bluuebunny/crossref_metadata_2025 huggingface dataset:
On subordinated distributions and random record processes
Authors: Embrechts P. , Omey E.
Published: November 2008

Consider a sequence of i.i.d. random variables attached to the points of an independent point process. The random record process is the process of epochs of successive maxima in this sequence. Various limit theorems are proved for the distribution of times to successive records and interrecord times. Some new results on the tail-behaviour of subordinated distributions are needed.
Pencils of real binary cubics
Authors: Wall C. T. C.
Published: November 2008

A complete and satisfying account of the classification of pencils of binary cubics over an algebraically closed field was given by Newstead (2). Extending these results to the real case is not a matter of mere routine since new questions arise, for example the separation of roots of the cubics in a pencil (as well as their reality).
On a conjecture of Watson
Authors: Raka Madhu
Published: November 2008

Let Qn be a real indefinite quadratic form in n variables x1, x2,…, xn, of determinant D ≠ 0 and of type (r, s), 0 < r < n, n = r + s. Let σ denote the signature of Qn so that σ = r − s. It is known (see e.g. Blaney(4)) that, given any real numbers c1 c2, …, cn, there exists a constant C depending upon n and σ only such that the inequality

has a solution in integers x1, x2, …, xn. Let Cr, s denote the infimum of all such constants. Clearly Cr, s = Cs, r, so we need consider non-negative signatures only. For n = 2, C1, 1 = ¼ follows from a classical result of Minkowski on the product of two linear forms. When n = 3, Davenport (5) proved that C2, 1 = 27/100. For all n and σ = 0, Birch (3) proved that Cr, r = ¼. In 1962, Watson(18) determined the values of Cr, s for all n ≥ 21 and for all signatures σ. He proved that

Watson also conjectured that (1·2) holds for all n ≥ 4. Dumir(6) proved Watson's conjecture for n = 4. For n = 5, it was proved by Hans-Gill and Madhu Raka(7, 8). The author (12) has proved the conjecture for σ = 1 and all n. In the preceding paper (13) we proved that C5, 1 = 1. In this paper we prove Watson's conjecture for σ = 2, 3 and 4.
Multiple images of stochastic processes
Authors: Berman Simeon M.
Published: November 2008

A simple sufficient condition is given for a stochastic process x(t), 0 ≤ t ≤ 1, to have the following property: There is an integer m ≥ 2 such that for any non-degenerate subinterval J ⊂ [0, 1], there exist m disjoint subintervals I1, …, Im ⊂ J such that the intersection of the images of I1,…, Im under the mapping by x(·) has positive Lebesgue measure, almost surely. There is also a version for vector random fields; and the main result is shown to apply to large classes of processes.
Some applications of Maz'ja's uniqueness theorem to a class of linear water wave problems
Authors: Hulme Andrew
Published: November 2008

This paper describes a criterion which, if satisfied, guarantees uniqueness of solution for the problem involving the radiation or diffraction of small amplitude water waves by a totally submerged body. This criterion was originally stated by a Russian mathematician, V. G. Maz'ja, although his work does not appear to be widely known. For this reason a brief outline of Maz'ja's proof is given here, together with a discussion of the condition to be satisfied by the submerged body.

Maz'ja's criterion is not satisfied by all submerged bodies and so his result does not provide a general proof of uniqueness. However, the criterion is satisfied in some important cases and examples are presented here. The partial nature of this result is due entirely to the method of proof and not to any intrinsic difficulty with the underlying hydrodynamics.
Polarization and the two-dimensional Grothendieck inequality
Authors: Tonge Andrew
Published: November 2008

Throughout this paper all scalars and vector spaces will be assumed to be complex unless there are specific indications to the contrary.
The transient behaviour of the Moran model in population genetics
Authors: Donnelly Peter
Published: November 2008

This paper presents an alternative analysis of the behaviour of the Moran model. Using some of the techniques developed in the study of interactive particle systems, a process which is dual to the Moran model is constructed. Exact analysis of this dual process is considerably easier than for the original model. Because of the relationship between the two processes it is then possible to find the distribution of the Moran model.
De Rham's theorem in a smooth topos
Authors: Moerdijk Ieke , Reyes Gonzalo E.
Published: November 2008

It has been persuasively argued (e.g. by Lawvere[8]) that the mathematical world picture needed to develop the physics of continuous bodies and fields should involve a cartesian closed category of smooth morphisms between smooth spaces. As far as the foundations of the calculus of variations are concerned, the need for such a category was recognized by K. T. Chen(cf. [2]).
A dualizing complex for Stanley–Reisner rings
Authors: Gräbe Hans-Gert
Published: November 2008

In this paper we construct a (multihomogeneous) dualizing complex for A [Δ], the Stanley–Reisner ring of Δ over an arbitrary commutative noetherian ring A with identity, admitting a dualizing complex. In addition, some consequences are discussed.
Characterizations of r-potent matrices
Authors: McCloskey Joseph P.
Published: November 2008

