bluuebunny/crossref_metadata_2025_split huggingface dataset:
Anzai and Furstenberg Transformations on the 2-Torus and Topologically Quasi-Discrete Spectrum
Authors: Kodaka Kazunori 
Published: December 2010

AbstractLet ϕ0 be an Anzai transformation on the 2-torus T2 defined by ϕ0(x,y) = (e2πiθx,xy) and ϕy a Furstenberg transformation on T2 defined by ϕf(x,y) = (e2πiθx,e2πif(x)xy) where θ is an irrational number and f is a real valued continuous function on the 1-torus T. In the present note we will show that ϕf has topologically quasi-discrete spectrum if and only if ϕf is topologically conjugate to ϕ0. Furthermore we will show that for any irrational number θ there is a real valued continuous function f on T such that ϕf does not have topologically quasi-discrete spectrum but is uniquely ergodic.
On Constrained L2-Approximation of Complex Functions
Authors: Bokhari M. A. 
Published: December 2010

AbstractA function f analytic in any disc of radius greater than 1 is approximated in the L2-sense over a class of polynomials which also interpolate f on a subset of the roots of unity. The resulting solution is used to discuss Walsh-type equiconvergence. The main theorem of the paper generalizes certain results of Walsh, Rivlin and Cavaretta et al.
Radii and the Sausage Conjecture
Authors: Bőrőczky Károly , Henk Martin 
Published: December 2010

AbstractIn 1975, L. Fejes Toth conjectured that in Ed, d ≥ 5, the sausage arrangement is denser than any other packing of n unit balls. This has been known if the convex hull Cn of the centers has low dimension. In this paper, we settle the case when the inner m-radius of Cn is at least O(ln d/m). In addition, we consider the extremal properties of finite ballpackings with respect to various intrinsic volumes.
Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields
Authors: Clark David A. , Kuwata Masato 
Published: December 2010

AbstractLet k = Fq be a finite field of characteristic p with q elements and let K be a function field of one variable over k. Consider an elliptic curve E defined over K. We determine how often the reduction of this elliptic curve to a prime ideal is cyclic. This is done by generalizing a result of Bilharz to a more general form of Artin's primitive roots problem formulated by R. Murty.
The Complete Continuity Property and Finite Dimensional Decompositions
Authors: Girardi Maria , Johnson William B. 
Published: December 2010

AbstractA Banach space has the complete continuity property (CCP) if each bounded linear operator from L1 into is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP has a subspace with a finite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such as fails cotype or is a lattice), then the decomposition may be strengthened to a basis.
Every Invertible Hilbert Space Operator is a Product of Seven Positive Operators
Authors: Christopher Phillips N. 
Published: December 2010

AbstractWe prove that every invertible operator in a properly infinite von Neumann algebra, in particular in L(H) for infinite dimensional H, is a product of 7 positive invertible operators. This improves a result of Wu, who proved that every invertible operator in L(H) is a product of 17 positive invertible operators.
Connectedness of the Invertibles in Certain Nest Algebras
Authors: Davidson Kenneth R. , Lindsay John , Pitts David R. 
Published: December 2010

AbstractWe show that if is a nest with no isolated atoms of finite multiplicity, then the invertibles in are connected. The key technical ingredient is that in such nest algebras, every operator with zero atomic diagonal part factors through the non-atomic part of . In particular, these results apply for the Cantor nest.
An Integral Representation for the Generalized Binomial Function
Authors: Heggie M. , Nicklason G. R. 
Published: December 2010

AbstractThe generalized binomial function can be obtained as the solution of the equation y = 1 +zyα which satisfies y(0) = 1 where α ≠ 1 is assumed to be real and positive. The technique of Lagrange inversion can be used to express as a series which converges for |z| < α-α|a — l|α-1. We obtain a representation of the function as a contour integral and show that if α > 1 it is an analytic function in the complex z plane cut along the nonnegative real axis. For 0 < α < 1 the region of analyticity is the sector |arg(—z)| < απ. In either case defined by the series can be continued beyond the circle of convergenece of the series through a functional equation which can be derived from the integral representation.
Facial Structures for the Positive Linear Maps Between Matrix Algebras
Authors: Kye Seung-Hyeok 
Published: December 2010

