bluuebunny/crossref_metadata_2025_split huggingface dataset:
Characterization of some classes of operators on spaces of vector-valued continuous functions
Authors: Bombal Fernando , Cembranos Pilar 
Published: November 2008

LetKbe a compact Hausdorff space andE, FBanach spaces. We denote byC(K, E)the Banach space of all continuous.E-valued functions defined onK,with the supremum norm. It is well known ([6], [7]) that every operator (= bounded linear operator)TfromC(K, E)toFhas a finitely additive representing measuremof bounded semi-variation, defined on the Borel σ-field Σ ofKand with values inL(E, F″)(the space of all operators fromEinto the second dual ofF),in such a way thatwhere the integral is considered in Dinculeanu's sense.
The group of the countable universal graph
Authors: Truss J. K. 
Published: November 2008

Let C be a set with at least two, and at most ℵ0, members, and for any set X let [X]2 denote the set of its 2-element subsets. If Γ is a countable set, and Fc is a function from [Γ]2 into C, then the structure Γc = (Γ, Fc) is called the countable universal C-coloured graph if the following condition is satisfied:Whenever α is a map from a finite subset of Γ into C there is xεΓ–dom α such that (∀yεdom α) Fc {x, y} = α(y).
Immersions in bordism classes
Authors: Szücs András 
Published: November 2008

1·1. The aim of the present paper is to prove the followingTheorem. Let Vi and Mn be closed smooth manifolds and i < n. Let f: Vi → Mn be a generic smooth map such that all of its singular points are of the type Σ;1, 0. (See [2].) Then there exists a non-zero integer N such that the bordism class N·[f]εΩi(Mn) contains an immersion.
The Hausdorff dimension of self-affine fractals
Authors: Falconer K. J. 
Published: November 2008

AbstractIf T is a linear transformation on ℝn with singular values α1 ≥ α2 ≥ … ≥ αn, the singular value function øs is defined by where m is the smallest integer greater than or equal to s. Let T1, …, Tk be contractive linear transformations on ℝn. Let where the sum is over all finite sequences (i1, …, ir) with 1 ≤ ij ≤ k. Then for almost all (a1, …, ak) ∈ ℝnk, the unique non-empty compact set F satisfying has Hausdorff dimension min{d, n}. Moreover the ‘box counting’ dimension of F is almost surely equal to this number.
Harmonic measure on 3-dimensional Brownian paths
Authors: Burdzy Krzysztof 
Published: November 2008

AbstractIt is well known that the trace X([0, ∞) of the 3-dimensional Brownian motion X has positive capacity and, therefore, the harmonic measure is well defined on this set. It is shown that a.s., this harmonic measure is singular with respect to the occupation measure Lebesgue ο X−1.
Arithmetic-geometric means of positive matrices
Authors: Cohen Joel E. , Nussbaum Roger D. 
Published: November 2008

AbstractWe prove the existence of unique limits and establish inequalities for matrix generalizations of the arithmetic–geometric mean of Lagrange and Gauss. For example, for a matrix A = (aij) with positive elements aij, define (contrary to custom) A½ elementwise by [A½]ij = (aij)½. Let A(0) and B(0) be d × d matrices (1 < d < ∞) with all elements positive real numbers. Let A(n + 1) = (A(n) + B(n))/2 and B(n + 1 ) = (d−1A(n)B(n))½. Then all elements of A(n) and B(n) approach a common positive limit L. When A(0) and B(0) are both row-stochastic or both column-stochastic, dL is less than or equal to the arithmetic average of the spectral radii of A(0) and B(0).
Sobrification and bicompletion of totally bounded quasi-uniform spaces
Authors: Künzi H. P. A. , Brümmer G. C. L. 
Published: November 2008

AbstractWe observe that if is a compatible totally bounded quasi-uniformity on a T0-space (X,), then the bicompletion of (X, ) is a strongly sober, locally quasicompact space. It follows that the b-closure S of (X, ) in is homeomorphic to the sobrification of the space (X, ). We prove that S is equal to if and only if (X, ) is a core-compact space in which every ultrafilter has an irreducible convergence set and is the coarsest quasi-uniformity compatible with . If is the Pervin quasi-uniformity on X, then S is equal to if and only if X is hereditarily quasicompact, or equivalently, is the Pervin quasi-uniformity on .
The Andersen-Jessen theorem revisited
Authors: Schmidt Klaus D. 
Published: November 2008