A matrix A is said to be tripotent whenever A3 = A. The study of tripotent matrices is of statistical interest since if the n × 1 real random vector X follows an N(0, I) distribution and A is a symmetric matrix then the real quadratic form X′AX is distributed as the difference of two independently distributed X2 variates if and only if A3 = A. In fact, a necessary and sufficient condition that A is tripotent is that there exist two idempotent matrices B and C such that A = B – C, and BC = 0. Using properties of diagonalizable matrices, we will prove several algebraic characterizations of r-potent matrices that extend the known results for tripotent matrices. Our first result will be to obtain an analogous decomposition for an arbitrary r-potent matrix.
Projections and embeddings of locally convex operator spaces and their duals
Authors: Fourie Jan H. , Ruckle William H.
Published: November 2008

Let E, F be Hausdorff locally convex spaces. In this note we consider conditions on E and F such that the dual space of the space Kb (E, F) (of quasi-compact operators) is a complemented subspace of the dual space of Lb (E, F) (of continuous linear operators). We obtain necessary and sufficient conditions for Lb(E, F) to be semi-reflexive.
Complex strict and uniform convexity and hyponormal operators
Authors: Mattila Kirsti
Published: November 2008

Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. The (spatial) numerical range of an operator TεB(X) is defined as the set

If V(T) ⊂ ℝ, then T is called hermitian. More about numerical ranges may be found in [8] and [9].
A homological criterion for the realizability of poly-Surface groups
Authors: Johnson F. E. A.
Published: November 2008

The Realizability Question for poly-Surface groups consists in asking whether, for any poly-Surface group G, one may find a smooth closed aspherical manifold XG with π1(XG)= G. It seems, on present evidence, that the answer is always ‘yes’ [2][3], although in any one case the details may be quite complicated [4].
Finite Bol loops: III
Authors: Burn R. P.
Published: November 2008

In this paper we prove that for any odd prime p, a Moufang loop of order 2p2 is a group and there is exactly one non-associative right Bol loop of order 2p2.
Brownian motion can see a knot
Authors: Varopoulos N. Th.
Published: November 2008

Let be the 3-dimensional sphere and let be a smooth knot, i.e. K is the image of a regular diffeomorphism . We say that K is unknotted if there exists a diffeomorphism of onto the unit sphere of , that brings K to the equatorial circle otherwise we say that K is knotted.
Knots which are branched cyclic covers of only finitely many knots
Authors: Strickland Paul
Published: November 2008

In [5] we proved two results: theorem 1, which said that if k was a simple (2q – 1)-knot, q 1, then it was equivalent to the m-fold branched cyclic cover of another knot if and only if there existed an isometry u of its Blanchfield pairing 〈,〉, whose mth power was the map induced by a generator t of the group of covering translations associated with the infinite cyclic cover of k; and theorem 2, which showed that if k were the m-fold b.c.c. of two such knots, then these would be equivalent if and only if the corresponding isometries were conjugate by an isometry of 〈,〉. Using this second result, we present two cases where k may only be the m-fold b.c.c. of finitely many knots.
On the Hausdorff dimension of Brownian cone points
Authors: Evans Steven N.
Published: November 2008

Let B(t) be a two-dimensional Brownian motion. For 0 < α < 2π, set

and, for 0 ≥ β< 2π, let F(α,β) be F(α) rotated through an angle β about the origin.
Generalized translations associated with an unbounded self-adjoint operator
Authors: Fishel B.
Published: November 2008

Delsarte [2], Povzner [9], Levitan [8], Leblanc [7], Dunford and Schwartz [3] (p. 1626) and Hutson and Pym [5] have discussed generalized translation operators (GTO) ‘associating with a differential operator’. The latter authors have also considered the topic in an abstract setting-the GTO ‘associates’ with a compact operator in a normed space. GTO are to have properties generalizing those of the translation operators defined by members of a group on a vector space E of functions defined on the group:

(πεE, s and t are group elements). In the case of a locally compact topological group the integration spaces E = L1,L2,L∞, for a Haar measure of the group, are of especial interest.
Structurally stable heteroclinic cycles
Authors: Guckenheimer John , Holmes Philip
Published: November 2008

This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of Cr vector fields equivariant with respect to a symmetry group. In the space X(M) of Cr vector fields on a manifold M, there is a residual set of vector fields having no trajectories joining saddle points with stable manifolds of the same dimension. Such heteroclinic connections are a structurally unstable phenomenon [4]. However, in the space XG(M) ⊂ X(M) of vector fields equivariant with respect to a symmetry group G, the situation can be quite different. We give an example of an open set U of topologically equivalent vector fields in the space of vector fields on ℝ3 equivariant with respect to a particular finite subgroup G ⊂ O(3) such that each X ∈ U has a heteroclinic cycle that is an attractor. The heteroclinic cycles consist of three equilibrium points and three trajectories joining them.
The group of homotopy self-equivalence classes using an homology decomposition
Authors: Rutter John W.
Published: November 2008

Exact sequences which can be used for calculating the group (X) of homotopy classes of homotopy self-equivalences of a space X are known in the case of cellular decompositions (some references are given in § 1 of [8]), and in the case of Postnikov decompositions (for example 3·1 of [5]). Here we obtain exact sequences which can be used to calculate (X) using a simply-connected homology decomposition.
A computation of the Littlewood exponent of stochastic processes
Authors: Blei Ron C. , Kahane J.-P.
Published: November 2008

