bluuebunny/crossref_metadata_2025 huggingface dataset:
Rings With Comparability
Authors: Ferrero Miguel , Sant’Ana Alveri
Published: December 2010

The class of rings studied in this paper properly contains the class of right distributive rings which have at least one completely prime ideal in the Jacobson radical. Amongst other results we study prime and semiprime ideals, right noetherian rings with comparability and prove a structure theorem for rings with comparability. Several examples are also given.
Commutators and Analytic Dependence of Fourier-Bessel Series on (0, ∞)
Authors: Guadalupe José J. , Pérez Mario , Varona Juan L.
Published: December 2010

In this paper we study the boundedness of the commutators [b, Sn] where b is a BMO function and Sn denotes the n-th partial sum of the Fourier-Bessel series on (0, ∞). Perturbing the measure by exp(2b) we obtain that certain operators related to Sn depend analytically on the functional parameter b.
On Benson’s Definition of Area in Minkowski Space
Authors: Thompson A. C.
Published: December 2010

Let (X, ‖ . ‖) be a Minkowski space (finite dimensional Banach space) with unit ball B. Various definitions of surface area are possible in X. Here we explore the one given by Benson [1], [2]. In particular, we show that this definition is convex and give details about the nature of the solution to the isoperimetric problem.
On the Moduli Space of a Spherical Polygonal Linkage
Authors: Kapovich Michael , Millson John J.
Published: December 2010

We give a “wall-crossing” formula for computing the topology of the moduli space of a closed n-gon linkage on 𝕊2. We do this by determining the Morse theory of the function ρn on the moduli space of n-gon linkages which is given by the length of the last side—the length of the last side is allowed to vary, the first (n − 1) side-lengths are fixed. We obtain a Morse function on the (n − 2)-torus with level sets moduli spaces of n-gon linkages. The critical points of ρn are the linkages which are contained in a great circle. We give a formula for the signature of the Hessian of ρn at such a linkage in terms of the number of back-tracks and the winding number. We use our formula to determine the moduli spaces of all regular pentagonal spherical linkages.
Minimal Separators
Authors: Polat Norbert
Published: December 2010

A separator of a connected graph G is a set of vertices whose removal disconnects G. In this paper we give various conditions for a separator to contain a minimal one. In particular we prove that every separator of a connected graph that has no thick end, or which is of bounded degree, contains a minimal separator.
Smooth Maps and Real Algebraic Morphisms
Authors: Bochnak J. , Kucharz W.
Published: December 2010

Let X be a compact nonsingular real algebraic variety and let Y be either the blowup of along a linear subspace or a nonsingular hypersurface of of bidegree (1, 1). It is proved that a C1 map f : X → Y can be approximated by regular maps if and only if , where is the subgroup of H1(X, Z/2) generated by the cohomology classes of algebraic hypersurfaces in X. This follows from another result on maps into generalized flag varieties.
A Remark on the Moser-Aubin Inequality for Axially Symmetric Functions on the Sphere
Authors: Pruss Alexander R.
Published: December 2010

Let Sr be the collection of all axially symmetric functions f in the Sobolev space H1(𝕊2) such that vanishes for i = 1, 2, 3. We prove that

and that this infimum is attained. This complements recent work of Feldman, Froese, Ghoussoub and Gui on a conjecture of Chang and Yang concerning the Moser-Aubin inequality.
Trivial Units in Group Rings
Authors: Farkas Daniel R. , Linnell Peter A.
Published: December 2010

Let G be an arbitrary group and let U be a subgroup of the normalized units in ℤG. We show that if U contains G as a subgroup of finite index, then U = G. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.
Complementary Series for Hermitian Quaternionic Groups
Authors: Muić Goran , Savin Gordan
Published: December 2010

Let G be a hermitian quaternionic group. We determine complementary series for representations of G induced from super-cuspidal representations of a Levi factor of the Siegel maximal parabolic subgroup of G.
Sets of Uniqueness for Univalent Functions
Authors: Overholt Marius
Published: December 2010

We observe that any set of uniqueness for the Dirichlet space 𝐷 is a set of uniqueness for the class S of normalized univalent holomorphic functions.
Cockcroft Properties of Thompson’s Group
Authors: Bogley W. A. , Gilbert N. D. , Howie James
Published: December 2010

