bluuebunny/crossref_metadata_2025 huggingface dataset:
Collapsing three-dimensional convex polyhedra: correction
Authors: Chillingworth D. R. J.
Published: November 2008

An ingenious construction due to Connelly and Henderson (2) has shown that there exists a rectilinearly triangulated convex polyhedron P in having the property that at least one vertex of the triangulation lies in the interior of a face of P, and yet there is no isomorphic triangulation of a convex polyhedron P′ all of whose vertices are vertices of P′. Thus the assertion beginning on the top line of p. 354 of (1) is false, which leaves a gap in the proof of essentially the main result of (1), namely that any rectilinearly triangulated convex polyhedron incan be simplicially collapsed onto its boundary minus a 2-simplex σ. The purpose of this note is to show that the theorem is nevertheless still true. In any case the Corollaries 2 and 3 in (1) are unaffected by the error.
A non-commutative Gel'fand-Naimark theorem
Authors: Mulvey Christopher J.
Published: November 2008

This paper presents a straightforward proof of the Gel'fand-Naimark theorem for non-commutative C*-algebras with identity, established by Dauns and Hofmann(2) in the context of fields of C*-algebras, by considering instead C*-algebras in categories of sheaves. The proof differs from that of (2,3,4) in obtaining an isometric *-isomorphism

from the C*-algebra A to the C*-algebra of sections of a C*-algebra Ax in the category of sheaves on the maximal ideal space X of the centre of A, without invoking any arguments which involve completeness (3, Theorem 7·9). Instead, the results of (7) yield immediately the existence of an algebraic isomorphism, the compactness of the maximal ideal space X then being used to prove that Ax is indeed a C*-algebra in the category of sheaves on X and that the isomorphism is isometric. One recovers the representation of (2) by noting (8) that any C*-algebra in the category of sheaves on X is isomorphic to the sheaf of sections of a canonical field of C*-algebras on X.
Rigid homogeneous chains
Authors: Glass A. M. W. , Gurevich Yuri , Holland W. Charles , Shelah Saharon
Published: November 2008

Classifying (unordered) sets by the elementary (first order) properties of their automorphism groups was undertaken in (7), (9) and (11). For example, if Ω is a set whose automorphism group, S(Ω), satisfies

then Ω has cardinality at most ℵ0 and conversely (see (7)). We are interested in classifying homogeneous totally ordered sets (homogeneous chains, for short) by the elementary properties of their automorphism groups. (Note that we use ‘homogeneous’ here to mean that the automorphism group is transitive.) This study was begun in (4) and (5). For any set Ω, S(Ω) is primitive (i.e. has no congruences). However, the automorphism group of a homogeneous chain need not be o-primitive (i.e. it may have convex congruences). Fortunately, ‘o-primitive’ is a property that can be captured by a first order sentence for automorphisms of homogeneous chains. Hence our general problem falls naturally into two parts. The first is to classify (first order) the homogeneous chains whose automorphism groups are o-primitive; the second is to determine how the o-primitive components are related for arbitrary homogeneous chains whose automorphism groups are elementarily equivalent.
On the Green's function for heterogeneous media in one-speed transport theory
Authors: Prinja A. K.
Published: November 2008

The Green's functions for semi-infinite and adjacent semi-infinite media are considered in one-speed transport theory. Chandrasekhar's Principles of Invariance are used to formulate integral equations that describe the emergent and interface angular distributions. It is shown that mathematically these are equivalent to subtracting from the transport equation known solutions to related, simpler problems. Duplication of effort is avoided in this way. For adjacent semi-infinite media, a difficulty encountered in the solutions of the integral equations necessitates the application of a Laplace transform for its resolution. Some virtues of using the transform are explored, e.g. in the determination of the internal distribution where it yields concise expressions for the Green's function.
On the L4 norm of spherical harmonics
Authors: Stanton Robert J. , Weinstein Alan
Published: November 2008

It is shown that, among all the L2 normalized spherical harmonics of a given degree, the L4 norm is locally maximized by the ‘highest weight’ function .
A pencil of four-nodal plane sextics
Authors: Edge W. L.
Published: November 2008

Wiman, in 1895, found ((5), p. 208) an equation for a 4-nodal plane sextic W that admits a group S of 120 Cremona self-transformations; of these, 24 are projectivities, the other 96 quadratic transformations. S is isomorphic to the symmetric group of degree 5 and Wiman emphasizes that S does permute among themselves 5 pencils (4 pencils of lines and 1 of conics) and 5 nets (4 nets of conics and 1 of lines). But he gives no geometrical properties of W. The omission should be repaired because, as will be explained below, W can be uniquely determined by elementary geometrical conditions. Furthermore: W is only one, though admittedly the most interesting, of a whole pencil P of 4-nodal sextics; every member of P is invariant under S+, the icosahedral subgroup of index 2 in S, while the transformations in the coset S/S+ transpose the members of P in pairs save for two that they leave fixed, W being one of these. When the triangle of reference is the diagonal point triangle of the quadrangle of its nodes the form of W is (7.2) below. Wiman referred his curve to a different triangle.
A simple proof of Müntz's theorem
Authors: Rogers L. C. G.
Published: November 2008