A stochastic process X = {X(t): t ∈ [0, 1]} on a probability space (Ω, , ℙ) is said to have finite expectation if the function defined on the measureable rectangles in Ω × [0, 1] by

for A ∈ and (s, t) ⊂ [0, 1] gives rise to a complex measure in each of its two coordinates (see [1], definition 1·1). Equivalently, X has finite expectation if

is finite. The function defined by (1), effectively a generalization of the Doléans measure (see e.g. [4] pp. 33–35), is extendible to a bona fide complex measure on Ω × [0, 1] if and only if its ‘total variation’
A geometric criterion for decomposition and multivalence
Authors: Abu-Muhanna Y. , Lyzzaik A.
Published: November 2008

We give a quite general geometric criterion for a function analytic in the unit disc to be a polynomial of a univalent function, and hence a criterion for multivalence. We believe that this is the essence why multivalent close-to-convex functions enjoy the latter decomposition property. As another application, we study, as suggested by T. Sheil-Small ‘9’, the geometry of classes of analytic functions which arise from his recent investigation of multivalent harmonic mappings.
Singular numbers of smooth kernels
Authors: Oehring Charles
Published: November 2008

In [12] we elaborate the vague principle that the behaviour at infinity of the decreasing sequence of singular numbers sn(K) of a Hilbert–Schmidt kernel K is at least as good as that of the sequence {n−1/qω(n−1;K)}, where ωp is an Lp-modulus of continuity of K and q = p/(p − 1), where 1 ≤ p ≤ 2. Despite the author's effort to justify his study of refinements of the half-century old theorem of Smithies [13], that theorem remains the central result of the subject (viz. that for 0 < a ≤ 1, K∈Lip(a, p) implies that sn(K) = O(n−α−1/q)). For example, Cochran's omnibus theorems [5, 6] that delimit the Schatten classes to which a kernel belongs are based on the blending of ‘smoothness’ conditions and emphasize the pivotal role of the principal corollary of Smithies' theorem (viz. {sn}∈lr if r−1 < α + q−1). Cochran later offered in [7] a very simple derivation of the corollary from a Fourier series theorem of Konyushkov (see [2], vol. II, p. 197), whose proof was, however, at least as intricate as Smithies' demonstration.
The loops onU(n)/O(n) andU(2n)/Sp(n)
Authors: Crabb M. C. , Mitchell S. A.
Published: November 2008

In [6] and [9] the second author and Bill Richter showed that the natural ‘degree’ filtration on the homology of ΩSU(n) has a geometric realization, and that this filtration stably splits (as conjectured by M. Hopkins and M. Mahowald). The purpose of the present paper is to prove the real and quaternionic analogues of these results. To explain what this means, consider the following two ways of viewing the filtration and splitting for ΩSU(n). Whenn= ∞, ΩSU=BU. The filtration isBU(1)⊆BU(2)⊆… and the splittingBU≅ V1≤<∞is a theorem of Snaith[14]. The result for ΩSU(n) may then be viewed as a ‘restriction’ of the result forBU. On the other hand there is a well-known inclusion ℂPn−1. This extends to a map ΩΣℂPn−1→ΩSU(n), and the filtration (or splitting) may be viewed, at least algebraically, as a ‘quotient’ of the James filtration (or splitting) of ΩΣℂPn−1. It is now clear what is meant by the ‘real and quaternionic analogues’. In the quaternionic case, we replaceBUbyBSp=Ω(SU/SP), ΩSU(n) by Ω(SU(2n)/SP(n))and ℂPn−1by ℍPn−1. The integral homology of Ω(SU(2n)/SP(n)) is the symmetric algebra on the homology of ℍPn−1, and may be filtered by the various symmetric powers. We show that this filtration can be realized geometrically, and that the spaces of the filtration are certain (singular) real algebraic varieties (exactly as in the complex case). The strata of the filtration are vector bundles over filtrations of Ω(SU(2n−2)/SP(n−1)), and the filtration stably splits. See Theorems (1·7) and (2·1) for the precise statement. In the real case we replaceBUby Ω(SU/SO), Ω(SU(n)/SO(n)) and ℂPn−1by ℝPn−1. Here integral homology must be replaced by mod 2 homology, and splitting is only obtained after localization at 2. (Snaith's splitting ofBOin [14] can be refined [2, 8] so as to be exactly analogous to the splitting ofBU:BO≅V1≤<∞MO(k).)
On harmonic maps between S3 and S2 of prescribed Hopf invariant
Authors: Ratto Andrea
Published: November 2008

In this paper we prove the following

Theorem. Each element of the group π3(S2) = ℤ can be rendered harmonic, i.e. admits a harmonic representative, provided that the domain S3is given a suitable riemannian metric.
The packing measure of the graphs and level sets of certain continuous functions
Authors: Rezakhanlou Fraydoun
Published: November 2008

The relationship between the local growth of a continuous function and the packing measure of its level sets and of its graph is studied. For the Weierstrass function with b an integer such that b ≥ 2 and with 0 < α < 1, and for x ∈ Range (W) outside a set of first category, the level set W−1(x) has packing dimension at least 1 − α. Furthermore, for almost all x ∈ Range (W), the packing dimension of f is at most 1 − α. Finer results on the occupation measure and the size of the graph of a continuous function satisfying the Zygmund Λ-condition are obtained.
Almost sure convergence of the Hill estimator
Authors: Deheuvels Paul , Haeusler Erich , Mason David M.
Published: November 2008

