bluuebunny/crossref_metadata_2025 huggingface dataset:
The last problem of Harald Bohr
Authors: Kahane Jean-Pierre
Published: April 2009

The first and last papers of Harald Bohr deal with ordinary Dirichlet series and their order (or Lindelöf) function μ(σ) (= inf{α;f(σ + it) + 0(|t|α)}). The Lindelöf hypothesis is μ(σ) = inf(0, ½ − t) when an = (−1)n. Are there ordinary Dirichlet series with −l < μ′ (σ) < 0 for some σ? A negative answer would imply Lindelöf's hypothesis. This is the last problem of Harald Bohr. This paper gives (1) a review on Bohr's results on ordinary Dinchlet series; (2) a review on results of the author and of Queffelec on “almost sure” and “quasi sure” properties of series with the solution of a previous problem of Bohr; (3) the following answer to the last problem: μ′(σ) can approach − ½, and necessarily μ(σ + μ(σ) + ½) = 0. The characterization of the order functions of ordinary Dirichlet series remains an open question.
The method of upper, lower solutions and monotone iterative scheme for higher order hyperbolic partial differential equations
Authors: Agarwal Ravi P.
Published: April 2009

Uniformly monotone convergent iterative methods for obtaining multiple solutions of (n + m)th order hyperbolic partial differential equations together with initial conditions are discussed. Appropriate partial differential inequalities which connect upper and lower solutions, and variation of parameters formula is developed.
Some subgroups of the Thompson group
Authors: Wilson Robert A.
Published: April 2009

We determine all conjugacy classes of maximal local subgroups of Thompson's sporadic simple group, and all maximal non-local subgroups except those with socle isomorphic to one of five particular small simple groups.
A generalisation of the quintuple product identity
Authors: Hirschhorn M. D.
Published: April 2009

The quintuple product identity has appeared many times in the literature. Indeed, no fewer than 12 proofs have been given. We establish a more general identity from which the quintuple product identity follows in two ways.
Recursive constructions and some properties of twofold designs with block size four
Authors: Phelps K. T. , Rosa A.
Published: April 2009

A direct construction for partially resolvable t-partitions is presented and then used to give a recursive construction for BIBDs (ν, 4, 2). In particular, we construct BIBD(ν, 4, 2) with BIBD(ν, 4, 2) embedded in it whenever ν = 3u + a, a ∈ {1, 4, 7}. This result allows us to give simple proofs for the existence of BIBD(ν, 4, 2) with various additioinal properties.
Everywhere Nonrecursive r.e. Sets in Recursively Presented Topological Spaces
Authors: Xiang Li
Published: April 2009

Recursively presented topological spaces are topological spaces with a recursive system of basic neighbourhoods. A recursively enumerable (r.e.) open set is a r.e. union of basic neighbourhoods. A set is everywhere r.e. open if its intersection with each basic neighbourhood is r.e. Similarly we define everywhere creative, everywhere simple, everywhere r.e. non-recursive sets and show that there exist sets both with and without these everywhere properties.
Pair-Countable, Closure-Preserving Covers of Compact Sets
Authors: Potoczny Henry
Published: April 2009

In this paper, we prove the following results: (1) if a topological space X has a pair-countable, closure-preserving cover of compact sets, then X is locally paracompact at each point of X and X has a dense open subspace which is locally σ-compact. In addition, if X is also collectionwise-T2, then X is paracompact. Locally paracompact is taken to mean that each point X has an open set with paracompact closure.
On normal complements to sections of finite groups
Authors: Dade Everett C.
Published: April 2009

Suppose that H/N is a section of a finite group G, i.e., that H is a subgroup of G and N is a normal subgroup of H. We are interested in the existence of normal subgroups M of G satisfying: Such an M can be called a normal complement to the section H/N in G.
The lateral completion of an arbitrary lattice group
Authors: Bernau S. J.
Published: April 2009

This paper shows that every lattice groupGcan be densely embedded in a unique laterally complete lattice groupH(the lateral completion ofG). All reasonable structure properties ofGare inherited byHand we have the following relationships between the ideal radicalL(G), the distributive radicalD(G) and the radicalR(G) ofGand the corresponding radicals ofH..
Free i-Groups and vector lattices
Authors: Bleier Roger D.
Published: April 2009

The purpose of this paper is to present three somewhat disparate results on free objects in three different classes of λ-groups. The first is that no proper ideal of a finitely generated free vector lattice can itself be a free vector lattice. Second, each free abelian lgroup is characteristically simple. The third result is that each disjoint subset of a free (non-abelian) lgroup is countable.
2-groups of almost maximal class
Authors: James Rodney
Published: April 2009

Let G be a group of order 2n and x, y ∈ G. We define the Commutator [x, y] as x−1y−1xy. Similarly, if X, Y are subsets of G, then [X, Y] denotes the sub-group genrated by all commutators of the form [x, y] where x ∈ X, y ∈ Y. Using this, we may define the lower central series of G inductively by The following results are well known.
Systems of derivations on topological algebras of power series
Authors: Schultz Henry J.
Published: April 2009