AbstractFor stochastic processes which are induced by a signed measure, the Andersen-Jessen theorem asserts almost sure convergence and yields the identification of the limit. This result has been extended to real and vector-valued stochastic processes which are induced by a finitely additive set function or a set function process. In the present paper, we study the structure of such induced stochastic processes in order to locate the Andersen-Jessen theorem and its extensions in the family of convergence theorems for martingales and their generalizations. As an application of these results, we also show that the Andersen-Jessen theorem and its extensions can be deduced from the convergence theorems for conditional expectations and positive supermartingales.
RUC-systems and Besselian systems in Banach spaces
Authors: Garling D. J. H. , Tomczak-Jaegermann N. 
Published: November 2008

Let (rj) be a Rademacher sequence of random variables – that is, a sequence of independent random variables, with , for each j. A biorthogonal system in a Banach space X is called an RUC-system[l] if for every x in [ej] (the closed linear span of the vectors ej), the seriesconverges for almost every ω. A basis which, together with its coefficient functionals, forms an RUC-system is called an RUC-basis. A biorthogonal system is an RLTC-svstem if and only if there exists 1 ≤ K < ∞ such thatfor each x in [ej]: the RUC-constant of the system is the smallest constant K satisfying (1) (see [1], proposition 1.1).
On (q + t)-arcs of type (0, 2, t) in a desarguesian plane of order q
Authors: Korchmáros Gábor , Mazzocca Francesco 
Published: November 2008

This paper is concerned with certain point-sets T in a projective plane PG (2, q) over GF (q) which have only three characters with respect to the lines. We assume throughout this paper that for any line l of πwhere It is easily seen that if t = 1 then T is a (q + 1)-arc, i.e. an oval; otherwise T is a (q+t, t)-arc of type (0, 2, t). Therefore (q+t, t)-arcs of type (0, 2, t) appear to be a generalization of ovals and there are interesting connections between ovals and (q + t, t)-arcs of type (0, 2, t) from various points of view. Our purpose is to investigate such particular (k, t)-arcs using some ideas of B. Segre developed for ovals in three fundamental papers [16, 17, 18]. For these papers and more recent results in this direction the reader is referred to [6], chapter 10 and [9]. General results concerning (k, n)-arcs may be found in [6], chapter 12; see also [4, 7, 20, 23].
Convolution estimates related to surfaces of half the ambient dimension
Authors: Drury S. W. , Guo Kanghui 
Published: November 2008

Let ƒ be a smooth function of compact support defined in the plane and consider the integralThe estimateis well-known, see for instance the work of Littman[4]. The operator T amounts to convolution with the measure σ carried by the parabola t → (t, ½t2) and given by dσ = dt. Usually one proves (1) by embedding σ in an analytic family of distributions σz in ℝ2 given by
Products of idempotent integer matrices
Authors: Fountain John 
Published: November 2008

AbstractLet E denote the set of non-identity idempotent matrices in the full matrix ring Mn(R) over a principal ideal domain R. A necessary and sufficient condition is found for the subsemigroup generated by E to be the set of all matrices in Mn(R) of rank less than n. The condition is satisfied when R is a discrete valuation ring and when R is the ring of integers. Thus every n × n matrix of rank less than n is a product of idempotent integer matrices.
Pseudo-Anosov homeomorphisms on a sphere with four punctures have all periods
Authors: Llibre Jaume , Mackay Robert S. 
Published: November 2008

AbstractIt is proved that if ƒ is a homeomorphism of the two-sphere with an invariant set V of cardinality N = 4, then either ƒ has periodic orbits of all periods or it belongs to one of a small number of algebraically finite isotopy classes relative to V. For N ≤ 4, the second case always holds. On the other hand, for each N ≥ 7 we give examples of pseudo-Anosov homeomorphisms of the sphere, relative to a set of N points, for which not all periods occur.
The connection between the universal enveloping C*-algebra and the universal enveloping von Neumann algebra of a JW-algebra
Authors: Jamjoom Fatmah B. 
Published: November 2008

AbstractThis article aims to study the relationship between the universal enveloping C*-algebra C*(M) and the universal enveloping von Neumann algebra W*(M), when M is a JW-algebra. In our main result (Theorem 2·7) we show that C*(M) can be realized as the C*-subalgebra of W*(M) generated by M.
Spectral inequalities for compact integral operators on Banach function spaces
Authors: Drnovšek Roman 
Published: November 2008

