabilistic argument: some Bessel functions can be represented by the probability distribution of partial sums of symmetrized independent and identically distributed random variables (Feller [4], p. 149). Stadje used this idea and the local limit theorem, which is well known in probability theory.
Deformations of hyperbolic structures
Authors: Kourouniotis Christos
Published: November 2008

In this paper I shall define a deformation of hyperbolic structures on n-manifolds, called ‘bending’, by constructing a family of quasiconformal homeomorphisms of hyperbolic (n+ l)-space. The deformation can be applied to manifolds which contain totally geodesic submanifolds of codimension 1.
Topologies and continuous functions on extreme points and pure states
Authors: Batty C. J. K.
Published: November 2008

There are various ways of using the affine geometry of a compact convex set K to topologize its extreme boundary ∂eK (see [2, 7, 10] and the references quoted therein). The best-known method is to take as closed sets the traces on ∂eK of the closed split faces of K. This topology is known as the facial topology [1, 2, 4], and is significant because the facially continuous functions correspond to the order-bounded linear operators on A(K) and to the multipliers in A(K) [1, 3, 20]. Typically, split faces are scarce, so that the facial topology is coarse. The Choquet topology [7, 15, 18], whose closed sets are the traces of compact extremal subsets of K, is finer, but is usually less easily recognized. The Bishop–de Leeuw theorem was extended in [5] by showing that a maximal measure on K induces a measure on a σ-algebra on ∂eK containing the Choquet closed sets as well as the traces of the Baire subsets of K. The maximal topology is finer even than the Choquet topology, and the Bishop-de Leeuw theorem was further extended in [18] to a σ-algebra including the maximally closed sets. Although the definition of the maximal topology in [18] made use of integral representation theory, a geometrical description of it will be given in Proposition 2·1 below. The Choquet and maximally continuous functions on ∂eK were characterized in [18] in terms of the geometry and integral representation theory of K, respectively. It will be shown in Theorem 2·4 that the Choquet and maximally continuous functions coincide if is a union of faces of K, even though the topologies may differ.
A sequence well distributed in the square
Authors: Pinch R. G. E.
Published: November 2008

Bollobás and Erdös[1] have posed the problem:

If a is irrational, show that for 1 ≤ i < j ≤ p the number of integers t with 1 ≤ t ≤ p such that {(t–i)2a} < d and {(t–j)2a} < d, 0 < d < 1, is d2p + o(p) uniformly in i, j.
Extensions of pro-pgroups of cohomological dimension two
Authors: Würfel Tilmann
Published: November 2008

The purpose of this note is to extend Brumer's characterization of pro-pgroups of cohomological dimension two ([1], corollary 5·3) to presentations more general than free ones. The result is then used to rid a proof in [7] of certain field theoretic ingredients. As a by-product we complete a result of Tsvetkov [6] about group extensions obtained by omitting relations.
Simultaneous Pellian equations
Authors: Pinch R. G. E.
Published: November 2008

In this paper we describe a method for finding integer solutions of simultaneous Pellian equations, that is, integer triples (x,y,z) satisfying equations of the form

where the coefficientsa,b,c,d,fare integers and we assume thata,c, andacare not square.
Morita equivalence for continuous groups
Authors: Moerdijk Ieke
Published: November 2008

This paper is essentially concerned with the following problem. LetGbe a topological group.AG-set is a setSequipped with a continuous action(whereSis given the discrete topology). TheseG-sets form a categoryBG. It is well known that ifGandHarediscretegroups,BGis equivalent toBHiffGis isomorphic toH. However, this result cannot be extended much beyond the discrete case. The problem is: when isBGequivalent toBH, for topological groupsGandH?
On fixed-point-free elements
Authors: Espuelas Alberto
Published: November 2008

In Theorem 1·2 of [3] the following extension of the classical theorem of Shult is proved.