AbstractLet denote the convex set of all positive linear maps from the matrix algebra Mn(ℂ) into itself. We construct a join homomorphism from the complete lattice of all faces of into the complete lattice of all join homomorphisms between the lattice of all subspaces of ℂn . We also characterize all maximal faces of .
Closed Symmetric Overgroups of Sn in On
Authors: Li Chi-Kwong , Whitney Wayne 
Published: December 2010

AbstractA norm on ℝn is said to be permutation invariant if its value is preserved under permutation of the coordinates of a vector. The isometry group of such a norm must be closed, contain Sn and —I, and be conjugate to a subgroup of On, the orthogonal group. Motivated by this, we are interested in classifying all closed groups G such that 〈—I,Sn〉 < G < On. We use the theory of Lie groups to classify all possible infinite groups G, and use the theory of finite reflection groups to classify all possible finite groups G. In keeping with the original motivation, all groups arising are shown to be isometry groups. This completes the work of Gordon and Lewis, who studied the same problem and obtained the results for n ≥ 13.
Mean Curvature of Riemannian Foliations
Authors: March Peter , Min-Oo Maung , Ruh Ernst A. 
Published: December 2010

AbstractIt is shown that a suitable conformai change of the metric in the leaf direction of a transversally oriented Riemannian foliation on a closed manifold will make the basic component of the mean curvature harmonic. As a corollary, we deduce vanishing and finiteness theorems for Riemannian foliations without assuming the harmonicity of the basic mean curvature.
A Completely General Rabinowi1sch Criterion for Complex Quadratic Fields
Authors: Mollin R. A. 
Published: December 2010

AbstractWe provide a criterion for the class group of a complex quadratic field to have exponent at most 2. This is given in terms of the factorization of a generalized Euler-Rabinowitsch polynomial and has consequences for consecutive distinct initial prime-producing quadratic polynomials which we cite as applications.
Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras
Authors: Okoh F. 
Published: December 2010

AbstractIf R is a Dedekind domain, then div splits i.e.; the maximal divisible submodule of every R-module M is a direct summand of M. We investigate the status of this result for some finite-dimensional hereditary algebras. We use a torsion theory which permits the existence of torsion-free divisible modules for such algebras. Using this torsion theory we prove that the algebras obtained from extended Coxeter- Dynkin diagrams are the only such hereditary algebras for which div splits. The field of rational functions plays an essential role. The paper concludes with a new type of infinite-dimensional indecomposable module over a finite-dimensional wild hereditary algebra.
Mean Convergence of Hermite-Fejér Interpolation Based on the Zeros of Lascenov Polynomials
Authors: Shi Ying Guang 
Published: December 2010

AbstractWeighted LP mean convergence of Hermite-Fejér interpolation based on the zeros of orthogonal polynomials with respect to the weight |x|2α+1(l — x2)β(α, β > — 1) is investigated. A necessary and sufficient condition for such convergence for all continuous functions is given. Meanwhile divergence of Hermite-Fejér interpolation in LP with p > 2 is obtained. This gives a possible answer to Problem 17 of P. Turân [J. Approx. Theory, 29(1980), p. 40].
On Positive Integer Solutions of the Equation xy + yz + xz = n
Authors: Hassan Al-Zaid , Brindza B. , Pintér Á. 
Published: December 2010

AbstractAs it had been recognized by Liouville, Hermite, Mordell and others, the number of non-negative integer solutions of the equation in the title is strongly related to the class number of quadratic forms with discriminant —n. The purpose of this note is to point out a deeper relation which makes it possible to derive a reasonable upper bound for the number of solutions.
Numbers Of Conjugacy Class Sizes And Derived Lengths for A-Groups
Authors: Marshall Mary K. 
Published: December 2010

AbstractAn A-group is a finite solvable group all of whose Sylow subgroups are abelian. In this paper, we are interested in bounding the derived length of an A-group G as a function of the number of distinct sizes of the conjugacy classes of G. Although we do not find a specific bound of this type, we do prove that such a bound exists. We also prove that if G is an A-group with a faithful and completely reducible G-module V, then the derived length of G is bounded by a function of the number of distinct orbit sizes under the action of G on V.
Complicated Bifurcations of Periodic Solutions in Some System of Ode
Authors: Soleev A. 
Published: December 2010

