bluuebunny/crossref_metadata_2025 huggingface dataset:
Curvature, causality and completeness in space-times with causally complete spacelike slices
Authors: Galloway Gregory J.
Published: November 2008

Let S be a spacelike slice (defined formally in Section 2) in a space-time M. We will say that S is future causally complete in M if for each p ε J+(S) the closure in S of the set J-(p) ∩ S is compact. Define past causal completeness time-dually. Then S is causally complete if it is both future and past causally complete. A compact spacelike slice is necessarily causally complete, as is any Cauchy surface, but the concept of causal completeness is much broader than either of these two conditions. For example the slices t = const. ≠ 0 in the space-time obtained by removing the origin from Minkowski space are causally complete, although they are neither Cauchy nor compact. The slice t = 0 in the previous example and the hyperboloid in Minkowski space (where (t, x1, …, xn) are standard inertial coordinates) are examples of slices which are not causally complete. Physically speaking, an edgeless slice S is future causally complete if the information from S which reaches a point in the future of S comes from a finite nonsingular region in S. The Maximal Reissner-Nordstrom space-time is a well-known example in which this finiteness condition is not fulfilled by any of its asymptotically flat partial Cauchy surfaces. Indeed for any such partial Cauchy surface S, J-(p) ∩ S is non-compact for any p ε H+(S). However, as has been discussed in the literature (e.g. [17], p. 625 f), it is believed that the Cauchy horizon in this situation is unstable with respect to perturbations of the initial data on S.
Simplicial minors and decompositions of graphs
Authors: Diestel Reinhard
Published: November 2008

The purpose of this paper is to give natural characterizations of the countable graphs that admit tree-decompositions or simplicial tree-decompositions into primes. Tree-decompositions were recently introduced by Robertson and Seymour in their series of papers on graph minors [7]. Simplicial tree-decompositions were first considered by Halin[6], being the most typical kind of ‘simplicial decomposition’ as introduced by Halin[5] in 1964. The problem of determining which infinite graphs admit a simplicial decomposition into primes has stood unresolved since then; a first solution for simplicial tree-decompositions was given in [2].
Improved estimates for continuous data dependence in linear elastodynamics
Authors: Knops R. J. , Payne L. E.
Published: November 2008

In a previous paper [6], the present authors established estimates for the continuous dependence of the solution on various data in the initial boundary value problem of linear elastodynamics on a bounded region of space. The main conclusion concerned continuous dependence on the body-force, but also it was shown how this result could be used to derive continuous dependence on the initial data, elasticities, boundary data and initial geometry. The method adopted was based upon logarithmic convexity arguments and hence led naturally to continuity in the sense of Hölder on compact sub-intervals of time. A special feature of the study entailed the lack of any sign-definiteness conditions on the elasticities which, of course, in the absence of any a priori constraint on the solution always gives rise to an ill-posed problem. (See, for instance, the comprehensive survey by Payne [10].)
Stably continuous frames
Authors: Banaschewski B. , Brummer G. C. L.
Published: November 2008

In the lattice theory that underlies topology, that is, in the study of frames, a class of frames arising naturally is that of the stably continuous frames (see §0 for definitions). On the one hand, they correspond to the most reasonable not necessarily Hausdorff compact spaces, and on the other, they are precisely the retracts of coherent frames. Moreover, an important special case of stably continuous frames are the compact regular frames which correspond to compact Hausdorff spaces.
Locally linear actions on 3-manifolds
Authors: Kwasik SŁawomir , Bai Lee Kyung
Published: November 2008

Let a finite groupGact topologically on a closed smooth manifoldMn. One of the most natural and basic questions is whether such an action can be smoothed. More precisely, let γ:G×Mn→Mnbe a topological action ofGonMn. The action γ can be smoothed if there exists a smooth actionand an equivariant homeomorphismIt is well known that forn≤ 2 every finite topological group action onMnis smoothable. However already forn= 3 there are examples of topological actions on 3-manifolds which cannot be smoothed (see [1, 2] and references there). All these actions fail to be smoothable because of bad local behaviour.
Extracting almost symmetric sequences in rearrangement invariant spaces
Authors: Raynaud Yves
Published: November 2008

We extend to a wider class of rearrangement invariant spaces a result of S. Guerre concerning the extraction of almost symmetric sequences from a given weakly null sequence in Lp.
Global analogues of the Brown–Grossman proper homotopy groups of an end
Authors: Hernandez L. J. , Porter T.
Published: November 2008

The Brown–Grossman proper homotopy groups at an end of a locally compact Hausdorff space,X, were introduced by E. M. Brown in 1974. In this note we define and study ‘global’ versions of these groups and compare these global groups with the groups ‘at infinity’. We also obtain several interlocking exact sequences relating these groups with the Hurewicz and Steenrod homotopy groups ofX.
Triangulating and recognising PL homology manifolds
Authors: Ayala R. , Quintero A. , Mitchell W. J. R.
Published: November 2008

An earlier recognition theorem of one of the authors is extended to the bounded case, and conditions yielding concordance of triangulations are established.
The growth of the expected number of real zeros of a random polynomial with dependent coefficients
Authors: Glendinning Richard
Published: November 2008

We determine the rate of growth of the expected number of real zeros of a class of random polynomials whose coefficients form a stationary uniformly mixing sequence.
Mordell's finite basis theorem revisited
Authors: Cassels J. W. S.
Published: November 2008

