bluuebunny/crossref_metadata_2025 huggingface dataset:
Rigid Continua With Many Embeddings
Authors: Terasawa Jun
Published: December 2010

A separable metric space X is called rigid if the identity 1X is the only autohomeomorphism, and homogeneous if, for any points x, y of X, there is an (onto) homeomorphism h: X → X such that h(x) = y.

In this note, we show that this onto-ness of the homeomorphism h could not be removed in the definition of homogeneity, by constructing a continuum X which is rigid and has many embeddings, that is, for any two points x, y, there is an embedding (= into homeomorphism) h: X→X such that h(x) = y.
The Proximal Subgradient and Constancy
Authors: Clarke F. H. , Redheffer R. M.
Published: December 2010

If f is a lower semicontinuous function mapping a connected open subset of ℝn to (—∞, ∞], and if the proximal subgradient of f reduces to zero wherever it exists, then f is constant.
Small Amplitude Limit Cycles for Cubic Systems
Authors: Guíñez V. , Sáez E. , Szántó I.
Published: December 2010

In this article we study the simultaneous generation of limit cycles out of singular points and infinity for the family of cubic planar systems

With a suitable choice of parameters, the origin and four other singularities are foci and infinity is a periodic orbit. We prove that it is possible to obtain the following configuration of limit cycles: two small amplitude limit cycles out of the origin, a small amplitude limit cycle out of each of the other four foci, and a large amplitude limit cycle out of infinity. We also obtain other configurations with fewer limit cycles.
A Characterization of Proximal Subgradient Set-Valued Mappings
Authors: Poliquin R. A.
Published: December 2010

In this paper we tackle the problem of identifying set-valued mappings that are subgradient set-valued mappings. We show that a set-valued mapping is the proximal subgradient mapping of a lower semicontinuous function bounded below by a quadratic if and only if it satisfies a monotone selection property.
E-Associative Rings
Authors: Feigelstock Shalom
Published: December 2010

A ring R is E-associative if φ(xy) = φ(x)y for all endomorphisms φ of the additive group of R, and all x,y ∊ R. Unital E-associative rings are E-rings. The structure of the torsion ideal of an E-associative ring is described completely. The E-associative rings with completely decomposable torsion free additive groups are also classified. Conditions under which E-associative rings are E-rings, and other miscellaneous results are obtained.
Quelques Formules Exactes Pour des Moyennes de Fonctions L de Dirichlet
Authors: Louboutin Stéphane
Published: December 2010

Nous donnons une expression finie pour la valeur L(1, X) dès lors que X est un caractère de Dirichlet modulo f ≥ 2, impair et non principal. Cette expression, valable même lorsque ce caractère n'est pas primitif, nous permet de généraliser au théorème 2 le résultat de H. Walum sur un comportement en moyenne de ces fonctions L (sa démonstration qui fait usage de sommes de Gauss ne semble pas pouvoir être adaptée au cas de caractères non primitifs.) Nous appliquons ces résultats à l'obtention de bornes pour le nombre de classes relatif des corps cyclotomiques: nous retrouvons celles de T. Metsänkylä et de K. Feng par une méthode nous permettant de les ensuite amender.
A Metastable Result for the Finite Multidimensional Contact Process
Authors: Mountford T. S.
Published: December 2010

We prove that for a contact process restricted to the cube [1,n]d and initially fully occupied, the time to die out, when it is suitably normalized, converges to an exponential random variable as n tends to infinity.
Limit Cycles of Liénard Equations With Non Linear Damping
Authors: Urbina A.M. , León De La Barra G. , León De La Barra M. , Cañas M.
Published: December 2010

We consider the Liénard's equation with f(x) polynomial. By using the generalized polar coordinates we establish the maximum possible number of small amplitude limit cycles of such equation in terms of the degree of f(x).
Coefficient Multipliers of Mixed Norm Spaces
Authors: Jevtić Miroljub , Jovanović Ivan
Published: December 2010

We give a simple characterization of coefficient multipliers from the mixed norm space Hp,q,α, 2 ≤ p ≤ ∞, into Hu,v,β, 0 ≤ u ≤ 2, which includes the main results of Wojtaszczyk in [5]. We also calculate multipliers from the Hardy space Hp, 2 ≤ p ≤ ∞, into Hq, 0 < q ≤ 2.
Hopf Bifurcation for Implicit Neutral Functional Differential Equations
Authors: Kaczynski Tomasz , Xia Huaxing
Published: December 2010

An analog of the Hopf bifurcation theorem is proved for implicit neutral functional differential equations of the form F(xt, D′(xt, α), α) = 0. The proof is based on the method of S1-degree of convex-valued mappings. Examples illustrating the theorem are provided.
Inner Functions and Toeplitz Operators
Authors: Murphy Gerard J.
Published: December 2010

We give characterizations of Toeplitz operators on generalised H2 spaces and derive some properties of the corresponding Toeplitz algebras. The proofs depend essentially on having a "sufficient" supply of inner functions.
Autour du Théorème du Sous-Groupe Algébrique
Authors: Roy Damien , Waldschmidt Michel
Published: December 2010

A known consequence of the theorem of the algebraic subgroup is a lower bound for the rank of matrices whose entries are linear combinations, with algebraic coefficients, of logarithms of algebraic numbers. We extend this kind of result to commutative algebraic groups.
Subgroup Separability of Generalized Free Products of Free-By-Finite Groups
Authors: Allenby R. B. J. T. , Tang C. Y.
Published: December 2010