Theorem. Let G be a p-solvable group and let V be a faithful KG-module, where char. Assume that G contains an element x of order pn acting fixed-pointfreely on V. If p is a Fermat prime suppose further that the Sylow 2-subgroups of G are abelian. If p = 2 assume that the Sylow q-subgroups of G for each Mersenne prime q less than 2n are abelian. Then
Pregroups and length functions
Authors: Hoare A. H. M.
Published: November 2008

Pregroups were defined by Stallings[7] who showed that the elements of the group they define have a normal form up to an equivalence called interleaving. Recently Rimlinger[5] has shown that subject to a discreteness and a boundedness condition any pregroup P defines a graph of groups. We show here that closer analysis of P makes the boundedness condition superfluous. In § 1 we give results of Stallings and Rimlinger and prove some key lemmas. In §2 we show that the discreteness condition gives an integer-valued length function in the sense of Lyndon [4]. It follows from the work of Chiswell [2] and Serre [6] that this defines a graph of groups. I would like to thank the referee for his careful reading and useful comments on this paper.
Filtrations, closure operations and prime divisors
Authors: Okon J. S. , Ratliff L. J.
Published: November 2008

Let ƒ = {In}n≽ 0be a filtration on a ringR, let

(In)w= {xεR;xsatisfies an equationxk+i1xk− 1+ … +ik= 0, whereijεInj} be the weak integral closure ofInand let ƒw= {(In)w}n≽ 0. Then it is shown that ƒ ↦ ƒwis a closure operation on the set of all filtrations ƒ ofR, and ifRis Noetherian, then ƒwis a semi-prime operation that satisfies the cancellation law: if ƒh≤ (gh)wand Rad (ƒ) ⊆ Rad (h), then ƒw≤gw. These results are then used to show that ifRand ƒ are Noetherian, then the sets Ass (R/(In)w) are equal for all largen. Then these results are abstracted, and it is shown that ifI↦Ixis a closure (resp.. semi-prime, prime) operation on the set of idealsIofR, then ƒ ↦ ƒx= {(In)x}n≤ 0is a closure (resp., semi-prime, prime) operation on the set of filtrations ƒ ofR. In particular, if Δ is a multiplicatively closed set of finitely generated non-zero ideals ofRand (In)Δ= ∪KεΔ(In, K: K), then ƒ ↦ ƒΔis a semi-prime operation that satisfies a cancellation law, and ifRand ƒ are Noetherian, then the sets Ass (R/(In)Δ) are quite well behaved.
Locally compact groups: maximal compact subgroups and N-groups
Authors: Bagley R. W. , Wu T. S. , Yang J. S.
Published: November 2008

If G is a locally compact group such thatG/G0contains a uniform compactly generated nilpotent subgroup, thenGhas a maximal compact normal subgroupKsuch thatG/Gis a Lie group. A topological groupGis an N-group if, for each neighbourhoodUof the identity and each compact setC⊂G, there is a neighbourhoodVof the identity such thatfor eachg∈G. Several results on N-groups are obtained and it is shown that a related weaker condition is equivalent to local finiteness for certain totally disconnected groups.
Group homomorphisms inducing an isomorphism of a functor
Authors: Minami Norihiko
Published: November 2008

Whenever a covariant (resp. contravariant) functor F from a category of groups is given, it is natural to ask the following question: if a homomorphismof groups induces the isomorphism (resp., ), is f itself an isomorphism?
Tangential H∞-images of boundary curves
Authors: Rudin Walter
Published: November 2008

1.Introduction. Suppose that Ω is a region (i.e. a connected open set) in ࠶n, for some fixedn≥ 1. We define (Γ, μ) to be aFatou pair inΩ if

(a) Γ is a continuous family of boundary curves γwin Ω, one ending at each w ∈ ∂Ω,

(b) μ is a positive finite Borel measure on ∂Ω, and

(c) the conclusion of Fatou's theorem holds with respect to Γ and μ. Let us state (a) and (c) in more detail:

(a) The map(w, t) → γw(t)is continuous, from ∂Ω × [0, 1) into Ω, and

for every w in the boundary ∂Ω of Ω.