0. Mordell proved his ‘Finite Basis Theorem’ in the paper [31] ‘On the rational solutions of the indeterminate equations of the third and fourth degrees’ which appeared in 1922 in Volume 21 of these Proceedings. It had been assumed, rather than conjectured, by Poincaré some 20 years previously, but it was not what he had set out to prove. The theorem and its generalizations are at the heart of many of the most interesting achievements and problems of the theory of numbers and also of algebraic geometry. Mordell himself had virtually no part in these developments: his great work was to lie elsewhere ([5]).
Additivity and superadditivity in Lp-spaces
Authors: Bernau S. J.
Published: November 2008

A simple proof is given that if X is a normed vector lattice, 1 ≼ p ≼ ∞, and the norm in X is p-additive, then the norm is p-superadditive if p < ∞. If p = ∞, then X satisfies Kakutani's classical M-space condition. The proof uses duality but is otherwise elementary.
On the global attractivity in a generalized delay-logistic differential equation
Authors: Gopalsamy K.
Published: November 2008

The purpose of this article is to derive a set of ‘easily verifiable’ sufficient conditions for the local asymptotic stability of the trivial solution of

and then examine the ‘size’ of the domain of attraction of the trivial solution of the nonlinear system (1·1) with a countable number of discrete delays.
Explicit expressions for Sturm sequences
Authors: Godwin H. J.
Published: November 2008

Sturm's theorem was announced in 1829 and various proofs were given soon after (see [2], p. 363 for details). It is given in various textbooks on algebra, e.g. in [1], pp. 448–453, where its application to finding the number and location of the real zeros of a polynomial is explained. It has been applied, in conjunction with Givens's method, to finding the eigenvalues of a matrix (see, e.g. [3], p. 494), and has been used recently in a neat computational form by Takeuchi [4] for investigating algebraic fields.
Random trees in a graph and trees in a random graph
Authors: Janson Svante
Published: November 2008

This paper treats two related sets of problems in the theory of random graphs. In Sections 2 and 3 we study random spanning subtrees of a complete graph (or, equivalently, random labelled trees). It is shown that the number of common edges of two such random trees asymptotically has a Poisson distribution with expectation 2. Similar results are obtained for the number of edges in the intersection or union of more than two random trees.
On the simple object associated to a diagram in a closed model category
Authors: Pascual-Gainza Pere
Published: November 2008

In this paper we develop a descent technique for generalized (co)-homology theories defined in the category of algebraic varieties. By such a theory we mean a functor Sch→C, where C is a closed model category in the sense of Quillen satisfying certain axioms (cf. §4). We have chosen to work in such a general context so as to include two situations for which the results of SGA 4 of Deligne and Saint-Donat are not applicable: descent of multiplicative structures (i.e. of differential graded algebras) and descent for generalized sheaf cohomology (such as the algebraic K-theory of coherent sheaves over a noetherian scheme).
Laws of the iterated logarithm for sums of the middle portion of the sample
Authors: Haeusler Erich , Mason David M.
Published: November 2008

Let X1, X2, …, be a sequence of independent random variables with common distribution function F in the domain of attraction of a stable law and, for each n ≥ 1, let X1, n ≤ … ≤ Xn, n denote the order statistics based on the first n of these random variables. It is shown that sums of the middle portion of the order statistics of the form , where (kn)n ≥ 1 is a sequence of non-negative integers such that kn → ∞ and kn/n → 0 as n → ∞ at an appropriate rate, can be normalized and centred so that the law of the iterated logarithm holds. The method of proof is based on the almost sure properties of weighted uniform empirical processes.
An investigation of countable B-groups
Authors: Cameron P. , Johnson K. W.
Published: November 2008

A group G is defined to be a B-group if any primitive permutation group which contains G as a regular subgroup is doubly transitive. In the case where G is finite the existence of families of B-groups has been established by Burnside, Schur, Wielandt and others and led to the investigation of S-rings. A survey of this work is given in [3], sections 13·7–13·12. In this paper the possibility of the existence of countable B-groups is discussed. Three distinct methods are given to embed a countable group as a regular subgroup of a simply primitive permutation group, and in each case a condition on the square root sets of elements of the group is necessary for the embedding to be carried out. It is easy to demonstrate that this condition is not sufficient, and the general question remains open.
Unitary representations of the mapsS1→ su(N, 1)
Authors: Chari Vyjayanthi , Pressley Andrew
Published: November 2008

For many questions, both in Mathematics and in Physics, the most important representations of a Lie algebraaare those which are unitarizable and highest weight (such representations are automatically irreducible). The classification of such representations whenais a finite-dimensional complex simple Lie algebra was completed only recently (see [3] for details and further references) and the corresponding question when a is an affine algebra was investigated by Jakobsen and Kac [5]. Theorem 3·1 of that paper contains a list of unitarizable highest weight representations which is claimed to be exhaustive. However, we shall show that this list is incomplete by constructing a further family of such representations. In fact, the classification problem in the affine case must be considered to be still open.
Singularities of convex-polygonally generated shape-densities
Authors: Le Hui-Lin
Published: November 2008

