bluuebunny/crossref_metadata_2025 huggingface dataset:
Quasi-bounded and singular thermal potentials
Authors: Watson N. A.
Published: November 2008

In his monograph [2], Doob presented the theories of quasi-bounded and singular functions associated with the Laplace and heat equations. In particular, on p. 712, he proved in the classical case that a potential is quasi-bounded if and only if its associated measure vanishes on polar sets. However, on p. 714, he proved only weaker results for the thermic case, namely that a potential is quasi-bounded (i) if its associated measure vanishes on semi-polar sets, and (ii) only if its measure vanishes on polar sets. The main purpose of this note is to establish that the exact analogue of the result for the classical case holds for the thermic case. We also use a related theorem on thermal potentials, to prove a second characterization of those which are quasi-bounded, analogous to one due to Arsove and Leutwiler for the classical case. We also give the corresponding characterizations of singular thermal potentials.
Finite soluble groups admitting an automorphism of prime power order with few fixed points
Authors: Hartley Brian , Turau Volker
Published: November 2008

Let G be a finite soluble group with Fitting subgroup F(G). The Fitting series of G is defined, as usual, by F0(G) = 1 and Fi(G)/Fi−1(G) = F(G/Fi−1(G)) for i ≥ 1, and the Fitting height h = h(G) of G is the least integer such that Fn(G) = G. Suppose now that a finite soluble group A acts on G. Let k be the composition length of A, that is, the number of prime divisors (counting multiplicities) of |A|. There is a certain amount of evidence in favour of the

CONJECTURE. |G:Fk(G)| is bounded by a number depending only on |A| and |CG(A)|.
Asymptotic behaviour of the H-transform in the complex domain
Authors: Carmichael Richard D. , Pathak Ram S.
Published: November 2008

Abelian theorems for the H-transform of functions and generalized functions are obtained as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Quasi-asymptotic behaviour (q.a.b.) of the H-transformable generalized functions is defined. A structure theorem for generalized functions possessing q.a.b. is proved and is applied to obtain the asymptotic behaviour of the H-transform of generalized functions having q.a.b. The theorems are illustrated by examples.
Change of rings and characteristic classes
Authors: Huebschmann Johannes
Published: November 2008

We construct characteristic classes for the change of rings spectral sequences. These have their values in appropriate Ext groups and provide descriptions of the first non-zero differentials in the spectral sequences. We use these classes to do some calculations in the cohomology spectral sequence of an extension of a finite cyclic group by a finite cyclic group.
Affine structure of facially symmetric spaces
Authors: Friedman Yaakov , Russo Bernard
Published: November 2008

In [7], the authors proposed the problem of giving a geometric characterization of those Banach spaces which admit an algebraic structure. Motivated by the geometry imposed by measuring processes on the set of observables of a quantum mechanical system, they introduced the category of facially symmetric spaces. A discrete spectral theorem for an arbitrary element in the dual of a reflexive facially symmetric space was obtained by using the basic notions of orthogonality, protective unit, norm exposed face, symmetric face, generalized tripotent and generalized Peirce projection, which were introduced and developed in this purely geometric setting.
Periods and special values of the hypergeometric series
Authors: Flach Matthias
Published: November 2008

The aim of this paper is to complement results by Wolfart [14] about algebraic values of the classical hypergeometric series

for rational parameters a, b, c and algebraic arguments z. Wolfart essentially determines the set of a, b, c ∈ ℚ,z ∈ ℚ for which F(a, b, c; z) ∈ ℚ and indicates, in a joint paper with F. Beukers[1], that some of these values can be expressed in terms of special values of modular forms. This method yields a few strikingly explicit identities like

but it does not give general statements about the nature of the algebraic values in question. In this paper we identify F(a, b, c; z) as a generator of a Kummer extension of a certain number field depending on z, which in particular bounds its degree as an algebraic number in terms of the degree of z. Our theorem in §2 seems to be the most precise statement one can make in general but sometimes improvements are possible as we point out at the end of §2.
On the shape of a random acyclic digraph
Authors: Mckay Brendan D.
Published: November 2008

If D is an acyclic digraph, define the height h = h(D) to be the length of the longest directed path in D. We prove that the values of h(D) over all labelled acyclic digraphs D on n vertices are asymptotically normally distributed with mean Cn and variance C′n, where C ≈ 0·764334 and C′ ≈ 0·145210. Furthermore, define V0(D) to be the set of sinks (vertices of out-degree 0) and, for r ≥ 1, define Vr(D) to be the set of vertices ν such that the longest directed path from ν to V0(D) has length r. For each k ≥ 1, let nk(D) be the number of sets Vt(D) which have size k. We prove that, for fixed k, the values of nk(D) over all labelled acyclic digraphs D on n vertices are asymptotically normally distributed with mean Ckn and variance C′kn, for positive constants Ck and C′k. Results of Bender and Robinson imply that our claim holds also for unlabelled acyclic digraphs.
Real projective representations of finite groups
Authors: Hoffmann P. N. , Humphreys J. F.
Published: November 2008