Let 0 < λ1 < λ2 < … be an increasing sequence of positive reals tending to infinity, and let ν1, ν2 be two (finite) signed measures on ℝ+ such that

for all k. It was originally proved by Müntz (12) that, if

then ν1 = ν2, and, conversely, if this condition fails, then there exist distinct ν1 and ν2 satisfying (1).
Small fractional parts of quadratic and additive forms
Authors: Baker R. C. , Harman G.
Published: November 2008

We denote by ∥…∥ the distance to the nearest integer. Let ε be an arbitrary positive number. Danicic(6) showed that for N > c1(s, ε) and a quadratic form Q(x1, …, xs) there exist integers n1, …, ns with

having
Representation theory for tensor products of Banach algebras
Authors: Carne T. K.
Published: November 2008

The algebraic tensor product A1⊗A2 of two Banach algebras is an algebra in a natural way. There are certain norms α on this tensor product for which the multiplication is continuous so that the completion, A1αA2, is a Banach algebra. The representation theory of such tensor products is the subject of this paper. It will be shown that, under certain simple conditions, the tensor product of two semi-simple Banach algebras is semi-simple although, without these conditions, the result fails.
Subgroup closed Fitting classes are formations
Authors: Bryce R. A. , Cossey John
Published: November 2008

Since their introduction by Fischer(12) and Fischer, Gaschütz and Hartley (13) Fitting classes of soluble groups have attracted attention on two fronts (all groups considered in this paper will be finite and soluble). On the one hand is their important role in the structure of finite soluble groups, a good account of which can be found in Gaschütz (14), and on the other is their intrinsic interest as classes of groups. This paper falls into the second category, and is a continuation and completion of (8). There we proved that a subgroup closed Fitting class is a formation if it consists of groups of nilpotent length at most three. Happily, at last, we can remove this qualification.
Norm preserving interpolation sets for polydisc algebras
Authors: Globevnik Josep
Published: November 2008

Let N > 1 and let AN be the polydisc algebra, i.e. the algebra of all continuous functions on the closed polydisc δ¯N ⊂ N, analytic on the open polydisc δN, with sup norm. Call a closed set F ⊂ δ¯N a peak interpolation set for AN if given any f ε C(F), f ≠ 0, there is an extension f ε AN of f such that ¦f˜(z)¦ < ‖ f ‖ (z ε δ¯N - F); call F a norm preserving interpolation set for AN if given any f ε C(F) there is an extension f˜ ε AN of f such that ‖f˜‖ = ‖f‖. The paper gives a complete description of norm preserving interpolation sets for AN in terms of peak interpolation sets for AM, M ≤ N.
Cohomological annihilators
Authors: Schenzel Peter
Published: November 2008

The local cohomology theory introduced by Grothendieck(1) is a useful tool for attacking problems in commutative algebra and algebraic geometry. Let A denote a local ring with its unique maximal ideal m. For an ideal I ⊂ A and a finitely generated A-module M we consider the local cohomology modules HiI (M), i є ℤ, of M with respect to I, see Grothendieck(1) for the definition. In particular, the vanishing resp. non-vanishing of the local cohomology modules is of a special interest. For more subtle considerations it is necessary to study the cohomological annihilators, i.e. aiI(M): = AnnΔHiI(M), iєℤ. In the case of the maximal ideal I = m these ideals were used by Roberts (6) to prove the ‘New Intersection Theorem’ for local rings of prime characteristic. Furthermore, we used this notion (7) in order to show the amiability of local rings possessing a dualizing complex. Note that the amiability of a system of parameters is the key step for Hochster's construction of big Cohen-Macaulay modules for local rings of prime characteristic, see Hochster(3) and (4).
On the tangent developable of a space curve
Authors: Mond David
Published: November 2008

In this paper we investigate the local form of the tangent developable of a curve in 3-space, and obtain results relating this to the order of vanishing of the torsion. In particular,

Theorem 1. If at the point γ(t) on the curve γ, the torsion vanishes to order k (0 ≼ k ≼ 4), then the germ of the tangent developable at that point has one curve of self intersection if k is odd, and none if k is even.
Locally symmetric homology spheres and an application of Matsushima's formula
Authors: Johnson Francis E. A.
Published: November 2008

It is a matter of some interest to determine which closed manifolds have the same homology as a closed aspherical manifold (7) (9). This paper is concerned with the more restrictive question of which spheres have the same homology as some closed aspherical manifold.
Probability measures with trivial Stam groups
Authors: Brown Gavin , Mohan William
Published: November 2008

Let μ be a probability measure on the real line ℝ, x a real number and δ(x) the probability atom concentrated at x. Stam made the interesting observation that either

or else

(ii) δ(x)* μn, are mutually singular for all positive integers n.
Appendix
Authors: Spaltenstein N.
Published: November 2008

The notations and the references are the same as in the article by Alvis and Lusztig (0).For a finite group H let H^ be the set of isomorphism classes of irreducible complex representations of H. Let |θ| denote the degree of θ∈H^
On a class of non-homogeneous Markov chains
Authors: Cohn Harry
Published: November 2008

Suppose that {Xn} is a countable non-homogeneous Markov chain and

If converges for any i, l, m, j with , then

whenever lim , whereas if converges, then

where and . The behaviour of transition probabilities between various groups of states is studied and criteria for recurrence and transience are given.
Geometric invariant theory of linear systems
Authors: Wall C. T. C.
Published: November 2008

In considering the geometric invariant theory of linear systems (pencils, nets, …) of geometrical objects (quadrics, cubic curves, binary forms,…) there are several ways to apply the basic theory. The object of this note is to point out the equivalence of different approaches and to apply this remark to a number of special cases.
The uniqueness of bundle transfers
Authors: Lewis L. G.
Published: November 2008