In earlier papers Kendall and Le[3,4] made a geometrical study of the structure and singularities of a convex-polygonally generated shape-density for any convex polygon K. The present work describes the singular tessellation T(K) in algebraic terms, and obtains explicit formulae for the ‘jump functions’ of m̃ across every edge of the tessellation. These results, combined with earlier work by Le[5] on the basic tile, make it possible to find m̃ explicitly in every tile by what we have called the ‘stepping-stone’ method. In a closing section the exact order of the differential singularity is found at the tile boundaries.
Absolute Nörlund matrix summability of Fourier series based on inclusion theorems
Authors: Kuttner B. , Rhoades B. E.
Published: November 2008

In a recent paper [39] the second author established sufficient conditions for a Nörlund matrix (N, p) to be stronger than a Cesaro matrix (C, α) of order α, for some positive α. This result was then used to show that a number of known theorems dealing with the Nörlund summability of Fourier series, or related series, can be more easily established, since the conditions placed on the Nörlund matrix imply that it is stronger than some (C, α) method, for which the summability theorem has already been established.
Multivariate Landau–Kolmogorov-type inequality
Authors: Ditzian Z.
Published: November 2008

Assuming that the nth iterate of the Laplacian Δnf belongs to L∞(ℝ), we show for 0 < k < 2n that

where ∂/∂ξi is the derivative in the ei direction. The result is also extended to other Banach spaces of functions on ℝd.
A weighted version of the Paley–Wiener theorem
Authors: Genchev T. G.
Published: November 2008

A generalization of the classical theorems of Paley and Wiener[5] and Plancherel and Polya[6] concerning entire functions of exponential type is obtained. The proof relies only on the Cauchy theorem and the Hardy–Littlewood inequality for the Fourier transform (see [8, 9]). Since the functions under consideration are supposed to be defined only in two opposite octants in ℂn, a version of the edge of the wedge theorem [7] is derived as a by-product.
Subgroups like Wielandt's in finite soluble groups
Authors: Bryce R. A.
Published: November 2008

In 1935 Baer[1] introduced the concept of kern of a group as the subgroup of elements normalizing every subgroup of the group. It is of interest from three points of view: that of its structure, the nature of its embedding in the group, and the influence of its internal structure on that of the whole group. The kern is a Dedekind group because all its subgroups are normal. Its structure is therefore known exactly (Dedekind [7]): if not abelian it is a direct product of a copy of the quaternion group of order 8 and an abelian periodic group with no elements of order 4. As for the embedding of the kern, Schenkman[13] shows that it is always in the second centre of the group: see also Cooper [5], theorem 6·5·1. As an example of the influence of the structure of the kern on its parent group we cite Baer's result from [2], p. 246: among 2-groups, only Hamiltonian groups (i.e. non-abelian Dedekind groups) have nonabelian kern.
The Morava K-theories of wreath products
Authors: Hunton John
Published: November 2008

In p-primary stable homotopy theory, recent developments have shown the importance of the Morava K-theory spectra K(n) for positive integers n. A current major problem concerns the behaviour of the K(n)-cohomologies on the classifying spaces of finite groups and on related spaces. In this paper we show how to compute the Morava K-theory of extended power constructions Here Xp is the p-fold product of some space X and Cp is the cyclic group of order p. In particular, if we take X as the classifying space BG for some group G, then Dp(X) forms the classifying space for , the wreath product of G by Cp.
Topological conjugation of Lorenz maps by β-transformations
Authors: Glendinning Paul
Published: November 2008

Necessary and sufficient conditions for a Lorenz map to be topologically conjugate to a piecewise linear map with constant slope (a β-transformation) are given, first in terms of kneading invariants of the maps and then in terms of the topological entropy restricted to basic sets. The dynamics of β-transformations is also described.
The natural ordering on a strictly real Banach algebra
Authors: Miller John Boris
Published: November 2008

A strictly real unital Banach algebra is one in which every element has real spectrum. An antilattice partial order and its associated open-interval topology are defined on by taking as positive cone the principal component of the maximal group of the algebra, and their properties are studied. The topology coincides with the semimetric topology of the spectral radius, which is a seminorm, making into a locally convex partially ordered topological algebra with continuous inversion and normal cone. Every positive element has a unique positive square root, and logarithm, and these functions and exp are continuous and monotone. The cone has the same closure in both open-interval and normal topologies, the closure being a wedge for an associated preorder on , this preorder coinciding with the preorder of Kelley and Vaught. The partial order and the associated preorder have the same dual cone. There is a modified Gelfand representation for (possibly non-commutative) , and a boundary integral representation for functionals in the order dual. The compact convex subset in the dual is metrizable if the cone of the partial order in is separable.
Lifting amalgams and other colimits of monoids
Authors: Heath Philip R.
Published: November 2008

Let U = [{Mi: i ∈ I}; U; {øi: i ∈ I}] be a monoid amalgam of inclusions, i.e. U and each Mi is a monoid, and øi: U → Mi are inclusions. Let be the monoid free product of the amalgam U (see for example [10] for these concepts), and let β: B → H be a homomorphism of monoids. The type of question we seek to answer in this paper is under what conditions (on β, B and H) can we deduce that B is isomorphic to the free product of the amalgam
Samuel compactification and completion of uniform frames
Authors: Banaschewski B. , Pultr A.
Published: November 2008