We prove that generalized free products of finitely generated free-byfinite groups amalgamating a cyclic subgroup are subgroup separable. From this it follows that if where t ≥ 1 and u, v are words on {a1,...,am} and {b1,...,bn} respectively then G is subgroup separable thus generalizing a result in [9] that such groups have solvable word problems.
Some Properties of Hankel Convolution Operators
Authors: Betancor J. J. , Marrero I.
Published: December 2010

Let be the Zemanian space of Hankel transformable generalized functions and let be the space of Hankel convolution operators for . This is the dual of a subspace of for which is also the space of Hankel convolutors. In this paper the elements of are characterized as those in and in that commute with Hankel translations. Moreover, necessary and sufficient conditions on the generalized Hankel transform are established in order that every such that in .
A Weak Hadamard Smooth Renorming of L1(Ω, μ)
Authors: Borwein Jonathan M. , Fitzpatrick Simon
Published: December 2010

We show that L1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L1.
Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
Authors: Rousseau C. , Toni B.
Published: December 2010

In this paper we study the local bifurcation of critical periods of periodic orbits in the neighborhood of a nondegenerate centre of a vector field with a homogeneous nonlinearity of the third degree. We show that at most three local critical periods bifurcate from a weak linear centre of finite order or from the linear isochrone and at most two local critical periods from the nonlinear isochrone. Moreover, in both cases, there are perturbations with the maximum number of critical periods.
Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable
Authors: Bremner Murray
Published: December 2010

We consider simple complex Lie algebras extended over the commutative ring C[z,(z — a1)-1, . . . ,(z — an)-1] where a1, . . . ,an ∊ C. We compute the universal central extensions of these Lie algebras and present explicit commutation relations for these extensions. These algebras generalize the untwisted affine Kac-Moody Lie algebras, which correspond to the case n = 1, a1 = 0.
Fields of Ga Invariants are Ruled
Authors: Deveney James K. , Finston David R.
Published: December 2010

The quotient field of the ring of invariants of a rational Ga action on Cn is shown to be ruled. As a consequence, all rational Ga actions on C4 are rationally triangulable. Moreover, if an arbitrary rational Ga action on Cn is doubled to an action of Ga × Ga on C2n, then the doubled action is rationally triangulable.
Subharmonic Extensions and Approximations
Authors: Gauthier P. M.
Published: December 2010

In this note we extend subharmonic functions defined on closed sets.
Structure Induced on Subsets of a Lattice Via Information Gathered from Tensor Products
Authors: Smith Brent
Published: December 2010

Suppose that a subset of a finite dimensional lattice has the property that there are many orthogonal tensor products that are almost 1 on the set, then the set is forced to have unusual concentrations of points in small cartesian products.
A Lattice Isomorphism Theorem for Nonsingular Retractable Modules
Authors: Zhengping Zhou
Published: December 2010

Let RM be a nonsingular module such that B = EndR(M) is left nonsingular and has as its maximal left quotient ring, where is the injective hull of RM. Then it is shown that there is a lattice isomorphism between the lattice C(M) of all complement submodules of RM and the lattice C(B) of all complement left ideals of B, and that RM is a CS module if and only if B is a left CS ring. In particular, this is the case if RM is nonsingular and retractable.
A Note on Quotient Fields of Power Series Rings
Authors: Chu Huah , Lang Yi-Chuan
Published: December 2010

Let R be an integral domain with quotient field K. If R has an overling S ≠ K, such that S[X] is integrally closed, then the "algebraic degree" of K((X)) over the quotient field of R[X] is infinite. In particular, it holds for completely integrally closed domain or Noetherian domain R.
Weak Amenability of Group Algebras of Locally Compact Groups
Authors: Despić M. , Ghahramani F.
Published: December 2010

A new proof is given for the weak amenability of the group algebras of locally compact groups.
Weighted Occupation Time for Branching Particle Systems and a Representation for the Supercritical Superprocess
Authors: Evans Steven N. , O'Connell Neil
Published: December 2010

We obtain a representation for the supercritical Dawson-Watanabe superprocessin terms of a subcritical superprocess with immigration, where the immigration at a given time is governed by the state of an underlying branching particle system. The proof requires a new result on the laws of weighted occupation times for branching particle systems.
A Singular Integral on L2(Rn)
Authors: Fan Dashan
Published: December 2010

We consider a convolution singular integral operator associated to a kernel K(x) = b(x)Ω(x)|x|-n, and prove that if b ∊ L∞(ℝn) is a radial function and Ω ∊ H(Σn-1) with mean zero condition (1), then is a bounded linear operator in the space L2(ℝn).
On Level 0 Affine Lie Modules
Authors: Britten D. J. , Lemire F. W.
Published: December 2010

It is proven that the dimensions of the homogeneous summands of a nontrivial Z graded module for an infinité dimensional Heisenberg algebra on which a central element acts as nonzero scalar are unbounded. This result is then applied to show that the central elements of an affine Lie algebra act trivially on any indecomposable diagonalizable module whose weight spaces are of bounded dimension.
A Unimodal Property of Purely Imaginary Zeros of Bessel and Related Functions
Authors: Kokologiannaki C. G. , Muldoon M. E. , Siafarikas P. D.
Published: December 2010