In this note we characterize those sequencesknsuch that the Hill estimator of the tail index based on theknupper order statistics of a sample of sizenfrom a Pareto-type distribution is strongly consistent.
Supercritical branching processes with density independent catastrophes
Authors: Grey D. R.
Published: November 2008

A Markov branching process in either discrete time (the Galton–Watson process) or continuous time is modified by the introduction of a process of catastrophes which remove some individuals (and, by implication, their descendants) from the population. The catastrophe process is independent of the reproduction mechanism and takes the form of a sequence of independent identically distributed non-negative integer-valued random variables. In the continuous time case, these catastrophes occur at the points of an independent Poisson process with constant rate. If at any time the size of a catastrophe is at least the current population size, then the population becomes extinct. Thus in both discrete and continuous time we still have a Markov chain with stationary transition probabilities and an absorbing state at zero. Some authors use the term ‘emigration’ as an alternative to ‘catastrophe’.
A note concerning Seifert manifolds for 2-knots
Authors: Trace Bruce
Published: November 2008

Elementary observations yield new classes of knotted 2-spheres in S4 which do not admit Punct (# S1 × S2) as a Seifert manifold. This provides a rather painless proof which re-establishes the existence of non-ribbon 2-knots.
Egorov measurability and generator cores
Authors: Jefferies Brian
Published: November 2008

Sufficient conditions are given for a set to be a core for the generator of a weakly integrable semigroup on a locally convex space. The conditions are illustrated by semigroups of unbounded operators on a Banach space.
Some remarks about extreme degrees in a random graph
Authors: Palka Zbigniew
Published: November 2008

Let Kn, p be a random subgraph of a complete graph Kn obtained by removing edges, each with the same probability q = 1 – p, independently of all other edges (i.e. each edge remains in Kn, p with probability p). Very detailed results devoted to probability distributions of the number of vertices of a given degree, as well as of the extreme degrees of Kn, p, have already been obtained by many authors (see e.g. [l]–[5], [7]–[9]). A similar subject for other models of random graphs has been investigated in [10]–[13], The aim of this note is to give some supplementary information about the distribution of the ith smallest (i ≥ 1 is fixed) and the ith largest degree in a sparse random graph Kn, p, i.e. when p = p(n) = o(1).
Random fractals
Authors: Falconer K. J.
Published: November 2008

There has been considerable interest of late in fractals, both in their occurrence in the sciences, and in their mathematical theory. A general account of fractals is given by Mandelbrot [10], whilst a more mathematical approach may be found in Falconer [5].
Characterization of matrix probability distributions by mean residual lifetime
Authors: Jupp P. E.
Published: November 2008

The mean residual lifetime of a real-valued random variable X is the function e defined by

One of the more important properties of the mean residual lifetime function is that it determines the distribution of X. See, for example, Swartz [10]. References to related characterizations are given by Galambos and Kotz [3], pages 30–35. It was established by Jupp and Mardia[6] that this property holds also for vector-valued X. As (1·1) makes sense if X is a random symmetric matrix, it is natural to ask whether the property holds in this case also. The purpose of this note is to show that, under certain regularity conditions, the distributions of such matrices are indeed determined by their mean residual lifetimes.
Presentations for (G, s)-transitive graphs of small valency
Authors: Weiss Richard
Published: November 2008

Given a groupG, a subgroupHand an elementa∈G, we define Γ(G, H, a) to be the graph on the set of left-cosets ofHinG, where two left-cosetsg1Handg2Hare adjacent whenever. We will consider this construction only in the case that

The first of these conditions assures that adjacency is a symmetric relation (i.e. that Γ(G, H, a) is an undirected graph) and the second assures that Γ(G, H, a) is connected.
Projective representations of rotation subgroups of Weyl groups
Authors: Theo D.
Published: November 2008

By exploiting the well known spin representations of the orthogonal groups O(l), Morris [12] was able to give a unified construction of some of the projective representations of Weyl groups W(Φ) which had previously only been available by ad hoc means [5]. The principal purpose of the present paper is to give a corresponding construction for projective representations of the rotation subgroups W+(Φ) of Weyl groups. Thus we construct non-trivial central extensions of W+(Φ) via the well-known double coverings of the rotation groups SO(l). This adaptation allows us to give a unified way of obtaining the basic projective representations of W+(Φ) from those of W(Φ) determined in [12]. Hence our work is a development of the recent work of Morris, and is an extension of Schur's work on the alternative groups [15].
Fitting functors in finite solvable groups: II
Authors: Beidleman James C. , Brewster Ben , Hauck Peter
Published: November 2008

This paper is a continuation of [1], where we introduced the concept and investigated the basic properties of Fitting functors for finite solvable groups. We recall that a map f which assigns to each finite solvable group G a non-empty set f(G) of subgroups of G is called a Fitting functor if the following property is satisfied: whenever α: G → H is a monomorphism with α(G) ⊴ H, then

The most prominent examples of conjugate Fitting functors are provided by injectors of Fitting classes. However, Fitting functors f in general do not behave as nicely as injectors. For instance, f(G) need not consist of pronormal subgroups of a group G (cf. [1], 4·3).
Coupled stationary bifurcations in non-flux boundary value problems
Authors: Armbruster D. , Dangelmayr G.
Published: November 2008

Coupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov–Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in ℂ2 of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.
A non-causal triangle function
Authors: McMaster T. B. M.
Published: November 2008

Schweizer and Sklar, in their book Probabilistic Metric Spaces, raise the question of whether every triangle function is causal. This note provides a negative answer, by observing certain properties of a suitable partial quaternary operation on the unit interval.
Real forms of cusp singularities. II
Authors: Wall C. T. C.
Published: November 2008

In [3] we classified the real forms of cusp singularities and described their topology; on the way we gave a detailed treatment of the automorphism group. In further work on deformations of real cusp singularities it has been found that these results need completing in certain aspects, and this is the object of the present paper.
Hereditary artinian rings of finite representation type and extensions of simple artinian rings
Authors: Schofield Aidan
Published: November 2008

In [1], Dowbor, Ringel and Simson consider hereditary artinian rings of finite representation type; it is known that if A is an hereditary artinian algebra of finite representation type, finite-dimensional over a field, then it corresponds to a Dynkin diagram in a natural way; they show that an hereditary artinian ring of finite representation type corresponds to a Coxeter diagram. However, in order to construct an hereditary artinian ring of finite representation type corresponding to a Coxeter diagram that is not Dynkin, they show that it is necessary though not sufficient to find an extension of skew fields such that the left and right dimensions are both finite but are different. No examples of such skew fields were known at the time. In [3], I constructed such extensions, and the main aim of this paper is to extend the methods of that paper to construct an extension of skew fields having all the properties needed to construct an hereditary artinian ring of finite representation type corresponding to the Coxeter diagram I2(5).
Finite-point order compactifications
Authors: Richmond Thomas A.
Published: November 2008

After the characterization of 1-point topological compactifications by Alexandroff in 1924, n-point topological compactifications by Magill [4] in 1965, and 1-point order compactifications by McCallion [5] in 1971, spaces that admit an n -point order compactification are characterized in Section 2. If X* and X** are finite-point order compactifications of X, sup{X*, X**} is given explicitly in terms of X* and X** in § 3. In § 4 it is shown that if an ordered topological space X has an m-point and an n-point order compactification, then X has a k-point order compactification for each integer k between m and n. The author is indebted to Professor Darrell C. Kent, who provided assistance and encouragement during the preparation of this paper.
Some sign properties of symmetric functions
Authors: Hunter D. B. , Macdonald I. G.
Published: November 2008

This paper is concerned with the sign properties of the S-functions sλ for real arguments. We show first that sλ is indefinite if any part of the partition λ is odd. Thus it is only if all parts of λ are even that sλ can possibly be positive definite or semi-definite. In this case we show that sλ(x) is positive provided that at least l(λ) of the components of x are non-zero, where l(λ) is the number of parts of the partition λ.
Mutations of homology spheres and Casson's invariant
Authors: Kirk Paul A.
Published: November 2008

Given an embedding of an oriented surface F in an oriented three-manifold M and a homeomorphism h of F, one can construct another three-manifold Mn by cutting M along F and re-glueing the two boundary components using h. Let F be a genus two surface and r the involution which exhibits F as the 2-fold branched cover of S2 branched over six points. In this special case we call Mr the mutation of M along F.
Iterating exponential functions with cyclic exponents
Authors: Baker I. N. , Rippon P. J.
Published: November 2008

This paper is concerned with expressions of the form

wherefa(x) = ax. Thus we have

Such expressions have been described variously as continued exponentials, iterated exponentials, towers of exponents or hyperpowers. We shall frequently make use of their elementary properties, as for example

and
KMS states for reduced groups, theta functions and the Powers–Størmer construction
Authors: Hannabuss K. C.
Published: November 2008

KMS states of a twisted convolution algebra of Schwartz functions on a vector group are classified and related to KMS states of twisted L1-algebras for certain subquotients. The KMS states for the subquotient algebras are also related to Fock states of vector groups. In the particular case of the subquotient Tn × ℤn of ℚ2n this links the Fock space construction of the theta functions with their appearance in KMS states of loop groups and in the Kac character formula.
The function field abstract prime number theorem
Authors: Cohen Stephen D.
Published: November 2008

For arithmetical semigroups modelled on the positive integers, there is an ‘abstract prime number theorem’ (see, for example, [1]). In order to study enumeration problems in the several arithmetical categories whose prototype instead is the ring of polynomials in an indeterminate over a finite field of order q, Knopfmacher[2, 3] introduced the following modification. An additive arithmetical semigroup G is a free commutative semigroup with an identity, generated by a countable set of ‘primes’ P and admitting an integer-valued degree mapping ∂ with the properties

(i) ∂(l) = 0,∂(p) > 0 for p∈P;

(ii) ∂(ab) = ∂(a) + ∂(b) for all a, b in G;

(iii) the number of elements in G of degree n is finite. (This number will be denoted by G(n).)
Deformations of reductive group actions
Authors: Müller Gerd
Published: November 2008