The aim of this paper is twofold: first, to construct the compact regular coreflection of uniform frames, that is, the frame counterpart of the Samuel compactification of uniform spaces (Samuel [10]), and then to use this for a new description of the completion of a uniform frame, as an alternative to those previously given by Isbell [6] on the one hand and Kříž [8] on the other. In addition, we present a few further results, as well as new proofs of known ones, that are naturally connected with completions and arise particularly easily from our approach to them. Most prominently among these, we identify the uniform space of minimal Cauchy filters of a uniform frame as the spectrum of its completion.
The Hausdorff dimension of certain sets of singular n-tuples
Authors: Rynne Bryan P.
Published: November 2008

In the paper [3] we obtained a lower bound for the Hausdorff dimension of certain sets of singular n-tuples in ℝn. In this paper we will obtain an upper bound for the dimension of these sets. These two bounds are not sharp enough to yield the exact dimension of all the sets considered but they do yield the dimension of the set of ‘highly singular’ (in a sense to be made precise below) n-tuples.
Annihilators in JB-algebras
Authors: Battaglia M.
Published: November 2008

Orthogonality is defined for all elements in a JB-algebra and Topping's results on annihilators in JW-algebras are generalized to the context of JB- and JBW-algebras. A pair (a, b) of elements in a JB-algebra A is said to be orthogonal provided that a2 ∘ b equals zero. It is shown that this relation is symmetric. The annihilator S⊥ of a subset S of A is defined to be the set of elements a in A such that, for all elements s in S, the pair (s, a) is orthogonal. It is shown that the annihilators are closed quadratic ideals and, if A is a JBW-algebra, a subset I of A is a w*-closed quadratic ideal if and only if I coincides with its biannihilator I⊥⊥. Moreover, in a JBW-algebra A the formation of the annihilator of a w*-closed quadratic ideal is an orthocomplementation on the complete lattice of w*-closed quadratic ideals which makes it into a complete orthomodular lattice. Further results establish a connection between ideals, central idempotents and annihilators in JBW-algebras.
Weak precompactness, strong boundedness, and weak complete continuity
Authors: Abbott Catherine A. , Bator Elizabeth M. , Bilyeu Russell G. , Lewis Paul W.
Published: November 2008

Weak precompactness in spaces of vector measures and in the space of Bochner integrable functions is studied. Uniform countable additivity and uniform integrability are characterized in terms of weak precompactness. Through this, a connection between strongly bounded operators and operators having weakly precompact adjoints on abstract continuous function spaces is established. These operators are compared with weakly completely continuous operators.
Entropy, character theory and centrality of finite quasigroups
Authors: Smith Jonathan D. H.
Published: November 2008

The paper introduces concepts of entropy and asymptotic entropy for finite quasigroups. A quasigroup is abelian if and only if its entropy is maximal. It is a З-quasigroup if and only if its asymptotic entropy is maximal.
A calculus for rational tangles: applications to DNA recombination
Authors: Ernst C. , Sumners D. W.
Published: November 2008

There exist naturally occurring enzymes (topoisomerases and recombinases), which, in order to mediate the vital life processes of replication, transcription, and recombination, manipulate cellular DNA in topologically interesting and non-trivial ways [24, 30]. These enzyme actions include promoting the coiling up (supercoiling) of DNA molecules, passing one strand of DNA through another via a transient enzyme-bridged break in one of the strands (a move performed by topoisomerase), and breaking a pair of strands and recombining them to different ends (a move performed by recombinase). An interesting development for topology has been the emergence of a new experimental protocol, the topological approach to enzymology [30], which directly exploits knot theory in an effort to understand enzyme action. In this protocol, one reacts artificial circular DNA substrate with purified enzyme in vitro (in the laboratory); the enzyme acts on the circular DNA, causing changes in both the euclidean geometry (supercoiling) of the molecules and in the topology (knotting and linking) of the molecules. These enzyme-caused changes are experimental observables, using gel electrophoresis to fractionate the reaction products, and rec A enhanced electron microscopy [15] to visualize directly and to determine unambiguously the DNA knots and links which result as products of an enzyme reaction. This experimental technique calls for the building of knot-theoretic models for enzyme action, in which one wishes mathematically to extract information about enzyme mechanism from the observed changes in the DNA molecules.
Short intervals containing numbers without large prime factors
Authors: Harman Glyn
Published: November 2008

We denote, as usual, the number of integers not exceeding x having no prime factors greater than y by Ψ(x, y). We also write

The function Ψ(x, y) is of great interest in number theory and has been studied by many researchers (see [3], [5] and [6] for example). The function Ψ(x, z, y) has also received some attention (see [2], [4–6]). In this paper we shall try to obtain a positive lower bound for Ψ(x, z, y) with y as small as possible when z is about x½ in magnitude. We note that the approach in [5] and [6] allows y to be much smaller than is permissible here, but requires x/z to be smaller than any power of x in [6] (unless some conjecture like the Riemann Hypothesis is assumed), or needs in [5]. The following result was obtained by Balog[1].
On the reciprocal Dunford-Pettis property in projective tensor products
Authors: Emmanuele G.
Published: November 2008