We show, among other things, that, for n = 0,1, the negative of the square of a purely imaginary zero of is unimodal on (n — 2, n — 1). One of the important tools in the proof is the Mittag-Leffler partial fractions expansion of .
A General Tauberian Condition that Implies Euler Summability
Authors: Parameswaran Mangalam R.
Published: December 2010

Let V be any summability method (whether linear or conservative or not), 0 < p < 1 and s a real or complex sequence. Let Ep denote the matrix of the Euler method. A theorem is proved, giving a condition under which the V-summability of Eps will imply the Ep-summability of s. This extends, in generalized form, an earlier result of N. H. Bingham who considered the case where s is a real sequence and V = B (Borel's method). It is also proved that even for real sequences, the condition given in the theorem cannot be replaced by the condition used by Bingham.
On Finite Coding Factors of a Class of Random Markov Chains
Authors: Rahe M.
Published: December 2010

For k-step Markov chains, factors generated by finite length codes split off with Bernoulli complement when maximal in entropy. Those not maximal are relatively finite in another factor which generates or splits off.

These results extend to random Markov chains with finite expected step size, implying that random Markov chains with finite expected step size can have only finitely many ergodic components, each of which is isomorphic to a finite rotation, a Bernoulli shift, or a direct product of a Bernoulli shift with a finite rotation. This result limits the type of zero entropy factors which occur in random Markov chains with finite expected step size, providing a counterpoint to the work of Kalikow, Katznelson, and Weiss, who have shown that each zero entropy process can be embedded in some random Markov chain.

Extending Rudolph and Schwarz, random Markov chains with finite expected step size are limits in of their canonical Markov approximants. The -closure of the class is the Bernoulli cross Generalized Von Neuman processes.

Finitary isomorphism of aperiodic ergodic random Markov chains with finite expected step size is considered.

Applications are made to a class of generalized baker's transformations.
Strong Commutativity Preserving Maps of Semiprime Rings
Authors: Brešar Matej , Robert Miers C.
Published: December 2010

In this paper we characterize maps f: R —> R where R is semiprime, f is additive, and [f(x),f(y)] = [x,y] for all x,y ∊ R. It is shown that f(x) = λx + ξ(x) where λ ∊ C, λ2 = 1, and ξ: R —> C is additive where C is the extended centroid of R.
Dismantlability Revisited for Ordered Sets and Graphs and the Fixed-Clique Property
Authors: Ginsburg John
Published: December 2010

We give a unified treatment of several fixed-point type theorems by using the concept of dismantlability, extended from ordered sets to arbitrary graphs. For a graph G and a vertex x of G we let NG(X) denote the set of neighbours of x in G. We say that x is a subdominant vertex of G if there is a vertex y of G, distinct from x, such that NG(x)∪{x} ⊆ NG(y)∪{y}. If G has n vertices we say that G is dismantlable if the vertices of G can be listed as x1, x2, ..., xi,..., xn such that, for all i = 1,2,..., n— 1, xi is a subdominant vertex of the graph Gi = G — {xj : j < i}
Touching Convex Sets in the Plane
Authors: Katchalski Meir , Pach János
Published: December 2010

Two subsets of the Euclidean plane touch each other if they have a point in common and there is a straight line separating one from the other.

It is shown that there exists a positive constant c such that if are families of plane convex sets with for some k ≥ 1 and if every touches every then either contains k members having nonempty intersection.
A Characterization of LCn Compacta in Terms of Gromov-Hausdorff Convergence
Authors: Kawamura Kazuhiro
Published: December 2010

It is proved that a compactum is locally n-connected if and only if it is the limit (in the sense of Gromov-Hausdorff convergence) of an "equi-locally n-connected" sequence of (at most) (n + 1)-dimensional compacta.
A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces
Authors: Steprans Juris , Watson Stephen , Just Winfried
Published: December 2010

We propose an analogue of the Banach contraction principle for connected compact Hausdorff spaces. We define a J-contraction of a connected compact Hausdorff space. We show that every contraction of a compact metric space is a J-contraction and that any J-contraction of a compact metrizable space is a contraction for some admissible metric. We show that every J-contraction has a unique fixed point and that the orbit of each point converges to this fixed point.
Every Countable Regular Space Without Isolated Points is Connectifiable
Authors: Tzannes V.
Published: December 2010

It is proved that every countable regular space without isolated points can be embedded densely in a connected Hausdorff space with a dispersion point.
Second Variation of the "Total Scalar Curvature" on Contact Manifolds
Authors: Blair D. E. , Perrone D.
Published: December 2010

Let M2n+1 be a compact contact manifold and 𝓐 the set of associated metrics. Using the scalar curvature R and the *-scalar curvature R*, in [5] we defined the "total scalar curvature", by and showed that the critical points of I(g) on 𝓐 are the K-contact metrics, i.e. metrics for which the characteristic vector field is Killing. In this paper we compute the second variation of I(g) and prove that the index of I(g) and of —I(g) are both positive at each critical point. As an application we show that the classical total scalar curvature A(g) = ∫M R dVg restricted to 𝓐 cannot have a local minimum at any Sasakian metric.
Conjugacy Separability of Generalized Free Products of Certain Conjugacy Separable Groups
Authors: Tang C. Y.
Published: December 2010

