bluuebunny/crossref_metadata_2025 huggingface dataset:
On the ‘strange formula’ of Freudenthal and de Vries
Authors: Fegan H. D. , Steer B.
Published: November 2008

Suppose that G is a semi-simple, compact, connected Lie group. Endow g, its Lie algebra, with the inner product which is the negative of the Killing form. Choose a fundamental Weyl Chamber and let R+ denote the positive roots so determined.
Non-singular Bianchi type VIIh solution of no-scale supergravity
Authors: Lorenz-Petzold D.
Published: November 2008

A non-singular solution of the bosonic SU(1, 1)/U(1) no-scale supergravity field equations is constructed for an anisotropic cosmological model which is of Bianchi type VIIh.
On elements of order four in certain free central extensions of groups
Authors: Stöhr Ralph
Published: November 2008

Let F be a non-cyclic free group, R a normal subgroup of F and G = F/R, i.e.

where π is the natural projection of F onto G, is a free presentation of G. Let R′ denote the commutator subgroup of R. The quotient F/[R′,F] is a free central extension

of the group F/R′, the latter being a free abelianized extension of G. While F/R′ is torsion-free (see, e.g. [2], p. 23), elements of finite order may occur in R′/[R′,F], the kernel of the free central extension (l·2). Since C. K. Gupta [1] discovered elements of order 2 in the free centre-by-metabelian group F/[F″,F] (i.e. (1·2) in the case R = F′), torsion in F/[R′,F] has been studied by a number of authors (see, e.g. [4–13]). Clearly the elements of finite order in F/[R′,F] form a subgroup T of the abelian group R′/[R′,F]. It will be convenient to write T additively. By a result of Kuz'min [5], any element of T has order 2 or 4. Moreover, it was pointed out in [5] that elements of order 4 may really occur. On the other hand, it has been shown in [11] that, if G has no 2-torsion, then T is an elementary abelian 2-group isomorphic to H4(G, ℤ2). So if T contains an element of order 4, then G must have 2-torsion. We also mention a result of Zerck [13], who proved that 2T is an invariant of G, i.e. it does not depend on the particular choice of the free presentation (1·1).
A different approach to unbounded operator algebras
Authors: Hennings M. A.
Published: November 2008

When considering *-algebras of unbounded operators, the usual approach is perhaps the one to be expected. One starts with a Hilbert space , and then defines a common dense domain X associated with some *-algebra of unbounded operators on . The algebra is then used to define a locally convex topology (the graph topology) on X, with respect to which the inner product on X is continuous, and this in turn defines a variety of topologies on , which are then studied.
Periodic groups with permutable subgroup products
Authors: Longobardi Patrizia , Maj Mercede , Rhemtulla Akbar
Published: November 2008

Let G be a group. If there exists an integer n > 1 such that for each n-tuple (H1, …, Hn) of subgroups of G there is a non-identity permutation σ of Σn such that the complexes H1,…Hn and Hσ(1)…Hσ(n) are equal, then G is said to have the property of permutable subgroup products, or to be a PSP group. We show that periodic groups with this property are locally finite and investigate the structure of such groups.
A Seifert-matrix interpretation of Cappell and Shaneson's approach to link cobordisms
Authors: Ko Ki Hyoung
Published: November 2008

We classified the set of Fm-cobordism classes of Fm-links by their Seifert matrices in [5]. On the other hand Cappell and Shaneson identified them with essentially a quotient group of their homology surgery obstruction group [2]. In this paper, we will find a description of their surgery obstruction in terms of a Seifert matrix. In relation to Ledimet's recent results [7], we hope this might provide some clue to whether Fm-cobordism or boundary cobordism is stronger than ordinary link cobordism. It also seems to be an interesting algebraic question to find an algorithm for obtaining a Seifert matrix from their surgery obstruction.
Stable quintuples and terminal quotient singularities
Authors: Sankaran G. K.
Published: November 2008

We shall prove below part of a conjecture made by Shigefumi Mori, David Morrison and Ian Morrison in the course of their investigations into the properties of isolated terminal cyclic quotient singularities of prime Gorenstein index in dimension four [1]. The reader of the present paper need have no knowledge of algebraic geometry, because we quickly reduce the problem to one about the geometry of numbers that can be solved by elementary calculations. The calculations are very lengthy and not quite routine, so what the reader does need is either patience, if he intends to check them, or faith, if he does not. We give only part of the calculations below. Full details may be obtained from the author.*
A note on centrality in 3-manifold groups
Authors: Kropholler P. H.
Published: November 2008

Centralizers in fundamental groups of 3-manifolds are well understood because of their relationship with Seifert fibre spaces. Jaco and Shalen's book [4] provides detailed information about Seifert fibre spaces in 3-manifolds, and consequently about centralizers in their fundamental groups. It is the purpose of this note to record two group-theoretic properties, both easily deduced from results of Jaco and Shalen. Doubtless many other authors could have established the same results had they needed them. Our motivation for writing this paper is that these properties can be used as a basis for group-theoretic proofs of certain fundamental results in 3-manifold theory: Proposition 1 below can be used as a basis for a proof of the Torus Theorem (cf. [8]) and Proposition 2 for the Torus Decomposition Theorem (cf. [9]).
A criterion for detecting inequivalent tunnels for a knot
Authors: Kobayashi Tsuyoshi
Published: November 2008

