bluuebunny/crossref_metadata_2025_split huggingface dataset:
Quadratic Diophantine equations and two generator Möbius groups
Authors: Tan Eng-Chye , Tan Ser-Peow 
Published: April 2009

AbstractIn this paper, we study the set of rational μ in (−2, 2) for which the group Gu generated by is not free by using quadratic Diophantine equations of the form ax2 −by2 = ±1. We give a new set of accumulation points for rational values of μ in (−2, 2) for which Gμ is not free, thereby extending the results of Beardon where he showed that are accumulation points, where N is an integer which is not a perfect square. In particular, we exhibit an infinite set of accumulation points for μ between 1 and 2 including the point 1.
Generalized regular variation of second order
Authors: de Haan Laurens , Stadtmüller Ulrich 
Published: April 2009

AbstractAssume that for a measurable funcionfon (0, ∞) there exist a positive auxiliary functiona(t)and some γ ∈ R such that. Thenfis said to be of generalized regular variation. In order to control the asymptotic behaviour of certain estimators for distributions in extreme value theory we are led to study regular variation of second order, that is, we assume thatexists non-trivially with a second auxiliary function a1(t). We study the possible limit functions in this limit relation (defining generalized regular variation of second order) and their domains of attraction. Furthermore we give the corresponding relation for the inverse function of a monotonefwith the stated property. Finally, we present an Abel-Tauber theorem relating these functions and their Laplace transforms.
Probabilistic convergence spaces
Authors: Richardson G. D. , Kent D. C. 
Published: April 2009

AbstractA basic theory for probabilistic convergence spaces based on filter convergence is introduced. As in Florescu's previous theory of probabilistic convergence structures based on nets, one is able to assign a probability that a given filter converges to a given point. Various concepts and theorems pertaining to convergence spaces are extended to the realm of probabilistic convergence spaces, and illustrated by means of examples based on convergence in probability and convergence almost everywhere. Diagonal axioms due to Kowalsky and Fischer are also studied, first for convergence spaces and then in the setting of probabilistic convergence spaces.
An extension of the Fejér-Jackson inequality
Authors: Brown Gavin , Wang Kun-Yang 
Published: April 2009

AbstractBest-possible results are established for positivity of the partial sums of Σ sin k θ (k + α)−1. In fact odd sums are positive for −1 ≤ α ≤ α0 = 2.1 …, while 2k terms are positive on the subinterval ]0, π − 2μ0π(4k +1)−1 [, μ0 = 0.8128 …. This is analagous to the Gasper extension of the Szegö-Rogosinski-Young inequality for cosine sums.
Further geometry of the mean curvature one-form and the normal plane field one-form on a foliated Riemannian manifold
Authors: Cairns Grant , Escobales Richard H. 
Published: April 2009

AbstractFor foliations on Riemannian manifolds, we develop elementary geometric and topological properties of the mean curvature one-form κ and the normal plane field one-form β. Through examples, we show that an important result of Kamber-Tondeur on κ is in general a best possible result. But we demonstrate that their bundle-like hypothesis can be relaxed somewhat in codimension 2. We study the structure of umbilic foliations in this more general context and in our final section establish some analogous results for flows.
Generalised spectral analysis of fractional random fields
Authors: Anh V. V. , Lunney K. E. 
Published: April 2009

AbstractThis paper considers a large class of non-stationary random fields which have fractal characteristics and may exhibit long-range dependence. Its motivation comes from a Lipschitz-Holder-type condition in the spectral domain.The paper develops a spectral theory for the random fields, including a spectral decomposition, a covariance representation and a fractal index. From the covariance representation, the covariance function and spectral density of these fields are defined. These concepts are useful in multiscaling analysis of random fields with long-range dependence.
Asymptotic behaviour of non-autonomous dissipative systems in Hilbert space
Authors: Guozhu Song 
Published: April 2009

AbstractIn this paper we discuss the asymptotic behaviour, as t → ∞, of the integral solution u(t) of the non-linear evolution equation where {A(t)}t≥0 is a family of m-dissipative operators in a Hilbert space H, and g ∈ Lloc (0, ∞ H).We give some sufficient conditions and some sufficient and necessary conditions to ensure that are weakly convergent.
The inner and outer space of 2-dimensional Laguerre planes
Authors: Polster B. , Steinke G. F. 
Published: April 2009