We prove that generalized free products of finitely generated free-byfinite or nilpotent-by-finite groups amalgamating a cyclic subgroup areconjugacy separable. Applying this result we prove a generalization of a conjecture of Fine and Rosenberger [7] that groups of F-type are conjugacy separable.
An Inverse Problem in the Calculus of Variations and the Characteristic Curves of Connections on SO(3)-Bundles
Authors: Atkins Richard , Ge Zhong
Published: December 2010

This paper concerns an inverse problem in the calculus of variations, namely, when a two-dimensional symmetric connection is globally a Riemannian or pseudo-Riemannian connection. Two new local characterizations of such connections in terms of the Ricci tensor and the Riemann curvature tensor respectively are given, together with a solution to the global problem. As an application, the problem of whether the characteristic curves of a connection on an SO(3)-bundle on a surface are the geodesies of a Riemannian metric on the surface is studied. Some applications to non-holonomic dynamics are discussed.
On t- Spec(R[[X]])
Authors: Dobbs David E. , Houston Evan G.
Published: December 2010

Let D be an integral domain, and let X be an analytic indeterminate. As usual, if I is an ideal of D, set It = ∪{JV = (J-1)-1 | J is a nonzero finitely generated subideal of I}; this defines the t-operation, a particularly useful star-operation on D. We discuss the t-operation on R[[X]], paying particular attention to the relation between t- dim(R) and t- dim(R[[X]]). We show that if P is a t-prime of R, then P[[X]] contains a t-prime which contracts to P in R, and we note that this does not quite suffice to show that t- dim(R[[X]]) ≥ t- dim(R) in general. If R is Noetherian, it is easy to see that t- dim(R[[X]]) ≥ t- dim(R), and we show that we have equality in the case of t-dimension 1. We also observe that if V is a valuation domain, then t-dim(V[[X]]) ≥ t- dim(V), and we give examples to show that the inequality can be strict. Finally, we prove that if V is a finite-dimensional valuation domain with maximal ideal M, then MV[[X]] is a maximal t-ideal of V[[X]].
Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains
Authors: Fu Siqi
Published: December 2010

In this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper can be stated as following:

Main Theorem. Let Ω be a strictly pseudoconvex domain with C∞ smooth boundary. Let FΩ(z,X) be either the Carathéodory or the Kobayashi metric of Ω. Let δ(z) be the signed distance from z to ∂Ω with δ(z) < 0 for z ∊ Ω and δ(z) ≥ 0 for z ∉ Ω. Then there exist a neighborhood U of ∂Ω, a constant C > 0, and a continuous function C(z,X):(U ∩ Ω) × ℂn -> ℝ such that

and|C(z,X)| ≤ C|X| for z ∊ U ∩ Ω and X ∊ ℂn
On the Periodic Radical of a Ring
Authors: Guo Xiuzhan
Published: December 2010

Let R be a ring and P(R) the sum of all periodic ideals of R. We prove that P(R) is the intersection of all prime ideals Pα such that contains no nontrivial periodic ideals. We also prove that P(R) = 0 if and only if Rs is a subdirect product of prime rings Rα with P(Rα) = 0.
An Elementary Example of a Banach Space not Isomorphic to its Complex Conjugate
Authors: Kalton N. J.
Published: December 2010

We give a simple and explicit example of a complex Banach space which is not isomorphic to its complex conjugate, and hence of two real-isomorphic spaces which are not complex-isomorphic.
Shuffling of Linear Orders
Authors: Orr John Lindsay
Published: December 2010

A linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.
Counterexamples in Nonstandard Measure Theory
Authors: Aldaz J. M. , Loeb P. A.
Published: December 2010

We show that several "good" properties of the standard part map on regular Hausdorff spaces do not hold for arbitrary Hausdorff spaces.
Tournaments and Ideal Class Groups
Authors: Kingan Robert J.
Published: December 2010

Results are given for a class of square {0,1}-matrices which provide information about the 4-rank of the ideal class group of certain quadratic number fields.
A Series of Elements of Order 4 in the Symplectic Cobordism Ring
Authors: Vershinin Vladimir V. , Anisimov Aleksandr L.
Published: December 2010

A series of elements of order 4 in the symplectic cobordism ring is constructed.
Quasi-Hereditary Endomorphism Algebras
Authors: Dlab V. , Heath P. , Marko F.
Published: December 2010

Quasi-hereditary algebras were introduced by Cline-Parshall-Scott (see [CPS] or [PS]) to deal with highest weight categories which occur in the study of semi-simple complex Lie algebras and algebraic groups. In fact, the quasi-hereditary algebras which appear in these applications enjoy a number of additional properties. The objective of this brief note is to describe a class of lean quasi-hereditary algebras [ADL] which possess such typical characteristics. A study of these questions originated in collaboration with C. M. Ringel (see [DR]).
A Note on the Relative Trace Formula
Authors: Levy Jason
Published: December 2010

This paper deals with the relative trace formula in the case of base change. Two truncations of the kernel are introduced, both based on the ideas of Arthur, and their integrals are shown to be asymptotic to each other. We also consider products of the kernel with automorphic forms, as these appear when comparing trace formulae (see [5]).
On Minimal Sets of Generators for Primitive Roots
Authors: Pappalardi Francesco
Published: December 2010