LetKbe a cohomology theory. Axioms are given which uniquely characterize the transfer inK-cohomology for bundles with structure group a compact Lie group and fibre a finite C.W. complex. Also, a family of generalized transfers is defined which includes both the standard transfer and Atiyah's holomorphic transfer.
A characterization of piecewise linear homology manifolds
Authors: Mitchell W. J. R.
Published: November 2008

We state and prove a theorem which characterizes piecewise linear homology manifolds of sufficiently large dimension among locally compact finite-dimensional absolute neighbourhood retracts (ANRs). The proof is inspired by Cannon's observation (3) that a piecewise linear homology manifold is a topological manifold away from a locally finite set, and uses Galewski and Stern's work on simplicial triangulations of topological manifolds, the Edwards–Cannon–Quinn characterization of topological manifolds and Siebenmann's work on ends (3, 6, 4, 13, 14, 15, 16). All these tools have suitable relative versions and so the theorem can be extended to the bounded case. However, the most satisfactory extension requires a classification of triangulations of homology manifolds up to concordance. This will be given in a subsequent paper and the bounded case will be postponed to that paper.
On 2-dimensional local rings with Artin's approximation property
Authors: Brown M. L.
Published: November 2008

Extending results of Popescu and Brown, the main result of this paper is that excellent henselian R1 and S1 2-dimensional local rings, at least in characteristic zero, have the approximation property of M. Artin.

Most of the paper consists of an extension of Néron's desingularization to rings which are R1 and S1; such a theorem was previously known for factorial domains. The main theorem is then deduced from this desingularization theorem using a theorem of Elkik.

Because of cohomological obstructions, the desingularization theorem is proved only for quasi-projective varieties. In the previously known case for factorial domains, these obstructions are always zero and the desingularization can be obtained by blowing up subschemes. The more general desingularization of this paper is obtained by blowing up locally free sheaves instead, the obstructions being zero for this case.
Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions
Authors: Ball J. M. , Schaeffer D. G.
Published: November 2008

In this paper we consider the equilibrium configurations of a homogeneous, incompressible, isotropic elastic body subjected to a uniform dead load surface traction of magnitude T whose direction is normal to the surface of the body in the reference configuration, and to no other forces. We concentrate on homogeneous equilibrium solutions, that is those for which the deformation gradient F is constant, and we study their bifurcations and stability (with respect to an appropriate static criterion) as T varies. Since it turns out that the equations for homogeneous equilibrium solutions, and the stability properties that we consider of these solutions, are independent of the shape of the body in the reference configuration, we can suppose if desired that this shape is a cube. (See Fig. 1.1.)
Spectral representation of local semigroups associated with Klein-Landau systems
Authors: Ricker W.
Published: November 2008

In their paper [5], Klein and Landau prove that given a symmetric ‘local semigroup’ of unbounded operators {T(t); t ≥ 0} on a Hilbert space, there exists a unique selfadjoint operator T such that T(t) is a restriction of e−tT, for each t ≥ 0. A similar representation theorem was proved earlier by Nussbaum [8]. The result of Klein and Landau was recently extended to the setting of reflexive Banach spaces by Kantorovitz ([4], theorem 2–3). More precisely, Kantorovitz presented necessary and sufficient conditions for a local semigroup of unbounded operators {T(t); t ≥ 0} to consist of restrictions of e−tT, t ≥ 0, for some unbounded spectral operator of scalar-type T with real spectrum (cf. [1] for the terminology).
Corrigenda
Authors: Kuhn Nicholas J.
Published: November 2008

In this note we show that Propositions 5·2 and 5·3 of [1] are incorrect as stated. Thus statement (5) of Theorem 1·3 must be considered as a conjecture and certainly does not follow from our constructions. Our error does not affect any other results in the paper, and, indeed, § 5 was included mainly to provide some conceptual motivation for our constructions.
Bounding finite groups acting on 3-manifolds
Authors: Kojima Sadayoshi
Published: November 2008

In Problem 3·39 (B) and (C) of Kirby's collection [10], Giffen and Thurston asked whether, for a closed 3-manifoldM, the order of finite subgroups of DiffMis bounded, so that it contains no infinite torsion subgroups unlessMadmits a circle action. In this paper, we answer this question affirmatively for homotopy geometric manifolds, and then discuss some hyperbolic 3-manifolds with only a few actions as examples showing poor symmetry of 3-manifolds in general.
Homogeneous elements of free algebras have free idealizers
Authors: Dicks Warren
Published: November 2008

Let k be a field, X a set, F = k 〈X〉 the free associative k-algebra, and b an element of F that is homogeneous with respect to the grading of F induced by some map . We show that the idealizer of b in F, S = {f∈F|fb∈bF}, is a free algebra.
Diophantine approximation and Dirichlet series
Authors: Everest G. R.
Published: November 2008

1. Given a sequence an of positive integers, one expects to obtain information on the distribution of these numbers by examining the Dirichlet series

In this paper we are going to show how such a series arises from Fröhlich's Galoismodule theory and the use the Thue–Siegel–Roth–Schmidt Theorem as one of the tools in the study of its singularities.
On the structure of certain arithmetic subgroups of SL2()
Authors: Maclachlan C.
Published: November 2008