If Do, D1, … are linear maps from an algebra A to an algebra B, both over the complexes, then {Do, D1, …} is a system of derivations if for all a, b in A and for all nonnegative integers k, we have Where C(k, i) is the binomial coefficient k!/i! (k—i)!. By (1.1) we see that Do must be a homomorphism and in case Do = I, where I is the identity map, D1 is a derivation and, for k ≧ 2, the Dk are higher derivations in the sense of Jacobson (1964), page 191. Gulick (1970), Theorem 4.2, proved that if A is a commutative regular semi-simple F-algebra with identity and {DO, D1, …} is a system of derivations from A to B = C(S(A)), the algebra of all continuous functions on the spectrum of A, where Dox = x, then the Dk are all continuous. Carpenter (1971), Theorem 5, shows that the regularity condition is unnecessary and Loy (1973) generalizes this a bit further. One of the many interesting features of systems of derivations is that they help determine analytic structure in Banach algebras (see for example, Miller (to appear)).
Natural extensions of probability measure in function space
Authors: Yeh R. Z.
Published: April 2009

Let {Xt}t ∈ T be a family of real (R) random variable defined on a probability space (Ω, A P) and having the ranges in a subset S of R, that is, Xt (Ω) ⊂ S for all t. Let X be the mapping of Ω into the function space St such that for any ω ∈ Ω We shall write X = {Xt}t ∈ T and call X the random fundtion arising from {Xt}t ∈ T. It is well-known that any finite subfamily of {Xt}t∈T induces a “finite joint distribution” in ST, and according to Kolmogorov (1933) these finite joint distributions can be simultaneously extended to a probability measure Po on the Borel class Bo of subsets of ST. This extension is natural in the sense that for any B∈B0P0(B) turns out to be exactly P[X−1(B)]. The Kolmogorov extension Po has however a shortcoming in that its domain B0 is not broad enough to include many events of practical interest.
Gauge invariant interactions of classical fields
Authors: Smrz P. K.
Published: April 2009

The theory of Yang-Mills fields is explicity formulated in terms of the theory of connections in principal and associated fiber bundles. Special attention is paid to the fiber bundles with Lorentz and Poincaré structures. Equations of the form ∇ψ = 0, where ∇ is a generalized convariant derivative, are shown to contain “mass” terms if the connection in the Poincaré fiber bundle is cononically associated to the connection in the Lorentz fiber bundle.
On the homotopy theory of monoids
Authors: Hurwitz Carol M.
Published: April 2009

Absract

In this paper, it is shown that any connected, small category can be embedded in a semi-groupoid (a category in which there is at least one isomorphism between any two elements) in such a way that the embedding includes a homotopy equivalence of classifying spaces. This immediately gives a monoid whose classifying space is of the same homotopy type as that of the small category. This construction is essentially algorithmic, and furthermore, yields a finitely presented monoid whenever the small category is finitely presented. Some of these results are generalizations of ideas of McDuff.
Continuity properties of the superposition operator
Authors: Appell Jürgen , Zabrejko Pjotr P.
Published: April 2009

Various continuity conditions (in norm, in measure, weakly etc.) for the nonlinear superposition operatorF x(s) =f(s, x(s)) between spaces of measurable functions are established in terms of the generating functionf = f(s, u). In particular, a simple proof is given for the fact that, ifFis continuous in measure, thenfmay be replaced by a functionfwhich generates the same superposition operatorFand satisfies the Carathéodory conditions. Moreover, it is shown that integral functional associated with the function f are proved.
The structure of crossed products by smooth actions
Authors: Williams Dana P.
Published: April 2009

Absract

Let ξ be a C*;-bundle over T with fibres {At}t∈A. Suppose that A is the C*-algebra of sections of ξ which vanish at infinity, and that (A, G, α) is a C*-dymanical system that, for each t ∈ T, the ideal It = {f ∈ A|f(t) =; 0} is G-invariant. If in addition, the stabiliser group of each P ∈ Prim(A) is amenable, then A ⋊αG is the section algebra of a C*-bundle with fibres {At ⋊αG}t∈T.

The above theorem may be used to prove a structure theorem for crossed products built from C*-dynamical systems (A, G, α) where the action of G on A is smooth. Assuming that the stabiliser groups are amenable, then A ⋊αG has a composition series such that each quotient is a section algebra of a C*-bundle where the fibres are of the form Aσ ⋊αG; moreover, the Aσ correspond to locally closed subsets of Prim(A), and G acts transitively on Prim(Aσ). In many cases, in particular when (G, A) is separable, the Aσ ⋊αG have been computed explicitly by other authors.

These results are actually proved for twisted C*dynamical systems.
The volumes of simplices, or, find the penguin
Authors: Klebaner Fima C. , Sudbury Aidan , Watterson G. A.
Published: April 2009

Given the equations for the n + 1 hyperplanes that bound an n-simplex in Rn, simple formulae are derived for the contents of the n − r simplices (0 ≦ r < n) embedded in it. For example, when n = 3, the formulae include the volume of the tetrahedron, the areas of its faces and the lengths of its edges.
On discontinuity of l2-angle
Authors: Jakóbczak Piotr , Mazur Tomasz
Published: April 2009

In this note the L2-angle between two concentric rings and between the ring and the exterior of the disc in the complex plane are calculated. In the second part we prove that the L2-angles between domains A and B and between A × C and B × C are equal. We give also some examples of discontinuity of the L2-angle between domains.
Sufficient conditions for the strong stability of the differential equation [p(D)+f(t)q(D)]y= 0
Authors: Howe A.
Published: April 2009