A conjecture of Brown and Zassenhaus (see [2]) states that the first log/? primes generate a primitive root (mod p) for almost all primes p. As a consequence of a Theorem of Burgess and Elliott (see [3]) it is easy to see that the first log2p log log4+∊p primes generate a primitive root (mod p) for almost all primes p. We improve this showing that the first log2p/ log log p primes generate a primitive root (mod p) for almost all primes p.
A Quantitative Estimate on Fixed-Points of Composite Meromorphic Functions
Authors: Zheng Jian-Hua
Published: December 2010

Let ƒ(z) be a transcendental meromorphic function of finite order, g(z) a transcendental entire function of finite lower order and let α(z) be a non-constant meromorphic function with T(r, α) = S(r,g). As an extension of the main result of [7], we prove that

where J has a positive lower logarithmic density.
A Sieve on Analytic Functions
Authors: Ramsay Keith
Published: December 2010

A sieve lemma is found, applicable to certain families of analytic functions on the unit disk, analogous to a large sieve lemma of P. X. Gallagher for sets of integers.
Nonexistence of Maxima for Perturbations of Some Inequalities with Critical Growth
Authors: Pruss Alexander R.
Published: December 2010

We study the question of nonexistence of extremal functions for perturbations of some sharp inequalities such as those of Moser-Trudinger (1971) and Chang- Marshall (1985). We shall show that for each critically sharp (in a sense that will be precisely defined) inequality of the form

where is a collection of measurable functions on a finite measure space (I, μ) and O a nonnegative continuous function on [0, ∞), we have a continuous Ψ on [0, ∞) with 0 ≤ Ψ ≤ Φ, but with

not being attained even if the supremum in (1) is attained. We then apply our results to the Moser-Trudinger and Chang-Marshall inequalities. Our result is to be contrasted with the fact shown by Matheson and Pruss (1994) that if Ψ(t) = o(Φ(t) as t —> ∞ then the supremum in (2) is attained. In the present paper, we also give a converse to that fact.
Nonnegative Linearization and Quadratic Transformation of Askey-Wilson Polynomials
Authors: Szwarc Ryszard
Published: December 2010

Nonnegative product linearization of the Askey-Wilson polynomials is shown for a wide range of parameters. As a corollary we obtain Rahman's result on the continuous q-Jacobi polynomials with α ≥ β > — 1 and α + β + 1 ≥ 0.
Nearrings of Continuous Functions From Topological Spaces into Topological Nearrings
Authors: Magill K. D.
Published: December 2010

Let λ be a map from the additive Euclideann-groupRninto the spaceRof real numbers and define a multiplication * onRnbyv * w = (λ(w))v. Then (Rn, + , *) is a topological nearring if and only if λ is continuous and λ(av) =aλ(v) for everyv€Rnand every a in the range ofλ. For any such mapλand any topological spaceXwe denote byNλ(X, Rn) the nearring of all continuous functions fromXinto (Rn, +, *) where the operations are pointwise. The ideals ofNλ(X, Rn) are investigated in some detail for certain λ and the results obtained are used to prove that two compact Hausdorff spacesXandYare homeomorphic if and only if the nearringsNλ(X, Rn) andNλ(Y, Rn) are isomorphic.
C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups
Authors: Goodearl K. R.
Published: December 2010

Examples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.
Convex functions on Banach spaces not containing ℓ1
Authors: Borwein Jon , Vanderwerff Jon
Published: December 2010

There is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of ℓ1. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.
A Universal Coefficient Decomposition for Subgroups Induced by Submodules of Group Algebras
Authors: Hartl Manfred
Published: December 2010

Dimension subgroups and Lie dimension subgroups are known to satisfy a ‘universal coefficient decomposition’, i.e. their value with respect to an arbitrary coefficient ring can be described in terms of their values with respect to the ‘universal’ coefficient rings given by the cyclic groups of infinite and prime power order. Here this fact is generalized to much more general types of induced subgroups, notably covering Fox subgroups and relative dimension subgroups with respect to group algebra filtrations induced by arbitrary N-series, as well as certain common generalisations of these which occur in the study of the former. This result relies on an extension of the principal universal coefficient decomposition theorem on polynomial ideals (due to Passi, Parmenter and Seghal), to all additive subgroups of group rings. This is possible by using homological instead of ring theoretical methods.
Sur les caractères d'une algèbre de Banach
Authors: Badea Catalin
Published: December 2010

A new proof for the Gleason-Kahane-Żelazko theorem concerning the characters of a Banach algebra is given. A theorem due to Pólya and Saxer is used instead of the Hadamard factorization theorem.
Monochromatic Homothetic Copies of {1, 1 + s, 1 + s + t}
Authors: Brown Tom C. , Landman Bruce M. , Mishna Marni
Published: December 2010

For positive integers s and t, let f(s, t) denote the smallest positive integer N such that every 2-colouring of [1, N] = {1, 2,...,N} has a monochromatic homothetic copy of {1, 1 + s, 1 + s + t}.

We show that f (s, t) = 4(s + t) + 1 whenever s/g and t/g are not congruent to 0 (modulo 4), where g = gcd(s, t). This can be viewed as a generalization of part of van der Waerden’s theorem on arithmetic progressions, since the 3-term arithmetic progressions are the homothetic copies of {1, 1 + 1, 1 + 1 + t}. We also show that f (s, t) = 4(s + t) + 1 in many other cases (for example, whenever s > 2t > 2 and t does not divide s), and that f (s, t) ≤ 4 (s + t) + 1 for all s, t.

