bluuebunny/crossref_metadata_2025 huggingface dataset:
A Relation Between the 2-Primary Parts of the Main Conjecture and the Birch-Tate-Conjecture
Authors: Kolster Manfred
Published: December 2010

It is shown that for totally real number fields the Main Conjecture in Iwasawa-Theory for p = 2 proposed by Fédérer implies the 2-primary part of the Birch-Tate-Conjecture in analogy with the case p odd.
Positive Harmonic Functions and Complete Metrics
Authors: Herron David A. , Schiff Joel L.
Published: December 2010

We introduce the class of Harnack domains in which a Harnack type inequality holds for positive harmonic functions with bounds given in terms of the distance to the domain's boundary. We give conditions connecting Harnack domains with several different complete metrics. We characterize the simply connected plane domains which are Harnack and discuss associated topics. We extend classical results to Harnack domains and give applications concerning the rate of growth of various functions defined in Harnack domains. We present a perhaps new characterization for quasidisks.
A Decomposition of Rings Generated by Faithful Cyclic Modules
Authors: Birkenmeier Gary F.
Published: December 2010

A ring R is said to be generated by faithful right cyclics (right finitely pseudo-Frobenius), denoted by GFC (FPF), if every faithful cyclic (finitely generated) right R-module generates the category of right R-modules. The class of right GFC rings includes right FPF rings, commutative rings (thus every ring has a GFC subring - its center), strongly regular rings, and continuous regular rings of bounded index. Our main results are: (1) a decomposition of a semi-prime quasi-Baer right GFC ring (e.g., a semiprime right FPF ring) is achieved by considering the set of nilpotent elements and the centrality of idempotnents; (2) a generalization of S. Page's decomposition theorem for a right FPF ring.
Normal Structure for Banach Spaces with Schauder Decomposition
Authors: Khamsi M. A.
Published: December 2010

We introduce a new constant in Banach spaces which implies, in certain cases, the weak- or weak*-normal structure.
Nilpotent-by-Noetherian Factorized Groups
Authors: Amberg Bernhard , Franciosi Silvana , de Giovanni Francesco
Published: December 2010

It is shown that a soluble-by-finite product G = AB of a nilpotent-by-noetherian group A and a noetherian group B is nilpotentby- noetherian. Moreover, a bound for the torsion-free rank of the Fitting factor group of G is given, in terms of the torsion-free rank of the Fitting factor group of A and the torsion-free rank of B.
Annihilating Polynomials for Group Rings and Witt Rings
Authors: Hurrelbrink Jurgen
Published: December 2010

Natural annihilating polynomials for group rings are produced; this yields, as a special case, the annihilating polynomials for Witt rings that have been discovered only recently.
A Regular Space on Which Every Real-Valued Function with a Closed Graph is Constant
Authors: Baggs Ivan
Published: December 2010

An example is given of a regular space on which every real-valued function with a closed graph is constant. It was previously known that there are regular spaces on which every continuous function is constant. It is also shown here that there are regular spaces that support only constant real-valued continuous functions, but support non-constant real-valued functions with a closed graph.
On Katětov Spaces
Authors: Porter Jack , Tikoo Mohan
Published: December 2010

Recent work by Krystock, Porter, and Vermeer has emphasized the importance of the concepts of Katětov spaces and H-sets in the theory of H-closed spaces. These properties are closely related to being the θ-closure of some set and being the adherence of an open filter. This relationship is developed by establishing, among other facts, that an H-closed space in which every closed set is the θ-closure of some set is compact and the θ-closure of a subset of an H-closed space is Katětov and characterizing the open filter adhérences of a space as precisely those sets which are the image of a closed set of the absolute of the space. Also, examples are given of a countable, scattered space which is not Katětov and an H-closed space with an H-closed subspace which is not the θ-closure of any subset of the given space.
A Note on the Distribution Function of Additive Arithmetical Functions in Short Intervals
Authors: Babu Gutti Jogesh , Erdös Paul
Published: December 2010

Let f be an additive arithmetical function having a distribution F. For any sequence let

In this note, we determine the slowest growing function b so that Qn{b, f) tends weakly to F, for various f.
Quadratic Non-Residues and Prime-Producing Polynomials
Authors: Mollin R. A. , Williams H. C.
Published: December 2010

We will be looking at quadratic polynomials having positive discriminant and having a long string of primes as initial values. We find conditions tantamount to this phenomenon involving another long string of primes for which the discriminant of the polynomial is a quadratic non-residue. Using the generalized Riemann hypothesis (GRH) we are able to determine all discriminants satisfying this connection.
lp-Norms of Some Generalized Hausdorff Matrices
Authors: Rhoades B. E.
Published: December 2010

In a recent paper D. Borwein [Math. Z. 183(1983), 483- 487] obtained an upper bound for the lp -norms of some generalized Hausdorff matrices, where the sequence (λn) satisfies the condition λn+1 ≦ λn + c, for some positive c. In this paper we obtained the lp -norms of these generalized Hausdorff matrices for which the mass functions are totally monotone.
On Skew Linear Groups Associated with Certain Soluble-by-Finite Groups
Authors: Wehrfritz B. A. F. , Shirvani M.
Published: December 2010

Let O1 denote the class of groups G such that every group ring of G (over a field) is an Ore domain. Several approaches to the correction of the proof of a result concerning subrings generated by certain O1-groups are given.
Solutions with Singular Initial Data for a Model of Electrophoretic Separation
Authors: Avrin Joel D.
Published: December 2010

