bluuebunny/crossref_metadata_2025 huggingface dataset:
On Density of Generalized Polynomials
Authors: Dyn N. , Lubinsky D. S. , Shekhtman Boris
Published: December 2010

We consider the density in C[a, b] of generalized polynomials of the form The main point of this note is that total positivity of K(x, t) has little relationship to density: There is a symmetric, analytic, totally positive (in fact ETP (∞)) kernel K for which these generalized polynomials are not dense.
Simplicity of Categories Defined by Symmetry Axioms
Authors: Lowen-Colebunders E. , Szabo Z. G.
Published: December 2010

We consider two generalizations R0w and R0 of the usual symmetry axiom for topological spaces to arbitrary closure spaces and convergence spaces. It is known that the two properties coincide on Top and define a non-simple subcategory. We show that R0W defines a simple subcategory of closure spaces and R0 a non-simple one. The last negative result follows from the stronger statement that every epireflective subcategory of R0 Conv containing all T1 regular topological spaces is not simple. Similar theorems are shown for the topological categories Fil and Mer.
Absolute Values of Toeplitz Operators and Hankel Operators
Authors: Nakazi Takahiko
Published: December 2010

Nehari's theorem for norms of bounded Hankel operators is revisited. Using it, the absolute values of Toeplitz operators are studied. This gives a theorem of Widom and Devinatz for invertible Toeplitz operators.
Notice of Retraction
Authors: Bashir M. A.
Published: December 2010

The result of a previous paper is retracted.
A Question of Valdivia on Quasinormable Fréchet Spaces
Authors: Bonet José
Published: December 2010

It is proved that a Fréchet space is quasinormable if and only if every null sequence in the strong dual converges equicontinuously to the origin. This answers positively a question raised by Valdivia. As a consequence a positive answer to a problem of Jarchow on Fréchet Schwartz spaces is obtained.
Variations on Müntz's Theme
Authors: Borwein Peter B.
Published: December 2010

We consider some variations of Muntz's classical theorem on when Span{xλi} is dense in C[0,1]. We prove, for example, that if then the collection of spaces is dense in C[0,1] if and only if lim sup(log n)/λn = ∞. Another variation concerns the denseness of the union of spaces of the form The derivations of these results require an examination of the location of the zeros of the associated Chebyshev polynomials.
The Behaviour of Homology in the Localization of Finite Groups
Authors: Casacuberta Carles
Published: December 2010

We show that, for a finite group G and a prime p, the following facts are equivalent: (i) the p-localization homomorphism l: G —> Gp induces p-localization on integral homology; (ii) the higher homotopy groups of the Bousfield-Kan Zp-completion of a K(G, 1) vanish; (iii) the group G is p-nilpotent.
Simultaneous Monotone Lp Approximation, p → ∞
Authors: Huotari Robert , Sahab Salem
Published: December 2010

Suppose that f, g € L∞ [0,1 ] have discontinuities of the first kind only. Using the measure, max{ ∥f — h∥p, ∥g — h∥p}, of simultaneous Lp approximation, we show that the best simultaneous approximations f and g by nondecreasing functions converge uniformly as p → ∞. Part of the proof involves a discussion of discrete simultaneous approximation in a general context. Assuming only that f and g are approximately continuous, we show that their simultaneous best monotone Lp approximation is continuous.
JV-Algèbres et JH*-Algèbres
Authors: Bensebah Ali
Published: December 2010

In the present article we generalize Theorem 2.3 of [6] in the case of JV algebras without a unit element and we obtain as a consequence that the multiplicativity of the involution ((xy)* = y*x*) in the definition of a JH*-algebra is redundant (see [3]). We end this paper with a theorem on unital JH*-algebra which is a nonassociative extension of the main result in [4].
Continuous Rings with Acc on Annihilators
Authors: Camillo Victor , Yousif Mohamed F.
Published: December 2010

It is shown that a two-sided continuous ring with ascending chain condition on left annihilators is quasi-Frobenius.
On Product Partitions of Integers
Authors: Harris V. C. , Subbarao M. V.
Published: December 2010

Let p*(n) denote the number of product partitions, that is, the number of ways of expressing a natural number n > 1 as the product of positive integers ≥ 2, the order of the factors in the product being irrelevant, with p*(1) = 1. For any integer if d is an ith power, and = 1, otherwise, and let . Using a suitable generating function for p*(n) we prove that
A Beckman-Quarles Type Theorem for Coxeter's Inversive Distance
Authors: Lester J. A.
Published: December 2010