AbstractThis article generalizes some spectral inequalities for non-negative matrices (see [2] and [3]) to compact integral operators with non-negative kernels defined on Banach function spaces. The spectral radius of a sum of such operators is estimated under certain conditions and a generalization of this inequality is given. An inequality for the spectral radius of a compact integral operator with the kernel equal to a weighted geometric mean of non-negative kernels is also proved.
Jacobian in genus 2
Authors: Cassels J. W. S. 
Published: November 2008

In [2] the author proposed the study of the geometry and arithmetic of the general curveof genus 2 over a general groundfield such as the rationals in order to attack Diophantine problems. He gave the form of the Jacobian, and Flynn[4, 5] determined the group law on it. This paper is preparatory to a planned study of heights under duality. It extends to a general groundfield the description of the Jacobian as the variety of lines on the intersection of two quadric surfaces in P5 given over the complexes in the last chapter of the textbook [7] of Griffiths and Harris. This description is a generalization of that of a curve of genus 1 as the intersection of two quadric surfaces in P3 and is a special case of a more general result [3]: its first appearances seem to be in [12] and [13].
On 3-dimensional Poincaré duality complexes and 2-knot groups
Authors: Hillman Jonathan A. 
Published: November 2008

AbstractWe show that a PD3-complex P such that π = π1(P) is infinite and has a non-trivial finite normal subgroup must be homotopy equivalent to RP2 × S1. Hence if A is an abelian normal subgroup of a 2-knot group πK which is not contained in the commutator subgroup πK′ and πK′ is infinite then A is torsion free.
Products of idempotent endomorphisms of an independence algebra of infinite rank
Authors: Fountain John , Lewin Andrew 
Published: November 2008

AbstractIn 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (under composition) of idempotent self-maps of the same set. In 1967, J. A. Erdos considered the analogous question for linear maps of a finite dimensional vector space and in 1985, Reynolds and Sullivan solved the problem for linear maps of an infinite dimensional vector space. Using the concept of independence algebra, the authors gave a common generalization of the results of Howie and Erdos for the cases of finite sets and finite dimensional vector spaces. In the present paper we introduce strong independence algebras and provide a common generalization of the results of Howie and Reynolds and Sullivan for the cases of infinite sets and infinite dimensional vector spaces.
Limiting properties of Inverse Beta and generalized Bleimann–Butzer–Hahn operators
Authors: Adell José A. , De La Cal Jesús 
Published: November 2008

AbstractIn this paper, we consider limiting properties concerning linear operators of probabilistic type. Specifically, we show that gamma operators are limits of inverse Beta operators and that Bleimann–Butzer–Hahn, Szász and Baskakov operators are limits of generalized Bleimann–Butzer–Hahn operators. By duality, these results are closely related to the convergence in the total variation distance of the probability measures involved. In each case, rates of convergence are given.
Invariant domains and singularities
Authors: Bergweiler Walter 
Published: November 2008

AbstractLet U be an invariant component of the Fatou set of an entire transcendental function f such that the iterates of f tend to ∞ in U. Let P(f) be the closure of the set of the forward orbits of all critical and asymptotic values of f. We show that there exists a sequence pn∈P(f) such that dist(pn, U) = o(|pn|), where dist(·, ·) denotes Euclidean distance. On the other hand, we give an example where dist (P(f), U) > 0. In this example, U is bounded by a Jordan curve.
Closed model categories for the n-type of spaces and simplicial sets
Authors: Elvira-Donazar Carmen , Hernandez-Paricio Luis-Javier 
Published: November 2008

AbstractFor each integer n ≥ 0, we give a distinct closed model category structure to the categories of spaces and of simplicial sets. Recall that a non-empty map is said to be a weak equivalence if it induces isomorphisms on the homotopy groups for any choice of base point. Putting the condition on dimensions ≥ n, we have the notion of a weak n-equivalence which is at the base of the nth closed model category structure given here.
Large deviations and overflow probabilities for the general single-server queue, with applications
Authors: Duffield N. G. , O'connell Neil 
Published: November 2008

AbstractWe consider queueing systems where the workload process is assumed to have an associated large deviation principle with arbitrary scaling: there exist increasing scaling functions (at, vt, t∈R+) and a rate function I such that if (Wt, t∈R+) denotes the workload process, thenon the continuity set of I. In the case that at = vt = t it has been argued heuristically, and recently proved in a fairly general context (for discrete time models) by Glynn and Whitt[8], that the queue-length distribution (that is, the distribution of supremum of the workload process Q = supt≥0Wt) decays exponentially:and the decay rate δ is directly related to the rate function I. We establish conditions for a more general result to hold, where the scaling functions are not necessarily linear in t: we find that the queue-length distribution has an exponential tail only if limt→∞at/vt is finite and strictly positive; otherwise, provided our conditions are satisfied, the tail probabilities decay like
A natural invariant algebra for the Harada-Norton group
Authors: Ryba A. J. E. 
Published: November 2008