In [6], p. 80, Serre showed that the group SL2(Z[1/p]) is a free product of two copies of SL2(Z) amalgamated along a sub-group of index p + 1 in both components. This result was obtained from the structure theory of groups acting on trees and the construction of a tree on which SL2 over a field with discrete valuation acts in a natural way. This result can be extended to other SL2 examples. Using the above description, Serre [6] also gave presentations for the groups SL2(Z[1/p]) where p = 2, 3.
A High–Low search game on the unit interval
Authors: Baston V. J. , Bostock F. A.
Published: November 2008

We consider the following two-person zero-sum game on the closed interval [0,1]. The hider chooses any real number h in [0,1]. The searcher successively chooses real numbers ξ1ξ2… in [0,1], where at each choice ξi he is told whether h = ξih < ξ1 or h > ξi and he may choose ξi+1 in the light of this information. The payoff (to the hider) is the sum of the distances of the searcher from the hider at each of the moves, that is .
The components of mKv for threefolds with x(V) = 0
Authors: Wilson P. M. H.
Published: November 2008

For V a complex algebraic threefold with k( V) = 0 and having at least one minimal model (for definition, see below), we show that (except possibly in one rather special case) the components of an effective divisor mKv are birationally ruled surfaces.
A note on k-uniformly convex spaces
Authors: Bae Jong Sook , Choi Sung Kyu
Published: November 2008

In this short note we prove that Istrǎƫescu's notion of k-uniform (k-locally uniform) convexity of a Banach space is actually equivalent to the notion of uniform (locally uniform) convexity. Thus theorem 2 in [3] and theorem 2·6·28 in [2] are trivially true.
Hermitian character and the first problem of R. H. Fox
Authors: Pizer Adrian
Published: November 2008

Let G be a group such that

(1) G is finitely presented with deficiency one,

(2) G/G' is infinite cyclic, with a distinguished generator t.
On the Fourier series of a finitely described convex curve and a conjecture of H. S. Shapiro
Authors: Sheil-Small T.
Published: November 2008

Let F(eis) denote a homeomorphism of the positively oriented unit circle onto a convex curve Γ and let f (eit) = F(eiΦ(t)), where Φ(t) is a non-decreasing function such that Φ(2π) – Φ(0) ≤ 2πN (N a positive integer). If f (eit) has Fourier coefficients cn, we show that is either constant or an N -valent analytic function in {|z| < 1}. We prove that where d is the distance from 0 to Γ and δ(N) > 0 depends only on N. This settles affirmatively a conjecture of H. S. Shapiro.
Another ‘short’ proof of the Riesz representation theorem
Authors: Garling D. J. H.
Published: November 2008

1. Introduction. In [2], a short synthetic proof of the Riesz representation theorem was given; this used the Hahn-Banach theorem, the Stone-Čech compactification of a discrete space and the Caratheodory extension procedure for measures. In this note, we show how the theorem can be proved using ultrapowers in place of the Stone-Čech compactification. We also describe how the proof can be expressed in a non-standard way (a rather different non-standard proof has been given by Loeb [4]).
Smoothness of functions and Fourier coefficients: a functional analyst's approach
Authors: Wojtaszczyk P.
Published: November 2008

We give new proofs of transference theorems which allow the transfer of the bad behaviour of Fourier coefficients from one complete orthonormal system to the other. We also present some results on Carleman-type singularities.
Proper pointed maps from ℝn+1to a σ-compact space
Authors: Hernandez Luis J. , Porter Timothy
Published: November 2008

In this paper we study the group of pointed proper homotopy classes of proper pointed maps from (ℝn+1, 0) to a pointed σ-compact space (X, x) and prove the existence of a diagram of exact sequences linking the groups with the Brown—Grossman groups, the Steenrod groups πn(X) and the classical Hurewicz homotopy groups πn(X).
Injective absolutely summing operators
Authors: Okada Susumu , Okazaki Yoshiaki
Published: November 2008

Let X be an infinite-dimensional Banach space. It is well-known that the space of X-valued, Pettis integrable functions is not always complete with respect to the topology of convergence in mean, that is, the uniform convergence of indefinite integrals (see [14]). The Archimedes integral introduced in [9] does not suffer from this defect. For the Archimedes integral, functions to be integrated are allowed to take values in a locally convex space Y larger than the space X while X accommodates the values of indefinite integrals. Moreover, there exists a locally convex space Y, into which X is continuously embedded, such that the space ℒ(μX, Y) of Y-valued, Archimedes integrable functions is identical to the completion of the space of X valued, simple functions with repect to the toplogy of convergence in mean, for each non-negative measure μ (see [9]).
On generalized albanese varieties for surfaces
Authors: Önsiper Hurşit
Published: November 2008

Given a variety X over a field k and a dense open subset U of X, the related generalized albanese problem has two parts. First we want to classify rational maps with domain U into commutative algebraic groups, into reasonable categories, and then in each category we want to find an object α which is universal in the sense that any β in this category factors through α.
Interpolation by analytic functions on c0
Authors: Aron Richard M. , Globevnik Josip
Published: November 2008

Let B be the open unit ball of c0. We give a geometric characterization of the sequences {xn} ⊂ bB with the property that, given any bounded sequence {αn} ⊂ ℂ, there is a continuous function , analytic in B, such that f(xn) = αn for all n and such that supi∈B|f(x)| = supn∈N|αn|.
On the Lk-UR and L-kR spaces
Authors: Chao-Xun Nan , Jian-Hua Wang
Published: November 2008