We prove that a bijective transformation on the set of circles in the real inversive plane which preserves pairs of circles a fixed inversive distance ρ > 0 apart must be induced by a Möbius transformation.
Convolutions with Unbounded Unity
Authors: Sitaramaiah V. , Subbarao M. V.
Published: December 2010

On the set F of complex-valued arithmetic functions we construct an infinite family of convolutions, that is, binary operations ψ of the form

so that (F, +, ψ) is a commutative ring, for which the unity is unbounded. Here + denotes pointwise addition.
A Tauberian Theorem Concerning Borel-Type and Riesz Summability Methods
Authors: Borwein David
Published: December 2010

It is proved that the summability of a series by the Borel-type summability method (B,α,β) together with a certain Tauberian condition implies its summability by the Riesz method (R, log(n + l),p).
Algebraic Ideals in Group Rings and Tensor Products
Authors: Lawrence John
Published: December 2010

It is shown that if a solvable group is not locally finite, then the group algebra over a field of characterisitc 0 has no nonzero algebraic ideals.
Sur un Problème Périodique
Authors: Guennoun Zine E. A.
Published: December 2010

Dans cet article, nous considérons le problème d'existence d'une solution périodique du problème de la forme: y″ = f(t,y,y′), 0 ≦ t ≦ 1 où f: [0,1 ] X R x R —> R est une fonction continue qui n'est pas nécessairement périodique et sans condition de croissance sur la variable y′. Nous obtenons certaines extensions d'un théorème du type Nirenberg ainsi que de l'équation de Liénard.
Norm One Multipliers on Subspaces of Lp
Authors: Hare Kathryn E.
Published: December 2010

We present a new elementary proof of the fact that a norm one multiplier ϕ on LP(T) satisfying ϕ(0) = ϕ(k) = 1 is k-periodic, and extend this result, when possible, to multipliers on translation invariant subspaces of LP. A consequence of our work is that all such multipliers on HP(T) are the restriction of a norm one multiplier on LP(T).
Comparison Theorems for the Eigenvalues of the Laplacian in the Unit Ball in RN
Authors: Hui Kin Ming
Published: December 2010

We obtain inequalities relating the eigenvalues of the Dirichlet and the Neumann problems for the Laplacian in the unit ball in Rn.
On the Stability of Equivariant Bifurcation Problems and Their Unfoldings
Authors: Lari-Lavassani Ali , Lu Yung-Chen
Published: December 2010

In their book Singularities and Groups in Bifurcation Theory M. Golubitsky, I. Stewart and D. Schaeffer have introduced an equivariant version of Martinet's notion of V (for variety)-equivalence with parameter. In this paper we give a unified proof that, in this context, infinitesimal stability is equivalent to stability at the local level of germs and that stability in the unfolding category is equivalent to versality.
Symmetrically Completely Bounded Linear Maps Between C*-Algebras
Authors: Tang Wai-Shing
Published: December 2010

We study the properties of a new class SCB(L, B) of bounded linear maps, called symmetrically completely bounded maps, from a linear subspace L of a C* -algebra to another C*-algebra B. This class contains the class of all completely bounded linear maps from L to B. In particular, we obtain a representation theorem for maps in SCB(L, B) when B is the algebra of all bounded linear operators on a Hilbert space.
Higher Dimensional Harmonic Volume Can be Computed as an Iterated Integral
Authors: Faucette William M.
Published: December 2010

In this paper it is shown that the computation of higher dimensional harmonic volume, defined in [1], can be reduced to Harris' computation in the onedimensional case (See [3]), so that higher dimensional harmonic volume may be computed essentially as an iterated integral. We then use this formula to produce a specific smooth curve , namely a specific double cover of the Fermat quartic, so that the image of the second symmetric product of in its Jacobian via the Abel-Jacobi map is algebraically inequivalent to the image of under the group involution on the Jacobian.
Null 2-Type Hypersurfaces in a Lorentz Space
Authors: Ferrández Angel , Lucas Pascual
Published: December 2010

In this paper, under certain hypothesis, we characterize generalized hyperbolic cylinders as the only null 2-type hypersurfaces in a Lorentz space.
A Method of Solving a Class of CIV Boundary Value Problems
Authors: Iraniparast Nezam
Published: December 2010