In a study of the word problem for groups, R. J. Thompson considered a certain group F of self-homeomorphisms of the Cantor set and showed, among other things, that F is finitely presented. Using results of K. S. Brown and R. Geoghegan, M. N. Dyer showed that F is the fundamental group of a finite two-complex Z2 having Euler characteristic one and which is Cockcroft, in the sense that each map of the two-sphere into Z2 is homologically trivial. We show that no proper covering complex of Z2 is Cockcroft. A general result on Cockcroft properties implies that no proper regular covering complex of any finite two-complex with fundamental group F is Cockcroft.
On the Prime Ideals in a Commutative Ring
Authors: Dobbs David E.
Published: December 2010

If n and m are positive integers, necessary and sufficient conditions are given for the existence of a finite commutative ring R with exactly n elements and exactly m prime ideals. Next, assuming the Axiom of Choice, it is proved that if R is a commutative ring and T is a commutative R-algebra which is generated by a set I, then each chain of prime ideals of T lying over the same prime ideal of R has at most 2|I| elements. A polynomial ring example shows that the preceding result is best-possible.
Examples of Half-Factorial Domains
Authors: Kim Hwankoo
Published: December 2010

In this paper, we determine some sufficient conditions for an A + XB[X] domain to be an HFD. As a consequencewe give new examples of HFDs of the type A + XB[X].
Twists of a General Class of L-Functions by Highly Ramified Characters
Authors: Shahidi Freydoon
Published: December 2010

It is shown that given a local L-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial Lfunction.
Some Semigroup Laws in Groups
Authors: Neumann B. H.
Published: December 2010

A challenge by R. Padmanabhan to prove by group theory the commutativity of cancellative semigroups satisfying a particular law has led to the proof of more general semigroup laws being equivalent to quite simple ones.
Growth Estimates on Positive Solutions of the Equation
Authors: Leung Man Chun
Published: December 2010

We construct unbounded positive C2-solutions of the equation in (equipped with Euclidean metric go) such that K is bounded between two positive numbers in , the conformal metric is complete, and the volume growth of g can be arbitrarily fast or reasonably slow according to the constructions. By imposing natural conditions on u, we obtain growth estimate on the -norm of the solution and show that it has slow decay.
The Zeta Function of a Pair of Quadratic Forms
Authors: Schueller Laura Mann
Published: December 2010

The zeta function of a nonsingular pair of quadratic forms defined over a finite field, k, of arbitrary characteristic is calculated. A. Weil made this computation when char k ≠ 2. When the pair has even order, a relationship between the number of zeros of the pair and the number of places of degree one in an appropriate hyperelliptic function field is established.
Hecke Operators on Jacobi-like Forms
Authors: Lee Min Ho , Myung Hyo Chul
Published: December 2010

Jacobi-like forms for a discrete subgroup are formal power series with coefficients in the space of functions on the Poincaré upper half plane satisfying a certain functional equation, and they correspond to sequences of certain modular forms. We introduce Hecke operators acting on the space of Jacobi-like forms and obtain an explicit formula for such an action in terms of modular forms. We also prove that those Hecke operator actions on Jacobi-like forms are compatible with the usual Hecke operator actions on modular forms.
A Proof of Casselman-Shahidi’s Conjecture for Quasi-split Classical Groups
Authors: Muić Goran
Published: December 2010

In this paper the author prove that standard modules of classical groups whose Langlands quotients are generic are irreducible. This establishes a conjecture of Casselman and Shahidi for this important class of groups.
Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses
Authors: Henniger J. P.
Published: December 2010

In answer to a question posed in [3], we give sufficient conditions on a Lie nilmanifold so that any ergodic rotation of the nilmanifold is metrically conjugate to its inverse. The condition is that the Lie algebra be what we call quasi-graded, and is weaker than the property of being graded. Furthermore, the conjugatingmap can be chosen to be an involution. It is shown that for a special class of groups, the condition of quasi-graded is also necessary. In certain examples there is a continuum of conjugacies.
Sums and Products of Weighted Shifts
Authors: Marcoux Laurent W.
Published: December 2010