A number of sufficient conditions for stability or strong stability, as used in the context of Hamiltonian systems, are found for the differential equationwhere the continuous functionf(t)is periodic ω int, D =d/dtandp(s),q(s)are real monic polynomials having special properties which allow the differential equation to be transformed into a canonical system ofksecond order equations.
On properly separable quotients of strict (LF) Spaces
Authors: Robertson W. J.
Published: April 2009

All known Banach spaces have an infinite-dimensional separable quotient and so do all nonnormable Fréchet spaces, although the general question for Banach spaces is still open. A properly separable topological vector space is defined, in such a way that separable and properly separable are equivalent for an infinite-dimensional complete metrisable space. The main result of this paper is that the strict inductive limit of a sequence of non-normable Fréchet spaces has a properly separable quotient.
Non-weak compactness of the integration map for vector measures
Authors: Okada S. , Ricker W. J.
Published: April 2009

Let m be a vector measure with values in a Banach space X. If L1(m) denotes the space of all m integrable functions then, with respect to the mean convergence topology, L1(m) is a Banach space. A natural operator associated with m is its integration map Im which sends each f of L1(m) to the element ∫fdm (of X). Many properties of the (continuous) operator Im are closely related to the nature of the space L1(m). In general, it is difficult to identify L1(m). We aim to exhibit non-trivial examples of measures m in (non-reflexive) spaces X for which L1(m) can be explicitly computed and such that Im is not weakly compact. The examples include some well known operators from analysis (the Fourier transform on L1 ([−π, π]), the Volterra operator on L1 ([0, 1]), compact self-adjoint operators in a Hilbert space); such operators can be identified with integration maps Im (or their restrictions) for suitable measures m.
On minimal Fitting classes of periodic, infinite groups
Authors: McCann Brendan
Published: April 2009

Examples of Fitting classes generated by certain periodic infinite groups are presented in this paper. The groups in question are finite extensions of direct products of quasi-cyclic (Prüfer) groups and are, in particular, Černikov groups. The methods applied follow closely those used for constructing Fitting classes of finite groups, especially in the case of nilpotent length three.
Ideal extensions of Γ-rings
Authors: Snyders A. J. M. , Veldsman S.
Published: April 2009

Given Γ-rings N1 and N2, a construction similar to the Everett sum of rings to find all possible extensions of N1 by N2 is given. Unlike the case of rings, it is not possible to find for any Γ-ring M an ideal extension that has a unity. Furthermore, contrary to the ring case, a Γ-ring with unity can not be characterized as a Γ-ring which is a direct summand in every extension thereof.
Homotopical aspects of Lie algebras
Authors: Ellis Graham J.
Published: April 2009

The Hurewicz theorem, Mayer-Vietoris sequence, and Whitehead's certain exact sequence are proved for simplicial Lie algebras. These results are applied, using crossed module techniques, to obtain information on the low dimensional homology of a Lie algebra, and information on aspherical presentations of Lie algebras.
The minimal volume of the plane
Authors: Bowditch B. H.
Published: April 2009

We give an account of the minimal volume of the plane, as defined by Gromov, and first computed by Bavard and Pansu. We also describe some related geometric inequalities.
Hyperbolic manifolds and degenerating handle additions
Authors: Scharlemann Martin , Wu Ying-Qing
Published: April 2009

A 2-handle addition on the boundary of a hyperbolic 3-manifold M is called degenerating if the resulting manifold is not hyperbolic. There are examples that some manifolds admit infinitely many degenerating handle additions. But most of them are not ‘basic’. (See Section 1 for definitions). Our first main theorem shows that there are only finitely many basic degenerating handle additions. We also study the case that one of the handle additions produces a reducible manifold, and another produces a ∂-reducible manifold, showing that in this case either the two attaching curves are disjoint, or they can be isotoped into a once-punctured torus. A byproduct is a combinatorial proof of a similar known result about degenerating hyperbolic structures by Dehn filling.
Almost identical imitations of (3,1)-dimensional manifold pairs and the manifold mutation
Authors: Kawauchi Akio
Published: April 2009

In this paper, we construct from any given good (3,1)-dimensional manifold pair finitely many almost identical imitations of it whose exteriors are mutative hyperbolic 3-manifolds. The equivariant versions with the mutative reduction property on the isometry group are also established. As a corollary, we have finitely many hyperbolic 3-manifolds with the same volume and the same isometry group.
Quasi-Fuchsian surfaces in hyperbolic knot complements
Authors: Adams Colin C. , Reid Alan W.
Published: April 2009

Examples of hyperbolic knots inS3are given such that their complements contain quasi-Fuchsian non-Fuchsian surfaces. In particular, this proves that there are hyperbolic knots that are not toroidally alternating.
On 4-manifolds with universal covering space a compact geometric manifold
Authors: Hillman Jonathan A.
Published: April 2009

There are 11 closed 4-manifolds which admit geometries of compact type (S4,CP2orS2×S2) and two other closely related bundle spaces (S2×S2and the total space of the nontrivialRP2-bundle overS2). We show that the homotopy type of such a manifold is determined up to an ambiguity of order at most 4 by its quadratic 2-type, and this in turn is (in most cases) determined by the Euler characteristic, fundamental group and Stiefel-Whitney classes. In (at least) seven of the 13 cases, a PL 4-manifold with the same invariants as a geometric manifold or bundle space must be homeomorphic to it.
Cusps, triangle groups and hyperbolic 3-folds
Authors: Conder Marston D. E. , Martin Gaven J.
Published: April 2009