A method will be introduced to solve problems utt — uss = h(s, t), u(t,t) - u(1+t,1 - t), u(s,0) = g(s), u(1,1) = 0 and for (s, t) in the characteristic triangle R = {(s,t) : t ≤ s ≤ 2 — t, 0 ≤ t ≤ 1}. Here represent the directional derivatives of u in the characteristic directions e1 = (— 1, — 1) and e2 = (1, — 1), respectively. The method produces the symmetric Green's function of Kreith [1] in both cases.
Boundary Links and Mutations
Authors: Jin Gyo Taek , Ko Ki Hyoung
Published: December 2010

Mutants of boundary links may not be boundary links, not even homology boundary links. Hence mutants of homology boundary links may not be homology boundary links.
bv0-Norms for Some Triangular Matrices
Authors: Rhoades B. E.
Published: December 2010

In this paper we obtain the bv0-norms for several well-known classes of matrix operators.
Topological Completeness of Function Spaces Arising in the Hausdorff Approximation of Functions
Authors: Beer Gerald
Published: December 2010

Let X be a complete metric space. Viewing continuous real functions on X as closed subsets of X × R, equipped with Hausdorff distance, we show that C(X, R) is completely metrizable provided X is complete and sigma compact. Following the Bulgarian school of constructive approximation theory, a bounded discontinuous function may be identified with its completed graph, the set of points between the upper and lower envelopes of the function. We show that the space of completed graphs, too, is completely metrizable, provided X is locally connected as well as sigma compact and complete. In the process, when X is a Polish space, we provide a simple answer to the following foundational question: which subsets of X × R arise as completed graphs?
Non-Archimedean t-Frames and FM-Spaces
Authors: De Grande-De Kimpe N. , Perez-Garcia C. , Schikhof W. H.
Published: December 2010

We generalize the notion of t-orthogonality in p-adic Banach spaces by introducing t-frames (§2). This we use to prove that a Fréchet-Montel (FM-)space is of countable type (Theorem 3.1), the non-archimedeancounterpart of a well known theorem in functional analysis over ℝ or ℂ ([6], p. 231). We obtain several characterizations of FM-spaces (Theorem 3.3) and characterize the nuclear spaces among them (§4).
Compact Sets in CP(X) and Calibers
Authors: Kalamidas N. D. , Spiliopoulos G. D.
Published: December 2010

This presentation concerns the relation of chain conditions on a space X, with the weights of compact sets in Cp(X), generalizing up to the class of dσ-bounded spaces, or stable spaces. In the last case, stronger results are obtained for Corson compact subsets of CP(X).
Generalized Second Fundamental form for Lipschitzian Hypersurfaces by Way of Second Epi Derivatives
Authors: Noll Dominikus
Published: December 2010

Using second epi derivatives, we introduce a generalized second fundamental form for Lipschitzian hypersurfaces. In the case of a convex hypersurface, our approach leads back to the classical second fundamental form, which is usually obtained from the second fundamental forms of the outer parallel surfaces by means of a limit procedure.
An Easy Proof for Some Classical Theorems in Plane Geometry
Authors: Thas C.
Published: December 2010

The main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).
Some Characterizations of Dedekind α-Completeness of a Riesz Space
Authors: Abramovich Y. A. , Wickstead A. W.
Published: December 2010

A vector lattice F is said to be Dedekind α-complete, where α is a cardinal number, provided that each non-empty order bounded subset D of F satisfying card(D) ≤ α has a supremum. Several characterizations of this property are presented here.
Soluble Right Orderable Groups are Locally Indicable
Authors: Chiswell I. M. , Kropholler P. H.
Published: December 2010

The object of this paper is to show that every soluble right orderable group is locally indicable. The proof identifies an interesting connection between the theory of right orderable groups and the theory of amenable groups and bounded cohomology.
A Multiparameter, Zero Density Subsequence Ergodic Theorem
Authors: Cogswell Kurt D.
Published: December 2010

We generalize a result of L. Sucheston on obtaining multiparameter ergodic theorems from their single parameter versions. This result is then employed to prove a multiparameter, subsequence ergodic theorem for operator averages along special zero density subsequences.
On Logarithmic Derivatives of Functions in a Class of Starlike Mappings
Authors: Gluchoff Alan D.
Published: December 2010