AbstractIn a vicinity of a stationary solution we consider a real analytic system of ODE of order four, depending on a small parameter. We look for families of periodic solutions which contract to the stationary solution, when the parameter tends to zero. We apply the general methods developed in [2] for the study of complex bifurcations and in [4] for local resolutions of singularities.
The Turaev-viro Invariant for 3-Manifolds is a Sum of Three Invariants
Authors: Sokolov M. V. 
Published: December 2010

AbstractWe show that every Turaev-Viro invariant for 3-manifolds is a sum of three new invariants and discuss their properties. We also find a solution of a conjecture of L. H. Kauffman and S. Lins. Tables of the invariants for closed orientable 3-manifolds of complexity ≤ 3 are presented at the end of the paper.
On A Brownian Motion Problem of T. Salisbury
Authors: Knight Frank B. 
Published: December 2010

AbstractLet B be a Brownian motion on R, B(0) = 0, and let f (t, x) be continuous. T. Salisbury conjectured that if the total variation of f (t, B(t)), 0 ≤ t ≤ 1, is finite P-a.s., then f does not depend on x. Here we prove that this is true if the expected total variation is finite.
Continuous Self-Maps of the Circle
Authors: Schaer J. 
Published: December 2010

AbstractGiven a continuous map δ from the circle S to itself we want to find all self-maps σ: S → S for which δ o σ. If the degree r of δ is not zero, the transformations σ form a subgroup of the cyclic group Cr. If r = 0, all such invertible transformations form a group isomorphic either to a cyclic group Cn or to a dihedral group Dn depending on whether all such transformations are orientation preserving or not. Applied to the tangent image of planar closed curves, this generalizes a result of Bisztriczky and Rival [1]. The proof rests on the theorem: Let Δ: ℝ → ℝ be continuous, nowhere constant, and limx→−∞ Δ(x) = −∞, limx→−∞ Δ(xx) = +∞; then the only continuous map Σ: R → R such that Δ o Σ = Δ is the identity Σ = idℝ.
Nonexistence Results of Positive Entire Solutions for Quasilinear Elliptic Inequalities
Authors: Naito Yūki , Usami Hiroyuki 
Published: December 2010

AbstractThis paper treats the quasilinear elliptic inequalitywhere N ≥ 2, m > 1, σ >m− 1, and p:ℝN → (0, ∞) is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When p has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results.
Fonctions Elliptiques et Équations Différentielles Ordinaires
Authors: Chouikha Raouf 
Published: December 2010

RésuméIn this paper, we detail some results of a previous note concerning a trigonometric expansion of the Weierstrass elliptic function . In particular, this implies its classical Fourier expansion. We use a direct integration method of the ODEwhere P(u) is a polynomial of degree n = 2 or 3. In this case, the bifurcations of (E) depend on one parameter only. Moreover, this global method seems not to apply to the cases n > 3.
Principe du Maximum et Lemme de Schwarz a Valeurs Vectorielles
Authors: Mazet Pierre 
Published: December 2010

RésuméNous établissons un théorème pour les fonctions holomorphes à valeurs dans une partie convexe fermée. Ce théorème précise la position des coefficients de Taylor de telles fonctions et peut être considéré comme une généralisation des inégalités de Cauchy. Nous montrons alors comment ce théorème permet de retrouver des versions connues du principe du maximum et d’obtenir de nouveaux résultats sur les applications holomorphes à valeurs vectorielles.
Reflexive Representations and Banach C*-Modules
Authors: Hadwin Don , Orhon Mehmet 
Published: December 2010