We provide a number of explicit examples of small volume hyperbolic 3-manifolds and 3-orbifolds with various geometric properties. These include a sequence of orbifolds with torsion of orderqinterpolating between the smallest volume cusped orbifold (q= 6) and the smallest volume limit orbifold (q→ ∞), hyperbolic 3-manifolds with automorphism groups with large orders in relation to volume and in arithmetic progression, and the smallest volume hyperbolic manifolds with totally geodesic surfaces. In each case we provide a presentation for the associated Kleinian group and exhibit a fundamental domain and an integral formula for the co-volume. We discuss other interesting properties of these groups.
On Mahler's compound bodies
Authors: Burger Edward B.
Published: April 2009

Let 1 ≤ M ≤ N − 1 be integers and K be a convex, symmetric set in Euclidean N-space. Associated with K and M, Mahler identified the Mth compound body of K, (K)m, in Euclidean (MN)-space. The compound body (K)M is describable as the convex hull of a certain subset of the Grassmann manifold in Euclidean (MN)-space determined by K and M. The sets K and (K)M are related by a number of well-known inequalities due to Mahler.

Here we generalize this theory to the geometry of numbers over the adèle ring of a number field and prove theorems which compare an adelic set with its adelic compound body. In addition, we include a comparison of the adelic compound body with the adelic polar body and prove an adelic general transfer principle which has implications to Diophantine approximation over number fields.
On Hausdorff dimension for attractors of iterated function systems
Authors: Yin Qinghe
Published: April 2009

A conjecture on the Hausdorff dimension for Markov attractors of disjoint hyperbolic iterated function systems was given by Ellis and Branton. This paper proves the conjecture and generalizes the result to more general cases.
Tubular sets and multivariate Polya algorithm
Authors: Huotari Robert
Published: April 2009

Some new results concerning tubular sets are presented, with applications to the convergence of the Polya algorithm in the contexts of simultaneous approximation and approximation of multivariate functions by univariate functions. (The Polya algorithm constructs a best uniform approximation from the limit, as p → ∞, of best Lp approximations.)
Pairs of rings with a bijective correspondence between the prime spectra
Authors: Jespers E. , Wauters P.
Published: April 2009

Let A be a subring of a commutative ring B. If the natural mapping from the prime spectrum of B to the prime spectrum of A is injective (respectively bijective) then the pair (A, B) is said to have the injective (respectively bijective) Spec-map. We give necessary and sufficient conditions for a pair of rings A and B graded by a free abelian group to have the injective (respectively bijective) Spec-map. For this we first deal with the polynomial case. Let l be a field and k a subfield. Then the pair of polynomial rings (k[X], l[X]) has the injective Spec-map if and only if l is a purely inseparable extension of k.
Hyperidentity bases for rectangular bands and other semigroup varieties
Authors: Wismath Shelly L.
Published: April 2009

Hyperidentities were introduced by Taylor, and their properties have been studied by Taylor, Bergman, Penner, Graczynska, Schweigert, Wismath, and others. In particular, Penner has produced bases for the hyperidentities of various types satisfied by the variety of semilattices.

In this paper, we look at bases for the hyperidentities satisfied by some other varieties of semigroups. We first investigate solid and hyper-associative varieties of semigroups, and use a result of Graczynska's to form a basis for the hyperidentities of type (2) for varieties with these properties. We then produce bases for the hyperidentities satisfied by the variety R B of rectangular bands, and prove that the collection of all hyperidentities satisfied by R B is not finitely based. Finally, we use the R B results to give hyperidentity bases for some varieties of nilpotent semigroups.
An order property for families of sets
Authors: Williams N. H.
Published: April 2009

We develop the idea of a θ-ordering (where θ is an infinite cardinal) for a family of infinite sets. A θ-ordering of the family A is a well ordering of A which decomposes A into a union of pairwise disjoint intervals in a special way, which facilitates certain transfinite constructions. We show that several standard combinatorial properties, for instance that of the family A having a θ-transversal, are simple consequences of A possessing a θ-ordering. Most of the paper is devoted to showing that under suitable restrictions, an almost disjoint family will have a θ-ordering. The restrictions involve either intersection conditions on A (the intersection of every λ-size subfamily of A has size at most κ) or a chain condition on A.
Formulas for some diophantine approximation constants
Authors: Cusick T. W. , Krass S.
Published: April 2009

Let M be a full Z-module in F a real number field of degree at least 3 with N(α) denoting the norm of α ∈ F. Given any nonzero number φ in M we make the plausible conjecture that one can find a number ß in M such that N(ß) = N(φ) and the algebraic conjugates of ß (not including ß) have ratios arbitraily near any given numbers consistent with the complex algebraic conjugates of elements of F. We use the conjecture to give explicit formulas for some diophantine approximation constants. Without the conjecture our methods lead to corresponding lower bounds for these constants.
Quasi-injective modules satisfying certain realtive finiteness conditions
Authors: Izawa Tatsuo
Published: April 2009

We study the endomorphism ring of a quasi-injective right R-module Q such that R satisfies certain finiteness conditions relative to Q. And we are concerned with a module sHomR(M, Q), where S is the endomorphism ring of QR.
Cumulants and partition lattices VI. variances and covariances of mean squares
Authors: Speed T. P. , Silcock H. L.
Published: April 2009