In this article it is shown that every bounded linear operator on a complex, infinite dimensional, separable Hilbert space is a sum of at most eighteen unilateral (alternatively, bilateral) weighted shifts. As well, we classify products of weighted shifts, as well as sums and limits of the resulting operators.
Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Authors: Azagra D. , Dobrowolski T.
Published: December 2010

We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinitedimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X/F is infinite-dimensional, then X and X \ F are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and the n-torus on certain Banach spaces.
Extrapolation of Lp Data from a Modular Inequality
Authors: Bloom Steven , Kerman Ron
Published: December 2010

If an operator T satisfies a modular inequality on a rearrangement invariant space Lρ(Ω, μ), and if p is strictly between the indices of the space, then the Lebesgue inequality holds. This extrapolation result is a partial converse to the usual interpolation results. A modular inequality for Orlicz spaces takes the form , and here, one can extrapolate to the (finite) indices i(Φ) and I(Φ) aswell.
On Gunning’s Prime Form in Genus 2
Authors: Grant David
Published: December 2010

Using a classical generalization of Jacobi’s derivative formula, we give an explicit expression for Gunning’s prime form in genus 2 in terms of theta functions and their derivatives.
Invariant Measures and Natural Extensions
Authors: Haas Andrew
Published: December 2010

We study ergodic properties of a family of intervalmaps that are given as the fractional parts of certain real Möbius transformations. Included are the maps that are exactly n-to-1, the classical Gauss map and the Renyi or backward continued fraction map. A new approach is presented for deriving explicit realizations of natural automorphic extensions and their invariant measures.
The Grade Conjecture and the S2 Condition
Authors: Marcelo Agustín , Marcelo Félix , Rodríguez César
Published: December 2010

Sufficient conditions are given in order to prove the lowest unknown case of the grade conjecture. The proof combines vanishing results of local cohomology and the S2 condition.
Uniform Distribution in Model Sets
Authors: Moody Robert V.
Published: December 2010

We give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the ‘physical’) space and its internal space. We prove, assuming only that the window defining themodel set ismeasurable with compact closure, that almost surely the distribution of points in any model set from such a family is uniform in the sense of Weyl, and almost surely the model set is pure point diffractive.
On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups
Authors: Connolly Francis X. , Prassidis Stratos
Published: December 2010

It is known that the K-theory of a large class of groups can be computed from the K-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the K-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of NK0-groups that appear in the calculation of the K0-groups of virtually infinite cyclic groups.
Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant
Authors: Xia Jingbo
Published: December 2010

A well-known theorem of Sarason [11] asserts that if [Tf, Th] is compact for every h ∈ H∞, then f ∈ H∞ + C(T). Using local analysis in the full Toeplitz algebra τ = τ(L∞), we show that the membership f ∈ H∞ + C(T) can be inferred from the compactness of a much smaller collection of commutators [Tf, Th]. Using this strengthened result and a theorem of Davidson [2], we construct a proper C*-subalgebra τ(L)) of τ which has the same essential commutant as that of τ. Thus the image of τ(ℒ) in the Calkin algebra does not satisfy the double commutant relation [12], [1]. We will also show that no separable subalgebra Ѕ of τ is capable of conferring the membership f ∈ H∞ + C(T) through the compactness of the commutators {[Tf, S] : S ∈ Ѕ}.
The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry
Authors: Fernández-López Manuel , García-Río Eduardo , Kupeli Demir N.
Published: December 2010

A partial differential equation, the local Möbius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local Möbius equation and an additional partial differential equation.
Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations
Authors: Berman Stephen , Morita Jun , Yoshii Yoji
Published: December 2010

We introduce the notion of Lie algebras with plus-minus pairs as well as regular plus-minus pairs. These notions deal with certain factorizations in universal enveloping algebras. We show that many important Lie algebras have such pairs and we classify, and give a full treatment of, the three dimensional Lie algebras with plus-minus pairs.
Local Complexity of Delone Sets and Crystallinity
Authors: Lagarias Jeffrey C. , Pleasants Peter A. B.
Published: December 2010

This paper characterizes when a Delone set X in is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let NX(T) count the number of translation-inequivalent patches of radius T in X and let MX(T) be the minimum radius such that every closed ball of radius MX(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a “gap in the spectrum” of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal.