Let K be an oriented knot in the 3-sphere S3. An exterior of K is the closure of the complement of a regular neighbourhood of K, and is denoted by E(K). A Seifert surface for K is an oriented surface S( ⊂ S3) without closed components such that ∂S = K. We denote S ∩ E(K) by Ŝ, and we regard S as obtained from Ŝ by a radial extension. S is incompressible if Ŝ is incompressible in E(K). A tunnel for K is an embedded arc τ in S3 such that τ ∪ K = ∂τ. We denote τ ∪ E(K) by τ, and we regard τ as obtained from τ by a radial extension. Let τ1, τ2 be tunnels for K. We say that τ1 and τ2 are homeomorphic if there is a self-homeomorphism f of E(K) such that f(τ1) = τ2. The tunnels τ1 and τ2 are isotopic if τ1 is ambient isotopic to τ2 in E(K). Then the main result of this paper is as follows: Theorem. Let K be a knot in S3, and let τ1, τ2 be tunnels for K. Suppose that there are incompressible Seifert surfaces S1 S2 for K such that S1 ∪ S2 = K, and τi ⊂ Si (i = 1, 2). If τ1 and τ2 are isotopic, then there is an ambient isotopyhτ (0 ≤ t ≤ 1) of S3 such that ht(K) = K, and h1(τ1) = τ2.
The dynamics of the Rikitake dynamo from the stiff limit
Authors: Chapman P. B. , Glover J. N. , Mees A. I.
Published: November 2008

The Rikitake two-disc system [10] has been proposed as a model of the Earth's magnetic dipole. Numerical integration of the system by Rikitake[10] and Allan [1] showed the phenomenon of polarity reversal which is seen in terrestrial paleomagnetic data [6]. Reversals in the simulations occurred at irregular and apparently unpredictable time intervals, in accord with the capricious character of the real data, though the agreement was qualitative rather than quantitative.
Uniform upper bounds for the complex divisor function
Authors: Hall R. R.
Published: November 2008

The function

has had several applications in the analytic theory of numbers. It was used by Ingham [10] to give a new proof that ζ(1 + iθ) ≠ 0. In [1] we introduced the modern notation on the left above and used τ(n, θ) to show that for almost all n the numbers log d are asymptotically uniformly distributed (mod 1). If we define

then it is known (Hall [2], Kátai[10]) that

(where p.p. means ‘on a sequence of asymptotic density 1’). It is still an open problem whether or not we may strike out the term (log 4/π) = 0.24156 & from the exponent in (3).
On the geometry of harmonic morphisms
Authors: Gudmundsson Sigmundur
Published: November 2008

Let π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.
Some inequalities concerning immanants
Authors: Heyfron Peter
Published: November 2008

In [13] T. H. Pate has recently proved an important inequality between immanants of Hermitian positive semi-definite matrices. In this paper we introduce some more inequalities with the eventual aim of better understanding the permanental dominance conjecture. Indeed the results in this paper together with known results show that the permanental dominance conjecture for immanants is true for all n × n Hermitian positive semi-definite matrices with n ≤ 8, except perhaps for the case of the partition (24) of 8.
Kähler groups and rigidity phenomena
Authors: Johnson F. E. A. , Rees E. G.
Published: November 2008

The class of fundamental groups of non-singular complex projective varieties is an interesting, but as yet imperfectly understood, class of finitely presented groups. Membership of is known to be extremely restricted (see [22, 23]). In this paper, we employ geometrical rigidity properties to realize some group extensions as elements of as in our previous papers, we find it convenient to work simultaneously with the class ℋ of fundamental groups of compact Kähler manifolds.
On the class number of the lpth cyclotomic number field
Authors: Nakagoshi Norikata
Published: November 2008

The first factor of the class number of a cyclotomic number field can be obtainable by the analytic class number formula and there are some tables which show the decompositions of the first factors into primes. But, using just the analytic formula, we cannot tell what kinds of primes will appear as the factors of the class number of a given cyclotomic number field, except for those of the genus number, or the irregular primes. It is significant to find in advance the prime factors, particularly those prime to the degree of the field. For instance, in the table of the first factors we can pick out some pairs (l, p) of two odd primes l and p such that the class number of each lpth cyclotomic number field is divisible by l even if p 1 (mod l). If p ≡ (mod l) for l ≥ 5 or p ≡ 1 (mod 32) for l = 3, then it is easy from the outset to achieve our intention of finding the factor l using the genus number formula. Otherwise it seems to be difficult. We wish to make it clear algebraically why the class number has the prime factor l.
Left orders in regular rings with minimum condition for principal one-sided ideals
Authors: Ánh Pham Ngoc , Márki László
Published: November 2008