The Harada-Norton group is one of the twenty-six sporadic simple groups. It has order 273, 030, 912, 000, 000 = 214.36.56.7.11.19. In this paper our main objective is:Theorem 1. The Harada-Norton group acts as a group of linear automorphisms of a 133-dimensional commutative, non-associative algebra defined over F5.
Representation of an element in SL(2, ,) as a short word in two generators
Authors: Bender Andreas 
Published: November 2008

It is one of the first theorems proved in the theory of modular forms [1, p. 78] that every element in SL (2, ℤ), and hence in SL(2, ), can be written as a product of the two generatorsWhile this is quite an easy result, it required more advanced tools such as spectral analysis on Riemann surfaces [2] to show that there is in fact always such a product of length O(log p). This result is not constructive and therefore immediately [2, p. 102] raises the following:Problem. Is there an algorithm polynomial in log p for constructing a monomial in S and T, of degree O(log p), whose value isIn this note, we construct such an algorithm. We will carry out all the details only for the particular elementbut it will become obvious that our method works for all elements in SL(2, ).
Invariant theory and Steenrod operations – maps between rings of invariants
Authors: Mahmud Zafer , Smith Larry 
Published: November 2008

AbstractLet G ′, G ″ be finite groups and p ′: G ↪ GL(n ′,ℚ), p ″: G ″ ↪ GL(n ″, ℚ) faithful rational representations. If T: V′ = ℚn′ → ℚn″ = V ″ is a linear transformation and Ξ: G ′ → G ″ a function such thatthen there are induced algebra homomorphisms ℚ[V ″] → ℚ[V ] and ℚ[V ″]G ″ → ℚ[V ′]G ′ making the diagramcommute. In this note we isolate the invariant theory portion of [1] and extend it to provide a necessary and sufficient condition that an algebra homomorphism between rings of invariants ℚ[V ″]G ″ → ℚ[V ′]G ′ arises in this way.
On block Behrend sequences
Authors: Tenenbaum G. 
Published: November 2008

Let A be a strictly increasing sequence of integers exceeding 1 and letdenote its set of multiples. We say that A is a Behrend sequence if M(A) has asymptotic density 1. The theory of sets of multiples was first developed in the late thirties, under the influence of Erdős, Besicovitch, and others. An account of the classical notions is presented in the book of Halberstam and Roth (1966), and recent progress in the area may be found in Hall and Tenenbaum [7], Erdős and Tenenbaum [4], Ruzsa and Tenenbaum [9]. As underlined by Erdős in [3], one of the central problems in the field is that of finding general criteria to decide whether a given sequence A is Behrend.
The dimension of self-affine fractals II
Authors: Falconer K. J. 
Published: November 2008

AbstractA family {S1, ,Sk} of contracting affine transformations on Rn defines a unique non-empty compact set F satisfying . We obtain estimates for the Hausdorff and box-counting dimensions of such sets, and in particular derive an exact expression for the box-counting dimension in certain cases. These estimates are given in terms of the singular value functions of affine transformations associated with the Si. This paper is a sequel to 4, which presented a formula for the dimensions that was valid in almost all cases.
On the braid index of links with nested diagrams
Authors: Chalcraft D. A. 
Published: November 2008

AbstractThe number of Seifert circuits in a diagram of a link is well known 9 to be an upper bound for the braid index of the link. The -breadth of the so-called P-polynomial 3 of the link is known 5, 2 to give a lower bound. In this paper we consider a large class of links diagrams, including all diagrams where the interior of every Seifert circuit is empty. We show that either these bounds coincide, or else the upper bound is not sharp, and we obtain a very simple criterion for distinguishing these cases.
Restriction implies Bochner–Riesz for paraboloids
Authors: Carbery Anthony 
Published: November 2008