The projective representations of a finite groupGover a fieldKare divided into sets, each parametrized by an element of the groupH2(G, Kx). The latter is the Schur multiplierM(G)whenK= ℂ.
Versal topological stratification and the bifurcation geometry of map-germs of the plane
Authors: Rieger J. H.
Published: November 2008

The set of critical values of a map of the plane (of corank 1) can be regarded as the apparent contour of a smooth surface. It is a classical result of Whitney[13] that generically the apparent contour is a smooth fold curve with isolated cusps and transverse fold crossings. More recent classifications of smooth map-germs of the plane of low codimension (occurring in generic 2- or 3-parameter families), e.g. in [1, 5, 7], were motivated by a question in differential geometry: given any smooth surface which is generically embedded in ℝ3, produce a list of all possible (orthogonal or central) projections of such a surface.
Sequences with bounded logarithmic discrepancy
Authors: Baker R. C. , Harman G.
Published: November 2008

Let {α} denote the fractional part of the real number α. Write χ(x, y) = 1 for {x} < y and χ(x, y) = 0 otherwise. A real sequence (xn) is uniformly distributed (mod 1) if

It is a consequence of (1·1) that DN = o(N),

Where

is the discrepancy of the sequence (xn).
Automatic continuity with application to C*-algebras
Authors: Palacios Angel Rodriguez
Published: November 2008

The fact proved by Cleveland [4], that the topology of any (non-complete) algebra norm on a C*-algebra is stronger than the topology of the usual norm, is reencountered as a direct consequence of a theorem, which we prove in this note, stating that homomorphisms from certain non-complete normed (associative) algebras onto some semisimple Banach algebras are automatically continuous.
Three-dimensional constitutive equations for rigid/perfectly plastic granular materials
Authors: Ostrowska-Maciejewska J. , Harris D.
Published: November 2008

A three-dimensional constitutive equation governing the flow of an isotropic rigid/perfectly plastic granular material is presented. The equation relates the strain-rate tensor to the Cauchy stress tensor and to the co-rotational rate of the Cauchy stress. It contains scalar functions of the scalar invariants involving the stress, stress-rate and strain-rate tensors together with parameters which characterize the material. The model generalizes the double-shearing model and its relationship to existing theories is demonstrated.
Quantum groups and representations of monoidal categories
Authors: Yettera David N.
Published: November 2008

This paper is intended to make explicit some aspects of the interactions which have recently come to light between the theory of classical knots and links, the theory of monoidal categories, Hopf-algebra theory, quantum integrable systems, the theory of exactly solvable models in statistical mechanics, and quantum field theories. The main results herein show an intimate relation between representations of certain monoidal categories arising from the study of new knot invariants or from physical considerations and quantum groups (that is, Hopf algebras). In particular categories of modules and comodules over Hopf algebras would seem to be much more fundamental examples of monoidal categories than might at first be apparent. This fundamental role of Hopf algebras in monoidal categories theory is also manifest in the Tannaka duality theory of Deligne and Mime [8a], although the relationship of that result and the present work is less clear than might be hoped.
Compactifications of discrete versions of semitopological semigroups by filters of zero sets
Authors: (Papazyan) Talin Budak
Published: November 2008

The maximal proper prime filters together with the ultrafilters of zero sets of any metrizable compact topological space are shown to have a compact Hausdorff topology in which the ultrafilters form a discrete, dense subspace. This gives a general theory of compactifications of discrete versions of compact metrizable topological spaces and some of the already known constructions of compact right topological semigroups are special cases of the general theory. In this way, simpler and more elegant proofs for these constructions are obtained.

In [8], Pym constructed compactifications for discrete semigroups which can be densely embedded in a compact group. His techniques made extensive use of function algebras. In [4] Helmer and Isik obtained the same compactifications by using the existence of Stone ech compactifications. The aim of this paper is to present a general theory of compactifications of semitopological semigroups so that Helmer and Isik's results in [4] are a simple consequence. Our proofs are different and are based on filters which provide a natural way of getting compactifications. Moreover we present new insights by emphasizing maximal proper primes which are not ultrafilters.

We start by defining filters of zero sets (called z-filters) on a given topological space X, and their convergence. In the case of compact metrizable topological spaces, we establish the connections between proper maximal prime z-filters on X and zultrafilters in β(X\{x})\(X\{x}) where β(X\{x}) is the Stone-ech compactification of X\{x}. We then define a topology on the set of all prime z-filters on X such that the subspace of all proper maximal primes is compact Hausdorff. We denote by the set of all proper maximal prime z-filters on X together with the z-ultrafilters and show that when X is a compact metrizable cancellative semitopological semigroup, is a compact right topological semigroup with dense topological centre. Also, when is considered for a compact Hausdorff metrizable group, the semigroup obtained is exactly the same (algebraically and topologically) as the semigroup obtained in [4]. Hence the result in [4] is just a consequence of the general theory presented in this paper.
On p-groups of maximal class. III
Authors: Vera-López Antonio , Fernández-Alcober Gustavo A.
Published: November 2008