Based on ideas from semigroup theory, Fountain and Gould [2, 3, 4] introduced a notion of order in a ring which need not have an identity. In some important cases of rings with identity, e.g. if the larger ring is a semisimple artinian ring, this notion coincides with the classical one. The most important result of Fountain and Gould (see [4]) is a Goldie-like characterization of two-sided orders in a regular ring with minimum condition on principal one-sided ideals. In addition, for the same class of rings, a generalization of the Faith–Utumi theorem has been proved by Gould and Petrich[7]. The methods of these papers seem not to work for one-sided orders.
Injective matricial Hilbert spaces
Authors: Robertson A. Guyan
Published: November 2008

Injective matricial operator spaces have been classified up to Banach space isomorphism in [20]. The result is that every such space is isomorphic to l∞, l2, B(l2), or a direct sum of such spaces. A more natural project, given the matricial nature of the definitions involved, would be the classification of such spaces up to completely bounded isomorphism. This was done for injective von Neumann algebras in [6] and for injective operator systems (i.e. unital injective operator spaces) in [19]. It turns out that the spaces l∞ and B(l2) are in a natural way uniquely characterized up to completely bounded isomorphism. However, as shown in [20], a problem arises in the case of l2. For there are two injective operator spaces which are each isometrically isomorphic to l2 but not completely boundedly isomorphic to each other. We shall resolve this problem by showing that these are the only two possibilities, in the sense that any injective operator space which is isometric to l2 is completely isometric to one of them. (See Corollary 3 below.) The Hilbert spaces in von Neumann algebras investigated in [17], [13] turn out to be injective matricial operator spaces and are therefore completely isometric to one of our two examples. Another Hilbert space in B(l2) which has been much studied in operator theory, complex analysis and physics is the Cartan factor of type IV [10]. This is the complex linear span of a spin system and generates the Fermion C*-algebra ([3], §5·2). We show that a Cartan factor of type IV is not even completely boundedly isomorphic to an injective matricial operator space. One curious property of all the aforementioned Hilbert spaces is that every bounded operator on them is actually completely bounded, a fact that is crucial in our proofs.
Effective mean value estimates for complex multiplicative functions
Authors: Hall R. R. , Tenenbaum G.
Published: November 2008

Quantitative estimates for finite mean values

of multiplicative functions are highly applicable tools in analytic and probabilistic number theory. Extending a result of Hall [4], Halberstam and Richert[3] proved a useful inequality valid for real, non-negative g satisfying for instance a Wirsing type condition, viz for all primes p, with constants λ1 ≥ 0, 0 ≤ λ2 < 2. Their upper bound is sharp to within a factor (l + o(l)), but even a weaker and easier to prove estimate, such as

(where the implied constants depend on λ1 and λ2), may become a surprisingly strong device. For instance, setting g(p) = l ± ε, where ε is an arbitrarily small positive number, provides immediately a proof of the famous Hardy–Ramanujan theorem on the normal order of the number of prime factors of an integer. This example, and many others, are discussed in detail in our book [5] where we make extensive use of (2) for various problems connected with the structure of the set of divisors of a normal number.
Hall–Littlewood polynomials at roots of 1 and modular representations of the symmetric group
Authors: Morris A. O. , Sultana N.
Published: November 2008

We first give a brief introduction to Hall–Littlewood functions; we follow closely the notation used in Macdonald [3].

Let λ = (λ1,…,λm) be a be a partition of n; that is λ1 + … + λm = n, λ1 ≥ λ2 ≥ … ≥ λm >0. We shall sometimes write l(λ) for m and refer to l(λ) as the length of λ and we shall write |λ| for ∑λi. Let x1, x2, … be an infinite set of indeterminates and t an indeterminate independent of the xi (i = 1,2, …). Let Pλ(x;t) = Pλ(x1, x2, …t) and Qλ(x,t) = Qλ(xl, x2, …t) be the Hall–Littlewood P- and Q-functions defined as in Macdonald.
On complete curves in moduli space II
Authors: González Díez Gabino , Harvey William J.
Published: November 2008

Introduction In a companion to this article [4], we gave a construction which furnishes complete curves, inside the moduli variety g of non-singular genus g curves, for each g ≥ 4; it was also shown there that the technique will not work in genus 3.
On the irrationality of certain series
Authors: Borwein Peter B.
Published: November 2008

We prove that the series

are irrational and not Liouville whenever q is an integer (q ╪ 0, ±1) and r is a nonzero rational (r ╪ −qn).
Locally free (ℙn)-modules
Authors: Coutinho S. C. , Holland M. P.
Published: November 2008

The purpose of this paper is to study the structure of locally free modules over the ring of differential operators on projective space. Let be a non-singular, complex, algebraic variety. Denote by the sheaf of rings of differential operators over and by its ring of global sections. A -module M is called locally free if the associated sheaf ⊗ M is locally free as a sheaf of -modules. Locally free modules arise naturally in -module theory as inverse images of determined modules; see [1] for definitions and examples.
Lacunary entire functions
Authors: Offord A. C.
Published: November 2008

It has been observed that lacunary functions and random functions often have many properties in common (cf. [5]). The present paper has the object of showing that lacunary entire functions behave in many respects like random entire functions. Both have the property of being large except in very small neighbourhoods of their zeros and these have a uniform angular distribution.
A coarse Mayer–Vietoris principle
Authors: Higson Nigel , Roe John , Yu Guoliang
Published: November 2008