Let Σ ⊆ ℝn be a (compact) hypersurface with non-vanishing Gaussian curvature, with suitable parameterizations, also called Σ: U → ℝn (U open patches in ℝn−1). The restriction problem for Σ is the question of the a priori estimate (for f ∈ S(ℝ))(^denoting the Fourier transform). The Bochner-Riesz problem for Σ is the question of whether the functionsdefine Lp-bounded Fourier multiplier operators on ℝn in the range.
Transmutation theory and rank for quantum braided groups
Authors: Majid Shahn 
Published: November 2008

AbstractLet f: H1 → H2be any pair of quasitriangular Hopf algebras over k with a Hopf algebra map f between them. We construct in this situation a quasitriangular Hopf algebra B(H1, f, H2) in the braided monoidal category of H1-modules. It consists in the same algebra as H2 with a modified comultiplication and has a quasitriangular structure given by the ratio of those of H1 and H2. This transmutation procedure trades a non-cocommutative Hopf algebra in the category of k-modules for a more cocommutative object in a more non-commutative category. As an application, every Hopf algebra containing the group algebra of ℤ2 becomes transmuted to a super-Hopf algebra.
On epimorphisms of non-commutative rings
Authors: Knight J. T. 
Published: November 2008

From a commutative ring A, Lazard(8) has made a flat injective epimorphism: A → B of commutative rings, such that if A → C is another flat injective epimorphism of commutative rings, then there is one and only one ring morphism: B → C such that the diagramcommutes; and he shows too that B → C is a flat injective epimorphism. The main aim of the present paper is to make a similar object for not necessarily commutative rings: this is achieved thanks to the notion of an A-prering, intermediate between that of an A-bimodule and that of an A-ring. In passing, prerings are also used to construct a kind of non-commutative ring of fractions.
On the relation of connective K-theory to homology
Authors: Smith Larry 
Published: November 2008

Let us denote by k*( ) the homology theory determined by the connective BU spectrum, bu, that is, in the notations of (1) and (9), bu2n = BU(2n,…,∞), bu2n+1 = U(2n + 1,…, ∞) with the spectral maps induced via Bott periodicity. The resulting spectrum, bu, is a ring spectrum. Recall that k*(point) ≅ Z[t], degree t = 2. There is a natural transformation of ring spectrainducing a morphismof homology functors. It is the objective of this note to establish: Theorem. Let X be a finite complex. Then there is a natural exact sequencewhere Z is viewed as a Z[t] module via the augmentationand, is induced by η*in the natural way.
On the periods of the exponential and elliptic functions
Authors: Masser D. W. 
Published: November 2008

Let ℘ be a Weierstrass elliptic function satisfying the differential equationand let ζ(z) be the associated Weierstrass ζ-function satisfying (z) = −℘(z). Corresponding to a pair of fundamental periods ω1, ω2 of ℘(z), there is a pair of quasi-periods η1, η2 of ζ(z) defined byand we have ηi = 2ζ(ωi/2) for i = 1, 2.
Averages of holomorphic mappings
Authors: Nestoridis V. 
Published: November 2008

In this paper we present two versions in several variables of the following result:Theorem 1([2, 3]). Let f be a function in the disc algebra (more generally in H1). Then for every point z0 in the open unit disc, there is an interval I on the unit circle T such that f(z0) = 1/|I| ∫Ifdσ, where 0 < |I| ≤ 2π denotes the length of I and σ the Lebesgue measure on T.
Superconductors in Alternating Magnetic Fields
Authors: Shoenberg D. 
Published: November 2008

A method of studying magnetic properties in alternating fields and its application to the intermediate state of a superconducting sphere are described. It is shown that the behaviour of the sphere in alternating fields of frequencies between 10 and 100 is different from that in very slowly varying fields, the difference becoming less for lower frequencies and for smaller radius. When the specimen is in the intermediate state, energy losses are produced in it by the alternating field, showing that the induced currents are out of phase with the alternating field. The induced currents do not, however, flow in the same way as in a homogeneous isotropic conductor, and this is probably on account of an anisotropic structure of the specimen when in the intermediate state. This structure depends strongly on the amplitude of the alternating field in such a way that the effective average conductivity is increased with decreasing amplitude, and this amplitude effect depends on the size of the specimen. Evidence is given for a time lag in the magnetocaloric effect, and this time lag decreases with decrease of the size of the specimen, being of order sec. for a sphere of about 1 cm. diameter.In conclusion I wish to thank Prof. Lord Rutherford and Dr Cockcroft for their interest in this work; Dr Peierls for suggesting the experiment and for much valuable advice and assistance; Mr Shire for advice on some technical points; and various members of the staff of the Royal Society Mond Laboratory for help in the measurements.