Formulae are given for the variances and covariances for mean squares in anova under the broadest possible assumptions. The results of ther authors are obtained by specializing appropriately: these include ones concerning randomization and/or random sampling models, as well as additive (linear) models consisting of mutually independent sets of exchangeable effects. Although the illustrations given refer only to doubly and triply-indexed arrays, the approach is quite general. Particular attention is drawn to the generalized cumulants (and their natural unbiased estimators) which vanish when additive models are assumed.
On the O'Nan-Scott theorem for finite primitive permutation groups
Authors: Liebeck Martin W. , Praeger Cheryl E. , Saxl Jan
Published: April 2009

We give a self-contained proof of the O'Nan-Scott Theorem for finite primitive permutation groups.
A note on group divisible designs with mutually orthogonal resolutions
Authors: Lamken E. R. , Vanstone S. A.
Published: April 2009

In this note, we use a geometric construction to produce group divisible designs with mutually orhogonal resolutions.
Isomorphic factorization of regular graphs of even degree
Authors: Ellingham M. N
Published: April 2009

A graph G is divisible by t if its edge set can be partitioned into t subsets, such that the subgraphs (called factors) induced by the subsets are all isomorphic. Such an edge partition is an isomorphic factorization. It is proved that a 2k-regular graph with an even number of vertices is divisble by 2k provided it contains either no 3-cycles or no 5-cycles. It is also shown that any 4-regular graph with an even number of vertices is divisible by 4. In both cases the components of the factors found are paths of length 1 and 2, and the factorizations can be constructed in polynomial time.
Analytic functions which operate on homogeneous algebras
Authors: Ward J. A.
Published: April 2009

It is well known that a complex-valued function ø, analytic on some open set Ω, extends to any commutative Banach algebra B so that the action of ø on B commutes with the action of the Gelfand transformation. In this paper, it is shown that if B is a homogeneous convolution Banach algebra over any compact group and if 0 ∈ Ω is a fixed point of ø, then a similar result holds, with the Gelfand transformation replaced by the Fourier-Stieltjes transformation. Care is required, in that discussion of this relation usually requires simultaneous consideration of the extension of ø to B and to certain operator algebras.
A general criterion for the existence of infinite Sidon sets
Authors: Wilson David C.
Published: April 2009

Let G be any compact group, connected or disconnected, with dual object Ĝ. We define a family of local Sidon subsets of Ĝ in terms of allowable images of the representations. Using this family we develop a straightforward criterion whereby the existence of infinite Sidon subsets of Ĝ may be decided.
On the characters of unitary representations
Authors: Cowling Michael
Published: April 2009

Let G be a locally compact group, and let D(G) be a dense subalgebra of the convolution algebra L1(G). Suppose that π is a unitary representation of G and that, for each u in D(G), π(u)) is a trace-class operator. Then the linear functional u → tr(π(u)) (the trace of π(u)) is called the D-character of π. We give a simple proof that the D-character of such a representation determines the representation up to unitary equivalence. As an application, we give an easy proof of the result of Harish-Chandra that the K-finite characters of unitary representations of semisimple Lie groups determine the representations.
Primitive permutation groups with a doubly transitive subconstituent
Authors: Praeger Cheryl E.
Published: April 2009

Let Gbe a primitive permutation group on a finite set Ω. We investigate the subconstitutents of G, that is the permutation groups induced by a point stabilizer on its orbits in Ω, in the cases where Ghas a diagonal action or a product action on Ω. In particular we show in these cases that no subconstituent is doubly transitive. Thus if G has a doubly transitive subconstituent we show that G has a unique minimal normal subgroup N and either N is a nonabelian simple group or N acts regularly on Ω: we investigate further the case where N is regular on Ω.
Hardy-Littlewood maximal functions on some solvable Lie groups
Authors: Gaudry G. , Giulini S. , Hulanicki A. , Mantero A. M.
Published: April 2009

Let N be a nilpotent simply connected Lie group, and A a commutative connected d-dimensional Lie group of automorphisms of N which correspond to semisimple endomorphisms of the Lie algebra of N with positive eigenvalues. Form the split extension S = N × A ≅ N × a, a being the Lie algebra of A. We consider a family of “rectangles” Br in S, parameterized by r > 0, such that the measure of Br behaves asymptotically as a fixed power of r. One can construct the Hardy-Littlewood maximal function operator f → Mf relative to left translates of the family {Br}. We prove that M is of weak type (1, 1). This complements a result of J.-O. Strömberg concerning maximal functions defined relative to hyperbolic balls in a symmetric space.
On commutator laws in groups
Authors: Macdonald I. D. , Neumann B. H.
Published: April 2009

There are some well-known laws that the commutator satisfies in groups, and that go by some or all of the names Jacobi, Witt, Hall; and there are also some lesser-known laws. This is an attempt at an axiomatic study of the interdependence and independence of these laws.
A note on the Lévy-Khinchin representation of negative definite functions on Hilbert spaces
Authors: Ritter Gunter
Published: April 2009

We study negative definite functions on a Hilbert space and use their properties to give a proof of the Lévy-Khinchin formula for an infinitely divisible probability distribution on .
A qualitative uncertainty principle for semisimple Lie groups
Authors: Cowling Michael , Price John F. , Sitaram Alladi
Published: April 2009