AbstractSuppose A is a unital C*-algebra and m:A → B(X) is unital bounded algebra homomorphism where B(X) is the algebra of all operators on a Banach space X. When X is a Hilbert space, a problem of Kadison [9] asks whether m is similar to a *-homomorphism. Haagerup [5] has shown that the answer is positive when m(A) has a cyclic vector or whenever m is completely bounded. We use this to show m(A) is reflexive (Alg Lat m(A) = m(A)−sot) whenever X is a Hilbert space. Our main result is that whenever A is a separable GCR C*-algebra and X is a reflexive Banach space, then m(A) is reflexive.
Stable Index Pairs for Discrete Dynamical Systems
Authors: Kaczynski Tomasz , Mrozek Marian 
Published: December 2010

AbstractA new shorter proof of the existence of index pairs for discrete dynamical systems is given. Moreover, the index pairs defined in that proof are stable with respect to small perturbations of the generating map. The existence of stable index pairs was previously known in the case of diffeomorphisms and flows generated by smooth vector fields but it was an open question in the general discrete case.
Equivalent Presentations of Modules Over Prüfer Domains
Authors: Fuchs Laszlo , Lee Sang Bum 
Published: December 2010

AbstractIf F and F′ are free R-modules, then M ≅ F/H and M ≅ F′/H′ are viewed as equivalent presentations of the R-module M if there is an isomorphism F → F′ which carries the submodule H onto H′. We study when presentations of modules of projective dimension 1 over Prüfer domains of finite character are necessarily equivalent.
Power Integral Bases in Composits of Number Fields
Authors: István Gaál  
Published: December 2010

AbstractIn the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary quadratic extensions of totally real cyclic number fields of prime degree. As an example we solve the index form equation completely in a two parametric family of fields of degree 10 of this type.
Percolation on Penrose Tilings
Authors: Hof A. 
Published: December 2010

AbstractIn Bernoulli site percolation on Penrose tilings there are two natural definitions of the critical probability. This paper shows that they are equal on almost all Penrose tilings. It also shows that for almost all Penrose tilings the number of infinite clusters is almost surely 0 or 1. The results generalize to percolation on a large class of aperiodic tilings in arbitrary dimension, to percolation on ergodic subgraphs of ℤd, and to other percolation processes, including Bernoulli bond percolation.
Brown-Halmos Type Theorems of Weighted Toeplitz Operators
Authors: Nakazi Takahiko 
Published: December 2010

AbstractThe spectra of the Toeplitz operators on the weighted Hardy space H2(Wdθ / 2π) and the Hardy space Hp(dθ / 2π), and the singular integral operators on the Lebesgue space L2(dθ / 2π) are studied. For example, the theorems of Brown-Halmos type and Hartman-Wintner type are studied.
The Growth Series of Compact Hyperbolic Coxeter Groups with 4 and 5 Generators
Authors: Worthington R. L. 
Published: December 2010

AbstractThe growth series of compact hyperbolic Coxeter groups with 4 and 5 generators are explicitly calculated. The assertions of J. Cannon and Ph. Wagreich for the 4-generated groups, that the poles of the growth series lie on the unit circle, with the exception of a single real reciprocal pair of poles, are verified. We also verify that for the 5-generated groups, this phenomenon fails.
The Normality in Products with a Countably Compact Factor
Authors: Yang Lecheng 
Published: December 2010

AbstractIt is known that the product ω1 × X of ω1 with an M1-spacemay be nonnormal. In this paper we prove that the product κ × X of an uncountable regular cardinal κ with a paracompact semi-stratifiable space is normal iff it is countably paracompact. We also give a sufficient condition under which the product of a normal space with a paracompact space is normal, from which many theorems involving such a product with a countably compact factor can be derived.
On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds
Authors: Fukuma Yoshiaki 
Published: December 2010

AbstractLet (X, L) be a polarized manifold over the complex number field with dim X = n. In this paper, we consider a conjecture of M. C. Beltrametti and A. J. Sommese and we obtain that this conjecture is true if n = 3 and h0(L) ≥ 2, or dim Bs |L| ≤ 0 for any n ≥ 3. Moreover we can generalize the result of Sommese.
On the Ideal-Triangularizability of Semigroups of Quasinilpotent Positive Operators on C(K)
Authors: Jahandideh M. T. 
Published: December 2010