Unique global strong solutions of a Cauchy problem arising in electrophoretic separation are constructed with arbitrary initial data in L1, thus generalizing an earlier global existence result. For small diffusion coefficients, the solutions can be viewed as approximate solutions for the corresponding zero-diffusion Riemann problem.
Exponential Estimates for the Conjugate Function on Locally Compact Abelian Groups
Authors: Asmar Nakhlé Habib
Published: December 2010

Let G be a locally compact Abelian group, with character group X. Suppose that X contains a measurable order P. For the conjugate function of f is the function whose Fourier transform satisfies the identity for almost all χ in X where sgnp(χ) = - 1 , 0, 1, according as We prove that, when f is bounded with compact support, the conjugate function satisfies some weak type inequalities similar to those of the Hilbert transform of a bounded function with compact support in ℝ. As a consequence of these inequalities, we prove that possesses strong integrability properties, whenever f is bounded and G is compact. In particular, we show that, when G is compact and f is continuous on G, the function is integrable for all p > 0.
On the Spectrum of the Bergman-Hilbert Matrix II
Authors: Davis Chandler , Ghatage Pratibha
Published: December 2010

We study a class of matrices (introduced by T. Kato) with principal homogeneous part, and use Mellin transform of the homogeneous kernel to determine spectral density of the positive infinite matrices.
Factors of Fields
Authors: Deveney James K. , Yanik Joe
Published: December 2010

Let L be a finitely generated extension of a field k. L is a k-rational factor if there is a field extension K of k such that the total quotient ring of L ꕕk K is a rational (pure transcendental) extension of K. We present examples of non-rational rational factors and explicitly determine both factors.
Automatic Continuity of Separating Linear Isomorphisms
Authors: Jarosz Krzysztof
Published: December 2010

A linear map A : C(T) → C(S) is called separating if f • g ≡ 0 implies Af • Ag = 0. We describe the general form of such maps and prove that any separating isomorphism is continuous.
On Multipliers into Bergman Spaces and Nevanlinna Class
Authors: Wojtaszczyk P.
Published: December 2010

We use the general factorisation theorems of Grothendieck, Nikishin and Maurey to characterise coefficient multipliers between Bergman spaces and into the Nevanlinna class.
Nearness Convergence
Authors: Naimpally S. A. , Tikoo Mohan L.
Published: December 2010

In this paper, a concept of nearness convergence is introduced which contains the proximal convergence of Leader as a special case. It is proved that uniform convergence and this nearness convergence are equivalent on totally bounded uniform nearness spaces. One of the features of this convergence is that it lies between uniform convergence and pointwise convergence, and implies uniform convergence on compacta. Some other weaker notions of nearness convergence which are sufficient to preserve nearness maps are also discussed.
On Some Combinatorial Interpretations of Slater's Identities
Authors: Lewis R. P.
Published: December 2010

Four combinatorial interpretations of identities due to L. J. Slater that have recently been published are slightly incorrect. I show how they may be corrected and also provide a new interpretation of one of these identities.
A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum
Authors: Rouhani H.
Published: December 2010

R. Ji asked whether or not a Furstenberg transformation of the 2-torus of the form (x,y) → (e2πiθx, f(x)y), where θ is irrational and f : T —> T is continuous with non-zero degree k, is topologically conjugate to the Anzai transformation (x, y) → (e2πiθx, xk y) or its inverse. In this paper this question is settled in the negative. Further, some sufficient conditions are given under which the crossed product C*-algebra associated with a Furstenberg transformation of the 2-torus has a unique tracial state.
The Product of two (Unbounded) Derivations
Authors: Pedersen Steen
Published: December 2010

We characterize when the product of two (unbounded) derivations of a C*-algebra is a derivation.
Representations of Lie Groups By Contact Transformations, I: Compact Groups
Authors: Herz Carl
Published: December 2010

The action of Lie groups as transitive groups of restricted contact transformations of compact manifolds are classified.
The Stability of a Functional Analogue of the Wave Equation
Authors: Bean Michael , Baker John A.
Published: December 2010

For h € ℝ and ϕ : ℝ2 → ℝ define Lhϕ: ℝ2 → ℝ by (Lhϕ)(x, y) = ϕ (x + h, y) + ϕ (x — h,y) — ϕ (x,y + h) — ϕ (x,y — h) for all (x,y) € ℝ2. The aim of the paper is to establish the following "stability" theorem concerning the functional equation

if δ > 0, f : ℝ2 → ℝ and

then there exists ɛ > 0 ami ϕ : ℝ2 → ℝ such that (Lhϕ)(x, y ) = 0 for all x, y,h ∊ ℝ and
On Completely Positive Maps Defined by an Irreducible Correspondence
Authors: Anantharaman-Delaroche C.
Published: December 2010

Completely positive maps defined by an irreducible correspondence between two von Neumann algebras M and N are introduced. We give results about their structure and characterize, among them, those which are extreme points in the convex set of all unital completely positive maps from M to N. As particular cases we obtain known results of M. D. Choi [4] on completely positive maps between complex matrices and of J. A. Mingo [8] on inner completely positive maps.
A Note on Sums of Primes
Authors: Granville Andrew
Published: December 2010