The purpose of this paper is to prove some facts about integral means of (d2/dz2)(log[f(z)/z])—or equivalently f″/f, for f in a class of starlike mappings of a "singular" nature. In particular it is noted that the Koebe function is not extremal for the Hardy means Mp(r,f″/f) for functions in this class.
On Homogeneous Expansions of Mixed Norm Space Functions in the Ball
Authors: Kwon E. G.
Published: December 2010

For f analytic in the complex ball having the homogeneous expansion conditions for f to be of Hardy space Hp or of weighted Bergman spaces are expressed in terms of lp properties of the sequence {∥Fk∥p}.
M-Ideals and Function Algebras
Authors: Seddighi K. , Zahedani H.
Published: December 2010

Let C(X) be the space of all continuous complex-valued functions defined on the compact Hausdorff space X. We characterize the M-ideals in a uniform algebra A of C(X) in terms of singular measures. For a Banach function algebra B of C(X) we determine the connection between strong hulls for B and its peak sets. We also show that M(X) the space of complex regular Borel measures on X has no M-ideal.
A Local Hopf Bifurcation Theorem for a Certain Class of Implicit Differential Equations
Authors: Kaczynski Tomasz , Krawcewicz Wieslaw
Published: December 2010

The local Hopf Bifurcation theorem is extended to implicit differential equations in Rn, of the form ẋ = f(x,ẋ, α), which are not solvable for the variable ẋ. The proof uses the S1 -degree of convex-valued mappings. An example of an implicit differential equation in R3 to which the presented theorem applies is provided.
The Canary Tree
Authors: Mekler Alan H. , Shelah Saharon
Published: December 2010

A canary tree is a tree of cardinality the continuum which has no uncountable branch, but gains a branch whenever a stationary set is destroyed (without adding reals). Canary trees are important in infinitary model theory. The existence of a canary tree is independent of ZFC + GCH.
Some Asymptotic Properties of Solutions of a Neutral Delay Equation With an Oscillatory Coefficient
Authors: Graef John R. , Spikes Paul W.
Published: December 2010

The authors consider the nonlinear neutral delay differential equation

and obtain results on the asymptotic behavior of solutions. Some of the results require that P(t) has arbitrarily large zeros or that P(t) oscillates about — 1
One-Dimensional Monoid Rings with n-Generated Ideals
Authors: Okon James S. , Paul Vicknair J.
Published: December 2010

A commutative ring R is said to have the n-generator property if each ideal of R can be generated by n elements. Rings with the n-generator property have Krull dimension at most one. In this paper we consider the problem of determining when a one-dimensional monoid ring R[S] has the n-generator property where R is an artinian ring and S is a commutative cancellative monoid. As an application, we explicitly determine when such monoid rings have the three-generator property.
On the Pole Order and Hodge Filtrations of Isolated Hypersurface Singularities
Authors: Scherk John
Published: December 2010

Unlike for a smooth projective hypersurface, for an isolated hypersurface singularity, the pole order and Hodge filtrations do not in general coincide. This note studies the difference between the two.
A Note on the Entire Cyclic Cohomology of a Finite Dimensional Noncommutative Space
Authors: Klimek Slawomir , Lesniewski Andrzej
Published: December 2010

We present sufficient conditions for entire cyclic cohomology to reduce to ordinary cyclic cohomology. These conditions are characteristic for finite dimensional (noncommutative) spaces.
On the Minimal Convex Shell of a Convex Body
Authors: Peri Carla
Published: December 2010

For any convex body C in ℝd we introduce the notion of the convex shell and we prove that there exists a unique "minimal" convex shell, extending the notion of the minimal spherical shell of C. Then we prove that a "typical" convex body touches the boundary of its minimal convex shell in precisely d + 2 points.
Existence and Nonexistence of Regular Generators
Authors: Adámek J.
Published: December 2010

A total category is constructed which has no regular generator although it has an object C such that every object is a regular quotient of a copower of C.
The Maximal Spectral Type of a Rank One Transformation
Authors: Choksi J. R. , Nadkarni M. G.
Published: December 2010

In this paper it is shown that the maximal spectral type of a general rank one transformation is given by a kind of generalized Riesz product, with possibly some discrete measure.
An Oscillation Result for Singular Neutral Equations
Authors: Gyori István , Turi Janos
Published: December 2010