Recently M. Benedicks showed that if a function f ∈ L2(Rd) and its Fourier transform both have supports of finite measure, then f = 0 almot everywhere. In this paper we give a version of this result for all noncompact semisimple connected Lie groups with finite centres.
Ergodic measures for the irrational rotation on the circle
Authors: Moran William
Published: April 2009

Riesz products are employed to give a construction of quasi-invariant ergodic measures under the irrational rotation of T. By suitable choice of the parameters such measures may be required to have Fourier-Stieltjes coefficients vanishing at infinity. We show further that these are the unique quasi-invariant measures on T with their associated Radon-Nikodym derivative.
Static modules and non-normal Clifford theory
Authors: Alperin J. L.
Published: April 2009

A version of the Dade-Cline equivalence from Clifford theory is proved for non-normal subgroups of a finite group in the context of a synthesis of a number of equivalences that arise in the representation theory of groups and algebras.
Stably free resolutions of lattices over finite groups
Authors: Gruenberg K. W.
Published: April 2009

For a ZG-lattice A, the nth partial free Euler characteristic εn(A) is defined as the infimum of all where F* varies over all free resolutions of A. It is shown that there exists a stably free resolution E* of A which realises εn(A) for all n≥0 and that the function n → εn(A) is ultimately polynomial no residue classes. The existence of E* is established with the help of new invariants σn(A) of A. These are elements in certain image groups of the projective class group of ZG. When ZG allows cancellation, E* is a minimal free resolution and is essentially unique. When A is periodic, E* is ultimately periodic of period a multiple of the projective period of A.
Lie rings of groups of prime exponent
Authors: Vaughan-Lee M. R.
Published: April 2009

We investigate the identities which hold in the associated Lie rings of groups of prime exponent. The multilinear identities which hold in these Lie rings are known, and it is conjectured that all the identities which hold in these Lie rings are consequences of multilinear ones. This is known to be the case for the associated Lie rings of two generator groups of exponent 5, and we provide some additional avidence for the conjecture by confirming that it also holds true for the associated Lie rings of three generator groups of exponent five.
Rank 1 preservers on the unitary Lie ring
Authors: Wong W. J.
Published: April 2009

The surjective additive maps on the Lie ring of skew-Hermitian linear transformations on a finite-dimensional vector space over a division ring which preserve the set of rank 1 elements are determined. As an application, maps preserving commuting pairs of transformations are determined.
The Coset lattices of E. S. Barnes and G. E. Wall
Authors: Hahn Alexander J.
Published: April 2009

John Conway's analysis in 1968 of the automorphism group of the Leech lattice and his discovery of three sporadic simple groups led to the immediate speculation that other Z-lattices might have interesting automorphism groups which give rise to (possibly new) finite simple groups. (The classification theorem for the finite simple groups has since told us that no new finite simple groups can arise in this or any other way.) For example in 1973, M. Broué and M. Enguehard constructed, in every dimension 2n, an even lattice (unimodular if n is odd) whose automorphism group is related to the simple Chevalley group of type Dn. This family of integral lattices received attention and acclaim in the subsequent literature. What escaped the attention of this literature, however, was the fact that these lattices had been discovered years earlier. Indeed in 1959, E. S. Barnes and G. E. Wall gave a uniform construction for a large class of positive definite Z-lattices in dimensions 2n which include those of Broué and Enguehard as special cases. The present article introduces an abstracted and generalized version of the construction of Barnes and Wall. In addition, there are some new observations about Barnes-Wall lattices. In particular, it is shown how to associate to each such lattice a continuous, piecewise linear graph in the plane from which all the important properties of the lattice, for example, its minimum, whether it is integral, unimodular, even, or perfect can be read off directly.
Computing subfields in algebraic number fields
Authors: Dixon John D.
Published: April 2009

Let K:= Q(α) be an algebraic number field which is given by specifying the minimal polynomial f(X) for α over Q. We describe a procedure for finding the subfields L of K by constructing pairs (w(X), g(X)) of polynomials over Q such that L= Q(w(α)) and g(X) is the minimal polynomial for w(α). The construction uses local information obtained from the Frobenius-Chebotarev theorem about the Galois group Gal(f), and computations over p-adic extensions of Q.
On flag varieties, hyperplane complements and Springer representations of Weyl groups
Authors: Lehrer G. I. , Shoji T.
Published: April 2009

Let G be a connected reductive linear algebraic group over the complex numbers. For any element A of the Lie algebra of G, there is an action of the Weyl group W on the cohomology Hi(BA) of the subvariety BA (see below for the definition) of the flag variety of G. We study this action and prove an inequality for the multiplicity of the Weyl group representations which occur ((4.8) below). This involves geometric data. This inequality is applied to determine the multiplicity of the reflection representation of W when A is a nilpotent element of “parabolic type”. In particular this multiplicity is related to the geometry of the corresponding hyperplane complement.
On tensor induction of group representations
Authors: Kovács L. G.
Published: April 2009

LetGbe a (not necessarily finite) group andρa finite dimensional faithful irreducible representation ofGover an arbitrary field; writeρ¯forρviewed as a projective representation. Suppose thatρis not induced (from any proper subgroup) and thatρ¯is not a tensor product (of projective representations of dimension greater than 1). LetKbe a noncentral subgroup which centralizes all its conjugates inGexcept perhaps itself, writeHfor the normalizer ofKinG, and suppose that some irreducible constituent, σ say, of the restrictionp↓Kis absolutely irreducible. It is proved that then (ρis absolutely irreducible and) ρ¯ is tensor induced from a projective representation ofH, namely from a tensor factor π ofρ¯↓Hsuch that π↓K= σ¯ and ker π is the centralizer ofKinG.
Structure of pseudo-semisimple rings
Authors: Mohamed Saad , Müller Bruno J.
Published: April 2009