AbstractThe classical 2-dimensional Laguerre plane is obtained as the geometry of non-trivial plane sections of a cylinder in R3 with a circle in R2 as base. Points and lines in R3 define subsets of the circle set of this geometry via the affine non-vertical planes that contain them. Furthemore, vertical lines and planes define partitions of the circle set via the points and affine non-vertical lines, respectively, contained in them.We investigate abstract counterparts of such sets of circles and partitions in arbitrary 2-dimensional Laguerre planes. We also prove a number of related results for generalized quadrangles associated with 2-dimensional Laguerre planes.
Integer points on algebraic curves with exceptional units
Authors: Poulakis Dimitrios 
Published: April 2009

AbstractLet F(X, Y) be an absolutely irreducible polynomial with coefficients in an algebraic number field K. Denote by C the algebraic curve defined by the equation F(X, Y) = 0 and by K[C] the ring of regular functions on Cover K. Assume that there is a unit ϕ in K[C] − K such that 1 − ϕ is also a unit. Then we establish an explicit upper bound for the size of integral solutions of the equation F(X, Y) = 0, defined over K. Using this result we establish improved explicit upper bounds on the size of integral solutions to the equations defining non-singular affine curves of genus zero, with at least three points at ‘infinity’, the elliptic equations and a class of equations containing the Thue curves.
Generic continuity of minimal set-valued mappings
Authors: Moors W. B. , Giles J. R. 
Published: April 2009

AbstractWe study classes of Banach spaces where every set-valued mapping from a complete metric space into subsets of the Banach space which satisfies certain minimal properties, is single-valued and norm upper semi-continuous at the points of a dense Gδ subset of its domain. Characterisations of these classes are developed and permanence properties are established. Sufficiency conditions for membership of these classes are defined in terms of fragmentability and σ-fragmentability of the weak topology. A characterisation of non membership is used to show that l∞ (N) is not a member of our classe of generic continuity spaces.
Bifurcation at infinity for equations in spaces of vector-valued functions
Authors: Diamond P. , Kloeden P. E. , Krasnosel'skii A. M. , Pokrovskii A. V. 
Published: April 2009

AbstractNew existence conditions, under which an index at infinity can be calculated, are given for bifurcations at infinity of asymptotically linear equations in spaces of vector-valued functions. The case where a bounded nonlinearity has discontinuous principal homogeneous part is considered. The results are applied to 2π-periodic problems for two-dimensional systems of ordinary differential equations and to a vector two-point boundary value problem.
Equivariant holomorphic maps into the Siegel disc and the metaplectic representation
Authors: Clerc Jean-Louis 
Published: April 2009

AbstractWe restrict the metaplectic representation to subgroupsGof the symplectic group associated to equivariant holomorphic maps into the Siegel disc. We describe the invariant subspaces of the decomposition, and reduce the problem to the decomposition of a space of ‘harmonic’ polynomials under the action of the maximal compact subgroup ofG.
The product of independent random variables with slowly varying truncated moments
Authors: Shimura Takaaki 
Published: April 2009

AbstractThe Mellin-Stieltjes convolution and related decomposition of distributions in M(α) (the class of distributions μ on (0, ∞) with slowly varying αth truncated moments ) are investigated. Maller shows that if X and Y are independent non-negative random variables with distributions μ and v, respectively, and both μ and v are in D2, the domain attraction of Gaussian distribution, then the distribution of the product XY (that is, the Mellin-Stieltjes convolution μ ^ v of μ and v) also belongs to it. He conjectures that, conversely, if μ ∘ v belongs to D2, then both μ and v are in it. It is shown that this conjecture is not true: there exist distributions μ ∈ D2 and v μ ∈ D2 such that μ ^ v belongs to D2. Some subclasses of D2 are given with the property that if μ ^ v belongs to it, then both μ and v are in D2.
Inverse semigroups with zero: covers and their structure
Authors: Bulman-Fleming Sydney , Fountain John , Gould Victoria 
Published: April 2009