Explicitly, for NX(T), if R is the covering radius of X then either NX(T) is bounded or NX(T) ≥ T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions.

For MX(T), either MX(T) is bounded or MX(T) ≥ T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has MX(T) ≥ c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.
Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type
Authors: Sirvent V. F. , Solomyak B.
Published: December 2010

We consider two dynamical systems associated with a substitution of Pisot type: the usual -action on a sequence space, and the -action, which can be defined as a tiling dynamical system or as a suspension flow. We describe procedures for checking when these systems have pure discrete spectrum (the “balanced pairs algorithm” and the “overlap algorithm”) and study the relation between them. In particular, we show that pure discrete spectrum for the -action implies pure discrete spectrum for the -action, and obtain a partial result in the other direction. As a corollary, we prove pure discrete spectrum for every -action associated with a two-symbol substitution of Pisot type (this is conjectured for an arbitrary number of symbols).
The Number of Fields Generated by the Square Root of Values of a Given Polynomial
Authors: Cutter Pamela , Granville Andrew , Tucker Thomas J.
Published: December 2010

The abc-conjecture is applied to various questions involving the number of distinct fields , as we vary over integers n.
Crossed Products by Semigroups of Endomorphisms and Groups of Partial Automorphisms
Authors: Larsen Nadia S.
Published: December 2010

We consider a class (A; S; α) of dynamical systems, where S is an Ore semigroup and α is an action such that each αs is injective and extendible (i.e. it extends to a non-unital endomorphism of the multiplier algebra), and has range an ideal of A. We show that there is a partial action on the fixed-point algebra under the canonical coaction of the enveloping group G of S constructed in [15, Proposition 6.1]. It turns out that the full crossed product by this coaction is isomorphic to A ⋊αS. If the coaction is moreover normal, then the isomorphism can be extended to include the reduced crossed product. We look then at invariant ideals and finally, at examples of systems where our results apply.
On Certain Finitely Generated Subgroups of Groups Which Split
Authors: Moon Myoungho
Published: December 2010

Define a group G to be in the class 𝒮 if for any finitely generated subgroup K of G having the property that there is a positive integer n such that gn ∈ K for all g ∈ G, K has finite index in G. We show that a free product with amalgamation A *CB and an HNN group A *C belong to 𝒮, if C is in 𝒮 and every subgroup of C is finitely generated.
Torsion Points on Certain Families of Elliptic Curves
Authors: Wieczorek Małgorzata
Published: December 2010

Fix an elliptic curve y2 = x3 + Ax + B, satisfying A, B ∈ , A ≥ |B| > 0. We prove that the -torsion subgroup is one of (0), /3, /9. Related numerical calculations are discussed.
Answer to a Question of S. Rolewicz
Authors: Sánchez Félix Cabello , Castillo Jesús M. F.
Published: December 2010

We exhibit examples of F-spaces with trivial dual which are isomorphic to its quotient by a line, thus solving a problem in Rolewicz's Metric Linear Spaces.
Beurling-Dahlberg-Sjögren Type Theorems for Minimally Thin Sets in a Cone
Authors: Miyamoto Ikuko , Yanagishita Minoru , Yoshida Hidenobu
Published: December 2010

This paper shows that some characterizations of minimally thin sets connected with a domain having smooth boundary and a half-space in particular also hold for the minimally thin sets at a corner point of a special domain with corners, i.e., the minimally thin set at ∞ of a cone.
Group Cohomology and Lp-Cohomology of Finitely Generated Groups
Authors: Puls Michael J.
Published: December 2010

Let G be a finitely generated, infinite group, let p > 1, and let Lp(G) denote the Banach space . In this paper we will study the first cohomology group of G with coefficients in Lp(G), and the first reduced Lp-cohomology space of G. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.
Localization of the Hasse-Schmidt Algebra
Authors: Traves William N.
Published: December 2010

The behaviour of theHasse-Schmidt algebra of higher derivations under localization is studied using André cohomology. Elementary techniques are used to describe the Hasse-Schmidt derivations on certain monomial rings in the nonmodular case. The localization conjecture is then verified for all monomial rings.
Cartan Subalgebras of
Authors: Neeb Karl-Hermann , Penkov Ivan
Published: December 2010