In this paper, extending the results in [ 1 ], we establish a necessary and sufficient condition for oscillation in a large class of singular (i.e., the difference operator is nonatomic) neutral equations.
Involutions Fixing the Disjoint Union of Odd-Dimensional Projective Spaces
Authors: Hou Duo , Torrence Bruce
Published: December 2010

We show that any differentiable involution on a closed manifold whose fixed point set is a disjoint union of odd-dimensional real projective spaces must be a bounding involution.
Poincare Duality and the Ring of Coinvariants
Authors: Kane Richard
Published: December 2010

It is shown that, in characteristic zero, a finite subgroup of a general linear group is generated by pseudo-reflections if and only if its ring of coinvariants satisfies Poincaré duality.
Finite Coverings of Rings by Ideals
Authors: Parmenter M. M.
Published: December 2010

Necessary and sufficient conditions are given for a ring to be a union of finitely many proper two-sided ideals.
Imaginary Verma Modules for Affine Lie Algebras
Authors: Futorny V. M.
Published: December 2010

We study a class of irreducible modules for Affine Lie algebras which possess weight spaces of both finite and infinite dimensions. These modules appear as the quotients of "imaginary Verma modules" induced from the "imaginary Borel subalgebra".
On a Characterization of Real Hypersurfaces of Type a in a Complex Space Form
Authors: Ki U-Hang , Suh Young-Jin
Published: December 2010

In this paper, under certain conditions on the orthogonal distribution T0, we give a characterization of real hypersurfaces of type A in a complex space form Mn(c), c ≠ 0.
Isotropic Immersions into a Real Space Form
Authors: Maeda Sadahiro , Tsukada Kazumi
Published: December 2010

The main purpose of this paper is to investigate isotropic immersions with low codimensions into a real space form.
Self-Affine Processes and the Ergodic Theorem
Authors: Vervaat Wim
Published: December 2010

Known results for strictly stable motions as finiteness of moments and local boundednessof sample-path variation are generalized to self-affine processes, i.e., self-similar processes with stationary increments. The proofs are new, even for stable motions, and are obtained by applying the ergodic theorem to powers of the (one-sided) increments.
Geometric Proofs of some Classical Results on Boundary Values for Analytic Functions
Authors: Villamor Enrique
Published: December 2010

In this note we are going to give a geometric proof, using the method of the extremal metric, of the following result of Beurling. For any analytic function f(z) in the unit disc Δ of the plane with a bounded Dirichlet integral, the set E on the boundary of the unit disc where the nontangential limits of f(z) do not exist has logarithmic capacity zero. Also, using an unpublished result of Beurling, we will prove different results on boundary values for different classes of functions.
On Closed Subsets of Root Systems
Authors: Doković D. Ž. , Check P. , Hée J.-Y.
Published: December 2010

Let R be a root system (in the sense of Bourbaki) in a finite dimensional real inner product space V. A subset P ⊂ R is closed if α, β ∊ P and α + β ∊ R imply that α + β ∊ P. In this paper we shall classify, up to conjugacy by the Weyl group W of R, all closed sets P ⊂ R such that R\P is also closed. We also show that if θ:R —> R′ is a bijection between two root systems such that both θ and θ-1 preserve closed sets, and if R has at most one irreducible component of type A1, then θ is an isomorphism of root systems.
On Rings whose Simple Modules are Flat
Authors: Hirano Yasuyuki
Published: December 2010

A ring R is called a right SF-ring if all of its simple right R-modules are flat. It is well known that a von Neumann regular ring is a right SF-ring. In this paper we study conditions under which the converse holds.
On Curves and Surfaces with Projectively Equivalent Hyperplane Sections
Authors: L'Vovsky S.
Published: December 2010

In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we make some remarks on connections between the mentioned property of a projective variety and its adjunction properties.
On an Upper Bound for the Heat Kernel on SU*(2n)/ Sp(n)
Authors: Sawyer P.
Published: December 2010

Jean-Philippe Anker made an interesting conjecture in [2] about the growth of the heat kernel on symmetric spaces of noncompact type. For any symmetric space of noncompact type, we can write

where ϕ0 is the Legendre function and q, "the dimension at infinity", is chosen such that limt—>∞Vt(x) = 1 for all x. Anker's conjecture can be stated as follows: there exists a constant C > 0 such that

where is the set of positive indivisible roots. The behaviour of the function ϕ0 is well known (see [1]).