In this paper, we prove that if X is a strictly convex Lk-UR space, then X is an L-kR space. However, the converse need not be true. Also, for each k ≥ 2, there exists a Lk-UR space which is URED but is not L-(k – 1)R.
Vogt's theorem on categories of homotopy coherent diagrams
Authors: Cordier Jean-Marc , Porter Timothy
Published: November 2008

Let Top be the category of compactly generated topological spaces and continuous maps. The category, Top, can be given the structure of a simplicially enriched category (or S-category, S being the category of simplicial sets). For A a small category, Vogt (in [22]) constructed a category, Coh (A, Top), of homotopy coherent A-indexed diagrams in Top and homotopy classes of homotopy coherent maps, and proved a theorem identifying this as being equivalent to Ho (TopA), the category obtained from the category of commutative A-indexed diagrams by localizing with respect to the level homotopy equivalences. Thus one of the important consequences of Vogt's result is that it provides concrete coherent models for the formal composites of maps and formal inverses of level homotopy equivalences which are the maps in Ho (TopA). The usefulness of such models and in general of Vogt's results is shown in the series of notes [14–17] by the second author in which those results are applied to give an obstruction theory applicable in prohomotopy theory.
Compact multipliers on weighted hypergroup algebras. II
Authors: Ghahramani F. , Medgalchi A. R.
Published: November 2008

In [7] we gave a description of compact multipliers of Lω(X), and left open the question of whether weakly compact multipliers on Lω(X) are compact. This had already been answered for some examples of hypergroup algebras ([1], [2], [6] and [10]). Here we give a positive answer to this question in the general setting of a weighted hypergroup algebra.
Multiplicative functions at consecutive integers
Authors: Hildebrand Adolf
Published: November 2008

Let λ(n) denote the Liouville function, i.e. λ(n) = 1 if n has an even number of prime factors, and λ(n) = − 1 otherwise. It is natural to expect that the sequence λ(n) (n ≥ 1) behaves like a random sequence of ± signs. In particular, it seems highly plausible that for any choice of εi = ± 1 (i = 0,…, k) we have
Schauder bases in locally solid lattice Banach spaces
Authors: Polyrakis Ioannis A.
Published: November 2008

Schauder bases in Banach spaces are studied in [5].

In ordered Banach spaces a special type of Schauder bases, the O.P. Schauder bases, are studied because then the properties of ordered spaces can be used.
Certain mapping properties of rational complex planar splines
Authors: Dikshit H. P. , Ojha A. , Sharma A.
Published: November 2008

Considering a certain partition of a given compact region in the complex plane, interpolatory, convergence and quasiconformal properties of interpolants from the class of continuous piecewise functions with pieces as quadratic polynomials in z and were studied recently in [3] and [7]. In the present paper we succeed in showing that the foregoing mapping properties continue to hold for interpolants from a certain class of continuous piecewise rational polynomial functions in z and
Unified proofs of Hilbert's basis theorem and its analogue in formal power series rings
Authors: Caruth A.
Published: November 2008

Let R denote a commutative Noetherian ring with an identity element. Hilbert's basis theorem states that the polynomial ring in a finite number of indeterminates over R is also Noetherian. (See Northcott ], theorem 8, p. 26; Zariski and Samuel [4], theorem 1, p. 201). Hilbert's original theorem in [2] is stated for the case when R is a field or the ring of integers. The standard proofs of this fundamental theorem are essentially of a direct type. The analogue of Hilbert's basis theorem in the ring of formal power series in a finite number of indeterminates over R is also true (Chevalley [1]; see also Northcott [3], theorem 3, p. 89; Zariski and Samuel [5], theorem 4, p. 138). In the present note we bring together concise proofs of Hilbert's and Chevalley's theorems by using a single indirect (i.e. reductio ad absurdum) argument. By induction it is sufficient to consider the case of a polynomial ring S and a formal power series ring T in a single indeterminate X over R.
When rings of differential operators are maximal orders
Authors: Chamarie M. , Stafford J. T.
Published: November 2008

Let A be a commutative domain, finitely generated as an algebra over a field k of characteristic zero and write (A) for the ring of k -linear differential operators. Then A is an Ore domain with quotient division ring, say Q. Our main result is that A is a maximal order in Q if and only if (i) A = ∩{Ap: height (p) = 1} and (ii) A is geometrically unibranched. In this case A is also a Krull domain with no reflexive ideals. We also determine some conditions under which A is simple.
Banach algebras whose duals consist of multipliers
Authors: Oshobi E. O. , Pym J. S.
Published: November 2008

A few years ago, the authors considered briefly Banach algebras whose duals could be identified ‘naturally’ with their multiplier algebras [17]. In this context, naturalness can be interpreted as meaning that, for each element b of the algebra B and each pair of elements u, v of the dual B′,

where 〈, 〉 denotes the dual pairing and the products are of elements of B′ regarded as left or right multipliers on B. In the present paper we return to the same circle of ideas but begin with a more general situation. We assume only that the algebra B is injectively embedded in its algebra of left, and in its algebra of right, multipliers and that its dual B′ can be injectively embedded in the algebra M(B) of double multipliers on B (definition below) in such a way that the above relation holds. From these assumptions we shall prove that there is a normed algebra A such that M(B) is the dual of A and is the algebra of continuous left multipliers on A (or, equally, right multipliers).
A note on a theorem of Stanton-Weinstein on the L4-norm of spherical harmonics
Authors: Lu Jiang-Hua
Published: November 2008