In this paper, we consider the family of the p-groups of maximal class and study some invariants related to the conjugacy classes of these groups. This subject was first taken up in [7] and [6], whose notation and terminology we maintain and give after this introduction. In [7], the invariants σG and k(G) are found for the p-groups of maximal class satisfying |G| ≤ p7. Here, apart from extending those results to the case when G has order p8 or p9, we consider the problem in all its generality and propose to determine their values for as large a family of p-groups of maximal class as possible. In this direction, we get some general results in the first paragraph, from which we want to point out the following ones.
Some self-dual local rings of integers not free over their associated orders
Authors: Byott N. P.
Published: November 2008

Let p be a prime number, and let K be a finite extension of the rational p-adic field ℚp. Let L/K be a finite abelian extension with Galois group G, and let L, K denote the valuation rings of L, K respectively. Then L is a free module of rank 1 over the group algebra KG. Defining the associated order of the extension L/K by

L can be viewed as a module over the ring , and a fortiori over the group ring KG.
On homogeneous chaos
Authors: Cutland Nigel , Ng Siu-Ah
Published: November 2008

This paper discusses the Wiener–Itô chaos decomposition of an L2 function φ over Wiener space, and is concerned in particular with the identification of the integrands ƒn in the chaos decomposition

First these are identified as Radon–Nikodým derivatives. Two elementary non-standard proofs of the Wiener–Itô chaos decomposition are given, based on Anderson's construction of Brownian motion and Itô integration.
Weakly compact homomorphisms between Banach algebras
Authors: Johnson B. E.
Published: November 2008

Compact homomorphisms between Banach algebras are not particularly unusual – for example if A is the algebra of complex sequences {an} with nan → 0 as n → ∞ and ∥{an}∥ = supn(nan) and B = c0 then the embedding map ø:A → B is a compact homomorphism. Nevertheless for really well behaved Banach algebras it is often the case that the only weakly compact homomorphisms are those with a finite-dimensional range. A number of interesting results in this area appear in [1] and elsewhere. The purpose of this paper is to extend those results.
Duals of vector-valued Köthe function spaces
Authors: Florencio Miguel , Paúl Pedro J. , Sáez Carmen
Published: November 2008

Let Λ be a perfect Köthe function space in the sense of Dieudonné, and Λ× its Köthe-dual. Let E be a normed space. Then the topological dual of the space Λ(E) of Λ-Bochner integrable functions equals the corresponding Λ×(E′) if and only if E′ has the Radon–Nikodým property. We also give some results concerning barrelledness for spaces of this kind.
A note on symmetric basic sequences in Lp(Lq)
Authors: Raynaud Yves
Published: November 2008

Subspaces of Lp spanned by symmetric independent identically distributed random variables were identified as Orlicz spaces by Bretagnolle and Dacunha-Castelle[1], who showed that, conversely, in the case p ≤ 2, every p-convex, 2-concave Orlicz space is isomorphic to a subspace of Lp. This was extended by Dacunha-Castelle [3] to subspaces of Lp with symmetric basis, which appear as ‘p-means’ of Orlicz spaces (see [9] for the corresponding finite-dimensional result, and [12] for the case of rearrangement invariant function spaces). On the contrary the only subspaces with symmetric basis of Lp for p ≥ 2 are lp and l2 (if one does not care about isomorphy constants).
On a problem in elementary number theory
Authors: Schinzel A. , Wójcik J.
Published: November 2008

Let ordq (a) be the exponent with which a prime q occurs in the factorization of a rational number a ≠ 0 and, if ordq (a) = 0, let Mq(a) be the multiplicative group generated by a modulo q. In the course of a group-theoretical investigation J. S. Wilson found he needed some results about integers a, b such that Mq(a) = Mq(b), indeed also for algebraic integers, and he proved some of what he needed. J. W. S. Cassels observed that Wilson's argument naturally proved the existence of infinitely many primes q with Mq(a) = Mq(b) for rational integers a, b with ab > 0, |a| > 1, |b| > 1. J. G. Thompson found a proof for the case of integers a, b with ab < 0, |a| > 1, |b| > 1. He also posed the problem for rational a, b (all this is unpublished). The aim of this paper is to prove that the answer to Thompson's question is affirmative. We also include the case ab > 0 settled by Thompson himself. We use the same technique devised by Wilson which has been elaborated by Cassels and Thompson. We thank Professor Cassels for the simplification of our original exposition and the referee for his suggestions.
Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group
Authors: Melbourne Ian , Dellnitz Michael
Published: November 2008

We obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.

Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.
Duality for base-changing morphisms of vector bundles, modules, Lie algebroids and Poisson structures
Authors: Higgins Philip J. , Mackenzie Kirill C. H.
Published: November 2008

The main result of this paper is an extension to Poisson bundles [4] and Lie algebroids of the classical result that a linear map of Lie algebras is a morphism of Lie algebras if and only if its dual is a Poisson morphism. In formulating this extension we introduce a second class of structural maps for vector bundles, which we call comorphisms, alongside the standard morphisms, and we further show that this concept of comorphism, in conjunction with a corresponding concept for modules, allows one to extend to arbitrary base-changing morphisms of arbitrary vector bundles the familiar duality and section functors which are normally denned only in the base-preserving case.
On asymptotics of a class of 1-dimensional diffusions
Authors: Rajeev B.
Published: November 2008