AbstractWe obtain analogues, in the setting of semigroups with zero, of McAlister's convering theoren and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a classCof semigroups defined by modifying one of the many characterisations ofE-unitary inverse semigroups, namely, that an inverse semigroups isE-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The classCis properly contained in the class of allE*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categoricalE*-unitary semigroups recently considered by Gomes and Howie.
A family of strongly singular operators
Authors: Folch-Gabayet Magali 
Published: April 2009

AbstractLet ψ be a positive function defined near the origin such lim1 →0+ ψ(t) = 0. We consider the operator Tzƒ, defined as the pricipal value of the convolution of function ƒ and a kernel K(t) = eiy(t)t−z /ψ(t)1−z, where z is a complex number, 0 ≤ Re(z) ≤ 1, 0 < t ≤ 1 and γ is a real function. Assuming certain regularity conditions on ψ and γ and certain relations between ψ and γ we show that Tθ is a bounded operator on Lp (R) for 1/p = (1+ θ) /2 and 0 ≤ θ < 1, and T1 is bounded from H1 (R) to L1 (R).
Congruence intersection properties for varieties of algebras
Authors: Agliano Paolo , Baker Kirby A. 
Published: April 2009

AbstractIt is shown that a variety ν has distributive congruence lattices if and only if the intersection of two principal congruence relations is definable by equations involving terms with parameters. The nature of the terms involved then provides a useful classification of congruence distributive varieties. In particular, the classification puts into proper perspective two stronger properties. A variety is said to have the Principal Intersection Property if the intersection of any two principal congruence relations is principal, or the Compact Intersection Property if the intersection of two compact congruence relations is compact. For non-congruence-distributive varieties, it is shown that some useful constuctions are nevertheless possible.
Amenability and semisimplicity for second duals of quotients of the Fourier algebraA(G)
Authors: Granirer Edmond E. 
Published: April 2009

AbstractLetF ⊂ Gbe closed andA(F) = A(G)/IF. IfFis a Helson set thenA(F)**is an amenable (semisimple) Banach algebra. Our main result implies the following theorem: LetGbe a locally compact group,F ⊂ Gclosed,a ∈ G. Assume either (a) For some non-discrete closed subgroupH, the interior ofF ∩ aHinaHis non-empty, or (b)R ⊂ G, S ⊂ Ris a symmetric set andaS ⊂ F. ThenA(F)**is a non-amenable non-semisimple Banach algebra. This raises the question: How ‘thin’ canFbe forA(F)**to remain a non-amenable Banach algebra?
Cesàro kernels on classical groups
Authors: Fan Dashan 
Published: April 2009

AbstractWe study the Cesàro operator on the classical group G and give a necessary and sufficient condition on the index α = α(G) for which the operator is convergent to f(U) for any continuous function f as N → ∞. The result in this paper solves a question posed by Gong in the book Harmonic analysis on classical groups.
On a conjecture of Crittenden and Vanden Eynden concerning coverings by arithmetic progressions
Authors: Simpson R. J. 
Published: April 2009

AbstractCrittenden and Vanden Eynden conjectured that ifnarithmetic progressions, each having modulus at leastk, include all the integers from 1 tok2n-k+1, then they include all the integers. They proved this for the casesk= 1 andk= 2. We give various necessary conditions for a counterexample to the conjecture; in particular we show that if a counterexample exists for some value ofk, then one exists for thatkand a value ofnless than an explicit function ofk.
Mixed cusp forms and parabolic cohomology
Authors: Lee Min Ho 
Published: April 2009

AbstractLet Sk, l(Γ, ω, χ) be the space of mixed cusp forms of type (k, l) associated to a Fuchsian group Γ, a holomorphic map ω: ℋ → ℋ of the upper half plane into itself and a homomorphism χ: Γ → SL(2, R) such that ω and χ are equivariant. We construct a map from Sk, l(Γ, ω, χ) to the parabolic cohomology space of Γ with coefficients in some Γ-module and prove that this map is injective.
The Dehn function and a regular set of normal forms for R. Thompson's group F
Authors: Guba V. S. , Sapir M. V. 
Published: April 2009

AbstractWe show that the group F discovered by Richard Thompson in 1965 has a subexponential upper bound for its Dehn function. This disproves a conjecture by Gersten. We also prove that F has a regular terminating confluent presentation.
Two-term Edgeworth expansion for M-estimators of a linear regression parameter without Cramér-type conditions and an application to the bootstrap
Authors: Karabulut I. , Lahiri S. N. 
Published: April 2009