A ring R is called right pseudo-semisimple if every right ideal not isomorphic to R is semisimpie. Rings of this type in which the right socle S splits off additively were characterized; such a ring has S2 = 0. The existence of right pseudo-semisimple rings with zero right singular ideal Z remained open, except for the trivial examples of semisimple rings and principal right ideal domains. In this work we give a complete characterization of right pseudo-semisimple rings with S2 = 0. We also give examples of non-trivial right pseudo-semisimple rings with Z = 0; in fact it is shown that such rings exist as subrings in every infinite-dimensional full linear ring. A structure theorem for non-singular right pseudo-semisimple rings, with homogeneous maximal socle, is given. The general case is still open.
Symmetric dual multiobjective fractional programming
Authors: Weir T.
Published: April 2009

A pair of symmetric dual multiobjective fractional programming problems is formulated and appropriate duality theorems are established.
The symmetric algebra of quotients of an ultraprime Banach algebra
Authors: Mathieu Martin
Published: April 2009

We present a symmetric version of a normed algebra of quotients for each ultraprime normed algebra. In addition, a C*-a1gebra of quotients of an arbitrary C*-a1gebra is introduced.
Multiplication operators on weighted spaces of vector-valued continuous functions
Authors: Singh R. K. , Manhas Jasbir Singh
Published: April 2009

If V is a system of weights on a completely regular Hausdorff space X and E is alocally convex space, then CV0(X, E) and CVb (X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.
Cup products and group extensions
Authors: Linnell P. A.
Published: April 2009

Let G be a finitely generated group and let R be a commutative ring, regarded as a G-module with G acting trivially. We shall determine when the cup product of two elements of H1(G, R) is zero. Our method will use the interpretation of H2(G, R) as extensions of G by R. This will give an alternative demonstration of results of Hillman and Würfel.
Classification of 4- and 5-arc-transitive cubic graphs of small girth
Authors: Morton Margaret J.
Published: April 2009

This paper classifies all finite connected 4- and 5-arc-transitive cubic graphs that contain circuits of length less than or equal to 11, or of length 13, and some of those graphs with circuits of length 12.
Hyponormal operators on uniformly smooth spaces
Authors: Chō Muneo
Published: April 2009

In this paper we will characterize the spectrum of a hyponormal operator and the joint spectrum of a doubly commuting n-tuple of strongly hyponormal operators on a uniformly smooth space. We also describe some applications of these results.
Elementary amenable groups and 4-manifolds with Euler characteristic 0
Authors: Hillman Jonathan A.
Published: April 2009

We extend earlier work relating asphericity and Euler characteristics for finite complexes whose fundamental groups have nontrivial torsion free abelian normal subgroups. In particular a finitely presentable group which has a nontrivial elementary amenable subgroup whose finite subgroups have bounded order and with no nontrivial finite normal subgroup must have deficiency at most 1, and if it has a presentation of deficiency 1 then the corresponding 2-complex is aspherical. Similarly if the fundamental group of a closed 4-manifold with Euler characteristic 0 is virtually torsion free and elementary amenable then it either has 2 ends or is virtually an extension of Z by a subgroup of Q, or the manifold is asphencal and the group is virtually poly- Z of Hirsch length 4.
Independent sets and lacunarity for hypergroups
Authors: Vrem Richard C.
Published: April 2009

Sets of independence are studied for compact abelian hypergroups and they are used, along with Riesz products, to investigate lacunarity questions on the dual object. It is shown that bounded Stechkin sets are always Sidon and that every bounded infinite subset of the dual contains an infinite Sidon set which is also a Λ set. Independent sets are shown to always be Sidon and a necessary condition for Sidonicity is provided. A result of Pisier is used to show that for compact non-abelian groups Sidon and central Λ are equivalent. Several applications are provided, primarily to questions regarding lacunarity on compact groups.
Critical associated metrics on contact manifolds III
Authors: Blair David E.
Published: April 2009

In the first paper of this series we studied on a compact regular contact manifold the integral of the Ricci curvature in the direction of the characteristic vector field considered as a functional on the set of all associated metrics. We showed that the critical points of this functional are the metrics for which the characteristic vector field generates a 1-parameter group of isometries and conjectured that the result might be true without the regularity of the contact structure. In the present paper we show that this conjecture is false by studying this problem on the tangent sphere bundle of a Riemannian manifold. In particular the standard associated metric is a critical point if and only if the base manifold is of constant curvature +1 or −1; in the latter case the characteristic vector field does not generate a 1-parameter group of isometries.
A characterization of uniserial rings via continuous and discrete modules
Authors: Jain S. K. , Lopez-Permouth S. R. , Rizvi S. Tariq
Published: April 2009

It is well-known that quasi-Frobenius rings are characterized by the property that all propective right modules are injective, as well as by the property that all injective right modules are projective. Similarly, either the property that every quasi-injective or that every quasi-injective is quasi-projective characterizes uniserial rings. Oshiro has given similar characterizations for generalized uniserial rings. The purpose of this paper is to characterize rings for which continuous right modules are discrete. We show that these rings are precisely the uniserial rings. The property that every discrete module is continuous is also investigated.
On r-graphs and r-multihypergraphs with given maximum degree
Authors: Füredi Zoltán
Published: April 2009