(c) For everyf ∈ H∞(Ω)(the class of all bounded holomorphic functions in Ω), the limit

exists a.e. [μ].
A ‘Hardy–Littlewood’ approach to the norm form equation
Authors: Everest G. R.
Published: November 2008

Suppose that K is a number field and n = [K: ℚ]. Write S∞(K) for the set of archimedean places of K, i.e. the set of all embeddings σ: K → ℂ. Suppose that is a linear form in t variables x1, …, xt, where the aj ∈ K. This gives rise to a norm form N(x), where
A survey of bordism and cobordism
Authors: Landweber Peter S.
Published: November 2008

In the paper ‘Bordism and Cobordism’, which appeared in vol. 57 (1961) of this journal [5], Michael Atiyah introduced and began the study of bordism and cobordism theory. The present article will trace developments in this area since this beginning.
Matchings and Radon transforms in lattices II. Concordant sets
Authors: Kung Joseph P. S.
Published: November 2008

Let and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.
Uniformly asymptotic expansions for an integral with a large and a small parameter
Authors: Ursell F.
Published: November 2008

The integral

involves a large real parameter N and a small real parameter ∈. Its asymptotic behaviour is non-uniform when N → ∞ and ∈ → 0. Thus, when ∈ > 0 is kept fixed and N → ∞, the integral decays exponentially at a rate depending on ∈; when ∈ → 0 the integral tends to

which decays algebraically when N → ∞. It is shown that several distinct uniformly asymptotic expansions can be obtained which each involve an infinite set of functions of the combination Certain related integrals are also treated.
Some remarks on the calculation of Born partial wave integrals
Authors: Piraux B. , Whelan Colm T.
Published: November 2008

The Born partial wave integrals of Seaton [3] are considered. It is shown that the treatment of Whelan [5] may be further simplified and that these integrals may be expressed as a finite sum of associated Legendre polynomials of the second kind. This provides a convenient method for their numerical evaluation and allows the relationship between the Born and Bethe reactance matrices to be given in explicit analytic form.
On representing sets of an almost disjoint family of sets
Authors: Komjath P. , Milner E. C.
Published: November 2008

For cardinal numbers λ, K, ∑ a (λ, K)-family is a family of sets such that || = and |A| = K for every A ε , and a (λ, K, ∑)-family is a (λ,K)-family such that |∪| = ∑. Two sets A, B are said to be almost disjoint if

and an almost disjoint family of sets is a family whose members are pairwise almost disjoint. A representing set of a family is a set X ⊆ ∪ such that X ∩ A = ⊘ for each A ε . If is a family of sets and |∪| = ∑, then we write εADR() to signify that is an almost disjoint family of ∑-sized representing sets of . Also, we define a cardinal number
Some infinite families in the stable homotopy of spheres
Authors: Lin Wen-Hsiung
Published: November 2008

The classical Adams spectral sequence [1] has been an important tool in the computation of the stable homotopy groups of spheres . In this paper we make another contribution to this computation.
Rigid cyclic group actions on cohomology complex projective spaces
Authors: Dovermann Karl Heinz
Published: November 2008

In this paper we discuss smooth and locally smooth cyclic actions on cohomology complex projective spaces. We shall show that in low dimensions the presence of a codimension-two fixed-point component forces many algebraic invariants to behave as they do in the linear examples.
A simplified approach to a three-part Wiener-Hopf problem arising in diffraction theory
Authors: Chakrabarti A.
Published: November 2008

A direct and simple approach, utilizing Watson's lemma, is presented for obtaining an approximate solution of a three-part Wiener-Hopf problem associated with the problem of diffraction of a plane wave by a soft strip.
Liénard systems with several limit cycles
Authors: Lloyd N. G.
Published: November 2008