AbstractA two-term Edgeworth expansion for the distribution of an M-estimator of a simple linear regression parameter is obtained without assuming any Cramér-type conditions. As an application, it is shown that certain modification of the naive bootstrap procedure is second order correct even when the error variables have a lattice distribution. This is in marked contrast with the results of Singh on the sample mean of independent and identically distributed random variables.
Value distribution of certain monomials of algebroid functions
Authors: Katajamäki Kari 
Published: April 2009

AbstractHayman has shown that iffis a transcendental meromorphic function andn≽ 3, thenfnf′ assumes all finite values except possibly zero infinitely often. We extend his result in three directions by considering an algebroid function ω, its monomial ωn0ω′n1, and by estimating the growth of the number of α-points of the monomial.
Free Lie algebras as modules for symmetric groups
Authors: Bryant R. M. , Kovács L. G. , Stöhr Ralph 
Published: April 2009

AbstractLet r be a positive integer, F a field of odd prime characteristic p, and L the free Lie algebra of rank r over F. Consider L a module for the symmetric group , of all permutations of a free generating set of L. The homogeneous components Ln of L are finite dimensional submodules, and L is their direct sum. For p ≤ r ≤ 2p, the main results of this paper identify the non-porojective indecomposable direct summands of the Ln as Specht modules or dual Specht modules corresponding to certain partitions. For the case r = p, the multiplicities of these indecomposables in the direct decompositions of the Ln are also determined, as are the multiplicities of the projective indecomposables. (Corresponding results for p = 2 have been obtained elsewhere.)
Some thin Lie algebras related to Albert-Frank algebras and algebras of maximal class
Authors: Caranti A. , Mattarei S. 
Published: April 2009

AbstractWe investigate a class of infinite-dimensional, modular, graded Lie algebra in which the homogeneous components have dimension at most two. A subclass of these algebras can be obtained via a twisted loop algebra construction from certain finite-dimensional, simple Lie algebras of Albert-Frank type.Another subclass of these algebras is strictly related to certain graded Lie algebras of maximal class, and exhibits a wide range of behaviours.
Enumerating p-Groups
Authors: Eick Bettina , O'Brien E. A. 
Published: April 2009

AbstractWe present a new algorithm which uses a cohomological approach to determine the groups of order pn, where p is a prime. We develop two methods to enumerate p-groups using the Cauchy-Frobenius Lemma. As an application we show that there are 10 494213 groups of order 29.1991 Mathematics subject classification (Amer. Math. Soc.): primary 20D15.
A recognition algorithm for non-generic classical groups over finite fields
Authors: Niemeyer Azice C. , Praeger Cheryl E. 
Published: April 2009

AbstractIn a previous paper the authors described an algorithm to determine whether a group of matrices over a finite field, generated by a given set of matrices, contains one of the classical groups or the special linear group. The algorithm was designed to work for all sufficiently large field sizes and dimensions of the matrix group. However, it did not apply to certain small cases. Here we present an algorithm to handle the remaining cases. The theoretical background of the algorithm presented in this paper is a substantial extension of that needed for the original algorithm.
Posets and differential graded algebras
Authors: Ramagge Jacqui , Wheeler Wayne W. 
Published: April 2009

AbstractIf P is a partially ordered set and R is a commutative ring, then a certain differential graded R-algebra A•(P) is defined from the order relation on P. The algebra A•() corresponding to the empty poset is always contained in A•(P) so that A•(P) can be regarded as an A•()-algebra. The main result of this paper shows that if R is an integral domain and P and P′ are finite posets such that A•(P)≅A•(P′) as differential graded A•()-algebras, then P and P′ are isomorphic.
A family of dominant Fitting classes of finite soluble groups
Authors: Ballester-Bolinches A. , Martínez-Pastor A. , Pérez-Ramos M. D. 
Published: April 2009

AbstractIn this paper a large family of dominant Fitting classes of finite soluble groups and the description of the corresponding injectors are obtained. Classical constructions of nilpotent and Lockett injectors as well as p-nilpotent injectors arise as particular cases.
Truncated tetrahedra and their reflection groups
Authors: Marshall T. H. 
Published: April 2009