Consider actions of a reductive complex Lie group G on an analytic space germ (X, 0). In a previous paper [16] we proved that such an action is determined uniquely (up to conjugation with an automorphism of (X, 0)) by the induced action of G on the tangent space of (X, 0). Here it will be shown that every deformation of such an action, parametrized holomorphically by a reduced analytic space germ, is trivial, i.e. can be obtained from the given action by conjugation with a family of automorphisms of (X, 0) depending holomorphically on the parameter. (For a more precise formulation in terms of actions on analytic ℂ-algebras, see Theorem 2 below. An analogue for actions on formal ℂ-algebras is given there too.)
On a class of non-causal triangle functions
Authors: Ying M. S.
Published: November 2008

In [2], B. Schweizer and A. Sklar proposed the problem of whether every triangle function is causal. In [1], T. B. M. McMaster solved the problem negatively by giving an example of a non-causal triangle function. In this note we provide a class of simpler non-causal triangle functions which are continuous on a dense subset of Δ+ but in general not continuous on Δ+. Since McMaster's triangle function is also not continuous on Δ+, the problem of determining whether or not every continuous triangle function is causal remains open.
Far field patterns and inverse scattering problems for imperfectly conducting obstacles
Authors: Angell T. S. , Colton David , Kress Rainer
Published: November 2008

We first examine the class of far field patterns for the scalar Helmholtz equation in ℝ2 corresponding to incident time harmonic plane waves subject to an impedance boundary condition where the impedance is piecewise constant with respect to the incident direction and continuous with respect to x ε ∂ D where ∂ D is the scattering obstacle. We then examine the class of far field patterns for Maxwell's equations in subject to an impedance boundary condition with constant impedance. The results obtained are used to derive optimization algorithms for solving the inverse scattering problem.
Maximally symmetric homogeneous metrics on manifolds
Authors: Bowers Philip L.
Published: November 2008

A metricdon a set hasmaximal symmetryprovided its isometry group is not properly contained in the isometry group of any metric equivalent tod. This concept was introduced by Janos [7] and subsequently Williamson and Janos [17] proved that the standard euclidean metric on ℝnhas maximal symmetry. In Bowers [2], an elementary proof that every convex, complete, two-point homogeneous metric for which small spheres are connected has maximal symmetry is presented. This result in turn implies that the standard metrics on the classical spaces of geometry – hyperbolic, euclidean, spherical and elliptic – are maximally symmetric. In this paper we study homogeneous metrics that possess maximal symmetry and, in particular, address the problem of the existence of such metrics and, to a lesser extent, their uniqueness.
Groups of automorphisms and centralizers
Authors: Turull Alexandre
Published: November 2008

Let G be a finite solvable group and A a group of automorphisms of G such that (|A|, |G|) = 1. We denote by h(G) the Fitting height of G and by l(A) the length of the longest chain of subgroups of A. Then, under some additional hypotheses, it is known from [5] that h(G) ≤ 2l(A) + h(CG(A)) and from [8] that, when CG(A) = 1, h(G) ≤ l(A), both results being best possible (see [6, 7]). The present paper attempts to explain the difference in the coefficient of l(A) in the two inequalities, from 2 to 1.
The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field
Authors: Flynn Eugene Victor
Published: November 2008

An embedding of the Jacobian variety of a curve of genus 2 is given, together with an explicit set of defining equations. A pair of local parameters is chosen, for which the induced formal group is defined over the same ring as the coefficients of . It is not assumed that has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field (of characteristic ╪ 2, 3, or 5).
Selections of multivalued maps and shape domination
Authors: Sanjurjo José M. R.
Published: November 2008

Some results are presented which establish connections between shape theory and the theory of multivalued maps. It is shown how to associate an upper-semi-continuous multivalued map F: X → Y to every approximative map f = {fk, X → Y} in the sense of K. Borsuk and it is proved that, in certain circumstances, if F is ‘small’ and admits a selection, then the shape morphism S(f) is generated by a map, and if F admits a coselection then S(f) is a shape domination.
On the computational complexity of the Jones and Tutte polynomials
Authors: Jaeger F. , Vertigan D. L. , Welsh D. J. A.
Published: November 2008

We show that determining the Jones polynomial of an alternating link is #P-hard. This is a special case of a wide range of results on the general intractability of the evaluation of the Tutte polynomial T(M; x, y) of a matroid M except for a few listed special points and curves of the (x, y)-plane. In particular the problem of evaluating the Tutte polynomial of a graph at a point in the (x, y)-plane is #P-hard except when (x − 1)(y − 1) = 1 or when (x, y) equals (1, 1), (−1, −1), (0, −1), (−1, 0), (i, −i), (−i, i), (j, j2), (j2, j) where j = e2πi/3
Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature
Authors: Bridges Thomas J.
Published: November 2008

When two purely imaginary eigenvalues of opposite Krein signature coalesce, in a Hamiltonian system, a small perturbation can drive them off of the imaginary axis resulting in a linear instability. The most celebrated example of this instability occurs in the restricted 3-body problem at Routh's critical mass ratio. In this paper the collision of eigenvalues is treated as a singularity. A variational form of the Lyapunov–Schmidt method and distinguished parameter ࡃ2-equivariant singularity theory, with the frequency as distinguished parameter, are used to determine the effect of the degeneracy on the branches of periodic solutions in a neighbourhood. Previous results of Meyer and Schmidt[13], Sokol'skij [16] and van der Meer [12] are recovered in the formulation as a co-dimension 1 singularity. The results are extended to include the effect of an additional degeneracy (a co-dimension 2 singularity). The theory is applied to a spinning double pendulum.
A semigroup embedding problem and an arithmetical function
Authors: Howie John M. , Selfridge J. L.
Published: November 2008

For unexplained terms in semigroup theory see [1] or [4].