Under the assumption of the prime /c-tuplets conjecture we show that it is possible to construct an infinite sequence of integers, such that the average of any two is prime.
LP Approximation by Reciprocals of Trigonometric and Algebraic Polynomials
Authors: Devore Ronald A. , Leviatan D. , Yu Xiang Ming
Published: December 2010

We give an estimate for the error of Lp approximation by reciprocals of polynomials. These estimates are the analogues of the Jackson and Ditzian - Totik estimates for polynomial approximation.
On An Affine Connection Which Admits A Volume-Like Form
Authors: Chi D. P. , Yoon Y. D.
Published: December 2010

A necessary and sufficient condition to obtain a volumelike form from an affine connection is given in terms of the Čech cohomology, after the volume-like form is naturally defined without a Riemannian metric. A necessary condition for an affine connection to be a Riemannian connection for some metric is also given.
The Limiting Behavior of Sequences of Quasiconformal Mappings
Authors: Aebischer Beat
Published: December 2010

The limiting behavior of sequences of quasiconformal homeomorphisms of the n-sphere Sn is studied using a substitute to the Poincaré extension of Möbius transformations introduced by Tukia. Adapted versions of the limit set and the conical limit set known in the theory of Kleinian groups are utilized. Most of the results also hold for families of homeomorphisms of Sn with the convergence property introduced by Gehring and Martin.
The Coherence Number of 2-Groups
Authors: McCool James
Published: December 2010

Let G be a finite group. A natural invariant c(G) of G has been defined by W.J. Ralph, as the order (possibly infinite) of a distinguished element of a certain abelian group associated to G. Ralph has shown that c(Zn) = 1 and c(Z2 ⴲ Z2) = 2. In the present paper we show that c(G) is finite whenever G is a dihedral group or a 2-group, and obtain upper bounds for c(G) in these cases.
On Values of the Riemann Zeta Function at Integral Arguments
Authors: Ewell John A.
Published: December 2010

For each nonnegative integer r,

is represented by a multiple series which is expressed in terms of rational numbers and the special values of the zeta function Thus, the set serves as a kind of basis for expressing all of the values
Units in Group Rings of the Infinite Dihedral Group
Authors: Mirowicz Maciej
Published: December 2010

This paper studies the group of units U(RD∞) of the group ring of the infinite dihedral group D∞ over a commutative integral domain R. The structures of U(Z2D∞) and U(Z3D∞) are determined, and it is shown that U(ZD∞) is not finitely generated.
A Karamata Method I. Elementary Properties and Applications
Authors: Baran Mirosław
Published: December 2010

In this paper we present a new approach to classical Karamata's results concerning the Hardy-Littlewood tauberian theorem.
Comparing Graded Versions of the Prime Radical
Authors: Beattie M. A. , S.X. Liu , Stewart P. N.
Published: December 2010

Let G be a group with identity e, let λ be a normal supernilpotent radical in the category of associative rings and let λref be the reflected radical in the category of G-graded rings. Then for A a G-graded ring, λref(A) is the largest graded ideal of A whose intersection with Ae is λ (Ae). For λ = B, the prime radical, we compare Bref(A) to BG(A) = B(A)G, the largest graded ideal in B(A).
On Extending Projectives of Finite Group-Graded Algebras
Authors: Harris Morton E.
Published: December 2010

Let G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.
Jacobi Sums, Irreducible Zeta-Polynomials, and Cryptography
Authors: Koblitz Neal
Published: December 2010

We find conditions under which the numerator of the zeta-function of the curve y2+y = xd over Fp, where d — 2g +1 is a prime, d ≠ p, is irreducible over Q. This leads to the generalized Mersenne problem of "almost primality" of the number of points on the jacobian of such a curve over an extension of Fp, which has application to public key cryptography.
On Some Conjectures on Neutral Differential Equations
Authors: Qian Chuanxi
Published: December 2010

In [2], Ladas and Sficas made two conjectures about the asymptotic behavior of solutions of some neutral differential equations. In this paper we confirm that these conjectures are indeed correct.
Simultaneous Triangularization of Algebras of Polynomially Compact Operators
Authors: Radjabalipour M.
Published: December 2010

If A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.
The Hilbert Problem—A Distributional Approach
Authors: Chaudhry M. A. , Pandey J. N.
Published: December 2010

A distributional solution to the Hilbert problem in dimension > 1 is given.
Two Continua Having A Property of J. L. Kelley
Authors: Ingram W. T. , Sherling D. D.
Published: December 2010

In proving the contractibility of certain hyperspaces J. L. Kelley identified and defined a certain uniformnessproperty which he called Property 3.2. It is known that the classes of locally connected continua, homogeneous continua and hereditarily indecomposable continua have Property 3.2. In this paper we prove that two examples of indecomposable continua developed respectively by the authors have Property 3.2. One is the example of a nonchainable atriodic tree-like continuum with positive span which was defined by the first author, and the other is a nonchainable, noncircle-like continuum which has the cone=hyperspace property which was defined by the second author. Each of the examples is an inverse limit of an inverse system having a single bonding map.
Special Principal Ideal Rings and Absolute Subretracts
Authors: Jespers Eric
Published: December 2010

A ringRis said to be an absolute subretract if for any ringSin the variety generated byRand for any ring monomorphismffromRintoS, there exists a ring morphismgfromStoRsuch that gf is the identity mapping. This concept, introduced by Gardner and Stewart, is a ring theoretic version of an injective notion in certain varieties investigated by Davey and Kovacs.