In this paper we study the almost sure asymptotics of htXt where (Xt) satisfies a stochastic differential equation and ht is a deterministic differentiable function, ht ↓ 0 as t → ∞. We give necessary and sufficient criteria, in terms of deterministic integrals, for the process htXt to converge to zero, to oscillate boundedly and for the case of infinite oscillations. Necessary and sufficient criteria for convergence to zero, in terms of a related integral, was studied by Chan and Williams in [1], for a class of diffusions that arise in simulated annealing. In Chan [2] the results are extended to higher dimensions. For Brownian motion, Jeulin and Yor[3] give a general criterion for convergence to zero, when the function ht is merely continuous and non-negative. The results of [1] and [3] are both generalizations of the well known ‘Kolmogorov criterion’ for Brownian motion. Our approach is very close to the techniques developed by Chan and Williams in [1]. Indeed, our method is essentially a fine tuning of those techniques. We apply our results, in Section 3, to a class of diffusions and compute the critical rate ht for which bounded oscillations occur. For Brownian motion this is the law of iterated logarithm, modulo the size of the oscillation. We also consider two parametrized families of diffusions for which the critical rate is seen to depend smoothly on the parameter. These results appear to be new. Our method also gives estimates on the size of the oscillations (Section 6).
How random is the characteristic polynomial of a random matrix ?
Authors: Hansen Jennie C. , Schmutz Eric
Published: November 2008

Every monic, degree n polynomial in Fq[x;] is the characteristic polynomial of at least one n × n matrix (with entries in the finite field Fq), but they do not appear with equal frequency. There is no a priori reason that the characteristic polynomial of a typical matrix should resemble a typical monic degree n polynomial. Nevertheless, we prove a precise version of the following heuristic statement: ‘Excepting its small factors, the characteristic polynomial of a random matrix is random.’
Versal unfoldings of equivariant linear Hamiltonian vector fields
Authors: Melbourne Ian
Published: November 2008

We prove an equivariant version of Galin's theorem on versal deformations of infinitesimally symplectic matrices. Matrix families of codimension zero and one are classified, and the results are used to study the movement of eigenvalues in one parameter families.
Curves with increasing chords
Authors: Rote Günter
Published: November 2008

A curve has increasing chords if AD ≥ BC for any four points A, B, C, D lying on the curve in that order. The length of such a curve that connects two points at distance 1 is at most 2π/Z in two dimensions, which is the optimal bound, and less than 30 in three dimensions.
On the cofiniteness of local cohomology modules
Authors: Delfino Donatella
Published: November 2008

Let (R,m) be a local, noetherian, d-dimensional ring and let M be a finitely generated R-module. Since the local cohomology modules are artinian, is finitely generated for all i and j (see [4], Remark 1*middot;3 and 2·1). Grothendieck[2] made the following conjecture: If I is an ideal of a noetherian ring R, thenis finitely generated for all j.
Ω theorems for the complex divisor function
Authors: Hall R. R.
Published: November 2008

This paper is a sequel to [6] and concerns the complex divisor function

which has had a number of applications in the analytic theory of numbers. Thus Hooley's Δ-function [8] defined by

satisfies the inequality

and Erdös' τ+-function, defined by

satisfies
Property (BB) and holomorphic functions on Fréchet-Montel spaces
Authors: Defant Andreas , Maestre Manuel
Published: November 2008

Two of the most important topologies on the space ℋ(E) of all holomorphic functions f:E → ℂ on a complex locally convex space E are the compact-open topology τ0 and the Nachbin-ported topology τε. We recall that a seminorm p on ℋ(E) is said to be τω-continuous if there is a compact K such that for every open set V with K contained in V there is a constant c > 0 satisfying

Clearly, the following natural question arises: when do the topologies τ0 and τω coincide? In the setting of Fréchet spaces equality of τ0 and τω forces E to be a Montel space; Mujica [21] proved τ0 = τω for Fréchet-Schwartz spaces and Ansemil-Ponte [1] showed that for Fréchet-Montel spaces this happens if and only if the space of all continuous n-homogeneous polynomials with the compact-open topology, (Pn(E), τ0), is barrelled. By duality, it turns out that the question τ0 = τω is intimately related to ‘Grothendieck's problème des topologies’ which asks whether or not for two Fréchet spaces E1 and E2 each bounded set B of the (completed) projective tensor product is contained in the closed absolutely convex hull of the set B1 ⊗ B2, where Bk is a bounded subset of Ek for k = 1, 2. If this is the case, then the pair (E1, E2) is said to have property (BB). Observe that every compact set B in can always be lifted by compact subsets Bk of Ek (see e.g. [20], 15·6·3). Hence, for Fréchet-Montel spaces E1 and E2, property (BB) of (El,E2) means that is Fréchet-Montel and vice versa. Taskinen[24] found the first counterexample to Grothendieck's problem. In [25] he constructed a Fréchet-Montel space E0 for which (E0,E0) does not have property (BB), and Ansemil-Taskinen [2] showed that τ0 ≠ τω on ℋ(E0).
Subquotients of UHF C*-algebras
Authors: Wassermann Simon
Published: November 2008