Let C, D be classes of semigroups such that every finite semigroup in the class C is embeddable in a finite semigroup in the class D. If n ≥ 2 then k is said to be a C – Dcover of n if every semigroup of order n in the class C is embeddable in a semigroup in the class D of order not greater than k. Let be the least C – D cover of n.
Nonsingular systems of two length three equations over a group
Authors: Howie James
Published: November 2008

In this paper we consider the conjecture of Kervaire, that a nonsingular system of equations in one or more variables over an arbitrary groupGhas a solution in some overgroup ofG.
Loop-theoretic properties of H-spaces
Authors: Arkowitz Martin , Lupton Gregory
Published: November 2008

If X is a topological space with base point, then a based map m: X × X → X is called a multiplication if m restricted to each factor of X × X is homotopic to the identity map of X. The pair (X, m) is then called an H-space. If A is a based topological space and (X, m) is an H-space, then the multiplication m induces a binary operation on the set [A, X] of based homotopy classes of maps of A into X. A classical result due to James [6, theorem 1·1 asserts that if A is a CW-complex and (X, m) is an H-space, then the binary operation gives [A, X] the structure of an algebraic loop. That is, [A, X] has a two-sided identity element and if a, b ∈[A, X], then the equations ax = b and ya = b have unique solutions x, y ∈ [A, X]. Thus it is meaningful to consider loop-theoretic properties of H-spaces. In this paper we make a detailed study of the following loop-theoretic notions applied to H-spaces: inversivity, power-associativity, quasi-commutativity and the Moufang property – see Section 2 for the definitions. If an H-space is Moufang, then it has the other three properties. Moreover, an associative loop is Moufang, and so a homotopy-associative H-space has all four properties. Since many of the standard H-spaces are homotopy-associative, we are particularly interested in determining when an H-space, in particular a finite CW H-space, does not have one of these properties.
On KMS states for self-dual CCR algebras and Bogoliubov automorphism groups
Authors: Ogi Hidekazu
Published: November 2008

Let be the self-dual CCR algebra over a triplet (K, r, Γ), where K is assumed to be a Hilbert space, and let {τt}t ∈ R be a Bogoliubov automorphism group of induced by a strongly continuous one-parameter unitary group on K. In this paper, we introduce some continuity for linear functionals on and, under this continuity, we study existence, uniqueness, and non-uniqueness of KMS states for .
Some free groups of matrices and the Burau representation of B4
Authors: Moran Siegfried
Published: November 2008

Using a criterion due to J. Tits [4] we shall show that it is easy to give a pair of conjugate matrices in GLn(ℂ) which freely generate a free group of rank two. The difficulty lies in producing two such matrices whose freeness does not follow directly from the known freeness of two 2 × 2 matrices. Finally we show that the well known problem as to whether the Burau representation of Artin's braid group B4 is faithful turns out to be arbitrarily close to being true in a large number of ways. Thanks are due to the referee for his helpful comments.
On the valence of some classes of harmonic maps
Authors: Lyzzaik Abdallah
Published: November 2008

We give examples which (i) disprove a conjecture of Sheil-Small regarding the valence of harmonic mappings of the unit disc to bounded convex domains, and (ii) answer negatively a question of the author regarding the valence of harmonic mappings with polynomial analytic and co-analytic parts.
The inhomogeneous minimum of binary quadratic forms
Authors: Berend Daniel , Moran William
Published: November 2008

An indefinite binary quadratic form ƒ gives rise to a certain function M on the torus. The properties of M, especially those related to its maximum – the so-called inhomogeneous minimum of ƒ – are the subject of numerous papers. Here we continue this study, putting more emphasis on the general behaviour of M.
Existence of periodic solutions to integro-differential equations of neutral type via limiting equations
Authors: Wu Jianhong , Xia Huaxing
Published: November 2008

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov–Razumikhin technique for neutral equations with finite delay to obtain existence of periodic solutions of Volterra neutral integro-differential equations (of infinite delay). Some comparisons between our results and the existing ideas are also provided.
Affine distance-transitive graphs with quadratic forms
Authors: Van Bon John
Published: November 2008

The classification of all finite primitive distance-transitive graphs is basically divided into two cases. In the one case, known as the almost simple case, we have an almost simple group acting primitively as a group of automorphisms on the graph. In the other case, known as the affine case, the vertices of the graph can be identified with the vectors of a finite-dimensional vector space over some finite field. In this case the automorphism group G of the graph Γ contains a normal p-subgroup N which is elementary Abelian and acts regularly on the set of vertices of Γ. Let G0 be the subgroup of G that stabilizes a vertex. Identifying the vertices of Γ with G0-cosets in G, one obtains a vector space V on which N acts as a group of translations, G0, stabilizes 0 and, as Γ is primitive, G0 acts irreducibly on V.
A formula for the number of branches for one-dimensional semianalytic sets
Authors: Szafraniec Zbigniew
Published: November 2008