Thus the set of homothetic copies of {1, 1 + s, 1 + s + t} is a set of triples with a particularly simple Ramsey function (at least for the case of two colours), and one wonders what other “natural” sets of triples, quadruples, etc., have simple (or easily estimated) Ramsey functions.
The Range of Group Algebra Homomorphisms
Authors: Kepert Andrew G.
Published: December 2010

A characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P. J. Cohen.
Theη-Invariants of Cusped Hyperbolic 3-Manifolds
Authors: Meyerhoff Robert , Ouyang Mingqing
Published: December 2010

In this paper, we define theη-invariant for a cusped hyperbolic 3-manifold and discuss some of its applications. Such an invariant detects the chirality of a hyperbolic knot or link and can be used to distinguish many links with homeomorphic complements.
D-Spaces and Resolution
Authors: Boudhraa Zineddine
Published: December 2010

A space X is a D-space if, for every neighborhood assignment f there is a closed discrete set D such that f(D) = X. In this paper we give some necessary conditions and some sufficient conditions for a resolution of a topological space to be a D-space. In particular, if a space X is resolved at each x ∊ X into a D-space Yx by continuous mappings fx: X − {x} → Yx, then the resolution is a D-space if and only if {x} × Bd(Yx) is a D-space.
A Uniform L∞ Estimate of the Smoothing Operators Related to Plane Curves
Authors: Guo Kanghui
Published: December 2010

In dealing with the spectral synthesis property for a plane curve with nonzero curvature, a key step is to have a uniform L∞ estimate for some smoothing operators related to the curve. In this paper, we will show that the same L∞ estimate holds true for a plane curve that may have zero curvature.
Approximation of Smooth Maps by Real Algebraic Morphisms
Authors: Kucharz Wojciech , Rusek Kamil
Published: December 2010

Let𝔾p,q(𝔽) be the Grassmann space of allq-dimensional𝔽-vector subspaces of𝔽p, where𝔽stands forℝ,ℂorℍ(the quaternions). Here𝔾p,q(𝔽) is regarded as a real algebraic variety. The paper investigates which C∞maps from a nonsingular real algebraic varietyXinto𝔾p,q(𝔽) can be approximated, in theC∞compact-open topology, by real algebraic morphisms.
On the Solvability of a Neumann Boundary Value Problem at Resonance
Authors: Kuo Chung-Cheng
Published: December 2010

We study the existence of solutions of the semilinear equations (1) in which the non-linearity g may grow superlinearly in u in one of directions u → ∞ and u → −∞, and (2) −Δu + g(x, u) = h, in which the nonlinear term g may grow superlinearly in u as |u| → ∞. The purpose of this paper is to obtain solvability theorems for (1) and (2) when the Landesman-Lazer condition does not hold. More precisely, we require that h may satisfy are arbitrarily nonnegative constants, . The proofs are based upon degree theoretic arguments.
A Short Proof of Euler’s Relation for Convex Polytopes
Authors: Lawrence Jim
Published: December 2010

The purpose of this paper is to present a short, self-contained proof of Euler’s relation. The ingredients of this proof are (i) the principle of inclusion and exclusion of combinatorics and (ii) the Euler characteristic; a development of the Euler characteristic is included.
Caractérisations Spectrales du Radical et du Socle d’Une Paire de Jordan-Banach
Authors: Maouche Abdelaziz
Published: December 2010

If f and g are two analytic functions from a domain D of the complex plane into respectively the Banach spaces V+ and V−, we prove that is an analytic multivalued function. From this derives the subharmonicity of the functions where ρ denotes the spectral radius. We apply these results to obtain nice caracterizations of the radical and the socle of a Banach Jordan pair, and finally we get an algebraic structural theorem.
Sequences with Translates Containing Many Primes
Authors: Brown Tom , Shiue Peter Jau-Shyong , Yu X.Y.
Published: December 2010

Garrison [3], Forman [2], and Abel and Siebert [1] showed that for all positive integers k and N, there exists a positive integer λ such that nk + λ is prime for at least N positive integers n. In other words, there exists λ such that nk + λ represents at least N primes.

We give a quantitative version of this result.We show that there exists λ ≤ xk such that nk + λ, 1 ≤ n ≤ x, represents at least primes, as x → ∞. We also give some related results.
Subordinacy Analysis and Absolutely Continuous Spectra for Sturm-Liouville Equations with Two Singular Endpoints
Authors: Clemence Dominic P.
Published: December 2010

The Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.
On Generalized Third Dimension Subgroups
Authors: Tahara Ken-Ichi , Vermani L.R. , Razdan Atul
Published: December 2010

Let G be any group, and H be a normal subgroup of G. Then M. Hartl identified the subgroup of G. In this note we give an independent proof of the result of Hartl, and we identify two subgroups of G for some subgroup K of G containing [H, G].
Pluriharmonic Symbols of Commuting Toeplitz Type Operators on the Weighted Bergman Spaces
Authors: Lee Young Joo
Published: December 2010

A class of Toeplitz type operators acting on the weighted Bergman spaces of the unit ball in the n-dimensional complex space is considered and two pluriharmonic symbols of commuting Toeplitz type operators are completely characterized.
Minimal Pencil Realizations of Rational Matrix Functions with Symmetries
Authors: Krupnik Ilya , Lancaster Peter
Published: December 2010