Over the last thirty years, the study of C*-algebras has proceeded in a number of directions. On one hand, much effort has been devoted to understanding the structure of particular classes of algebras, such as the approximately finite (AF) algebras. On the other, general structure theorems have been sought. Classes of algebras defined by certain abstract properties have been investigated with a view to obtaining more concrete descriptions of the algebras. One of the earliest results of this type was the theorem of Glimm [13], later extended by Sakai [20] to the inseparable case, characterizing the non-type I C*-algebras as those algebras which contain a subalgebra with a quotient *-isomorphic to the CAR algebra.
The generalized Yosida–Hewitt theorem
Authors: Basile A. , Bukhvalov A. V. , Yakubson M. Ya.
Published: November 2008

The Yosida–Hewitt (YH, for short) theorem [YH] has many versions and generalizations in diverse settings, e.g. functionals on vector lattices and spaces of vector-valued functions, measures with values in Banach spaces, topological groups and vector lattices, etc. In this paper we derive a very general form of the YH theorem dealing with the much more general case of operators acting in vector lattices (VLs, for short) and Banach spaces (BSs, for short). A unified approach to all settings mentioned above may be founded on decompositions for operators in VLs.
Evaluation operators on the Bergman space
Authors: Zhu Kehe
Published: November 2008

Let D be the open unit disc in the complex plane C and let dA be the normalized area measure on D. The Bergman space is the space of analytic functions f in D such that
On multigraded resolutions
Authors: Bruns Winfried , Herzog Jürgen
Published: November 2008

This paper was initiated by a question of Eisenbud who asked whether the entries of the matrices in a minimal free resolution of a monomial ideal (which, after a suitable choice of bases, are monomials) divide the least common multiple of the generators of the ideal. We will see that this is indeed the case, and prove it by lifting the multigraded resolution of an ideal, or more generally of a multigraded module, keeping track of how the shifts ‘deform’' in such a lifting; see Theorem 2·1 and Corollary 2·2.
Symmetric powers, metabelian Lie powers and torsion in groups
Authors: Stöhr Ralph
Published: November 2008

In this paper we study the homology of groups with coefficients in metabelian Lie powers, and apply the results to obtain information about elements of finite order in certain free central extensions of groups. Perhaps the most prominent example to which our results apply is the relatively free group

where Fd is the (absolutely) free group of rank d. Thus Fd(Bc) is the free group of rank d in the variety Bc of all groups which are both centre-by-(nilpotent of class ≤ c − 1)-by-abelian and soluble of derived length ≤ 3. It was pointed out in [1] that the order of any torsion element in Fd(Bc) divides c if c is odd and 2c if c is even. This, however, is a conditional result as it does not answer the question of whether or not there are any torsion elements in (1·1). Up to now, this question had only been answered in case when c is a prime number [1] or c = 4 [8]. In these cases Fd (Bc) is torsion-free if d ≤ 3, and elements of finite order do occur in Fd(Bc) if d ≥ 4. Moreover, the torsion elements in Fd(Bc) form a subgroup, and the precise structure of this torsion subgroup was exhibited in [1] in the case when c is a prime and in [8] for c = 4. In the present paper we add to this knowledge. On the one hand, we show that for any prime p dividing c the group Fd(Bc) has no elements of order p for all d up to a certain upper bound, which takes arbitrarily large values as c varies over all multiples of p. On the other hand, we show that for prime powers does contain elements of order p whenever d ≥ 4. Finally, we exhibit the precise structure of the p-torsion subgroup of when p ≠ 2. Precise statements are given below (Corollaries 1 and 2). Our results on (1·1) are a special case of more general results (Theorems 1′−3′) which refer to a much wider class of groups, and which are, in their turn, a consequence of our main results on the homology of metabelian Lie powers (Theorems 1–3).
Representation of a quotient of a subalgebra of B(X)
Authors: Le Merdy Christian
Published: November 2008

Let X be an SQp-space, i.e. a quotient of a subspace of some Lp-space. Let B ⊂ B(X) be a subalgebra of all bounded operators on X and let I ⊂ B be a closed ideal. We show that the quotient algebra B/I is isometrically homomorphic to a subalgebra of B(Y) for some SQp-space Y. This generalizes a theorem of Bernard and Cole, corresponding to p = 2, which states that any quotient of an operator algebra is an operator algebra.
On a problem in algebraic number theory
Authors: Wójcik J.
Published: November 2008

Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’
Geometric characterization of linearisable second-order differential equations
Authors: Martínez Eduardo , Cariñena José F.
Published: November 2008

Given an Ehresmann connection on the tangent bundle τ: TM → M we define a linear connection on the pull-back bundle τ*(TM). With the aid of this tool, necessary and sufficient conditions are derived for the existence of local coordinates in which a system of second-order differential equations is linear.
Superoptimal approximation by meromorphic functions
Authors: Peller V. V. , Young N. J.
Published: November 2008