Let F = (F1, …, Fn-1): (ℝn, 0)→(ℝn-1, 0) and G:(ℝn, 0)→(ℝ, 0) be germs of analytic mappings, and let X = F-1(0). Assume that 0 ∈ ℝn is an isolated singular point in X, i.e. 0 ∈ ℝn is isolated in {x ∈ X|rank[DF(x)] < n-1}. Hence a germ of X/{0} at the origin is either void or a finite disjoint union of analytic curves. Let b denote the number of branches, i.e. connected components, of X/{0} and let b+ (resp. b-, b0) denote the number of branches of X/{0} on which G is positive (resp. G is negative, G vanishes). The problem is to calculate the numbers b, b+, b-, b0 in terms of F and G.
Equivariant prequantization and admissible coadjoint orbits
Authors: Robinson P. L.
Published: November 2008

The orbit method has as its primary goal the construction and parametrization of the irreducible unitary representations of a (simply-connected) Lie group in terms of its coadjoint orbits. This goal was achieved with complete success for nilpotent groups by Kirillov[8] and for type I solvable groups by Auslander and Kostant[l] but is known to encounter difficulties when faced with more general groups. Geometric quantization can be viewed as an outgrowth of the orbit method aimed at providing a geometric passage from classical mechanics to quantum mechanics. Whereas the original geometric quantization scheme due to Kostant[9] and Souriau[14] enabled such a passage in a variety of situations, it too encounters difficulties in broader contexts.
A note on coverage error of bootstrap confidence intervals for quantiles
Authors: Angelis D. De , Hall Peter , Young G. A.
Published: November 2008

An interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of sizen−½, wherendenotes sample size. By way of contrast, the error would beO(n−1)for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved too(n−½)by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage errorO(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-tare also analysed.
On existence varieties of locally inverse semigroups
Authors: Auinger K. , Doyle J. , Jones P. R.
Published: November 2008

A locally inverse semigroup is a regular semigroup S with the property that eSe is inverse for each idempotent e of S. Motivated by natural examples such as inverse semigroups and completely simple semigroups, these semigroups have been the subject of deep structure-theoretic investigations. The class ℒ ℐ of locally inverse semigroups forms an existence variety (or e-variety): a class of regular semigroups closed under direct products, homomorphic images and regular subsemigroups. We consider the lattice ℒ(ℒℐ) of e-varieties of such semigroups. In particular we investigate the operations of taking meet and join with the e-variety CS of completely simple semigroups. An important consequence of our results is a determination of the join of CS with the e-variety of inverse semigroups – it comprises the E-solid locally inverse semigroups. It is shown, however, that not every e-variety of E-solid locally inverse semigroups is the join of completely simple and inverse e-varieties.
Bounded distortion and dimension for non-conformal repellers
Authors: Falconer K. J.
Published: November 2008

We obtain an expression for the dimension of a mixing repeller of a non-conformal mapping analogous to the well-known Bowen-Ruelle formula for conformal repellers. The dimension is given in terms of a generalized pressure defined in the context of the thermodynamic formalism. In the course of the paper we develop a subadditive version of the thermodynamic formalism that is suited to our needs and also obtain a ‘bounded distortion’ principle applicable to the non-conformal situation.
Type of blowing-up over a Buchsbaum ring
Authors: Yamagishi Kikumichi
Published: November 2008

Throughout this paper (A, , k) denotes a Noetherian local ring of dimension d and stands for the ith local cohomology functor with respect to . We refer the reader to [16] for any unexplained terminology.
Convolution estimates for some degenerate curves
Authors: Pan Yibiao
Published: November 2008

Let k ∈ R, k ≥ 3. Consider the curve of class C3 in R3 defined by

Let σk(t) = t(k−3)/6dt be the affine arclength measure on γk. Define the convolution operator T (= Tk) by
Duality of induction and restriction for abelian twisted covariant systems
Authors: Echterhoff Siegfried
Published: November 2008

Let (A, G, α, τ) be a twisted covariant system such that G/Nτ is abelian, and let Nτ ⊆ M ⊆ H be closed subgroups of G. We show that inducing covariant representations from A ⋊α, τM to A ⋊α, τH is in a certain sense dual to restricting representations from (A⋊α, τG)⋊άM┴ to (A⋊α, τG)⋊άH┴, and that, similarly, restricting representations from A⋊α, τH to A⋊α, τM is dual to inducing representations from (A⋊τG)⋊άH┴ to (A ⋊α, τG)⋊άM┴.
On the number of finite non-isomorphic Abelian groups in short intervals
Authors: Hongze Li
Published: November 2008

Let a(n) denote the number of non-isomorphic Abelian groups of order n. It is well-known that

for a natural number k we define

and
Finite classical groups and multiplication groups of loops
Authors: Vesanen Ari
Published: November 2008

Let Q be a loop; then the left and right translations La(x) = ax and Ra(x) = xa are permutations of Q. The permutation group M(Q) = 〈La, Ra | a ε Q〉 is called the multiplication group of Q; it is well known that the structure of M(Q) reflects strongly the structure of Q (cf. [1] and [8], for example). It is thus an interesting question, which groups can be represented as multiplication groups of loops. In particular, it seems important to classify the finite simple groups that are multiplication groups of loops. In [3] it was proved that the alternating groups An are multiplication groups of loops, whenever n ≥ 6; in this paper we consider the finite classical groups and prove the following theorems