There is an extensive literature on Liénard's equation

and numerous criteria for the existence of limit cycles have been developed: see the survey of Staude[7], for example. Broadly speaking, such results are proved in one of two ways: a bounded solution is shown to exist and the Poincaré–Bendixson theorem used, or an ‘a priori’ bound for periodic solutions is obtained and the methods of degree theory utilized.
Symmetries of generalized Klein–Gordon (including sine-Gordon) equations in two dimensions
Authors: Gordon T. J.
Published: November 2008

Much attention has been devoted over the years to the sine-Gordon equation φuv = sin φ (e.g. [2] and references therein). Of fundamental significance is the existence of a countably infinite set of conservation laws, which arises from a corresponding set of symmetries (e.g. [6, 7]).
The parallel rank of a submanifold of Euclidean space
Authors: Flegmann A. M.
Published: November 2008

The aim of this paper is to make some remarks about the theory of parallel immersions in ℝn. We show that the existence of parallels to a curve in ℝndepends on the values of the integrals of then− 1 curvature functions along the curve. We then give examples of immersions ofS1in ℝ3and of immersions of codimension 2 with local parallel rank zero, thereby answering certain questions in [1].
Liftings of formal groups and the Artinian completion of BP
Authors: Baker Andrew , Würgler Urs
Published: November 2008

Let BP denote the localization at υn, of the Brown-Peterson spectrum (associated to the prime p). There is a related ring spectrum E(n) with homotopy ring

(as a quotient ring of in fact the cohomology theory E(n)*( ) is determined via a Conner-Floyd type isomorphism from on finite complexes, and moreover E(n) and BP are in the same Bousfield class (see [2, 14]). Although it is known (essentially from [17]) that BP cannot be a product of suspensions of E(n) in a multiplicative sense, D. Ravenel conjectured that such a splitting might occur after suitable completion of these spectra (see the introduction to [14]). This question was the original motivation of the present paper; however in proving Ravenel's conjecture we were naturally led to the consideration of some fundamental results in the theory of liftings of formal group laws and ‘change of ring’ results for Ext groups occurring in connection with the work of [10, 11, 12].
A generalization of a result of Iwasawa on the capitulation problem
Authors: Cremona J. E. , Odoni R. W. K.
Published: November 2008

The aim of this note is to prove

Theorem 1. Let n ≥ 3, and let p1, p2,…, Pn be primes in ℕ: = {z ∈ ℤ:z > 0}, each congruent to 1 (mod 4), which satisfy both of the following conditions:

(i) every unit in ℚ(√(p1p2)) has norm + 1;

(ii) the graph γ = γ(p1, p2, …, pn) associated with p1, p2, …, pn is odd (in the sense of [1]).
A class of representations of involutive bialgebras
Authors: Schürmann Michael
Published: November 2008

A class of representations on Fock space is associated to a representation of the *-algebra structure of a cocommutative graded bialgebra with an involution. We prove that the Gelfand–Naimark–Segal (GNS) representation given by the convolution exponential of a conditionally positive linear functional can be embedded into a representation of this class. Our theory generalizes a well-known construction for infinitely divisible positive definite functions on a group. Applying our general result, we obtain a complete characterization of the GNS representations given by infinitely divisible states on involutive Lie superalgebras.
The Schwartz property and nuclearity of spaces of smooth and holomorphic functions in infinite dimensions
Authors: Bjon Sten
Published: November 2008

In [8] it was shown that a locally convex space E is a Schwartz space if and only if the convergence algebras Hc(U) and He(U) of holomorphic functions on an open subset of E coincide, i.e. if and only if continuous convergence c (see [1]) and the associated equable convergence structure e (= local uniform convergence, see [2, 13]) coincide.
On the correspondence between gerbes and bouquets
Authors: Ulbrich K.-H.
Published: November 2008

Duskin [1, 2] showed that gerbes over a Grothendieck toposEcan be interpreted by certain internal groupoids ofEwhich he called bouquets. He proved that for any bouquetBofEthe fibred category Fors(B) ofB-torsors is a gerbe overE, and conversely that any gerbe G gives rise to a bouquetBsatisfying G ≅ F ors(B). We want to give here a somewhat different approach to these results, based on a construction of gerbes given in [3].
The uniform compactification of a locally compact abelian group
Authors: Filali M.
Published: November 2008