The main goal of this paper is to establish the conjecture for the spaces SU*(2n)/ Sp(n).
Universal Spaces for Closed Images of σ-Discrete Metric Spaces
Authors: Tsuda Kôichi
Published: December 2010

We present a proof of a theorem announced by van Douwen concerning existences of universal spaces for certain closed images of σ-discrete metric spaces.
Overrings of Half-Factorial Domains
Authors: Anderson David F. , Chapman Scott T. , Smith William W.
Published: December 2010

An atomic integral domain D is a half-factorial domain (HFD) if for any irreducible elements α1,..., αn, β1,..., βm of D with α1... αn = β1 ...βm, then n = m. In [3], Anderson, Anderson, and Zafrullah explore factorization problems in overrings of HFDs and ask whether a localization of a HFD is again a HFD. We construct an example of a Dedekind domain which is a HFD, but with a localization which is not a HFD. We also give an example of a Dedekind domain where each localization is a HFD, but with an overring which is not a HFD.
Trace, Symmetry and Orthogonality
Authors: Craigen R.
Published: December 2010

Does there exist a circulant conference matrix of order > 2? When is there a symmetric Hadamard matrix with constant diagonal? How many pairwise disjoint, amicable weighing matrices of order n can there be? These are questions concerning which the trace function gives a great deal of insight. We offer easy proofs of the known solutions to the first two, the first being new, and develop new results regarding the latter question. It is shown that there are 2t disjoint amicable weighing matrices of order 2tp, where p is odd, and that this is an upper bound for t ≤ 1. An even stronger bound is obtained for certain cases.
Presentations of the Free Metabelian Group of Rank 2
Authors: Evans Martin J.
Published: December 2010

Let F3 denote the free group of rank 3 and M2 denote the free metabelian group of rank 2. We say that x * F3 is a primitive element of F3 if it can be included a in some basis of F3. We establish the existence of presentations such that N does not contain any primitive elements of F3.
Finite Complexes Whose Self-Homotopy Equivalence Groups Realize the Infinite Cyclic Group
Authors: Ken-Ichi Maruyama
Published: December 2010

Examples of finite complexes are given whose self-homotopy equivalences group is isomorphic to the group of integers.
Torsion Points of Drinfeld Modules
Authors: Bae Sunghan , Koo Jakyung
Published: December 2010

The finiteness of K-rational torsion points of a Drinfeld module of rank 2 over a locally compact complete field K with a discrete valuation is proved.
Lip α Approximation on Closed Sets with Lip α Extension
Authors: Bonilla A. , Fariña J. C.
Published: December 2010

Let F be a relatively closed subset of a domain G in the complex plane. Let f be a function that is the limit, in the Lip α norm on F, of functions which are holomorphic or meromorphic on G (0 < α < 1). We prove that, under the same conditions that give Lip α-approximation (0 < α < 1 ) on relatively closed subsets of G, it is possible to choose the approximating function m in such a way that f — m can be extended to a function belonging to lip
A Remark on a Weighted Landau Inequality of Kwong and Zettl
Authors: Brown R. C. , Hinton D. B. , Kwong M. K.
Published: December 2010

In this note we extend a theorem of Kwong and Zettl concerning the inequality

The Kwong-Zettl result holds for 1 ≤ p < ∞ and real numbers α, β, γ such that the conditions (i) β = (α + γ)/2, (ii) β > - 1 , and (iii) γ - 1 - p hold. Here the inequality is proved with β satisfying (i) for all α, γ except p — 1,-1 — p. In this case the inequality is false; however u is shown to satisfy the inequality
Semisimplicity of Free Centred Extensions
Authors: Ferrero Miguel
Published: December 2010

We prove that a free centred extension R[E] is a semisimple ring if R is a semisimple ring and C[E] is semisimple for every field C which is the extended centroid of a primitive factor of R.
Anzai and Furstenberg Transformations on the 2-Torus and Topologically Quasi-Discrete Spectrum
Authors: Kodaka Kazunori
Published: December 2010

Let 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

A 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

In 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

Let 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.
Second Fox Subgroups of Arbitrary Groups
Authors: Curzio Mario , Kanta Gupta C.
Published: December 2010