We prove the following result: if a Banach space E does not contain l1 and F has the (RDPP), then E ⊗nF has the same property, provided that L(E, F*) = K(E, F*). Hence we prove that if E ⊗n F has the (RDPP) then at least one of the spaces E and F must not contain l1. Some corollaries are then presented as well as results concerning the necessity of the hypothesis L(E, F*) = K(E, F*).
An identity theorem for multi-relator groups
Authors: Bogley William A.
Published: November 2008

In this paper, the Identity Theorem of R. C. Lyndon and the Freiheitssatz of W. Magnus are extended to a large class of multi-relator groups. Included are the two-relator groups introduced by I. L. Anshel in her thesis, where the Freiheitssatz was proved for those groups. The Identity Theorem provides cohomology computations and a classification of finite subgroups. The methods are geometric; technical tools include the original theorems of Magnus and Lyndon, as well as an amalgamation technique due to J. H. C. Whitehead.
Is every quartic a conic of conics?
Authors: Wall C. T. C.
Published: November 2008

The question of the title is to be interpreted as follows. Given a homogeneous nonzero quartic polynomial ø(x1, x2, x3), can one always find homogeneous quadraticsc, q1, q2, q3in three variables such that

I am indebted to Ulf Persson for asking this question, the answer to which is intimately related to the singularities of the projective quartic curve Γ defined by ø = 0. We work throughout over the field ℂ of complex numbers.
Weighted homogeneous maps from the plane to the plane
Authors: Gaffney T. , Mond D. M. Q.
Published: November 2008

An analytic map-germf:(ℂn, 0)→(ℂp, 0) is said to be quasi-homogeneous, or weighted homogeneous, if there are positive integersw1, …,wn, theweights, and positive integersd1, …,dp, thedegrees, such that for each monomialappearing in the Taylor expansion of theith componentfioff, we have
Analytic functions with values in lattices and symmetric spaces of measurable operators
Authors: Xu Quanhua
Published: November 2008

Let 0 < p,pi ≤ ∞, 0 < q,qi < ∞ (i = 1, 2) such that

Let E be a quasi-Banach lattice which fails to contain c0 and whose α-convexity constant is equal to 1 for some 0 < α < ∞. Then for every f∈H(E(q)) there exist g∈Hp, 0(E(q0)), h∈Hp1(E(q1)) such that

Consequently, E is q-concave for some finite q if and only if E is uniformly H1-convexifiable in the sense of [24]. Analogous results are also obtained for symmetric spaces of measurable operators. Another result proved in the paper says that if E is a symmetric quasi-Banach function space on (0, ∞) having the analytic Radon–Nikodym property then LE(M, τ) also possesses this property for any semifinite von Neumann algebra (M, τ).
Covering a sphere by equal circles, and the rigidity of its graph
Authors: Tarnai T. , Gáspár Zs.
Published: November 2008

How must a sphere be covered by n equal circles so that the angular radius of the circles will be as small as possible? In this paper, conjectured solutions of this problem for n = 15 to 20 are given and some sporadic results for n > 20 (n = 22, 26, 38, 42, 50) are presented. The local optima are obtained by using a ‘cooling technique’ based on the theory of bar-and-joint structures. Thus the graph of the coverings by circles is considered as a spherical cable net in which the edge lengths are uniformly decreased, e.g. due to a uniform decrease in the temperature, until the graph becomes rigid and tensile stresses appear in the cables.
Dimensions associated with recurrent self-similar sets
Authors: Deliu Anca , Geronimo J. S. , Shonkwiler R. , Hardin D.
Published: November 2008

The Hausdorff and box dimensions for measures associated with recurrent self-similar sets generated by similitudes is explicitly given. The box dimension of the attractor associated with a class of two-dimensional affine maps is also computed.
Elliptic ruled surfaces on Calabi–Yau threefolds
Authors: Wilson P. M. H.
Published: November 2008

In [5], we studied the behaviour of the Kähler cone of Calabi–Yau threefolds under deformations. We saw that the Kähler cone is locally constant in a smooth family of Calabi–Yau threefolds, unless some of the threefolds Xb contain elliptic ruled surfaces. Moreover, if X is a Calabi–Yau threefold containing an elliptic ruled surface, then the Kähler cone is not invariant under a generic small deformation.
Invariance groups and convergence of types of measures on Lie groups
Authors: Dani S. G.
Published: November 2008

Let G be a connected Lie group and let {λi} be a sequence of probability measures on G converging (in the usual weak topology) to a probability measure λ. Suppose that {αi} is a sequence of affine automorphisms of G such that the sequence {αi,(λi)} also converges, say to a probability measure μ. What does this imply about the sequence {αi}? It is a classical observation that if G = ℝn for some n, and neither of λ and μ is supported on a proper affine subspace of ℝn, then under the above condition, {αi} is relatively compact in the group of all affine automorphisms of ℝn.
Strong convergence of Kleinian groups and Carathéodory convergence of domains of discontinuity
Authors: Ohshika Ken'ichi
Published: November 2008