Let V be a vector space over a field of characteristic zero and V* be a space of linear functionals on V which separate the points of V. We consider V ⊗ V* as a Lie algebra of finite rank operators on V, and set (V, V*) := V ⊗ V*. We define a Cartan subalgebra of (V, V*) as the centralizer of a maximal subalgebra every element of which is semisimple, and then give the following description of all Cartan subalgebras of (V;V*) under the assumption that is algebraically closed. A subalgebra of (V, V*) is a Cartan subalgebra if and only if it equals for some one-dimensional subspaces Vj ⊆ V and (Vj)* ⊆ V* with (Vi)* (Vj) = δij and such that the spaces . We then discuss explicit constructions of subspaces Vj and (Vj)* as above. Our second main result claims that a Cartan subalgebra of (V, V*) can be described alternatively as a locally nilpotent self-normalizing subalgebra whose adjoint representation is locally finite, or as a subalgebra h which coincides with the maximal locally nilpotent h-submodule of (V, V*), and such that the adjoint representation of is locally finite.
Singular Integrals With Rough Kernels
Authors: Al-Salman Ahmad , Pan Yibiao
Published: December 2010

In this paper we establish the Lp boundedness of a class of singular integrals with rough kernels associated to polynomial mappings.
Universal Singular Inner Functions
Authors: Gorkin Pamela , Mortini Raymond
Published: December 2010

We show that there exists a singular inner function S which is universal for noneuclidean translates; that is one for which the set is locally uniformly dense in the set of all zero-free holomorphic functions in bounded by one.
Existence of Leray's Self-Similar Solutions of the Navier-Stokes Equations In 𝒟 ⊂ ℝ3
Authors: He Xinyu
Published: December 2010

Leray's self-similar solution of the Navier-Stokes equations is defined by

where . Consider the equation for U(y) in a smooth bounded domain D of with non-zero boundary condition:

We prove an existence theorem for the Dirichlet problem in Sobolev space W1,2(D). This implies the local existence of a self-similar solution of the Navier-Stokes equations which blows up at t = t* with t* < +∞, provided the function is permissible.
Suborbit Structure of Permutation p-Groups and an Application to Cayley Digraph Isomorphism
Authors: Alspach Brian , Du Shaofei
Published: December 2010

Let P be a transitive permutation group of order pm, p an odd prime, containing a regular cyclic subgroup. The main result of this paper is a determination of the suborbits of P. The main result is used to give a simple proof of a recent result by J. Morris on Cayley digraph isomorphisms.
On Maximal k-Sections and Related Common Transversals of Convex Bodies
Authors: Makai Endre , Martini Horst
Published: December 2010

Generalizing results from [MM1] referring to the intersection body IK and the cross-section body CK of a convex body K ⊂ , d ≥ 2, we prove theorems about maximal k-sections of convex bodies, k ∈ {1, … ,d − 1}, and, simultaneously, statements about common maximal (d − 1)- and 1-transversals of families of convex bodies.
On the Berger-Coburn-Lebow Problem for Hardy Submodules
Authors: Seto Michio
Published: December 2010

In this paper we shall give an affirmative solution to a problem, posed by Berger, Coburn and Lebow, for C*-algebras on Hardy submodules.
A New Characterization of Hardy Martingale Cotype Space
Authors: Bekjan Turdebek N.
Published: December 2010

We give a new characterization of Hardy martingale cotype property of complex quasi- Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.
Isotropic Immersions with Low Codimension of Complex Space Forms into Real Space Forms
Authors: Boumuki Nobutaka
Published: December 2010

The main purpose of this paper is to determine isotropic immersions of complex space forms into real space forms with low codimension. This is an improvement of a result of S. Maeda.
A Residue Formula for SU(2)-Valued Moment Maps
Authors: Plamenevskaya Olga
Published: December 2010

Jeffrey and Kirwan gave expressions for intersection pairings on the reduced space M0 = μ−1(0)/G of a Hamiltonian G-space M in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian SU(2)-space. The definition of quasi-Hamiltonian G-spaces was introduced by Alekseev, Malkin and Meinrenken.
Hankel Convolution Operators on Spaces of Entire Functions of Finite Order
Authors: Betancor Jorge J.
Published: December 2010