Also recall that a special principal ideal ring is a local principal ring with nonzero nilpotent maximal ideal. In this paper (finite) special principal ideal rings that are absolute subretracts are studied.
A Limit Theorem for Brownian Motion in a Random Scenery
Authors: Remillard Bruno , Dawson Donald A.
Published: December 2010

We find the limiting distribution of , where {Bu}u≧0 is the standard Brownian motion on ℝd, V is a particular random potential and {an}n≧1 is a normalizing sequence.
Δ-Moves On Links and Jones Polynomial Evaluations
Authors: Silver Daniel S.
Published: December 2010

We determine the effect on the Jones polynomial evaluated att = iand t = eπi/3of an oriented link whenever certain twists are performed.
On the Dual of Projective Varieties
Authors: Ballico E.
Published: December 2010

Here we give examples and classifications of varieties with strange behaviour for the enumeration of contacts (answering a question raised by Fulton, Kleiman, MacPherson). Then we give upper and lower bounds (in terms of the degree) for the non-zero ranks of a projective variety.
The Minimal Primal Ideal Space of a C*-Algebra and Local Compactness
Authors: Beckhoff Ferdinand
Published: December 2010

This paper is concerned with local compactness of the minimal primal ideal space of a C*-algebra, a sufficient condition is given. The property in question has bad hereditary properties as is shown by examples.
A Finitely Generated Modular Ortholattice
Authors: Bruns Gunter , Roddy Michael
Published: December 2010

We discuss [2] of the same title and offer an alternative example. This example is a subalgebra of the ortholattice of closed subspaces of separable real Hilbert space.
The Entrance Space of a Measure-Valued Markov Branching Process Conditioned on Non-Extinction
Authors: Evans Steven N.
Published: December 2010

We explicitly identify the possible probability entrance laws for a class of measure-valued processes that are constructed by taking a particular measure-valued Markov branching process and conditioning it to stay away from the zero measure trap. The set of extreme points of the entrance space is larger than the state space of the conditioned process, and contains elements which correspond tostartingthe conditioned process at the zero measure.
The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval
Authors: Hofbauer Franz , Raith Peter
Published: December 2010

We consider a piecewise monotonie and piecewise continuous map T on the interval. If T has a derivative of bounded variation, we show for an ergodic invariant measure μ with positive Ljapunov exponent λμ that the Hausdorff dimension of μ equals hμ / λμ.
The Poset of Conjugacy Classes and Decomposition of Products in the Symmetric Group
Authors: Bédard François , Goupil Alain
Published: December 2010

The action by multiplication of the class of transpositions of the symmetric group on the other conjugacy classes defines a graded poset as described by Birkhoff ([2]). In this paper, the edges of this poset are given a weight and the structure obtained is called the poset of conjugacy classes of the symmetric group. We use weights of chains in the posets to obtain new formulas for the decomposition of products of conjugacy classes of the symmetric group in its group algebra as linear combinations of conjugacy classes and we derive a new identity involving partitions of
n.
Universal Compact T1 -Spaces
Authors: Mysior Adam
Published: December 2010

For every infinite cardinal k we construct a space Ck universal for all compact T1 -spaces of weight ≤ k. It follows, in particular, that there are only 2k topologically different compact T1 -spaces. We show that Cw is universal for all second countable developable T1 -spaces. The existence of closely universal compact T1 -spaces is discussed.
An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials
Authors: Jones William B. , Thron W. J. , Wyshinski Nancy J.
Published: December 2010

It is known that the n-th denominators Qn (α, β, z) of a real J-fraction

where

form an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formula

the convergence being uniform on compact subsets of
On the Residual Finiteness of Polygonal Products of Nilpotent Groups
Authors: Kim Goansu , Tang C. Y.
Published: December 2010

In general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.
Weakness of the Topology of a JB*-Algebra
Authors: Bensebah Ali
Published: December 2010

The main purpose of this paper is to prove, that the topology of any (non-complete) algebra norm on a JB* -algebra is stronger than the topology of the usual norm. The proof of this theorem consists of an adaptation of the recent Rodriguez proof [8] that every homomorphism from a complex normed (associative) Q-algebra onto a B*-algebra is continuous.
Conditions for the Separability of Objects in Two-Dimensional Velocity Fields
Authors: Foldes Stephan
Published: December 2010

We consider the directed graph representing the obstruction relation between objects moving along the streamlines of a two-dimensional velocity field. A collection of objects is sequentially separable if and only if the corresponding graph has no directed cycles. A sufficient condition for this is the permeability of closed Jordan curves.
Conorme et Inverse Généralisé Dans Les C*-Algèbres
Authors: Mbekhta Mostafa
Published: December 2010

Dans ce travail, on étudie les propriétés de la conorme, c(a) d'un élément a d'une C*-algèbre A. Nous montrons que c(a) est aussi douée de la condition de B*- algèbre, c'est-à-dire qu'elle vérifie l'égalité: c(a)2 = c(a*a) = c(aa*) = c(a*)2. Nous remarquons que la conorme est invariante par restriction à toute sous-C*-algèbre de A, propriété connue pour le spectre.