In the theory of Kleinian groups, important examples of Kleinian groups are frequently constructed as algebraic limits of known sequences of Kleinian groups, for example quasi-conformal deformations of a Kleinian group. It is an important problem to determine the properties of the limit Kleinian group from information on the sequence converging to the limit. The topological properties of the domain of discontinuity and the limit set of a Kleinian group provide valuable pieces of information about the Kleinian group. It is reasonable to expect that in a good situation, the domain of discontinuity of the limit Kleinian group is the Carathéodory limit of the domains of discontinuity of the sequence, or, equivalently, the limit set of the limit Kleinian group is the Hausdorif limit of the limit sets of the sequence. Our main theorem (Theorem 5) shows that this is true when the sequence strongly converges to the limit, and the Kleinian groups of the sequence and the limit preserve the parabolicity in both directions and satisfy the condition (*) introduced by Bonahon.
On L1-kernels of unitary representations of semisimple Lie groups
Authors: Bekka Mohammed E. B. , Ludwig Jean
Published: November 2008

Let G be a locally compact group with fixed left Haar measure dx. Recall that G is said to be amenable if there exists a left translation invariant mean on the space L∞(G), i.e. if there exists a positive, linear functional M on L∞(G) such that M(lG) = 1 and M(xø) = Mø for all ø∈L∞(G), x∈G, where xø denotes the left translate xø(y) = ø(xy). The class of amenable groups includes all soluble and all compact groups (concerning the theory of amenable groups we refer to [9]). It is easy to see that G is amenable if and only if ℂ1G, the space of the constant functions on G, has a closed left translationinvariant complement in L∞(G). This reformulation of amenability leads to the following more general question.
The determination of convex bodies from the mean of random sections
Authors: Goodey Paul , Weil Wolfgang
Published: November 2008

Random sectioning of particles (compact sets in ℝ3with interior points) is a familiar procedure in stereology where it is used to estimate particle quantities like volume or surface area from planar or linear sections (see, for example, the survey [23] or the book [20]). In the following, we study the problem whether the whole shape of a convex particleKcan be estimated from random sections. IfEis an IUR (isotropic, uniform, random) line or plane intersectingKthen the intersection Xk=K∩Eis a (k-dimensional,k= 1 or 2) random set. It is clear that the distribution ofXkdeterminesKuniquely and that ifE1,…, Enare such flats, the most natural estimator forKwould be the convex hull
Asymptotic distributions of weighted compound Poisson bridges
Authors: Szyszkowicz Barbara
Published: November 2008

Let S(N(t)) be defined by

where {N(t), t ≥ 0} is a Poisson process with intensity parameter 1/μ > 0 and {Xi i ≥ 1} is a family of independent random variables which are also independent of {N(t), t ≥ 0}.
Some results of Lindelöf type involving the segmental behaviour of holomorphic functions
Authors: Bravo Francisca , Girela Daniel
Published: November 2008

A classical theorem of Lindelöf asserts that if ƒ is a function analytic and bounded in the unit disc δ which has the asymptotic value L at a point ξ ε ∂ δ then it has the non-tangential limit L at ξ. This result does not remain true for functions f analytic in δ whose maximum modulus grows to infinity arbitrarily slowly. However, the second author has recently obtained some results of Lindelöf type valid for these functions. In this paper we obtain new results of this kind. We prove that if f is an analytic function of slow growth in δ and ξ ε ∂ δ, then certain restrictions on the growth of ƒ′ along a segment which ends at ξ do imply that ƒ has a non-tangential limit at ξ.
Skeins and mapping class groups
Authors: Roberts Justin
Published: November 2008

The protective unitary representations of the mapping class groups of surfaces corresponding to the Jones–Witten topological quantum field theory for SU(2) are expressed as representations in algebras of skeins in the surface. The skein-theoretic construction of the representations uses neither Kirby's surgery theorem nor a presentation of the group. Using these representations and the Reidemeister–Singer classification of Heegaard splittings gives a proof of the existence of the moduli of the Witten invariants of 3-manifolds.
Links of prime ideals
Authors: Corso Alberto , Polini Claudia , Vasconcelos Wolmer V.
Published: November 2008

Roughly speaking, a link of an ideal of a Noetherian ring R is an ideal of the form I = (z): , where z = z1, …, zg is a regular sequence and g is the codimension of . This is a very common operation in commutative algebra, particularly in duality theory, and plays an important role in current methods to effect primary decomposition of polynomial ideals (see [2]).
Fractal properties of products and projections of measures in ℝd
Authors: Hu Xiaoyu , Taylor S. James
Published: November 2008

Borel measures in ℝd are called fractal if locally at a.e. point their Hausdorff and packing dimensions are identical. It is shown that the product of two fractal measures is fractal and almost all projections of a fractal measure into a lower dimensional subspace are fractal. The results rely on corresponding properties of Borel subsets of ℝd which we summarize and develop.
Triple points of unknotting discs and the Arf invariant of knots
Authors: Fiedler Thomas
Published: November 2008

An unknotting disc is the ‘trace’ in ℝ4of a homotopy of a diagram of a knot in ℝ3, which shrinks the diagram to a point. In this paper we study unknotting discs which have as singularities only ordinary triple points. It turns out that the Arf invariant of the knot is determined by the number of triple points in which all three branches of the disc intersect pairwise with the same index. We call such a triple pointcoherent. This interpretation of the Arf invariant has a surprising consequence:

LetS⊂ ℝ4be a taut immersed sphere which has as singularities only ordinary triple points. Then the number of coherent triple points inSis even. For example, it is easy to show that there is a taut immersed sphereSwith Euler number six of the normal bundle and which has exactly three ordinary double points and no other singularities. So, our result implies that the three double points ofScan not be pushed together to create an ordinary triple point without the appearance of new singularities.