In [1], [4], and [6] the authors have studied index problems associated with the ‘coarse geometry’ of a metric space, which typically might be a complete noncompact Riemannian manifold or a group equipped with a word metric. The second author has introduced a cohomology theory, coarse cohomology, which is functorial on the category of metric spaces and coarse maps, and which can be computed in many examples. Associated to such a metric space there is also a C*-algebra generated by locally compact operators with finite propagation. In this note we will show that for suitable decompositions of a metric space there are Mayer–Vietoris sequences both in coarse cohomology and in the K-theory of the C*-algebra. As an application we shall calculate the K-theory of the C*-algebra associated to a metric cone. The result is consistent with the calculation of the coarse cohomology of the cone, and with a ‘coarse’ version of the Baum–Connes conjecture.
Fractional parts of powers of rational numbers
Authors: Bennett M.
Published: November 2008

The author uses Padé approximation techniques and an elementary lemma on primes dividing binomial coefficients to sharpen a theorem of F. Beukers on fractional parts of powers of rationals. In particular, it is proven that ‖((N+ l)/N)k‖ > 3–k holds for all positive integers N and k satisfying 4 ≤ N ≤ k · 3k. Other results are described including an effective version of a theorem of K. Mahler for a restricted class of rationals.
Nielsen's commutator test for two-generator groups
Authors: Gupta Narain , Shpilrain Vladimir
Published: November 2008

Nielsen [14] gave the following commutator test for an endomorphism of the free group F = F2 = 〈x, y; Ø〉 to be an automorphism: an endomorphism ø: F → F is an automorphism if and only if the commutator [ø(x), ø(y)] is conjugate in F to [x, y]±1. He obtained this test as a corollary to his well-known result that every IA-automorphism of F (i.e. one which fixes F modulo its commutator subgroup) is an inner automorphism. Bachmuth et al. [4] have proved that IA-automorphisms of most two-generator groups of the type F/R′ are inner, and it becomes natural to ask if Nielsen's commutator test remains valid for those groups as well. Durnev[7] considered this question for the free metabelian group F/F″ and confirmed the validity of the commutator test in this case. Here we prove that Nielsen's test does not hold for a large class of F/R′ groups (Theorem 3·1) and, as a corollary, deduce that it does not hold for any non-metabelian solvable group of the form F/R″ (Corollary 3·2). In view of our Theorem 3·1, Nielsen's commutator test in these situations seems to have less appeal than his result that the IA-automorphisms of F are precisely the inner automorphisms of F. We explore some applications of this important result with respect to non-tameness of automorphisms of certain two- generator groups F/R (i.e. automorphisms of F/R which are not induced by those of the free group F). For instance, we show that a two-generator free polynilpotent group F/V, , has non-tame automorphisms except when V = γ2(F) or V = γ3(F), or when V is of the form [yn(U), γ(U)], n ≥ 2 (Theorem 4·2). This complements the results of [9] and [16] rather nicely, and is shown to follow from a more general result (Proposition 4·1). We also include an example of an endomorphism θ: x → xu, y→y of F which induces a non-tame automorphism of F/γ6(F) while the partial derivative ∂(u)/∂(x) is ‘balanced’in the sense of Bryant et al. [5] (Example 4·4). This gives an alternative solution of a problem in [5] which has already been resolved by Papistas [15] in the negative. In our final section, we consider groups of the type F/[R′,F] and, in contrast to groups of the type F/R′, we show that the Nielsen's commutator test does hold in most of these groups (Theorem 5·1). We conclude with a sufficiency condition under which Nielsen's commutator test is valid for a given pair of generating elements ofF modulo [R′,F] (Proposition 5·2).
A remark on the global indices of ℚ–Calabi–Yau 3-folds
Authors: Oguiso Keiji
Published: November 2008

It is well known that the so-called Beauville number B = 25.33.52.7.11.13.17.19 is a universal bound of the global indices of ℚ–Calabi–Yau 3-folds, but it has been unknown whether this number is best possible or not.
On Ford isometric spheres in complex hyperbolic space
Authors: Parker John R.
Published: November 2008

The complex hyperbolic version of Shimizu's lemma gives an upper bound on the radii of isometric spheres of maps in a discrete subgroup of PU(n, 1) containing a vertical Heisenberg translation. The purpose of this paper is to show that in a neighbourhood of this bound radii of isometric spheres only take values in a particular discrete set. When the group contains certain ellipto-parabolic maps this upper bound can be improved and the set of values of the radii is more restricted. Examples are given that show that these results cannot be improved.
Generalized interpolation in finite maximal subdiagonal algebras
Authors: Saito Kichi-Suke
Published: November 2008

Non-selfadjoint operator algebras have been studied since the paper of Kadison and Singer in 1960. In [1], Arveson introduced the notion of subdiagonal algebras as the generalization of weak *-Dirichlet algebras and studied the analyticity of operator algebras. After that, we have many papers about non-selfadjoint algebras in this direction: nest algebras, CSL algebras, reflexive algebras, analytic operator algebras, analytic crossed products and so on. Since the notion of subdiagonal algebras is the analogue of weak *-Dirichlet algebras, subdiagonal algebras have many fruitful properties from the theory of function algebras. Thus, we have several attempts in this direction: Beurling–Lax–Halmos theorem for invariant subspaces, maximality, factorization theorem and so on.
An elementary proof of the Birkhoff-Hopf theorem
Authors: Eveson Simon P. , Nussbaum Roger D.
Published: November 2008