In recent years, the Stone-Čech compactification of certain semigroups (e.g. discrete semigroups) has been an interesting semigroup compactification (i.e. a compact right semitopological semigroup which contains a dense continuous homomorphic image of the given semigroup) to study, because an Arens-type product can be introduced. If G is a non-compact and non-discrete locally compact abelian group, then it is not possible to introduce such a product into the Stone-Čech compactification βG of G (see [1]). However, let UC(G) be the Banach algebra of bounded uniformly continuous complex functions on G, and let UG be the spectrum of UC(G) with the Gelfand topology. If f∈ UC(G), then the functions f and fy defined on G by

are also in UC(G).
Amalgamation and the invariant trace field of a Kleinian group
Authors: Neumann Walter D. , Reid Alan W.
Published: November 2008

Let Γ be a Kleinian group of finite covolume and denote by Γ(2) the subgroup generated by {γ2:γ ∈ Γ}. In [9] the trace field of Γ(2) was shown to be an invariant of the commensurability class of Γ. In [8] this field was termed the invariant trace field of Γ and further properties of this field were studied. Following the notation of [8] we denote the invariant trace field of Γ by k(Γ).
On a question of R. Godement about the spectrum of positive, positive definite functions
Authors: Bekka Mohammed B.
Published: November 2008

Let G be a locally compact group, and let P(G) be the convex set of all continuous, positive definite functions ø on G normalized by ø(e) = 1, where e denotes the group unit of G. For ø∈P(G) the spectrum spø of ø is defined as the set of all indecomposable ψ∈P(G) which are limits, for the topology of uniform convergence on compact subsets of G, of functions of the form

(see [5], p. 43). Denoting by πø the cyclic unitary representation of G associated with ø, it is clear that sp ø consists of all ψ∈P(G) for which πψ is irreducible and weakly contained in πø (see [3], chapter 18).
Minimal surfaces in ℂPn with constant curvature and Kähler angle
Authors: Bolton J. , Woodward L. M.
Published: November 2008

In [2] we used the theory of harmonic sequences to obtain a congruence theorem for minimal immersions of surfaces into ℂPn. In this paper we show how these ideas may be used to give a simplified and unified treatment of some results of Kenmotsu [9, 10], Bryant [4] and Ohnita [13].
On sums of two squarefull numbers
Authors: Baker R. C. , Brüdern J.
Published: November 2008

A natural number n is said to be squarefull if p|n implies p2|n for primes p. The set of all squarefull numbers is not much more dense in the natural numbers than the set of perfect squares but their additive properties may be rather different. We are more precise only in the case of sums of two such integers as this is the problem with which we are concerned here. Let U(x) be the number of integers not exceeding x and representable as the sum of two integer squares. Then, according to a theorem of Landau [4],

as x tends to infinity.
The 2-modular characters of Conway's group Co2
Authors: Suleiman Ibrahim A. I. , Wilson Robert A.
Published: November 2008

We use computational methods to find the irreducible 2-modular characters of Conway's second group. Three of these are produced by probabilistic methods, which means that we have very strong evidence that they are correct, but we do not yet have a complete proof.
Quantum stochastic integration and quantum stochastic differential equations
Authors: Barnett Chris , Goldstein Stanisław , Wilde Ivan
Published: November 2008

Quantum stochastic integrals are constructed using the non-commutativeLp-space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution. Various examples of the theory are discussed, and quantum Ornstein-Uhlenbeck processes are obtained as explicit solutions.
The coloured Jones function and Alexander polynomial for torus knots
Authors: Morton H. R.
Published: November 2008

In [2] it was conjectured that the coloured Jones function of a framed knot K, or equivalently the Jones polynomials of all parallels of K, is sufficient to determine the Alexander polynomial of K. An explicit formula was proposed in terms of the power series expansion , where JK, k(h) is the SU(2)q quantum invariant of K when coloured by the irreducible module of dimension k, and q = eh is the quantum group parameter.