Here ‘taut’ means that the restriction of one of the coordinate functions onShas exactly two (non-degenerate) critical points, i.e. is a perfect Morse function.
The L2--problem on manifolds with piecewise strictly pseudoconvex boundaries
Authors: Darko Patrick W.
Published: November 2008

Ever since the solution of the -Neumann problem by Kohn [4], refinements, extensions and estimates of the solution have been made by a lot of people up to the present day. Kohn discovered that, where the -Neumann problem was solvable, the space of harmonic forms is finite dimensional and it followed from Hörmander's solution [3] that on bounded pseudoconvex domains in ℂn the appropriate spaces of harmonic forms are zero dimensional.
A construction of a compact right topological semigroup
Authors: El-Mabhouh Ahmed
Published: November 2008

It is well-known that the structure of βℕ, the Stone—Čech compactification of the discrete semigroup (ℕ, +), is very complex. For example, it has 2c minimal left ideals and 2c minimal right ideals, its minimal ideal contains 2c copies of the free group on 2c generators, see [5], and Lisan[8] proved the existence of 2c copies of the same group outside the closure of the minimal ideal.
Holonomies of Yang–Mills connections for bundles on a surface with disconnected structure group
Authors: Huebschmann Johannes
Published: November 2008

Let Σ be a closed surface of genus ≥ 1, G a compact Lie group, not necessarily connected with Lie algebra g, ξ,: P → Σ a principal G-bundle, and suppose Σ equipped with a Riemannian metric and g with an invariant scalar product so that the Yang—Mills equations on ξ are defined. Further, let

be the universal central extension of the fundamental group π of Σ and ΓR the group obtained from Γ when its centre Z is extended to the additive group R of the reals. We show that there are bijective correspondences between various spaces of classes of Yang—Mills connections on ξ and spaces of representations of Γ and ΓR (as appropriate) in G. In particular, we show that the holonomy establishes a homeomorphism between the moduli space N(ξ) of central Yang–Mills connections on ξ and the space Repξ(Γ, G) of representations of Γ in G determined by ξ. Our results rely on a detailed study of the holonomy of a central Yang–Mills connection and extend corresponding ones of Atiyah and Bott for the case where G is connected.
Bounded geodesics and Hausdorff dimension
Authors: Aravinda C. S.
Published: November 2008

Let M be a Riemannian manifold of constant negative curvature and finite Riemannian volume. It is well-known that the geodesic flow on the unit tangent bundle SM of M is ergodic. In particular, it follows that for almost all (p, v)∈ SM, where p ∈M and v is a unit tangent vector at p, the geodesic through p in the direction of v is dense in M. A theorem of Dani [Dl] says that the set of all (p, v)∈SM for which the corresponding geodesic is bounded (namely those with compact closure in M) is ‘large’ in the sense that its Hausdorff dimension is equal to that of the unit tangent bundle itself. In fact, Dani generalized this result to a more general algebraic situation (cf. [D2]).
Links with alternating diagrams on closed surfaces of positive genus
Authors: Hayashi Chuichiro
Published: November 2008

We consider links in an orientable 3-manifold M which have an alternating diagram on a closed orientable surface F of positive genus. We see that if the diagram is ‘complex’ enough and if F gives a Heegaard splitting of M, then such a link L is prime and M—L does not contain an essential torus.
On arithmetic progressions of equal lengths with equal products
Authors: Saradha N. , Shorey T. N. , Tijdeman R.
Published: November 2008

It is shown that apart from

there are only finitely many arithmetic progressions with given differences of equal lengths ≥ 2 and with equal products and that they can be effectively determined.
A generalization of the Liouville–Arnol'd theorem
Authors: Prince G. E. , Byrnes G. B. , Sherring J. , Godfrey S. E.
Published: November 2008

We show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the evolution space ℝ × TM of a manifold M. Both the original theorem and its generalization rely on a certain bijection between symmetries of the system and its first integrals. We give two examples of the use of the theorem for systems on ℝ2 which are not Euler-Lagrange.
On the average number of divisors of quadratic polynomials
Authors: Mckee James
Published: November 2008

Let d(n) denote the number of positive divisors of n, and let f(x) be a polynomial in x with integer coefficients, irreducible over ℤ. Erdös[3] showed that there exist constants λ1, λ2 (depending on f) such that
Discrete subadditive functions as Gomory functions
Authors: Rhodes Frank , Williams H. Paul
Published: November 2008

Our aim, in this paper, is to study a class of functions which occurs in pure integer programming, and to investigate conditions under which discrete subadditive functions belong to that class. The inspiration for the paper was the problem of classifying discrete metrics used in pattern recognition, while the methods of proof of the main theorem are those of pure integer programming.
Normality for elementary subgroup functors
Authors: Bak Anthony , Vavilov Nikolai
Published: November 2008

We define a notion of group functor G on categories of graded modules, which unifies previous concepts of a group functor G possessing a notion of elementary subfunctor E. We show under a general condition which is easily checked in practice that the elementary subgroup E(M) of G(M) is normal for all quasi-weak Noetherian objects M in the source category of G. This result includes all previous ones on Chevalley and classical groups G of rank ≥ 2 over a commutative or module finite ring M (since such rings are quasi-weak Noetherian) and settles positively unanswered cases of normality for these group functors.
Oriented bordism groups of immersions
Authors: Li Gui-Song
Published: November 2008

Let IΩn, k denote the bordism group of immersions of closed oriented n-manifolds into (n + k)-space. The object of this paper is to study certain group extension problems arising from Pastor's calculations of IΩn, k.