In important work some thirty years ago, G. Birkhoff[2, 3] and E. Hopf [16, 17] showed that large classes of positive linear operators behave like contraction mappings with respect to certain ‘almost’ metrics. Hopf worked in a space of measurable functions and took as his ‘almost’ metric the oscillation ω(y/x) of functionsyandxwithx(t)> 0 almost everywhere, defined by
Hausdorff dimension of sets of non-differentiability points of Cantor functions
Authors: Darst Richard
Published: November 2008

Each number a in the segment (0, ½) produces a Cantor set, Ca, by putting b = 1 − 2a and recursively removing segments of relative length b from the centres of the interval [0, 1] and the intervals which are subsequently generated. The distribution function of the uniform probability measure on Ca is a Cantor function, fa. When a = 1/3 = b, Ca is the standard Cantor set, C, and fa is the standard Cantor function, f. The upper derivative of f is infinite at each point of C and the lower derivative of f is infinite at most points of C in the following sense: the Hausdorff dimension of C is ln(2)/ln(3) and the Hausdorff dimension of S = {x ∈ C: the lower derivative of f is finite at x} is [ln(2)/ln(3)]2. The derivative of f is zero off C, the derivative of f is infinite on C — S, and S is the set of non-differentiability points of f. Similar results are established in this paper for all Ca: the Hausdorff dimension of Ca is ln (2)/ln (1/a) and the Hausdorff dimension of Sa is [ln (2)/ln (1/a)]2. Removing k segments of relative length b and leaving k + 1 intervals of relative length a produces a Cantor set of dimension ln(k + l)/ln(1/a); the dimension of the set of non-differentiability points of the corresponding Cantor function is [ln (k + l)/ln (1/a)]2.
On a conjecture of Smith's
Authors: Lianchao Xu
Published: November 2008

In this paper we prove a conjecture of Smith's on the number of simple modules of algebras which are similar to the enveloping algebra of sl(2).
An example concerning Alexeev's boundedness results on log surfaces
Authors: Blache Raimund
Published: November 2008

In this note, we construct a sequence of l.t. surfaces (Xn)n ∈ ℕ such that KXn is ample for all n and such that (K2Xn)n ∈ ℕ is a strictly increasing series with limit equal to 1. This answers (in the affirmative) a question by Alexeev, cf. [Al], 11·1. Here, an l.t. surface is a normal complex projective surface with at most quotient singularities (which is the same as ‘at most log terminal singularities’). A main result of [Al] implies that it is impossible to find a sequence (Xn)n ∈ ℕ of l.t. surfaces with KXn ample for all n such that K2Xn is strictly decreasing. Although our construction is not too difficult, the example is new and has several interesting implications, see Section 4.

Without further explanation, we use some fundamental tools concerning l.t. surfaces like Mumford's intersection theory or the notion of minimality; the reader should consult [Blb] and the references quoted there.
Pointwise convergence of spherical means
Authors: Seeger Andreas , Wainger Stephen , Wright James
Published: November 2008

For a function f ∈ Lp(ℝd) we define the spherical means

where dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. We consider the problem of pointwise convergence of the means , for any particular sequence tj → 0.
Strong and weak duality principles for fractal dimension in Euclidean space
Authors: Cutler Colleen D.
Published: November 2008

Tricot [27] provided apparently dual representations of the Hausdorff and packing dimensions of any analytic subset of Euclidean d-space in terms of, respectively, the lower and upper pointwise dimension maps of the finite Borel measures on ℝd. In this paper we show that Tricot's two representations, while similar in appearance, are in fact not duals of each other, but rather the duals of two other ‘missing’ representations. The key to obtaining these missing representations lies in extended Frostman and antiFrostman lemmas, both of which we develop in this paper. This leads to the formulation of two distinct characterizations of dim (A) and Dim (A), one which we call the weak duality principle and the other the strong duality principle. In particular, the strong duality principle is concerned with the existence, for each analytic set A, of measures on A that are (almost) of the same exact dimension (Hausdorff or packing) as A. The connection with Rényi (or information) dimension and a variational principle of Cutler and Olsen[12] is also established.
The Hausdorff dimension of Julia sets of entire functions II
Authors: Stallard Gwyneth M.
Published: November 2008

Letfbe a transcendental entire function such that the finite singularities of f−1lie in a bounded set. We show that the Hausdorff dimension of the Julia set of such a function is strictly greater than one.
On the almost sure approximation of self-adjoint operators in L2 (0, 1)
Authors: Ciach L. J. , Jajte R. , Paszkiewicz A.
Published: November 2008