AbstractWe outline the classification, up to isometry, of all tetrahedra in hyperbolic space with one or more vertices truncated, for which the dihedral angles along the edges formed by the truncations are all π/2, and those remaining are all submultiples of π. We show how to find the volumes of these polyhedra, and find presentations and small generating sets for the orientation-preserving subgroups of their reflection groups.For particular families of these groups, we find low index torsion free subgroups, and construct associated manifolds and manifolds with boundary. In particular, for each g ≥ 2, we find a sequence of hyperbolic manifolds with totally geodesic boundary of genus g, which we conjecture to be of least volume among such manifolds.
A note on Engel groups and local nilpotence
Authors: Burns R. G. , Medvedev Yuri 
Published: April 2009

AbstractThis paper is concerned with the question of whether n-Engel groups are locally nilpotent. Although this seems unlikely in general, it is shown here that it is the case for the groups in a large class C including all residually soluble and residually finite groups (in fact all groups considered in traditional textbooks on group theory). This follows from the main result that there exist integers c(n), e(n) depending only on n, such that every finitely generated n-Engel group in the class C is both finite-of-exponent-e(n)–by–nilpotent-of-class≤c(n) and nilpotent-of-class≤c(n)–by–finite-of-exponent-e(n). Crucial in the proof is the fact that a finitely generated Engel group has finitely generated commutator subgroup.
Crossed products of Hilbert C*-bimodules by bundles
Authors: Kajiwara Tsuyoshi , Watatani Yasuo 
Published: April 2009

AbstractWe present the definition of crossed products of Hilbert C*-bimodules by Hilbert bundles with commuting finite group actions and finite dimensional fibers. This is a general construction containing the bundle construction and crossed products of Hilbert C*-bimodule by finite groups. We also study the structure of endomorphism algebras of the tensor products of bimodules. We also define the multiple crossed products using three bimodules containing more than 2 bundles and show the associativity law. Moreover, we present some examples of crossed product bimodules easily computed by our method.
Contracting spacelike hypersurfaces by their inverse mean curvature
Authors: Holder Michael 
Published: April 2009

AbstractIn this work we study the behaviour of compact, smooth, orientable, spacelike hypersurfaces without boundary, which are immersed in cosmological spacetimes and move under the inverse mean curvature flow. We prove longtime existence and regularity of a solution to the corresponding nonlinear parabolic system of partial differential equations.
The arithmetic of a semigroup of series of Walsh functions
Authors: Il'inskaya I. P. 
Published: April 2009

AbstractLet be the classical system of the Walsh functions, the multiplicative semigroup of the functions represented by series of functions Wk(t)with non-negative coefficients which sum equals 1. We study the arithmetic of . The analogues of the well-known [ related to the arithmetic of the convolution semigroup of probability measures on the real line are valid in . The classes of idempotent elements, of infinitely divisible elements, of elements without indecomposable factors, and of elements without indecomposable and non-degenerate idempotent factors are completely described. We study also the class of indecomposable elements. Our method is based on the following fact: is isomorphic to the semigroup of probability measures on the groups of characters of the Cantor-Walsh group.
Hyperbolic knot complements without closed embedded totally geodesic surfaces
Authors: Ichihara Kazuhiro , Ozawa Makoto 
Published: April 2009

AbstractIt is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces cannot be totally geodesic.
A remark on robustness and weak continuity of M-estimators
Authors: Clarke Brenton R. 
Published: April 2009

AbstractGlobal weak continuity of M-functionals in a neighbourhood of the parametric distribution is established. This has implications for robustness of M-estimators vis a vis definitions put forward by Hampel. For instance the Tukey bisquare location estimator is robust on neighbourhoods of the parametric model, but the median is not.
Asymptotic Behaviour of Continuous Time and State Branching Processes
Authors: Li Zeng-Hu 
Published: April 2009

AbstractWe prove some limit theorems for contiunous time and state branching processes. The non-degenerate limit laws are obtained in critical and non-critical cases by conditioning or introducing immigration processes. The limit laws in non-critical cases are characterized in terms of the cononical measure of the cumulant semigroup. The proofs are based on estimates of the cumulant semigroup derived from the forward and backward equations, which are easier than the proffs in the classical setting.