The bordism group of immersions was first studied by Wells [12] who calculated the unoriented bordism group I Rn, k for k = n and k = n − 1 ≡ 3(4). Later these unoriented bordism groups were completely determined by Koschorke and Olk for k ≥ n − 2 with the help of an exact sequence measuring the difference between IRn, k and Rn (see [4]). A similar program has been carried out by Pastor [7] to determine the oriented bordism group I Ωn, k for k ≥ n − 2 except for certain group extension problems and some low dimensional cases.
The distribution of the values of an entire function whose coefficients are independent random variables (II)
Authors: Offord A. C.
Published: November 2008

This is a study of entire functions whose coefficients are independent random variables. When the space of such functions is symmetric it is shown that independence of the coefficients alone is sufficient to ensure that almost all such functions will, for large z, be large except in certain small neighbourhoods of the zeros called pits. In each pit the function takes every not too large value and these pits have a certain uniform distribution.
Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type
Authors: Majid Shahn , Markl Martin
Published: November 2008

We introduce an associative glueing operation ⊕q on the space of solutions of the Quantum Yang–Baxter Equations of Hecke type. The corresponding glueing operations for the associated quantum groups and quantum vector spaces are also found. The former involves 2×2 quantum matrices whose entries are themselves square or rectangular quantum matrices. The corresponding glueing operation for link-invariants is introduced and involves a state-sum model with Boltzmann weights determined by the link invariants to be glued. The standard su(n) solution, its associated quantum matrix group, quantum space and link-invariant arise at once by repeated glueing of the one-dimensional case.
Truncated symmetric powers and modular representations of GLn
Authors: Doty Stephen , Walker Grant
Published: November 2008

Several results are obtained relating to the modular representation theory of the general linear group GLn in the defining characteristic p > 0. In Section 1, embeddings of certain simple modules in symmetric powers of the natural module, or in tensor products of truncated symmetric powers, are constructed. In Section 2, cases are found where simple quotientsof Schur modules H0(λ) can be constructed by extending theidea of truncation to these modules in a natural way. In Section 3, the characters of those simple modules which can be constructed as twisted tensor products of truncated symmetric powers are expressed in terms of Schur functions.
Compactifications and A-compactifications of frames. Proximal frames
Authors: Dimov Georgi D. , Tironi Gino
Published: November 2008

The aim of this paper is to give two new descriptions of the ordered set of all (up to equivalence) regular compactifications of a completely regular frame. F and to introduce and study the notion of A-frame as a generalization of the notion of Alexandroff space (known also as zero-set space) (Alexandroff[l], Gordon[15]). A description of the ordered set of all (up to equivalence) A-compactifications of an A-frame by means of an ordered by inclusion set of some distributive lattices (called AP-sublattices) is obtained. It implies that any A-frame has a greatest A-compactification and leads to the descriptions of A new category isomorphic to the category of proximal frames is introduced. A question for compactifications of frames analogous to the R. Chandler's question [8, p. 71] for compactifications of spaces is formulated and solved. Many results of [1], [3], [15], [23], [9], [10] and [11] are generalized.
Attaching cells to finite complexes, with an application to elliptic spaces
Authors: Powell Geoffrey M. L.
Published: November 2008

Suppose that f; Sn → E is a continuous map from the n-sphere to a 1-connected CW complex E, with n ≥ 2. One may suppose that f is a cofibration, so that there is a cofibration sequence , with f the attaching map of the cell en+1. Consider the homotopy fibre F of the inclusion E ↪ B, so that there is a homotopy fibration let δ; ΩB → F be the connectant of this fibration. The following definition is given by Félix and Lemaire in [11]:
Definition 1·1. Suppose that k is a field of characteristic p ≥ 0. The attaching map f:Sn → E is:
1. p-inert if is surjective;
2. p-lazy if is zero;
where H˜ denotes reduced homology and coefficients are taken in the field k.
Fundamental groups of 4-manifolds with circle actions
Authors: Kwasik Sławomir , Schultz Reinhard
Published: November 2008

Topological circle actions on 4-manifolds are studied using modifications of known techniques for smooth actions. This yields topological versions of some previously known restrictions on the fundamental groups of 4-manifolds admitting smooth circle actions.
Harmonic typically real mappings
Authors: Bshouty D. , Hengartner W. , Hossian O.
Published: November 2008

We give an example of a univalent orientation-preserving harmonic mapping f = h + g¯ defined on the unit disc U which is real on the real axis, satisfies and is not typically real. Furthermore, we give a geometric characterization for univalent, harmonic and typically real mappings.
Positivity of more Jacobi polynomial sums
Authors: Brown Gavin , Koumandos Stamatis , Wang Kun-Yang
Published: November 2008

Our main result can be stated as follows:

Theorem.

for all λ ≥ λ0, where λ0 is the unique root in (0, 1) of the equation

andis the Gegenbauer polynomial of degree 2k and order λ. The only cases of equality in (1·1) are when θ = 0 and n is odd.