There are several important theorems concerning the almost sure convergence of (monotone) sequences of orthogonal projections in L2-spaces. Let us mention here the martingale convergence theorems or the results on the developments of functions with respect to orthogonal systems. On the other hand every self-adjoint operator with the spectrum on the interval [0, 1] is a limit of some sequence of orthogonal projections in the weak operator topology (see [1]). This paper is devoted to a problem of approximation of a self-adjoint operator A acting in L2 (0, 1) by a sequence Pn of orthogonal projections in the sense that
The elliptic Mahler measure
Authors: Everest G. R. , Fhlathúin Bríd Ní
Published: November 2008

In this paper, we are going to introduce an elliptic analogue of the classical Mahler measure of an integral polynomial. The measure is shown to vanish if and only if the roots of the polynomial are attached to division points of the curve. This is the exact analogue of the statement that the Mahler measure of an integral polynomial vanishes if and only if all of its roots are division points of the circle (in other words, roots of unity). The proof of this result exploits an integral representation for the local canonical heights on the elliptic curve. The integral is that of a simple polynomial function over the complete curve in the appropriate valuation. Attention then shifts to the calculation of local integrals of arbitrary rational functions on elliptic curves. Results are proved which show these integrals may be computed as effective limits of Riemann sums. Finally, consideration is given to analogous behaviour for abelian varieties. We give a method, in principle, for computing the global canonical height of a rational point on an abelian variety denned over an algebraic number field, once again exploiting the integral representation of the local heights. The methods used include recent inequalities for linear forms in elliptic and abelian logarithms.
The Haagerup invariant for tensor products of operator spaces
Authors: Sinclair Allan M. , Smith Roger R.
Published: November 2008

In [7, 8] Haagerup introduced two isomorphism invariants and for C*-algebras and von Neumann algebras , based on appropriate forms of the completely bounded approximation property defined below. These definitions have obvious extensions to operator spaces and dual operator spaces respectively, and in [16] we established the multiplicativity of A on the ultraweakly closed spatial tensor product of two dual operator spaces and :
Compact tripotents in bi-dual JB*-triples
Authors: Edwards C. Martin , Rüttimann Gottfried T.
Published: November 2008

The set consisting of the partially ordered set of tripotents in a JBW*-triple C with a greatest element adjoined forms a complete lattice. This paper is mainly concerned with the situation in which C is the second dual A** of a complex Banach space A and, more particularly, when A is itself a JB*-triple. A subset of consisting of the set of tripotents compact relative to A (denned in Section 4) with a greatest element adjoined is studied. It is shown to be an atomic complete lattice with the properties that the infimum of an arbitrary family of elements of is the same whether taken in or in and that every decreasing net of non-zero elements of has a non-zero infimum. The relationship between the complete lattice and the complete lattice where B is a Banach space such that B** is a weak*-closed subtriple of A** is also investigated. When applied to the special case in which A is a C*-algebra the results provide information about the set of compact partial isometries relative to A and are closely related to those recently obtained by Akemann and Pedersen. In particular it is shown that a partial isometry is compact relative to A if and only if, in their terminology, it belongs locally to A. The main results are applied to this and other examples.
Semigroups whose idempotents form a subsemigroup
Authors: Almeida J. , Pin J.-E. , Weil P.
Published: November 2008

We prove that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to those of Birget, Margolis and Rhodes, and of Jones and Szendrei on finite E-semigroups.
Seifert-fibred homology 3-spheres,V-surfaces and the Floer index
Authors: Nasatyr Emile Ben
Published: November 2008

Let Σ be a Seifert-fibred homology 3-sphere. We are interested in the chain complex for the Floer homology of Σ. This is generated by the critical points of the ChernSimons functional acting on the moduli space of irreducibleSU(2)-connections modulo gauge-equivalence, i.e. the equivalence classes of flat connections: see [6]. Specifically, we ask the question: given the holonomy ρ of a flat connectionCρ, what is the index ofCρin the chain complex? By definition thisFloer indexis given by the spectral flow of a family of twisted signature operators with coefficients in the adjoint bundle (with fibre su(2)) corresponding to any path of connections joining the trivial connection toCρ. We will calculate this spectral flow by an almost entirely direct method, obtaining a formula in terms of the dimensions of spaces of π1(Σ)- automorphic functions. These dimensions will be evaluated to give the numerical result previously obtained using a different method by Fintushel and Stern: see [5].
Invariant measures for families of circle maps
Authors: Quas Anthony
Published: November 2008

In this paper, we establish conditions for a continuous family of circle maps to have a continuous family of invariant measures in the appropriate topologies, and demonstrate the necessity of some of the conditions.
Knots, matroids and the Ising model
Authors: Schwärzler W. , Welsh D. J. A.
Published: November 2008

A polynomial is defined on signed matroids which contains as specializations the Kauffman bracket polynomial of knot theory, the Tutte polynomial of a matroid, the partition function of the anisotropic Ising model, the Kauffman–Murasugi polynomials of signed graphs. It leads to generalizations of a theorem of Lickorish and Thistlethwaite showing that adequate link diagrams do not represent the unknot. We also investigate semi-adequacy and the span of the bracket polynomial in this wider context.
Convergence in distribution of lightly trimmed and untrimmed sums are equivalent
Authors: Kesten Harry
Published: November 2008