1. Let El (l = 0,1,2, …) be the eigenspaces of the Laplacian on the standard 2-sphere S2. Consider the function r2. 4: El −{0} → R given by

Stanton and Weinstein proved in [1] that r2, 4 was locally maximized by the ‘highest weight’ function . This note is to simplify part of their proof, namely that of the negativity of .
Completely 0-simple semigroups of quotients III
Authors: Fountain John , Petrich Mario
Published: November 2008

In a recent paper [6] the authors introduced the concept of a completely 0-simple semigroup of quotients. This definition has since been extended to the class of all semigroups giving a definition of semigroup of quotients which may be regarded as an analogue of the classical ring of quotients. WhenQis a sernigroup of quotients of a semigroupS, we also say thatSis an order inQ.
Categories of diametric frames
Authors: Pultr A.
Published: November 2008

The aim of this paper is to discuss categories arising when we extend the metric structure to pointless spaces (frames or locales). The classical distance function is here being replaced by the notion of diameter satisfying certain natural properties (monotonicity, subadditivity for intersecting elements, etc.).
A-generators for certain polynomial algebras
Authors: Peterson Franklin. P.
Published: November 2008

R. M. W. Wood has proved a conjecture we made about dimensions of A generators of H*(RP∞ × … × RP∞). In this note we give some of the consequences of this conjecture.
Amenability of Banach algebras
Authors: Gourdeau Frédéric
Published: November 2008

We consider the problem of amenability for a commutative Banach algebra. The question of amenability for a Banach algebra was first studied by B. E. Johnson in 1972, in [5]. The most recent contributions, to our knowledge, are papers by Bade, Curtis and Dales [1], and by Curtis and Loy [3]. In the first, amenability for Lipschitz algebras on a compact metric space K is studied. Using the fact, which they prove, that LipαK is isometrically isomorphic to the second dual of lipαK, for 0 < α < 1, they show that lipαK is not amenable when K is infinite and 0 < α < 1. In the second paper, the authors prove, without using any serious cohomology theory, some results proved earlier by Khelemskii and Scheinberg [8] using cohomology. They also discuss the amenability of Lipschitz algebras, using the result that a weakly complemented closed two-sided ideal in an amenable Banach algebra has a bounded approximate identity. Their result is stronger than that of [1].
Tempered distributions with spectral gaps
Authors: Gabardo Jean-Pierre
Published: November 2008

A tempered distribution on ℝ whose Fourier transform is supported in an interval [−Ω,Ω], where Ω>0, can be characterized by the behaviour of its successive derivatives. On the other hand, a tempered distribution on ℝ whose Fourier transform vanishes in an interval (−Ω,Ω), where Ω>0, can be characterized by the behaviour of a particular sequence of successive antiderivatives. Similar considerations apply to general convolution operators acting on J′(ℝn) and yield characterizations for tempered distributions having their Fourier transforms supported in sets of the form or , where and Ω>0.
The failure of the amalgamation property for representable varieties of l-groups
Authors: Powell Wayne B. , Tsinakis Constantine
Published: November 2008

A variety satisfies the amalgamation property if given G, H1, and embeddings τ1: G → H1 and τ2: G → H2, there exist and embeddings σ1: H1 → K and σ2: H2 → K such that σ1τ1 = σ2τ2.
Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernel
Authors: Bushell P. J. , Okrasinski W.
Published: November 2008

The non-linear Volterra integral equation

has been studied recently in connection with non-linear diffusion and percolation problems [4, 6, 10]. The existence, uniqueness and qualitative behaviour of non-negative, non-trivial solutions are the questions of physical interest.
Geometric interpretations of the ‘natural’ generators of the Mathieu groups
Authors: Curtis R. T.
Published: November 2008

In [1] we used the alternating group A5 to produce a set of five permutations of order three acting on 12 letters; this set was normalized by A5 and generated the Mathieu group M12. We analogously used the linear group PSL2(7) to produce a set of seven involutions acting on 24 letters which was normalized by our PSL2(7) and generated M24. In this paper we describe the combinatorial and geometric interpretations of our generators, and aim to justify our use of the word ‘natural’. The generators for M12 are defined both as permutations of twelve 5-cycles in a conjugacy class of A5, and as permutations of the faces of a dodecahedron. The outer automorphism of M12 emerges as a bonus. The generators of M24 are defined analogously both as permutations of twenty-four 7-cycles in the action of PSL2(7) on seven letters, and as permutations of the 24 faces of a certain cubic graph drawn on a surface of genus three. In addition we mention the connection between the latter construction and the binary Golay code.
Completely right pure monoids on which ℋ is a right congruence
Authors: Gould Victoria
Published: November 2008

An S-system over a monoid S is a set A together with a function ø: A × S → A such that (a, 1) ø = a and (a, st) ø = ((a, s) ø, t) ø for all a ∈ A and for all s, t ∈ S. So an S-system is a set on which S acts unitarily on the right. For (a, s) ø we write simply as: the notions of S-homomorphism, S-subsystem etc. are defined in the obvious manner. Many papers have been written characterizing monoids by properties of their S-systems; here we are concerned with injectivity and a related concept, absolute purity. Further details of the terms we use are given in Section 2.
Structure theory for L*-algebras
Authors: Cuenca Mira José Antonio , Martín Amable García , González Cándido Martín
Published: November 2008