In this paper I show that the explicit formula does give the Alexander polynomial when K is any torus knot.
Genus of nilpotent groups of Hirsch length six
Authors: Cassidy Charles , Lajoie Caroline
Published: November 2008

In this paper, we characterize the genus of an arbitrary torsion-free finitely generated nilpotent group of class two and of Hirsch length six by means of a finite number of arithmetical invariants. An algorithm which permits the enumeration of all possible genera that can occur under the conditions above is also given.
A family of Fitting classes of supersoluble groups
Authors: Menth Martin
Published: November 2008

A class of groups that is closed with respect to subnormal subgroups and normal products is called a Fitting class. Given a finite soluble group G, one may ask for the Fitting class (G) generated by G, that is the intersection of all Fitting classes containing G. For simple or nilpotent groups G it is easy to compute (G), but in other cases the determination of (G) seems to be surprisingly difficult, and there is no general method of solving this problem. In recent years there has been a lot of work in this area, see for instance Bryce and Cossey[l], [2], Hawkes[6] (or [5], IX. 9. Var. II), Heineken[7] and McCann[10].
Tangent sequences in Orlicz and rearrangement invariant spaces
Authors: Hitczenko Paweł , Montgomery-Smith Stephen J.
Published: November 2008

Let (fn) and (gn) be two sequences of random variables adapted to an increasing sequence of σ-algebras (ℱn) such that the conditional distributions of fn and gn given ℱn coincide. Suppose further that the sequence (gn) is conditionally independent. Then it is known that where the number C is a universal constant. The aim of this paper is to extend this result to certain classes of Orlicz and rearrangement invariant spaces. This paper includes fairly general techniques for obtaining rearrangement invariant inequalities from Orlicz norm inequalities.
Isomorphisms between the second duals of group algebras of locally compact groups
Authors: Farhadi Hamid-Reza
Published: November 2008

Let G be a locally compact group and L1(G) be the group algebra of G. We show that G is abelian or compact if every continuous automorphism of L1(G)** maps L1(G) onto L1(G) This characterizes all groups with this property and answers a question raised by F. Ghahramani and A. T. Lau in [7]. We also show that if G is a compact group and θ is any (algebra) isomorphism from L1(G)** onto L1(H)**, then H is compact and θ maps L1(G) onto L1(H).
Path homomorphisms
Authors: Nešetřil Jaroslav , Zhu Xuding
Published: November 2008

We investigate homomorphisms between finite oriented paths. We demonstrate the surprising richness of this perhaps simplest case of homomorphism between graphs by proving the density theorem for oriented paths. As a consequence every two dimensional countable poset is represented finite paths and their homomorphisms, and every finite dimensional poset is represented finite oriented trees and their homomorphisms. We then consider related problems of universal representability and extendability and on-line representability.
Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles
Authors: Bruzzo Ugo , Maciocia Antony
Published: November 2008

By using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfacesXthe Hilbert schemes Hilbn(X) can be identified for alln≥ 1 with moduli spaces of Gieseker stable vector bundles onX. We also introduce a new Fourier-Mukai type transform for such surfaces.
Minimal ideals in group algebras and their biduals
Authors: Baker J. W. , Filali M.
Published: November 2008

LetGbe a locally compact group andFa left introverted subalgebra ofC(G). For each of the algebrasL1(G),M(G),F* andL∞(G)* we determine the finite-dimensional minimal left ideals of the algebra (if any); in some cases we also determine the finite-dimensional minimal two-sided ideals, and in certain cases show that all minimal ideals of the algebra are finite-dimensional.
Continuous linear operators onC(K, X) and pointwise weakly precompact subsets ofC(K, X)
Authors: lger A.
Published: November 2008