A theory of minimal realizations of rational matrix functionsW(λ) in the “pencil” formW(λ) =C(λA1−A2)−1Bis developed. In particular, properties of the pencil λA1−A2are discussed whenW(λ) is hermitian on the real line, and whenW(λ) is hermitian on the unit circle.
Mazur Intersection Properties for Compact and Weakly Compact Convex Sets
Authors: Vanderwerff Jon
Published: December 2010

Various authors have studied when a Banach space can be renormed so that every weakly compact convex, or less restrictively every compact convex set is an intersection of balls. We first observe that each Banach space can be renormed so that every weakly compact convex set is an intersection of balls, and then we introduce and study properties that are slightly stronger than the preceding two properties respectively.
New Characterizations of the Reflexivity in Terms of the Set of Norm Attaining Functionals
Authors: Acosta Mariá D. , Galán Manuel Ruiz
Published: December 2010

As a consequence of results due to Bourgain and Stegall, on a separable Banach space whose unit ball is not dentable, the set of norm attaining functionals has empty interior (in the norm topology). First we show that any Banach space can be renormed to fail this property. Then, our main positive result can be stated as follows: if a separable Banach space X is very smooth or its bidual satisfies the w*-Mazur intersection property, then either X is reflexive or the set of norm attaining functionals has empty interior, hence the same result holds if X has the Mazur intersection property and so, if the norm of X is Fréchet differentiable. However, we prove that smoothness is not a sufficient condition for the same conclusion.
Characterizing Continua by Disconnection Properties
Authors: Tymchatyn E. D. , Yang Chang-Cheng
Published: December 2010

We study Hausdorff continua in which every set of certain cardinality contains a subset which disconnects the space. We show that such continua are rimfinite. We give characterizations of this class among metric continua. As an application of our methods, we show that continua in which each countably infinite set disconnects are generalized graphs. This extends a result of Nadler for metric continua.
Normal Invariants of Lens Spaces
Authors: Young Carmen M.
Published: December 2010

We show that normal and stable normal invariants of polarized homotopy equivalences of lens spacesandare determined by certainl-polynomials evaluated on the elementary symmetric functions. Each polynomiallkappears as the homogeneous part of degreekin the Hirzebruch multiplicativeL-sequence. Whenn= 8, the elementary symmetric functions alone determine the relevant normal invariants.
Band-Limited Wavelets with Subexponential Decay
Authors: Dziubański Jacek , Hernández Eugenio
Published: December 2010

It is well known that the compactly supported wavelets cannot belong to the class . This is also true for wavelets with exponential decay. We show that one can construct wavelets in the class that are “almost” of exponential decay and, moreover, they are band-limited. We do this by showing that we can adapt the construction of the Lemarié-Meyer wavelets [LM] that is found in [BSW] so that we obtain band-limited, C∞-wavelets on R that have subexponential decay, that is, for every 0 < ε < 1, there exits Cε > 0 such that . Moreover, all of its derivatives have also subexponential decay. The proof is constructive and uses the Gevrey classes of functions.
Convolution with Measures on Curves in ℝ3
Authors: Oberlin Daniel M.
Published: December 2010

We study convolution properties ofmeasures on the curves (ta1 , ta2 , ta3) in .
Dow’s Principle andQ-Sets
Authors: Brendle Jörg
Published: December 2010

AQ-set is a set of reals every subset of which is a relative Gδ. We investigate the combinatorics ofQ-sets and discuss a question of Miller and Zhou on the sizeqof the smallest set of reals which is not aQ-set. We show in particular that various natural lower bounds forqare consistently strictly smaller thanq.
Embedding Coverings in Bundles
Authors: Edmonds Allan L.
Published: December 2010

IfV→Xis a vector bundle of fiber dimensionkandY→Xis a finite sheeted covering map of degreed, the implications for the Euler class e(V) inHk(X)ofVimplied by the existence of an embeddingY→Vlifting the covering map are explored. In particular it is proved that dd′e(V) = 0 where d′ is a certain divisor of d – 1, and often d′ = 1.
On the Square of the First Zero of the Bessel Function Jv(z)
Authors: Elbert Árpád , Siafarikas Panayiotis D.
Published: December 2010

Let Jv,1 be the smallest (first) positive zero of the Bessel function Jv(z), v > −1, which becomes zero when v approaches −1. Then can be continued analytically to −2 < v < −1, where it takes on negative values. We show that is a convex function of v in the interval −2 < v ≤ 0, as an addition to an old result [Á. Elbert and A. Laforgia, SIAM J. Math. Anal. 15(1984), 206–212], stating this convexity for v > 0. Also the monotonicity properties of the functions are determined. Our approach is based on the series expansion of Bessel function Jv(z) and it turned out to be effective, especially when −2 < v < −1.
On Analytic Functions of Bergman BMO in the Ball
Authors: Kwon E. G.
Published: December 2010

Let B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for which

if 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.
Instabilité de vecteurs propres d’opérateurs linéaires
Authors: Nikolskaia Ludmila
Published: December 2010