The structure theory of separable complex L*-algebras was given by Schue in [10] and [11]. In [3] Balachandran makes a study of infinite-dimensional complex topologically simple L*-algebras of classical type and poses the question whether these algebras exhaust the class of all infinite-dimensional complex topologically simple L*-algebras. In this paper we give an affirmative answer by determining all the complex topologically simple infinite-dimensional L*-algebras. The case of the real L*-algebras was studied previously in [4], [9] and [12] also under the separability condition. Applying the result of Balachandran, our result yields the structure theory for real L*-algebras. The main tool used here is the ‘approximation’ of the L*-algebra by topologically simple separable L*-algebras via an ultraproduct construction.
Closure properties of the quasi-centre of a Banach algebra
Authors: Rennison J. F.
Published: November 2008

Throughout the paper, A will denote a unital Banach algebra with centre Z over the complex field ℂ. An element a of A is called quasi-central if, for some K ≥ 1,

The set of elements a satisfying (1) for a particular value of K will be denoted by Q(K) and Q = UK≥1Q(K) will be called the quasi-centre of A.
Radial variation of analytic functions with non-tangential boundary limits almost everywhere
Authors: Hallenbeck D. J. , Samotij K.
Published: November 2008

The purpose of this paper is to investigate the asymptotic behaviour as r → 1− of the integrals

and f is an analytic function on the unit disk Δ which has non-tangential limits at almost every point on ∂Δ. The paper is divided into three parts. In the first part we consider the case where λ ≠ 1/k, in the second the somewhat more delicate case when λ = 1/k and in the third part we concentrate on some problems related to the case λ = k = 1.
The Pompeiu problem for groups
Authors: Carey Alan L. , Kaniuth Eberhard , Moran William
Published: November 2008

The Pompeiu problem has its origins in classical analysis in ℝn (see [2, 3, 4, 8] for a discussion and some history). In this context it may be stated as follows. Let D ⊂ ℝn be a bounded measurable set of positive Lebesgue measure and f a locally integrable function on ℝn. Then, if ∫σ(D)f = 0 for all rigid motions σ of ℝn, is f = 0?
A torus reduction theorem for regular coverings of 3-manifolds by homology 3-spheres
Authors: Luft E. , Sjerve D.
Published: November 2008

For any regular covering p:M→M of 3-dimensional manifolds M, M with M a homology 3-sphere we construct a regular covering p′: M′ → M′ of 3-manifolds M′, M′ with the same group of covering transformations and a degree 1 map f:M → M′ so that M′ is a homology 3-sphere, M′ (and hence M′) is irreducible and does not contain incompressible tori, and the regular covering p:M→M is induced from the regular covering p′: M′ → M′ by the map f. Assuming Thurston's geometrization conjecture it follows that M′ (and hence M′) is either hyperbolic or Seifert fibred.
Joint reductions and Rees algebras
Authors: Verma J. K.
Published: November 2008

Let R be a Cohen-Macaulay local ring of dimension d, multiplicity e and embedding dimension v. Abhyankar [1] showed that v − d + 1 ≤ e. When equality holds, R is said to have minimal multiplicity. The purpose of this paper is to study the preservation of this property under the formation of Rees algebras of several ideals in a 2-dimensional Cohen-Macaulay (CM for short) local ring. Our main tool is the theory of joint reductions and mixed multiplicities developed by Rees [9] and Teissier[12].
Topological pseudofree actions on spheres
Authors: Kwasik Sławomir , Schultz Reinhard
Published: November 2008

In topology and geometry it is often instructive to consider objects with isolated singularities. Frequently such objects turn out to be relatively tractable and to provide useful insights into more general situations. For actions of finite cyclic groups on manifolds the standard notion of singularity is a point that is left fixed by some non-trivial element of the group (but not necessarily by the whole group). If the singular set is isolated the action is said to bepseudofree. Special cases of pseudofree actions have been studied in several independent contexts; in particular, previous papers of Cappell and Shaneson [4] and the authors [15] considered classes of ‘nice’ pseudofree actions on spheres. References to other works are given at the beginning of [15] (and in the meantime there has also been considerable further activity).
Constructive complete distributivity II
Authors: Rosebrugh Robert , Wood R. J.
Published: November 2008

A complete lattice, L, is constructively completely distributive, (CCD) (L), if the sup map defined on down-closed subobjects has a left adjoint. It was known that in Boolean toposes (CCD) (L) is equivalent to (CCD) (Lop). We show here that the latter property for all L (sufficiently, for Ω.) characterizes Boolean toposes.
Bifurcation in the traction problem for a transversely isotropic material
Authors: Danescu A.
Published: November 2008

The traction problem for a transversely isotropic incompressible elastic material is considered, and it is shown that when only pure homogeneous deformations are considered, the problem can be formulated as a two-dimensional ℤ2-equivariant bifurcation problem in which the bifurcation parameter is the dead-load. Using imperfect bifurcation theory, conditions for bifurcation phenomena are given and, considering a general non-linear form for the stored energy function, the recognition problem is solved in the simplest cases. The last section treats transversely isotropic non-linear perturbations for a Mooney–Rivlin material and a neo-Hookean material and the corresponding bifurcations.
The mod-p cohomology rings of some p-groups
Authors: Leary I. J.
Published: November 2008