LetKbe a compact Hausdorif space,Xa Banach space andC(K, X) the Banach space of all continuous functions :KXequipped with the supremum norm. A subsetHofC(K, X) is pointwise weakly precompact if, for eachtinK, the setHt) = {(t):H} is weakly precompact. In this note we study the images of a bounded pointwise weakly precompact subsetHofC(K, X) under several classes of linear operators onC(K, X).
Interpolation problems for ideals in nest algebras
Authors: Anoussis M. , Katsoulis E. G. , Moore R. L. , Trent T. T.
Published: November 2008

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation Txt = yt, for i = 1, 2,, n. In this article, we continue the investigation of the one-vector interpolation problem for nest algebras that was begun by Lance. In particular, we require the interpolating operator to belong to certain ideals which have proved to be of importance in the study of nest algebras, namely, the compact operators, the radical, Larson's ideal, and certain other ideals. We obtain necessary and sufficient conditions for interpolation in each of these cases.
A criterion for a smooth surface to be Del Pezzo
Authors: Maeda B. Hidetoshi
Published: November 2008

In this paper we assume throughout that the ground field k is algebraically closed and of characteristic zero.
On Fréchet Montel spaces and their projective tensor product
Authors: Díaz Juan Carlos , Miñarro M.Angeles
Published: November 2008

The main result in this note is as follows. Let E be a Fréchet Montel space which belongs to the large class of decomposable (FG)-spaces introduced by Bonet, Díaz, Taskinen and let F be a Fréchet Montel (resp. distinguished) space. Then the projective tensor product is Montel (resp. distinguished). We also give examples of Montel decomposable (FG)-spaces without an unconditional basis.
On the Liénard system which has no periodic solutions
Authors: Sugie Jitsuro , Yoneyama Toshiaki
Published: November 2008

The problem of periodicity of solutions of the generalized Liénard equation

has attracted much attention. Many efforts have been made to give sufficient conditions to guarantee the existence and the uniqueness of periodic solutions (limit cycles) of (1·1). There are also some papers on the number of limit cycles of (1·1) (see, for example, [3, 5, 6, 13]). However, there are only a few results on non-existence of periodic solutions of (1·1).
Compact left ideal groups in semigroup compactification of locally compact groups
Authors: Baker J. W. , Lau A. T.
Published: November 2008

LetGbe a locally compact group and letUGdenote the spectrum of theC*-algebraLUC(G)of bounded left uniformly continuous complex-valued functions onG, with the Gelfand topology. Then there is a multiplication onUGextending the multiplication onG(when naturally embedded inUG) such thatUGis a semigroup and for eachx ∈ UG, the mapy ↦ yxfromUGintoUGis continuous, i.e.UGis a compact right topological semigroup. ConsequentlyUGhas a unique minimal idealKwhich is the union of minimal (closed) left idealsUG. FurthermoreKis the union of the set of maximal subgroups ofK(see [3], theorem 3·ll).
An embedding theorem for HCF-rings
Authors: Gilmer Robert
Published: November 2008

Let D be an integral domain with identity. In (3), Cohn has shown that if D is a Schreier ring, then D can be inertly embedded in a pre-Bezout domain B(D), which Cohn calls the pre-Bezout hull of D. Further, D is an HCF-ring if and only if B(D) is a Bezout domain, and D is a UFD if and only if B(D) is a PID. Using a modification of Cohn's techniques, Samuel in (8) has shown that a Krull domain can be inertly embedded in a Dedekind domain. In this paper, we show that these embedding theorems are also obtained by considering the embedding of a v-ring in its Kronecker function ring with respect to the v-operation. To wit, if D is a v-ring and if Dv is the Kronecker function ring of D with respect to the v-operation, then Dv is a Bezout domain, and we show that D is inertly embedded in Dv if an only if D is an HCF-ring. Moreover, D is a UFD if and only if Dv is a PID, and if D is a Krull domain, D is inertly embedded (in Samuel's sense) in Dv, a Dedekind domain.