We show that trimming a fixed number of terms from sums of i.i.d. random variables (so-called light trimming) can have only a modest effect on limiting behaviour. More specifically, the trimmed sums, after centralization and normalization, have a limit distribution, if and only if the untrimmed sums have a limit distribution (with the same centralization and normalization constants).
Topologies in vector lattices
Authors: Roberts G. T.
Published: November 2008

This paper is concerned with topologies for vector lattices (in the sense of (1)) or spaces that satisfy the axioms K 1, 2, 3′ and 4 of (5) that are given by neighbourhoods. The notions of convergence introduced by Kantorovitch(5) and Birkhoff(1) do not in general lead to topologies which can be denned in terms of open sets, as, even for directed systems, the notion of closure derived from them is not such that the closure of every set is closed. In order to ensure this Kantorovitch introduces an axiom (his K6) which excludes even some Banach lattices. These notions of convergence are based more on the lattice aspect than the vector-space aspect of a vector lattice. In this paper the reverse is true, and it deals essentially with the application of the theory of topological vector spaces, as developed by von Neumann(9), Mackey (6, 7) and others, to vector lattices.
On powers of ideals generated by R-sequences in a Noetherian local ring
Authors: Caruth A.
Published: November 2008

In a Noetherian commutative ring with identity, every ideal can be expressed (not necessarily uniquely) as a finite intersection of primary ideals (called a primary decomposition). This note is concerned with powers of ideals generated by subsets of an R-sequence in a local ring R (i.e. a Noetherian commutative ring R with identity possessing a unique maximal ideal m) and with a decomposition of such ideals.
The statistics of Weil's trigonometric sums
Authors: Odoni R. W. K.
Published: November 2008

Let F be the finite field of q = pn elements and let F0 be its prime subfield; thus, card F0 = p. For polynomials f ∈ F[x] and non-principal additive characters η of F A. Weil (1) proved the estimate
A “Scale-of-two” High-Speed Counter Using Hard Vacuum Triodes
Authors: Lewis W. B.
Published: November 2008

A high-speed recording counter circuit is described which has proved very reliable. The basic circuit element employs two triodes in a symmetrical circuit which has two stable conditions. The circuit is triggered alternately from one stable state to the other by the applied impulses acting through a circuit comprising two “Westector” cuprous oxide rectifiers and an inductance.

It is easily possible to make a counter operate accurately at a speed of 20,000 random impulses a minute, provided that the associated recording meter operates in less than 1/100 sec.

A “watch-dog” thyratron recording circuit is also described. This is useful where the slow speed of the mechanical recording meter would introduce loss.
Modelling operating system structures by timed stream processing functions
Authors: Broy Manfred , Dendorfer Claus
Published: November 2008

Some extensions of the basic formalism of stream processing functions are useful to specify complex structures such as operating systems. In this paper we give the foundations of higher order stream processing functions. These are functions which send and accept not only messages representing atomic data, but also complex elements such as functions. Some special notations are introduced for the specification and manipulation of such functions. A representation of time is outlined, which enables us to model time dependent behaviour. Finally, we demonstrate how characteristic operating system structures can be modelled by timed higher order stream processing functions.
Lessons from the design of a Standard ML library
Authors: Berry Dave
Published: November 2008

We describe the Edinburgh SML Library and draw lessons from its development. These lessons are of two kinds. The first concerns how to use SML to write a library, and shows some of the design choices that have to be considered. Most of the paper concerns this topic. The second kind of lesson concerns ways in which the language hinders the construction of a library. We suggest some changes to the language as a result of this experience, the most important being the addition of higher-order functors. We also suggest that language designers should consider the needs of libraries early on in the design of a language.
Residual theory in λ-calculus: a formal development
Authors: Huet Gérard
Published: November 2008

We present the complete development, in Gallina, of the residual theory of β-reduction in pure λ-calculus. The main result is the Prism Theorem, and its corollary Lévy's Cube Lemma, a strong form of the parallel-moves lemma, itself a key step towards the confluence theorem and its usual corollaries (Church-Rosser, uniqueness of normal forms). Gallina is the specification language of the Coq Proof Assistant (Dowek et al., 1991; Huet 1992b). It is a specific concrete syntax for its abstract framework, the Calculus of Inductive Constructions (Paulin-Mohring, 1993). It may be thought of as a smooth mixture of higher-order predicate calculus with recursive definitions, inductively defined data types and inductive predicate definitions reminiscent of logic programming. The development presented here was fully checked in the current distribution version Coq V5.8. We just state the lemmas in the order in which they are proved, omitting the proof justifications. The full transcript is available as a standard library in the distribution of Coq.
On the generation of specializers
Authors: Glück Robert
Published: November 2008

Self-applicable specializers have been used successfully to automate the generation of compilers. Specializers are often rather sophisticated, for which reason one would like to adapt and transform them with the aid of the computer. But how to automate this process? The answer to this question is given by three specializer projections. While the Futamura projections define the generation of compilers from interpreters, the specializer projections define the generation of specializers from interpreters. We discuss the potential applications of the specializer projections, and argue that their realization is a real touchstone for the effectiveness of the specialization principle. In particular, we discuss generic specializers, bootstrapping of subject languages and the generation of optimizing specializers from interpretive specifications. The Futamura projections are regarded as a special case of the specializer projections. Recent results confirm that the specializer projections can be performed in practice using partial evaluators.
Type Reconstruction for Type Classes
Authors: Nipkow Tobias , Prehofer Christian
Published: November 2008