Soit {an} une suite d'éléments réguliers telle que an → a régulier. Nous donnons des conditions nécessaires et suffisantes pour que où a† désigne l'inverse de Moore-Penrose de a.
Nörlund Operators On lp
Authors: Borwein David
Published: December 2010

The Nörlund matrix Na is the triangular matrix {an-k /An}, where an ≥ 0 and An := a0 + a1 + • • • + an > 0. It is proved that, subject to the existence of α := lim nan/An, Na ∊ B(lp) for 1 < p < ∞ if and only if α < ∞. It is also proved that it is possible to have Na ∊ B(lp) for 1 < p < ∞ when sup nan/An = ∞.
Descriptions of the Characteristic Sequence of an Irrational
Authors: Brown Tom C.
Published: December 2010

Let α be a positive irrational real number. (Without loss of generality assume 0 < α < 1.) The characteristic sequence of α is

f(α) =f1f2 ···, where fn = [(n + 1)α] - [nα].

We make some observations on the various descriptions of the characteristic sequence of α which have appeared in the literature. We then refine one of these descriptions in order to obtain a very simple derivation of an arithmetic expression for [nα] which appears in A. S. Fraenkel, J. Levitt, and M. Shimshoni [17]. Some concluding remarks give conditions on n which are equivalent to fn = 1.
Weighted Restriction for Curves
Authors: Lakey Joseph D.
Published: December 2010

We prove weighted norm inequalities for the Fourier transform of the form

where v is a nonnegative weight function on ℝd and ψ: [— 1,1 ] —> ℝd is a nondegenerate curve. Our results generalize unweighted (i.e. v = 1) restriction theorems of M. Christ, and two-dimensional weighted restriction theorems of C. Carton-Lebrun and H. Heinig.
A Sequence of Results on Class Number Congruences
Authors: Costa Antone
Published: December 2010

Let p ≡ 1 mod 8 be a rational prime and let h(—p) be the class number of . In [1], Barrucand and Cohn show that h(-p) = 0 mod 8 iff p = x2 + 32y2 for some x,y € Z. In this article, we generalize their result to a family of relative quadratic extensions K/F, where Fk is the maximum totally real subfield of Q(ζ2k+2 ), and a power of a prime of Fk from a family of positive density.
On Maximal Residue Difference Sets Modulo p
Authors: Fabrykowski J.
Published: December 2010

A residue difference set modulo p is a set A = {a1,a2,...,ak} of integers 1 ≤ ai ≤ p — 1 such that for all i and j with i ≠ j, where is the Legendre symbol. We give a lower and an upper bound for mp—the P maximal cardinality of such set A in the case of p ≡ 1 (mod 4).
Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua
Authors: Grispolakis J. , Nikiel J. , Simone J. N. , Tymchatyn E. D.
Published: December 2010

Let X be a Hausdorff space which is the continuous image of an ordered continuum. We prove that every irreducible separator of X is metrizable. This is a far reaching extension of the 1967 theorem of S. Mardešić which asserts that X has a basis of open sets with metrizable boundaries. Our first result is then used to show that, in particular, if Y is an hereditarily locally connected continuum, then for subsets of Y quasi-components coincide with components, and that the boundary of each connected open subset of Y is accessible by ordered continua. These results answer open problems in the literature due to the fourth and third authors, respectively.
Orlicz Spaces Without Strongly Extreme Points and Without H-Points
Authors: Hudzik Henryk
Published: December 2010

W. Kurc [5] has proved that in the unit sphere of Orlicz space LΦ(μ) generated by an Orlicz function Φ satisfying the suitable Δ2-condition and equipped with the Luxemburg norm every extreme point is strongly extreme. In this paper it is proved in the case of a nonatomic measure μ that the unit sphere of the Orlicz space LΦ(μ) generated by an Orlicz function Φ which does not satisfy the suitable Δ2-condition and equipped with the Luxemburg norm has no strongly extreme point and no H-point.
Bicyclic and Bass Cyclic Units in Group Rings
Authors: Jespers E. , Leal G. , Parmenter M. M.
Published: December 2010

The subgroup generated by the Bass cyclic and bicyclic units is of infinite index in the group of units of the integral group ring ZG when G is either D or
A Topology for the Solid Subsets of a Topological Space
Authors: Lucchetti Roberto , Torre Anna , Wets Roger J.-B.
Published: December 2010

A new topology for the closed subsets of a topological space X which are the closure of their interiors is defined and investigated. Some applications to convergence of regular measures are also given.
On PP-Endomorphism Rings
Authors: Nicholson W. K.
Published: December 2010

A characterization is given of when all kernels (respectively images) of endomorphisms of a module are direct summands, a necessary condition being that the endomorphism ring itself is a left (respectively right) PP-ring. This result generalizes theorems of Small, Lenzing and Colby-Rutter and shows that R is left hereditary if and only if the endomorphism ring of every injective left module is a right PP-ring.
A Remark on Convolution With Measures Supported on Curves
Authors: Pan Yibiao
Published: December 2010

Let λ be a certain measure supported on a curve in R3. We prove that
if the curve has nonzero curvature and torsion, then λ * L3/2 ⊂ L2.
Barnes' First Lemma and its Finite Analogue
Authors: Helversen-Pasotto Anna , Solé Patrick
Published: December 2010

We give a parallel proof of Barnes' first lemma and of its finite analogue. In both cases we use the Mellin transform. In the classical case, the proof avoids the residue theorem. In the finite case the Gamma function is replaced by the Gaussian sum function and the beta function by the Jacobi sum function.
Representations of Compact Right Topological Groups
Authors: Milnes Paul
Published: December 2010