Let G be a matrix function of type m × n and suppose that G is expressible as the sum of an H∞ function and a continuous function on the unit circle. Suppose also that the (k – 1)th singular value of the Hankel operator with symbol G is greater than the kth singular value. Then there is a unique superoptimal approximant to G in : that is, there is a unique matrix function Q having at most k poles in the open unit disc which minimizes s∞(G – Q) or, in other words, which minimizes the sequence

with respect to the lexicographic ordering, where

and Sj(·) denotes the jth singular value of a matrix. This result is due to the present authors [PY1] in the case k = 0 (when the hypothesis on the Hankel singular values is vacuous) and to S. Treil[T2] in general. In this paper we give a proof of uniqueness by a diagonalization argument, a high level algorithm for the computation of the superoptimal approximant and a recursive parametrization of the set of all optimal solutions of a matrix Nehari—Takagi problem.
On the contractibility to a point of the linear groups of reflexive non-commutative Lp-spaces
Authors: Ferleger Sergei V. , Sukochev Fyodor A.
Published: November 2008

For every Banach space X, denote by GL(X) the linear group of X, i.e. the group of all linear continuous invertible operators on X with the topology induced by the operator norm. One says that GL(X) is contractible to a point if there exists a continuous map F: GL(X) × [0, 1] → GL(X) such that F(A,0) = A and F(A, 1) = Id, for every A ∈ GL(X).
On the complement of a nef and big divisor on an algebraic variety
Authors: Russo Francesco
Published: November 2008

LetXbe an algebraic (complete) variety over a fixed algebraically closed fieldk. To every Cartier divisorDonX, we can associate the gradedk-algebra. As is known, for a semi-ample divisorD,R(X,D) is a finitely generatedk-algebra (see [21] or [9]), while this property is no longer true for arbitrary nef and big divisors (see [21]).
Ends of graphs
Authors: Mller Rgnvaldur G.
Published: November 2008

It is shown how questions about ends of locally finite graphs can be reduced to questions about trees. Several applications are given; for example, locally finite connected graphs with infinitely many ends and automorphism groups that act transitively on the ends are classified.
A remark on the containment of c0 in spaces of compact operators
Authors: Emmanuele G.
Published: November 2008

Let X, Y be two Banach spaces. By L(X, Y) (resp. K(X, Y)) we denote the Banach space of all bounded, linear (resp. compact, bounded, linear) operators from X into Y. Several papers have been devoted to the question of when c0 embeds isomorphically into K(X, Y) (see 5, 8, 9 and their references) and its relationship with the following question:

(i) is K(X, Y) always uncomplemented in L(X, Y) when L(X, Y)K(X, Y)?
New classes of Banach spaces which are M-ideals in their biduals
Authors: Werner Dirk
Published: November 2008

A subspace X of a Banach space Y is called an M-ideal if there is an L-projection P on Y* whose kernel is X1, the annihilator of X; that is, we have

In the case that Y is the bidual of X, a natural linear projection on X*** = Y* with kernel X1 is available, namely .
Nonlinear integral inequalities of the Volterra type
Authors: Szwarc Ryszard
Published: November 2008

We are studying the integral inequality

where all functions appearing are defined and increasing on the right half-axis and take the value zero at zero. We are interested in determining when the inequality admits solutions u(x) which are non-vanishing in a neighbourhood of zero. It is well-known that if ψ(x) is the identity function then no such solution exists. This due to the fact that the operator defined by the integral on the right-hand side of the equation is linear and compact. So if we are interested in non-trivial solutions it is natural to require that ψ(x) > 0 at least for all non-zero points in some neighbourhood of zero. One of the typical examples is the power function ψ(x) = xα, where α < 1. This situation was explored in [2]. The functions a(x) that admit non-zero solutions were characterized by Bushell in [1]. For a general approach to the problem we refer to [2], [3] and [4].
Braid groups and the group of homeomorphisms of a surface
Authors: Scott G. P.
Published: November 2008

Braid groups on the plane were denned by Artin(1) in 1925. More recently Fox(8) defined braid groups on arbitrary topological spaces, the situation being particularly interesting if the space is a 2-manifold. Presentations of the braid groups on R2, S2 and P2 can be found in (2), (6) and (13) respectively, and some general results on braid groups of compact 2-manifolds can be found in (7). In section 1 of this paper, we give finite presentations for the braid groups on all closed 2-manifolds except S2 and P2.
Supersonic wing-body interference
Authors: Clark R. W.
Published: November 2008

We consider here the supersonic inviscid flow past a wing-body combination consisting of a semi-infinite plane wing symmetrically placed about an infinite convex cylinder. When the cylinder is circular in cross-section a formal solution for the Laplace transform of the velocity potential exists (Neilson(l), and Stewartson, 1951, unpublished). This solution is given in the form of a series which is only slowly convergent near the boundary surface separating the disturbed and the undisturbed regions. However, this slow convergence has been overcome by Waechter(4) using the Poisson Summation formula on the series solution. This enables the solution to be expressed in terms of integrals which can be evaluated as a convergent residue series, taking on different forms in the different regions of the interaction.
On the Calculation of Pair Creation by Fast Charged Particles and the Effect of Screening
Authors: Bhabha H. J.
Published: November 2008