We study the type inference problem for a system with type classes as in the functional programming language Haskell. Type classes are an extension of ML-style polymorphism with overloading. We generalize Milner's work on polymorphism by introducing a separate context constraining the type variables in a typing judgement. This leads to simple type inference systems and algorithms which closely resemble those for ML. In particular, we present a new unification algorithm which is an extension of syntactic unification with constraint solving. The existence of principal types follows from an analysis of this unification algorithm.
Generating action compilers by partial evaluation
Authors: Bondorf Anders , Palsberg Jens
Published: November 2008

Compiler generation based on Mosses' action semantics has been studied by Brown, Moura, and Watt, and also by the second author. The core of each of their systems is a handwritten action compiler, producing either C or machine code. We have obtained an action compiler in a much simpler way: by partial evaluation of an action interpreter. Even though our compiler produces Scheme code, the code runs as fast as that produced by the previous action compilers.
On cubism
Authors: Jacobs Bart
Published: November 2008

A number of difficulties in the formalism of Pure Type Systems (PTS) is discussed and an alternative classification system for typed calculi is proposed. In the new approach the main novelty is that one first explicitly specifies the dependencies that may occur. This is especially useful to describe constants, but it also facilitates the description of other type theoretic features like dependent sums.
Functional Pearls
Authors: Kennedy Andrew J.
Published: November 2008

This article describes the application of functional programming techniques to a problem previously studied by imperative programmers, that of drawing general trees automatically. We first consider the nature of the problem and the ideas behind its solution (due to Radack), independent of programming language implementation. We then describe a Standard ML program which reflects the structure of the abstract solution much better than an imperative language implementation. We conclude with an informal discussion on the correctness of the implementation and some changes which improve the algorithm's worst-case time complexity.
On the numerical evaluation of electrostatic fields in composite materials
Authors: Greengard Leslie , Moura Monique
Published: November 2008

A classical problem in electrostatics is the determination of the effective electrical conductivity in a composite material consisting of a collection of piecewise homogeneous inclusions embedded in a uniform background. We discuss recently developed fast algorithms for the evaluation of the potential and electrostatic fields induced in multiphase composites by an applied potential, from which the desired effective properties may be easily obtained. The schemes are based on combining a suitable boundary integral equation with the Fast Multipole Method and the GMRES iterative method; the CPU time required grows linearly with the number of points in the discretization of the interface between the inclusions and the background material.

A variety of other questions in electrostatics, magnetostatics and diffusion can be formulated in terms of interface problems. These include the evaluation of electrostatic fields in the presence of dielectric inclusions, the determination of magnetostatic fields in media with variable magnetic permeability, and the calculation of the effective thermal conductivity of a composite material. The methods presented here apply with minor modification to these other situations as well.
WHERE ARE ALL THE BOYS?
Authors: Brunn Rachelle , Kao Grace
Published: November 2008

We explore the gender gap in college completion among Blacks and Whites. Using the National Education Longitudinal Study of 1988, we examine how early school achievement and educational expectations affect attainment by following a nationally representative sample of youths from 1988 (approximately age fourteen) to 2000 (approximately age twenty-six). The odds of attaining an associate's or a bachelor's degree among Black women are greater than the odds among White men after controlling for family socioeconomic status. However, the difference between Black men and White men is additionally dependent on differences in middle school and high school achievement and in high school sequencing.
Between Two Worlds
Authors: Berant Ety , Zim Shraga
Published: November 2008

The present article describes the process of integration of psychological tests in personality assessment. This process is presented by means of a case study. The article underscores the importance of integrating all sources of information about the client. It also emphasizes the benefits of the feedback meeting for the client as well as for the therapist.
Exneriana – II – The Scientific Legacy of John E. Exner, Jr. 1Part of this paper was presented at the XIXth International Congress of Rorschach and Projective Methods, July 22–26, 2008, Louvain, Belgium.
Authors: Andronikof Anne
Published: November 2008

Based on an analysis of John Exner’s peer-reviewed published work from 1959 to 2007, plus a brief comment for an editorial in Rorschachiana, the author draws a comprehensive picture of the scientific work of this outstanding personality. The article is divided into three sections: (1) the experimental studies on the Rorschach, (2) the clinical studies using the Rorschach, and (3) Exner’s “testament,” which we draw from the last paper he saw published before his death (Exner, 2001/2002). The experimental studies were aimed at better understanding the nature of the test, in particular the respective roles of perception and projection in the response process. These fundamental studies led to a deeper understanding of the complex mechanisms involved in the Rorschach responses and introduced some hypotheses about the intentions of the author of the test. The latter were subsequently confirmed by the preparatory sketches and documents of Hermann Rorschach, which today can be seen at the H. Rorschach Archives and Museum in Bern (Switzerland). Exner’s research has evidenced the notion that the Rorschach is a perceptive-cognitive-projective test.