Compact right topological groups arise naturally as the enveloping semigroups of distal flows. Recently, John Pym and the author established the existence of Haar measure μ on such groups, which invites the consideration of the regular representations. We start here by characterizing the continuous representations of a compact right topological group G, and are led to the conclusion that the right regular representation r is not continuous (unless G is topological). The domain of the left regular representation l is generally taken to be the topological centre

or a tractable subgroup of it, furnished with a topology stronger than the relative topology from G (the goals being to have l both defined and continuous). An analysis of l and r on H = L2(G) for some non-topological compact right topological groups G shows, among other things, that:

(i)

for the simplest (perhaps) G generated by ℤ, (l, H) decomposes into one copy of each irreducible representation of ℤ and c copies of the regular representation.

(ii)

for the simplest (perhaps) G generated by the euclidean group of the plane , (l, H) decomposes into one copy of each of the continuous one-dimensional representations of and c copies of each continuous irreducible representation Ua,a > 0.

(iii)

when Λ(G) is not dense in G, it can seem very reasonable to regard r as a continuous representation of a related compact topological group, and also, G can be almost completely "lost" in the measure space (G, μ).
On Ideals Annihilating the Toral Class of BP*((BZ/PK)N)
Authors: Nakos George
Published: December 2010

A sequence of ideals Ik,n ⊆ BP* is introduced, with the property: Ik,n ⊆ Ann(γk,n), where γk,n is the toral class of the Brown-Peterson homology of the n-fold product BZ/pk × ··· × BZ/pk. These ideals seem to play an interesting and yet unclear role in understanding Ann(γk,n). They are defined by using the formal group law of the Brown-Peterson spectrum BP, and some of their elementary properties are established. By using classical theorems of Landweber and of Ravenel-Wilson, the author computes the radicals of Ik,n and Ann(γk,n), and discusses a few examples.
The Collineation Groups of Figueroa Planes
Authors: Batten Lynn M. , Johnson Peter M.
Published: December 2010

We describe the structure of the collineation groups of Figueroa planes, giving examples and explanations that show why the description in Dempwolff [3] is not completely accurate. We also give criteria for when Figueroa planes are isomorphic, and show that certain subplanes are Figueroa or Pappian planes.
Oscillations of Second Order Neutral Differential Equations
Authors: Ruan Shigui
Published: December 2010

In this paper, we consider the oscillatory behavior of the second order neutral delay differential equation

wheret ≥ t0,Tandσare positive constants,a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.
Blow Analytic Mappings and Functions
Authors: Yoshinaga Etsuo
Published: December 2010

Let π: M —> Rn be the blowing-up of Rn at the origin. Then a continuous map-germ f: (Rn — 0,0) —> Rm is called blow analytic if there exists an analytic map-germ such that Then an inverse mapping theorem for blow analytic mappings as a generalization of classical theorem is shown. And the following is shown. Theorem: The analytic family of blow analytic functions with isolated singularities admits an analytic trivialization after blowing-up.
A Note on the Analogue of the Bogomolov Type Theorem on Deformations of CR-Structures
Authors: Akahori Takao , Miyajima Kimio
Published: December 2010

Let (M, °T″) be a compact strongly pseudo-convex CR-manifold with trivial canonical line bundle. Then, in [A-M2], a weak version of the Bogomolov type theorem for deformations of CR-structures was shown by an analogy of the Tian- Todorov method. In this paper, we show that: in the very strict sense, there is a counterexample.
The σ-Linkedness of the Measure Algebra
Authors: Dow Alan , Steprans Juris
Published: December 2010

It is shown that the measure algebra on the space 22ω is σ-n-linked for each n ∊ ω.
Small Sets of k-th Powers
Authors: Ding Ping , Freedman A. R.
Published: December 2010

Let k ≥ 2 and q = g(k) — G(k), where g(k) is the smallest possible value of r such that every natural number is the sum of at most r k-th powers and G(k) is the minimal value of r such that every sufficiently large integer is the sum of r k-th powers. For each positive integer r ≥ q, let Then for every ε > 0 and N ≥ N(r, ε), we construct a set A of k-th powers such that |A| ≤ (r(2 + ε)r + l)N1/(k+r) and every nonnegative integer n ≤ N is the sum of k-th powers in A. Some related results are also obtained.
On a Property of Nilpotent Groups
Authors: Dokuchaev Michael
Published: December 2010

Let g be an element of a group G and [g, G] = 〈g-1a-1ga | a ∊ G〉. We prove that if G is locally nilpotent then for each g,t ∊ G either g[g, G] = t[t, G] or g[g, G] ∩ t[t, G] = Ø. The converse is true if G is finite.
Atomless Lattice-Ordered Groups
Authors: Glass A. M. W.
Published: December 2010

We show the existence of atomless lattice-ordered groups which have doubly transitive representations. In so doing, we answer a question of M. Giraudet from 1981 [4].
One Sided SF-Rings with Certain Chain Conditions
Authors: Xiao Yufei
Published: December 2010

We prove that with some weak chain conditions, left SF-rings are semisimple Artinian or regular. We also prove that MERT left SF-rings are really regular.
On The Tails of the Exponential Series
Authors: Yalçin Yildirim C.
Published: December 2010

A relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.
Factorization in LCM Domains with Conjugation
Authors: Beauregard Raymond A.
Published: December 2010

An atomic integral domain with conjugation has unique (in the sense of Theorem 6 below) factorization of atomic factors if it is an LCM domain. If the LCM hypothesis is dropped not even the number of atomic factors in a complete factorization of an element need be unique.
A Note on Epi-Convergence
Authors: Beer Gerald
Published: December 2010

Let LSC(X) denote the set of extended real valued lower semicontinuous functions on a metrizable space X. If f, f1, f2, f3,... is a sequence in LSC(X), we say 〈fn〉 is epi-convergent to f provided the sequence of epigraphs 〈epi fn〉 is Kuratowski- Painlevé convergent to epi f. In this note we address the following question: what conditions on f and/or on X are necessary and sufficient for this mode of convergence to force epigraphical convergence with respect to the stronger Hausdorff metric and Vietoris topologies?
Global Hypoellipticity of a Class of Second Order Operators
Authors: Bergamasco Adalberto P. , Zani Sérgio Luís
Published: December 2010

We show that almost all perturbations P — λ, λ € C, of an arbitrary constant coefficient partial differential operator P are globally hypoelliptic on the torus. We also give a characterization of the values λ € C for which the operator is globally hypoelliptic; in particular, we show that the addition of a term of order zero may destroy the property of global hypoellipticity of operators of principal type, contrary to that happens with the usual (local) hypoellipticity.
Parareductive Operators on Banach Spaces
Authors: Drnovšek Roman
Published: December 2010

This note gives a Banach space extension of the Hilbert space result due to P. A. Fillmore (see [3]). In particular, it is shown that the adjoint T* = A — iB of an operator T = A + iB (with A and B hermitian) is a polynomial in T if and only if T* leaves invariant every linear subspace invariant under T, and this is equivalent to the assertion that T* leaves invariant every paraclosed subspace invariant under T.
Angular Derivative and Compactness of Composition Operators on Large Weighted Hardy Spaces
Authors: Zorboska Nina
Published: December 2010

We show that a restriction on the angular derivative of the inducing map does not determine compact composition operators on large weighted Hardy spaces, thus answering in the negative a question posed by T. Kriete.
Inherently Nonfinitely Based Solvable Algebras
Authors: Kearnes Keith , Willard Ross
Published: December 2010

We prove that an inherently nonfinitely based algebra cannot generate an abelian variety. On the other hand, we show by example that it is possible for an inherently nonfinitely based algebra to generate a strongly solvable variety.
On Infinite Locally Finite Groups
Authors: Rhemtulla Akbar , Smith Howard
Published: December 2010

If G is a group such that every infinite subset of G contains a commuting pair of elements then G is centre-by-finite. This result is due to B. H. Neumann. From this it can be shown that if G is infinite and such that for every pair X, Y of infinite subsets of G there is some x in X and some y in Y that commute, then G is abelian. It is natural to ask if results of this type would hold with other properties replacing commutativity. It may well be that group axioms are restrictive enough to provide meaningful affirmative results for most of the properties. We prove the following result which is of similar nature.

If G is a group such that for each positive integer n and for every n infinite subset X1,...,Xn of G there exist elements xi of Xii = 1,... ,n, such that the subgroup generated by {x1,... ,xn} is finite, then G is locally finite.
Hopf's Ergodic Theorem for Particles with Different Velocities and the "Strong Sweeping out Property"
Authors: Bellow A. , Calderón A. P. , Krengel U.
Published: December 2010

In an earlier paper we provided a counterexample to an old conjecture of Hopf. In this note we show that the "strong sweeping out property" obtains for the Hopf operators (Tt) both when t —> +∞ and when t —> 0+, that is a.e. convergence fails in the worst possible way.
The Class Number Formula of a Real Quadratic Field and an Estimate of the Value of a Unit
Authors: Mitsuhiro T. , Nakahara T. , Uehara T.
Published: December 2010

Our aim is to give an arithmetical expression of the class number formula of real quadratic fields. Starting from the classical Dirichlet class number formula, our proof goes along arithmetical lines not depending on any analytical method such as an estimate for
On Traces of Separable Simple Sub Algebras in Matrix Rings
Authors: Nagahara Takasi , Yokota Seiya
Published: December 2010

For the trace map on an irreducible semigroup of n × n matrices over a field, I. N. Herstein presented a theorem in [3] which enables us to limit the nature of matrix groups of a certain kind. However, this is incorrect in general. For the theorem, we shall present a counter example, a revision, and some generalizations to non-irreducible semigroups.
Positive Linear Mappings Between C*-Algebras
Authors: Zhong Yong
Published: December 2010

We prove that a positive unital linear mapping from a von Neumann algebra to a unital C*-algebra is a Jordan homomorphism if it maps invertible selfadjoint elements to invertible elements, and that for any compact Hausdorff space X, all positive unital linear mappings from C(X) into a unital C*-algebra that preserve the invertibility for self-adjoint elements are *-homomorphisms if and only if X is totally disconnected.
An Extension Theorem Concerning Frechet Measures
Authors: Blei Ron C.
Published: December 2010