In a recent paper I developed a method for calculating the probability of the creation of an electron pair in the collision of two charged particles moving with a relative velocity very near that of light. I showed there that under certain conditions it is legitimate to treat one of the colliding particles, say the heavier one of charge Z2 and rest mass M2, which we shall call the particle 2, as fixed at the origin of coordinates, and the other, of charge Z1 and rest mass M1, which we shall call the particle 1, as moving classically along a straight line with uniform velocity V in the direction of the z-axis, passing the other particle 2 at a minimum distance of approach (impact parameter) b. I developed expressions (given by (18) to (22) of A) giving the probability of the transition of an electron from an initial state of negative energy E0 and momentum p0 lying in an element of momentum space dp0 to a final state of energy E and momentum p lying in an element of momentum space dp, under the combined perturbing influence of the two colliding particles when they pass at a minimum distance b. The initial state of the electron, left vacant after the transition, appears as a positron of momentum p+ = − p0. To get the differential effective cross-section for the creation of the above pair, we must integrate this probability over all values of the impact parameter b, and this integration can be performed easily as shown in A. The final result can be written as a sum of a finite number of doubly infinite integrals (A, (24)). The purpose of this paper is to carry through the evaluation of these integrals for certain special cases, and to consider the effects of screening. The results have already been communicated in A.
On the Smoothing of Observed Data
Authors: Jeffreys Harold
Published: November 2008

1. It often happens that we have a series of observed data for different values of the argument and with known standard errors, and wish to remove the random errors as far as possible before interpolation. In many cases previous considerations suggest a form for the true value of the function; then the best method is to determine the adjustable parameters in this function by least squares. If the number required is not initially known, as for a polynomial where we do not know how many terms to retain, the number can be determined by finding out at what stage the introduction of a new parameter is not supported by the observations*. In many other cases, again, existing theory does not suggest a form for the solution, but the observations themselves suggest one when the departures from some simple function are found to be much less than the whole range of variation and to be consistent with the standard errors. The same method can then be used. There are, however, further cases where no simple function is suggested either by previous theory or by the data themselves. Even in these the presence of errors in the data is expected. If ε is the actual error of any observed value and σ the standard error, the expectation of Σε2/σ2 is equal to the number of observed values. Part, at least, of any irregularity in the data, such as is revealed by the divided differences, can therefore be attributed to random error, and we are entitled to try to reduce it.
Specific Heats of Solids due to Molecular Rotations
Authors: Chang T. S.
Published: November 2008

Bethe's method, used in the problem of order-disorder transitions in alloys, is applied formally to the problem of molecular rotations in solids. To apply this method, we assume that the solid is entirely homogeneous, and that the state of rotation is the same throughout the solid. Without this assumption, the application of this method is impossible.

A particular form of the mutual potential energy between two neighbouring molecules has been chosen, and classical statistics is employed throughout. The calculations are made entirely after the manner of Bethe, and the similarities of the two problems are pointed out. The result is that there is a critical temperature, and also a discontinuity in the specific heat of the magnitude of some ten times the Boltzmann constant per molecule, arising from the sudden setting in of the rotations as the temperature is increased beyond the critical point. Agreement with the experiments is bad, indicating that a more profound theory is necessary.
Extended natural semantics
Authors: Hannan John
Published: November 2008

We extend the definition of natural semantics to include simply typed λ-terms, instead of first-order terms, for representing programs, and to include inference rules for the introduction and discharge of hypotheses and eigenvariables. This extension, which we call extended natural semantics, affords a higher-level notion of abstract syntax for representing programs and suitable mechanisms for manipulating this syntax. We present several examples of semantic specifications for a simple functional programming language and demonstrate how we achieve simple and elegant manipulations of bound variables in functional programs. All the examples have been implemented and tested in λProlog, a higher-order logic programming language that supports all of the features of extended natural semantics.
Empirical and analytic study of stack versus heap cost for languages with closures
Authors: Appel Andrew W. , Shao Zhong
Published: November 2008

We present a comprehensive analysis of all the components of creation, access and disposal of heap-allocated and stack-allocated activation records. Among our results are:

•Although stack frames are known to have a better cache read-miss rate than heap frames, our simple analytical model (backed up by simulation results) shows that the difference is too trivial to matter.

•The cache write-miss rate of heap frames is very high; we show that a variety of miss-handling strategies (exemplified by specific modern machines) can give good performance, but not all can.

•Stacks restrict the flexibility of closure representations (for higher-order functions) in important (and costly) ways.

•The extra load placed on the garbage collector by heap-allocated frames is small.

•The demands of modern programming languages make stacks complicated to implement efficiently and correctly.