It is well-known that if G is a multigraph (that is, a graph with multiple edges), the maximum number of pairwise disjoint edges in G is ν(G) and its maximum degree is D(G), then |E(G)| ≤ ν [3D/2’. We extend this theorem for r-graphs (that is, families of r-element sets) and for r-multihypergraphs (that is, r-graphs with repeated edges). Several problems remain open.
Integral and p-modular semisimple deformations for p-solvable groups of finite representation type
Authors: Schaps Mary
Published: April 2009

We prove that the split integral group ring of a finite p-solvable group of finite representation type has a structure analogous to that of the p-modular semisimple deformation. The split integral deformation can be put in the same form as the p-modular deformation by an appropriate substitution for the parameter T. As an application we derive a simple formula for the matrix units in the semisimple group algebra over a nonmodular prime.
Operations preserving the pfaffian property of a graph
Authors: Little C. H. C. , Rendl F.
Published: April 2009

Pfaffian graphs are those which can be oriented so that the 1-factors have equal sign, as calculated according to the prescription of Kasteleyn. We consider various operations on graphs and examine their effect on the Pfaffian property. We show that the study of Pfaffian graphs may be reduced to the case of subcubic graphs (graphs in which no vertex has degree greater than 3) or bricks (3-connected bicritical graphs).
Admissible solutions of the Schwarzian differential equation
Authors: Ishizaki Katsuya
Published: April 2009

Let R(z, w) be a rational function of w with meromorphic coefficients. It is shown that if the Schwarzian equation possesses an admissible solution, then , where αj, are distinct complex constants. In particular, when R(z, w) is independent of z, it is shown that if (*) possesses an admissible solution w(z), then by some Möbius transformation u = (aw + b) / (cw + d) (ad – bc ≠ 0), the equation can be reduced to one of the following forms: where τj (j = 1, … 4) are distinct constants, and σj (j = 1, … 4) are constants, not necessarily distinct.
Centralizer near-rings over free ring modules
Authors: Maxson C. J. , Van Der Walt A. P. J.
Published: April 2009

We treat centralizer near-rings over ring modules in general, with particular emphasis on the case of free modules. Questions like the following are answered. When is the near-ring a nonring? When is the near-ring simple? What are its maximal and minimal left ideals? What is its subgroup structure? What is the radical? The cases where the ring concerned is a PID or a field are treated in some detail.
Kronecker classes of field extensions of small degree
Authors: Praeger Cheryl E.
Published: April 2009

The structure of Kronecker class of an extension K: k of algebraic number fields of degree |K: k| ≤ 8 is investigated. For such classes it is shown that the width and socle number are equal and are at most 2, and for those of width 2 the Galois group is given. Further, if |K: k | is 3 or 4, or if 5 ≤ |K: k| ≤ 8 and K: k is Galois, then the groups corresponding to all “second minimal” fields in K are determined.
Some inequalities of Bessel and modified Bessel functions
Authors: Joshi C. M. , Bissu S. K.
Published: April 2009

Two-sided inequalties for the ratio of modified Bessel functions of first kind are given, which provide sharper upper and lower bounds than had been known earlier. Wronskian type inequalities for Bessel functions are proved, and in the sequel alternative proofs of Turan-type inequalities for Bessel and modified Bessel functions are also discussed. These then lead to a two-sided inequality for Bessel functions. Also incorporated in the discussion is an inequality for the ratio of two Bessel functions for 0 <x< 1. Verifications of these inequalities are pointed out numerically.
Continuous selection theorem, coincidence theorem and intersection theorems concerning sets with H-convex sections
Authors: Ding Xie-Ping
Published: April 2009

A continuous selection and a coincidence theorem are proved in H-spaces which generalize the corresponding results of Ben-El-Mechaiekh-Deguire-Granas, Browder, Ko-Tan, Lassonde, Park, Simon and Takahashi to noncompact and/or nonconvex settings. By applying the two theorems, some intersection theorems concerning sets with H-convex sections are obtained which generalize the corresponding results of Fan, Lassonde and Shih-Tan to H-spaces. Some applications to minimax principle are given.
On group distributively generated near-rings
Authors: Fray R. L.
Published: April 2009

The group near-ring constructed from a right near-ring R and a group G is studied in the special case where the near-ring is distributively generated. In particular, results concerning homomorphisms of near-rings or of groups and the augmentation ideal are obtained which resemble closely those obtained for group rings.
Semigroups with atomistic congruence lattices
Authors: Auinger Karl
Published: April 2009

In this note a characterization of semigroups with atomistic consruence lattices, given for weakly reductive semigroups, is generalized to arbitrary semigroups. Also, it is shown that there is a complete congruence on the congruence lattice of such a semigroup that decomposes it into a disjoint union of intervals of the partition lattice.
On the Lebesgue function for lagrange interpolation with equidistant nodes
Authors: Mills T. M. , Smith Simon J.
Published: April 2009

Properties of the Lebesgue function associated with interpolation at the equidistant nodes, are investigated. In particular, it is proved that the relative maxima of the Lebesgue function are strictly decreasing from the outside towards the middle of the interval [0, n], and upper and lower bounds, and an asymptotic expansion, are obtained for the smallest maximum whennis odd.