We give a complete description of the second Fox subgroup G ∩ (1 + Δ2(G)Δ(H)) relative to a given normal subgroup H of an arbitrary finitely generated group G.
The Contragredient Isotypic Component of the Regular Representation of Pseudoreflection Groups
Authors: Destrempes F. , Pianzola A.
Published: December 2010

For the regular representation of a pseudoreflection group G we characterize the occurrences of the contragredient representation as the gradient spaces of a set of Chevalley generators of the invariants of G.
The Complete Continuity Property and Finite Dimensional Decompositions
Authors: Girardi Maria , Johnson William B.
Published: December 2010

A 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

We 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.
(Z2)k-Actions Fixing a Product of Spheres and a Point
Authors: Pergher Pedro L. Q.
Published: December 2010

In the paper we identify up to bordism all manifolds with (Z2)k-action whose fixed point set is Sn × Sm U point.
Connectedness of the Invertibles in Certain Nest Algebras
Authors: Davidson Kenneth R. , Lindsay John , Pitts David R.
Published: December 2010

We 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

The 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

Let 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

A 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

It 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

We 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

If 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

Weighted 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 Some Geometric Invariants Associated to the Space of Flat Connections on an Open Space
Authors: Biswas I. , Guruprasad K.
Published: December 2010

A geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.
On the Representation of an Idempotent as a Sum of Nilpotent Elements
Authors: Ferrero M. , Puczyłowski E. R. , Sidki S.
Published: December 2010

In this paper we study in which rings a non-zero idempotent element can be presented as a sum of two nilpotent elements.
On Positive Integer Solutions of the Equation xy + yz + xz = n
Authors: Hassan Al-Zaid , Brindza B. , Pintér Á.
Published: December 2010

As 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.
A Characterization of Varieties with a Difference Term
Authors: Lipparini Paolo
Published: December 2010

We characterize, by means of congruence identities, all varieties having a weak difference term, and all neutral varieties. Our characterization of varieties with a difference term is new even in the particular case of locally finite varieties.
Numbers Of Conjugacy Class Sizes And Derived Lengths for A-Groups
Authors: Marshall Mary K.
Published: December 2010

An 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

In 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

We 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.
Deformation of the Universal Enveloping Algebra of Γ (σ1, σ2, σ3)
Authors: Zou Yi Ming
Published: December 2010

The defining relations for the Lie superalgebra Γ (σ1, σ2, σ3) as a contragredient algebra are discussed and a PBW type basis theorem is proved for the corresponding q-deformation.
On A Brownian Motion Problem of T. Salisbury
Authors: Knight Frank B.
Published: December 2010

Let 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

Given 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

This paper treats the quasilinear elliptic inequality

where 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.
Subdiagonal Algebras for Subfactors II (Finite Dimensional Case)
Authors: Saito Kichi-Suke , Watatani Yasuo
Published: December 2010

We show that finite dimensional subfactors do not have subdiagonal algebras unless the Jones index is one.
A Characterization of Real Hypersurfaces in Complex Space Forms in Terms of the Ricci Tensor
Authors: Baikoussis Christos
Published: December 2010

We study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T0.
Fonctions Elliptiques et Équations Différentielles Ordinaires
Authors: Chouikha Raouf
Published: December 2010

In 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 ODE

where 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

Nous 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.
The Dual Pair PGL3 × G2
Authors: Gross Benedict H. , Savin Gordan
Published: December 2010

Let H be the split, adjoint group of type E6 over a p-adic field. In this paper we study the restriction of the minimal representation of H to the closed subgroup PGL3 × G2.
Reflexive Representations and Banach C*-Modules
Authors: Hadwin Don , Orhon Mehmet
Published: December 2010

Suppose 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

A 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.
Coefficient Multipliers of Bergman Spaces Ap, II
Authors: Lou Zengjian
Published: December 2010

We show that the multiplier space , where X is BMOA, VMOA, B, B0 or disk algebra A. We give the multipliers from , we also give the multipliers from , C0, BMOA, and Hp.
Equivalent Presentations of Modules Over Prüfer Domains
Authors: Fuchs Laszlo , Lee Sang Bum
Published: December 2010

If 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

In 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

In 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

The 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

The 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

It 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.
Dihedral Groups of Automorphisms of Compact Riemann Surfaces
Authors: Yang Qingjie
Published: December 2010

In this note we determine which dihedral subgroups of GLg(ℂ) can be realized by group actions on Riemann surfaces of genusg> 1.