Overall, the execution cost of stack-allocated and heap-allocated frames is similar; but heap frames are simpler to implement and allow very efficient first-class continuations.
Proving the correctness of compiler optimisations based on a global analysis: a study of strictness analysis†
Authors: Burn Geoffrey , Le Métayer Daniel
Published: November 2008

A substantial amount of work has been devoted to the proof of correctness of various program analyses but much less attention has been paid to the correctness of compiler optimisations based on these analyses. In this paper we tackle the problem in the context of strictness analysis for lazy functional languages. We show that compiler optimisations based on strictness analysis can be expressed formally in the functional framework using continuations. This formal presentation has two benefits: it allows us to give a rigorous correctness proof of the optimised compiler; and it exposes the various optimisations made possible by a strictness analysis.
Continuation and path following
Authors: Allgower Eugene L. , Georg Kurt
Published: November 2008

The main ideas of path following by predictor–corrector and piecewise-linear methods, and their application in the direction of homotopy methods and nonlinear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed. Complexity issues and available software are also discussed.
Iterative solution of systems of linear differential equations
Authors: Miekkala Ulla , Nevanlinna Olavi
Published: November 2008

Parallel processing has made iterative methods an attractive alternative for solving large systems of initial value problems. Iterative methods for initial value problems have a history of more than a century, and in the works of Picard (1893) and Lindelöf (1894) they were given a firm theoretical basis. In particular, the superlinear convergence on finite intervals is included in Lindelöf (1894).
Choice of norms for data fitting and function approximation
Authors: Watson G. A.
Published: November 2008

For the approximation of functions and data, it is often appropriate to minimize a norm. Many norms have been considered, and a review is presented of methods for solving a range of problems using a wide variety of norms.
THE HYDRA OF HOROWITZIAN HISTORY
Authors: Dottin Paul Anthony
Published: November 2008

Whether to provide reparations to African Americans for the atrocities of slavery and segregation is arguably the most controversial public matter concerning race in the United States today. This debate, a clash over the economics and ethics of equality, is nothing less than a struggle over the future of racial identity, race relations, and racial progress in the current post–civil rights movement era.

With the stakes for African Americans so high, and the prospects for affirmative action dim, public intellectuals have weighed in heavily on each side of the issue. Randall Robinson—author of the best-known work advocating for reparations,The Debt: What America Owes to Blacks(2000)—and David Horowitz—the reparationist movement's most reviled nemesis and author ofUncivil Wars: The Controversy over Reparations for Slavery(2002)—have become the alpha and omega of almost any deliberation on Black reparations.

Not surprisingly, rancorous rhetoric has often overshadowed rigorous research on the veracity of antireparations and proreparations claims. This essay aims to correct this problem with an extensive analysis of David Horowitz's (2002) arguments, providing a synthesis of data, concepts, theories, and methodologies from the disciplines of sociology, history, economics, and anthropology. This essay finds that Horowitz's use of academic scholarship to discredit African American reparations fails to meet the “scientific” standards he demands of his opponents.
Zur Differentialdiagnose der echoarmen Schilddrüse
Authors: Mosser H. , Hruby W. , Braun U. , Stellamor K. , Habsburg E.
Published: November 2008

Die Hypothyreose als funktioneller Endzustand einer abgelaufenen Thyreoiditis stellt aufgrund der uncharakteristischen und oft schleichend verlaufenden Klinik ein diagnostisches Problem dar (8, 11, 13). In der reichlich vorhandenen Schilddrüsenliteratur gibt es kaum systematische Berichte über die sonographische Organstruktur bei diesem Krankheitsbild.

In einer prospektiven Studie fanden wir für diese Entität eine charakteristische Sonomorphologie des Organs hinsichtlich Struktur, Größe und Kontur.
Sonographische und farbdopplersonographische Befunde beim Osteosarkom
Authors: Wild F. , Erhardt J. , Beck J. D. , Deeg K. H. , Stehr K.
Published: November 2008

Bislang ist die Diagnostik von Knochentumoren eine Domäne der Radiologie. In der vorliegenden Arbeit werden sonographische und farbdopplersonographische Befunde bei 5 Patienten mit bioptisch gesichertem Osteosarkom beschrieben. Bei allen Patienten fand sich ein ausgedehnter Weichteiltumor mit echogenen osteosklerotischen Bezirken und echoarmen Kavernen. Charakteristisch waren außerdem deutliche Kortikalisdefekte im Bereich des Tumors. Beim Übergang von gesundem zu befallenem Knochen fanden sich typische Periostabhebungen. Farbdopplersonographisch gelang der Nachweis einer deutlich vermehrten Durchblutung des Tumors im Vergleich zu gesundem Gewebe. Sonographie und Farbdopplersonographie stellen eine wichtige Ergänzung zur konventionellen Radiologie dar. Mit der Sonographie können Struktur, Ausdehnung und Durchblutung von Osteosarkomen dargestellt werden.
Das Krankheitsbild und die Behandlung der Toxocara-canis-Uveitis im Kindesalter
Authors: Végh M. , Danka J.
Published: November 2008

Die durch Toxocara canis verursachte Uveitis hat bei Kindern einen schwereren Verlauf als bei Erwachsenen. Mit spezifischen Medikamenten (Mintezol) und Kortikosteroiden kann die Heilung erzielt und können die entzündlichen Herde reduziert werden. Bei Endophthalmitis-Patienten kann auch eine Vitrektomie in Frage kommen. Die Sehschärfeverbesserung hängt von der Lokalisation der Degeneration und von der Dauer der Erkrankung ab. Wir halten die Ultraschalluntersuchung zur Differentialdiagnose für unentbehrlich.