An F-measure on a Cartesian product of algebras of sets is a scalar-valued function which is a scalar measure independently in each coordinate. It is demonstrated that an F-measure on a product of algebras determines an F-measure on the product of the corresponding σ-algebras if and only if its Fréchet variation is finite. An analogous statement is obtained in a framework of fractional Cartesian products of algebras, and a measurement of p-variation of F-measures, based on Littlewood-type inequalities, is discussed.
Homéomorphismes Uniformes Entre les Sphères Unité des Espaces D'Interpolation
Authors: Daher Mohamad
Published: December 2010

Si (A0,A1) est un couple d'interpolation et si A0 est uniformément convexe on montre que pour tous θ1, θ2 ∊ ]0,1 [ il existe un homéomorphisme uniforme entre la sphère unité de (A0,A1)θ1 et la sphère unité de (A0, A1)θ2.
m-Dimensional Schlömilch Series
Authors: Miller Allen R.
Published: December 2010

By using the principle of mathematical induction a simple algebraic formula is derived for an m-dimensional Schlömilch series. The result yields a countably infinite number of representations for null-functions on increasingly larger open intervals.
Finite-Dimensional Subspaces of the p-Adic Space ℓ∞
Authors: Perez-Garcia C. , Schikhof Wim H.
Published: December 2010

For finite-dimensional subspaces of ℓ∞ over a non-archimedean valued base field K we study orthocomplementation as related to the Hahn-Banach property and strictness. As a corollary we obtain that, if K is not spherically complete, a closed hyperplane in c0 having the Hahn-Banach property is orthocomplemented (Theorem 2.1, Remark 2).
Semiprime Rings with Hypercentral Derivations
Authors: Lee Tsiu-Kwen
Published: December 2010

LetRbe a semiprime ring with a derivationd, λ a left ideal ofRandk, ntwo positive integers. Suppose that[d(xn),xn]k= 0 for allx∊ λ. Then [λ,R]d(R)= 0. That is, there exists a central idempotente∊U, the left Utumi quotient ring ofR, such thatdvanishes identically oneUand λ(l —e) is central in (1 —e)U
Divisor Sums of Generalised Exponential Polynomials
Authors: Everest G. R. , Shparlinski I. E.
Published: December 2010

A study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units. In the case of an integral binary recurrence sequence, similar (but stronger) results were obtained by P. Erdős, P. Kiss and C. Pomerance.
The Division Algorithm in Complex Bases
Authors: Gilbert William J.
Published: December 2010

Complex numbers can be represented in positional notation using certain Gaussian integers as bases and digit sets. We describe a long division algorithm to divide one Gaussian integer by another, so that the quotient is a periodic expansion in such a complex base. To divide by the Gaussian integer w in the complex base b, using a digit set D, the remainder must be in the set wT(b,D) ∩ ℤ[i], where T(b,D) is the set of complex numbers with zero integer part in the base. The set T(b,D) tiles the plane, and can be described geometrically as the attractor of an iterated function system of linear maps. It usually has a fractal boundary. The remainder set can be determined algebraically from the cycles in a certain directed graph.
On Self-Injective Perfect Rings
Authors: Herbera Dolors , Shamsuddin Ahmad
Published: December 2010

Let R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A ∩ B) = r(A) + r(B) for all left ideals A and B of R.
Backward Continued Fractions and their Invariant Measures
Authors: Gröchenig Karlheinz , Haas Andrew
Published: December 2010

This paper continues our investigation of backward continued fractions, associated with the generalized Renyi maps on [0,1). We first show that the dynamics of the shift map on a specific class of shift invariant spaces of nonnegative integer sequences exactly models the maps Tu for u € (0,4). In the second part we construct a new family of explicit invariant measures for certain values of the parameter u.
Purely Infinite Simple C*-Crossed Products II
Authors: Jeong JA A. , Kodaka Kazunori , Osaka Hiroyuki
Published: December 2010

We study the pure infiniteness of C* -crossed products by endomorphisms and automorphisms. Let A be a purely infinité simple unital C*-algebra. At first we show that a crossed product A × p N by a corner endomorphism p is purely infinite if it is simple. From this observation we prove that any simple C*-crossed products A ×αZ by an automorphism α is purely infinite. Combining this with the result in [Je] on pure infiniteness of crossed products by finite groups, one sees that if α is an outer action by a countable abelian group G then the simple C*-algebra A ×α G is purely infinite.
Quasi-Duality, Linear Compactness and Morita Duality for Power Series Rings
Authors: Xue Weimin
Published: December 2010

AS a generalization of Morita duality, Kraemer introduced the notion of quasi-duality and showed that each left linearly compact ring has a quasi-duality. Let R be an associative ring with identity and R[[x]] the power series ring. We prove that (1) R[[x]] has a quasi-duality if and only if R has a quasi-duality; (2) R[[x]] is left linearly compact if and only if R is left linearly compact and left noetherian; and (3) R[[x]] has a Morita duality if and only if R is left noetherian and has a Morita duality induced by a bimodule RUS such that S is right noetherian.
Uniform Kadec-Klee Lorentz Spaces Lw,1 and Uniformly Concave Functions
Authors: Dilworth S. J. , Lennard C. J.
Published: December 2010

We consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces Lw,1 that have the weak-star uniform Kadec-Klee property as precisely those for which the antiderivative ϕ of w is uniformly concave; building on recent work of Dilworth and Hsu. We also derive a quite general sufficient condition for a twice-differentiable ϕ to be uniformly concave; and explore the extent to which this condition is necessary.