AbstractIt is known that a semigroup of quasinilpotent integral operators, with positive lower semicontinuous kernels, on L2(X, μ), where X is a locally compact Hausdorff-Lindelöf space and μ is a σ-finite regular Borel measure on X, is triangularizable. In this article we use the Banach lattice version of triangularizability to establish the ideal-triangularizability of a semigroup of positive quasinilpotent integral operators on C(K) where K is a compact Hausdorff space.
A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive
Authors: Lipparini Paolo 
Published: December 2010

AbstractWe provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to the TC-commutator iff it has a (weak) difference term (is neutral) with respect to the linear commutator. We show that a variety V is congruence meet semi-distributive iff V is neutral, iff M3 is not a sublattice of Con A, for A ∈ V, iff there is a positive integer n such that .
Extremal Values of
Authors: P. Codecà  , Nair M. 
Published: December 2010

AbstractThe function Δ(x, N) as defined in the title is closely associated via Δ(N) = supx |Δ(x, N)| to several problems in the upper bound sieve. It is also known via a classical theorem of Franel that certain conjectured bounds involving averages of Δ(x, N) are equivalent to the Riemann Hypothesis. We improve the unconditional bounds which have been hitherto obtained for Δ(N) and show that these are close to being optimal. Several auxiliary results relating Δ(Np) to Δ(N), where p is a prime with pN, are also obtained and two new conjectures stated.
Inequalities for Baer Invariants of Finite Groups
Authors: Burns John , Ellis Graham 
Published: December 2010

AbstractIn this note we further our investigation of Baer invariants of groups by obtaining, as consequences of an exact sequence of A. S.-T. Lue, some numerical inequalities for their orders, exponents, and generating sets. An interesting group theoretic corollary is an explicit bound for |γc+1 (G)| given that G, Zc(G) is a finite p-group with prescribed order and number of generators.
Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball
Authors: Mascioni Vania , Molnár Lajos 
Published: December 2010

AbstractThe aim of this paper is to characterize those linear maps from a von Neumann factor A into itself which preserve the extreme points of the unit ball of A. For example, we show that if A is infinite, then every such linear preserver can be written as a fixed unitary operator times either a unital *-homomorphism or a unital *-antihomomorphism.
Dependent Automorphisms in Prime Rings
Authors: Brešar Matej , Martindale W. S. , Robert Miers C. 
Published: December 2010

AbstractFor each n ≥ 4 we construct a class of examples of a minimal C dependent set of n automorphisms of a prime ring R, where C is the extended centroid of R. For n = 4 and n = 5 it is shown that the preceding examples are completely general, whereas for n = 6 an example is given which fails to enjoy any of the nice properties of the above example.
Separating Singularities of Holomorphic Functions
Authors: Müller Jürgen , Wengenroth Jochen 
Published: December 2010

AbstractWe present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results for other classes of functions.
Some Norm Inequalities for Operators
Authors: Kittaneh Fuad 
Published: December 2010

AbstractLet Ai , Bi and Xi (i = 1, 2,…,n) be operators on a separable Hilbert space. It is shown that if f and g are nonnegative continuous functions on [0, ∞) which satisfy the relation f(t)g(t) = t for all t in [0, ∞), thenfor every r > 0 and for every unitarily invariant norm. This result improves some known Cauchy-Schwarz type inequalities. Norm inequalities related to the arithmetic-geometric mean inequality and the classical Heinz inequalities are also obtained.
A Note on Finite Dehn Fillings
Authors: Boyer S. , Zhang X. 
Published: December 2010

AbstractLet M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in H1(∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.
Non Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants
Authors: Campbell H. E. A. , Geramita A. V. , Hughes I. P. , Shank R. J. , Wehlau D. L. 
Published: December 2010

AbstractThis paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring of vector invariants ofmcopies of that representation is not Cohen-Macaulay for m ≥ 3. In the second section of the paper we use Poincaré series methods to produce upper bounds for the degrees of the generators for the ring of invariants as long as that ring is Gorenstein. We prove that, for a finite non-trivial group G and a faithful representation of dimension n with n > 1, if the ring of invariants is Gorenstein then the ring is generated in degrees less than or equal to n(|G| − 1). If the ring of invariants is a hypersurface, the upper bound can be improved to |G|.