Throughout this paper p denotes an odd prime. The groups we shall consider are central extensions of a cyclic subgroup by Cp ⊕ Cp, and may be presented as

The group P(n) is defined for each n ≥ 3, and has order pn. The group P(3) is the non-abelian group of order p3 and exponent p. The mod-p cohomology rings of the other groups of order p3 have been known for some time (see [14] or [5] for that of the non-abelian metacyclic group), and so this paper completes the calculation of the mod-p cohomology rings of the groups of order p3.
On pairs of additive forms modulo one
Authors: Schäffer S.
Published: November 2008

Throughout this paper ∈ denotes an arbitrary positive number. For real α, ‖α‖ denotes the distance from α to the nearest integer. For natural numbers k we write K = 2k−1. In 1948 Heilbronn [8] showed that for any real α and N > C1(∈)

This theorem has since been generalized in many ways. In particular, results of the following type have been proved for natural numbers k ≥ 2, h = 1,2 and s.
On Behrend sequences
Authors: Hall R. R. , Tenenbaum G.
Published: November 2008

Let denote a sequence of integers exceeding 1, and let τ(n, ) be the number of those divisors of n which belong to . We say that is a Behrend sequence if

where, here and in the sequel, we use the notation p.p. to indicate that a relation holds on a set of asymptotic density one.
Uniform annihilation of local cohomology and of Koszul homology
Authors: Raghavan K.
Published: November 2008

Let R be a ring (all rings considered here are commutative with identity and Noetherian), M a finitely generated R-module, and I an ideal of R. The jth local cohomology module of M with support in I is defined by

In this paper, we prove a uniform version of a theorem of Brodmann about annihilation of local cohomology modules. As a corollary of this, we deduce a generalization of a theorem of Hochster and Huneke about uniform annihilation of Koszul homology.
Applying rewriting methods to special monoids
Authors: Zhang Louxin
Published: November 2008

A special monoid is a monoid presented by generators and defining relations of the form w = e, where w is a non-empty word on generators and e is the empty word. Groups are special monoids. But there exist special monoids that are not groups. Special monoids have been extensively studied by Adjan[1] and Makanin[7] (see also [2]).
An elementary proof of the Ambartzumian–Pleijel identity
Authors: Cabo A. J.
Published: November 2008

In [5], Pleijel proved an identity relating the area A of a convex plane domain and the length L of its boundary (of class C1). In particular, it contains the isoperimetric inequality L2 –4πA ≥ 0.
Symmetry characterizations of certain distributions, 2: Discounted additive functionals and large deviations
Authors: Baxter Martin , Williams David
Published: November 2008

This paper may be read independently of Baxter and Williams [1], hereinafter denoted by [BW1].

As in [BW1], we are mainly concerned with discounted additive functionals. We find that the large-deviation behaviour of the average depends on the precise average used. We derive, in certain cases, a link (but not equality) between the Cesàro average and Abel average limits, and would expect that other averages would produce other limiting behaviours. We have focused on the exponentially discounted (Abel average) case, both because of its tractability and because of its frequent appearance in decision/control problems and models of financial markets. We do give in subsection (e) the promised ‘excursion’ treatment of symmetry characterizations of the type announced in [BW1]; and this new treatment is simpler, more illuminating and more general. First, however, we focus attention on a different kind of asymptotic behaviour from that studied in [BW1], and on differential equations for exact results.
Characterizing connected K-theory by homotopy groups
Authors: Rognes John
Published: November 2008

In this note we provide proofs for two facts related to connected topological K-theory, expected by Ib Madsen.
A class of groups producing simple, unique trace C*-algebras
Authors: Promislow S. David
Published: November 2008

We define and study a class of groups which produce simple, unique trace, C*-algebras. This class strictly contains the class of weak Powers groups, as shown by the fact that it is closed under extensions. We provide answers to some open problems involving Powers and weak Powers groups.
The upper Perron method for labelled complexes with applications to circle packings
Authors: Bowers Philip L.
Published: November 2008

The construction of geometric surfaces via labelled complexes was introduced by Thurston[16, chapter 13], and subsequent applications and developments have appeared in [1, 3, 4, 5, 14, 15]. The basic idea of using labelled complexes to produce geometric structures is that the vertices of a simplicial triangulation of a surface can be labelled with positive real numbers that collectively determine a metric of constant curvature ±1 or 0, with possible singularities at vertices, by using the label values to identify 2-simplices of the triangulation with geometric triangles. Beardon and Stephenson[1] developed a particularly simple method for producing non-singular surfaces via labelled complexes that is modelled after the classical Perron method for producing harmonic functions, and they applied their method in [2] to construct a fairly comprehensive theory of circle packings in general Riemann surfaces. This Perron method was developed more fully by Stephenson and the author in [3, 4] and applied to the study of circle packing points in moduli space. At about the same time and independently of Beardon, Stephenson, and Bowers, Carter and Rodin [5] and Doyle [8] developed the method for flat surfaces and Minda and Rodin [14] developed the method for finite type surfaces. Minda and Rodin [14] applied their development to give partial solutions to the labelled complex version of the classical Schwarz-Picard problem that concerns the construction of singular hyperbolic metrics on surfaces with prescribed singularities. In this paper, we modify the aforementioned approaches and examine the upper Perron method for producing non-singular geometric surfaces. This upper method has several advantages over the Perron method as developed previously and provides a complete solution to the labelled complex version of the Schwarz-Picard problem.