We consider some geometric properties of eigenvectors of linear operators on infinite dimensional Hilbert space. It is proved that the property of a family of vectors (xn) to be eigenvectors of a bounded operator T (admissibility property) is very instable with respect to additive and linear perturbations. For instance, (1) for the sequence to be admissible for every admissible (xn) and for a suitable choice of small numbers it is necessary and sufficient that the perturbation sequence be eventually scalar: there exist such that (Theorem 2); (2) for a bounded operator A to transform admissible families (xn) into admissible families (Axn) it is necessary and sufficient that A be left invertible (Theorem 4).
Modular Vector Invariants of Cyclic Permutation Representations
Authors: Smith Larry
Published: December 2010

Vector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group of prime order in characteristic p the image of the transfer homomorphism is a prime ideal, and the quotient algebra is a polynomial algebra on the top Chern classes of the action.
Heat Kernels of Lorentz Cones
Authors: Ding Hongming
Published: December 2010

We obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of timetand two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.
Generating Ideals in Rings of Integer-Valued Polynomials
Authors: Rush David E.
Published: December 2010

LetRbe a one-dimensional locally analytically irreducible Noetherian domain with finite residue fields. In this note it is shown that if I is a finitely generated ideal of the ring Int(R) of integer-valued polynomials such that for eachx∈ R the idealis stronglyn-generated,n≥ 2, thenIisn-generated, and some variations of this result.
The Classification of Pin4-Bundles over a 4-Complex
Authors: Weber Christian
Published: December 2010

In this paper we show that the Lie-group Pin4 is isomorphic to the semidirect product (SU2 × SU2) Z/2 where Z/2 operates by flipping the factors. Using this structure theorem we prove a classification theorem for Pin4-bundles over a finite 4-complex X.
Semigroup Algebras and Maximal Orders
Authors: Jespers Eric , Okniński Jan
Published: December 2010

We describe contracted semigroup algebras ofMalcev nilpotent semigroups that are prime Noetherian maximal orders.
Positive Definite Distributions and Subspaces of L_p With Applications to Stable Processes
Authors: Koldobsky Alexander
Published: December 2010

We define embedding of an n-dimensional normed space into L_p, 0 < p < n by extending analytically with respect to p the corresponding property of the classical Lp-spaces. The well-known connection between embeddings into Lp and positive definite functions is extended to the case of negative p by showing that a normed space embeds in L_p if and only if ‖x‖−p is a positive definite distribution. We show that the technique of embedding in L_p can be applied to stable processes in some situations where standard methods do not work. As an example, we prove inequalities of correlation type for the expectations of norms of stable vectors. In particular, for every , where X1,…,Xn and Y1,…,Yn are jointly q-stable symmetric random variables, 0 < q ≤ 2, so that, for some k ∈ ℕ, 1 ≤ k < n, the vectors (X1,…,Xk) and (Xk+1,…,Xn) have the same distributions as (Y1,…,Yk) and (Yk+1,…Yn), respectively, but Yi and Yj are independent for every choice of 1 ≤ i ≤ k, k + 1 ≤ j ≤ n.
Multilinear Proofs for Convolution Estimates for Degenerate Plane Curves
Authors: Bak Jong-Guk
Published: December 2010

Suppose that γ ∈ C2 ([0, ∞)) is a real-valued function such that γ(0) = γ′(0) = 0, and γ″(t) ≈ tm−2, for some integer m ≥ 2. Let Γ(t) = (t, γ(t)), t > 0, be a curve in the plane, and let dλ = dt be a measure on this curve. For a function ƒ on R2, let

An elementary proof is given for the optimal Lp-Lq mapping properties of T.
Subdifferential Regularity of Directionally Lipschitzian Functions
Authors: Bounkhel M. , Thibault L.
Published: December 2010

Formulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established.
On the Entire Coloring Conjecture
Authors: Sanders Daniel P. , Zhao Yue
Published: December 2010

The Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four colors. Vizing’s Theorem says that the edges of a graph with maximum degree Δ may be colored with Δ + 1 colors. In 1972, Kronk and Mitchem conjectured that the vertices, edges, and faces of a plane graph may be simultaneously colored with Δ + 4 colors. In this article, we give a simple proof that the conjecture is true if Δ ≥ 6.
Sur l’annulation de certains modules de cohomologie d’André-Quillen
Authors: Soto José J. M.
Published: December 2010

Soient A un anneau noethérien, B un anneau régulier essentiellement de type fini sur A. Si la cohomologie d’André-Quillen Hq(A, B, B) = 0 pour tout q ≥ 2 alors A est un anneau régulier.
Maximal Subbundles of Rank 2 Vector Bundles on Projective Curves
Authors: Ballico E.
Published: December 2010

Let E be a stable rank 2 vector bundle on a smooth projective curve X and V(E) be the set of all rank 1 subbundles of E with maximal degree. Here we study the varieties (non-emptyness, irreducibility and dimension) of all rank 2 stable vector bundles, E, on X with fixed deg(E) and deg(L), L ∈ V(E) and such that .
A Gauge Theoretic Proof of the Abel-Jacobi Theorem
Authors: Ionesei Gheorghe
Published: December 2010

We present a new, simple proof of the classical Abel-Jacobi theorem using some elementary gauge theoretic arguments.
Continued Fractions, Jacobi Symbols, and Quadratic Diophantine Equations
Authors: Mollin R. A. , van der Poorten A. J.
Published: December 2010

The results herein continue observations on norm form equations and continued fractions begun and continued in the works [1]−[3], and [5]−[6].