In this paper we study Hankel transforms and Hankel convolution operators on spaces of entire functions of finite order and their duals.
A Restriction Theorem for a k-Surface in ℝn
Authors: Oberlin Daniel M.
Published: December 2010

We establish a sharp Fourier restriction estimate for a measure on a k-surface in ℝn, where n = k(k + 3)/2.
Diagonal Plus Tridiagonal Representatives for Symplectic Congruence Classes of Symmetric Matrices
Authors: Đoković D. Ž. , Szechtman F. , Zhao K.
Published: December 2010

Let n = 2m be even and denote by Spn(F) the symplectic group of rank m over an infinite field F of characteristic different from 2. We show that any n × n symmetric matrix A is equivalent under symplectic congruence transformations to the direct sum of m × m matrices B and C, with B diagonal andC tridiagonal. Since the Spn(F)-module of symmetric n × n matrices over F is isomorphic to the adjoint module spn(F), we infer that any adjoint orbit of Spn(F) in spn(F) has a representative in the sum of 3m − 1 root spaces, which we explicitly determine.
Logarithms and the Topology of the Complement of a Hypersurface
Authors: Zeron E. S.
Published: December 2010

This paper is devoted to analysing the relation between the logarithm of a non-constant holomorphic polynomial Q(z) and the topology of the complement of the hypersurface defined by Q(z) = 0.
On the Generalized d’Alembert's and Wilson's Functional Equations on a Compact Group
Authors: Bouikhalene Belaid
Published: December 2010

Let G be a compact group.

Let σ be a continuous involution of G. In this paper, we are concerned by the following functional equation

where f , g, h: G ⟼ ℂ, to be determined, are complex continuous functions on G such that f is central. This equation generalizes d’Alembert's and Wilson's functional equations. We show that the solutions are expressed by means of characters of irreducible, continuous and unitary representations of the group G.
Separation of Variables for
Authors: Lopes Samuel A.
Published: December 2010

Let be the positive part of the quantized enveloping algebra . Using results of Alev–Dumas and Caldero related to the center of , we show that this algebra is free over its center. This is reminiscent of Kostant's separation of variables for the enveloping algebra U(g) of a complex semisimple Lie algebra g, and also of an analogous result of Joseph–Letzter for the quantum algebra Ŭq(g). Of greater importance to its representation theory is the fact that is free over a larger polynomial subalgebra N in n variables. Induction from N to provides infinite-dimensional modules with good properties, including a grading that is inherited by submodules.
Hyperplanes of the Form f1(x, y)z1 + · · · + fk(x, y)zk + g(x, y) Are Variables
Authors: Vénéreau Stéphane
Published: December 2010

The Abhyankar–Sathaye Embedded Hyperplane Problem asks whether any hypersurface of ℂn isomorphic to ℂn–1 is rectifiable, i.e., equivalent to a linear hyperplane up to an automorphism of ℂn. Generalizing the approach adopted by Kaliman, Vénéreau, and Zaidenberg, which consists in using almost nothing but the acyclicity of ℂn–1, we solve this problem for hypersurfaces given by polynomials of ℂ[x, y, z1, … , zk] as in the title.
Going-Down Results for Ci-Fields
Authors: Bevelacqua Anthony J. , Motley Mark J.
Published: December 2010

We search for theorems that, given a Ci-field K and a subfield k of K, allow us to conclude that k is a Cj -field for some j. We give appropriate theorems in the case K = k(t) and K = k((t)). We then consider the more difficult case where K/k is an algebraic extension. Here we are able to prove some results, and make conjectures. We also point out the connection between these questions and Lang's conjecture on nonreal function fields over a real closed field.
Additive Riemann–Hilbert Problem in Line Bundles Over ℂℙ1
Authors: Dwilewicz Roman J.
Published: December 2010

In this note we consider -problem in line bundles over complex projective space ℂℙ1 and prove that the equation can be solved for (0, 1) forms with compact support. As a consequence, any Cauchy-Riemann function on a compact real hypersurface in such line bundles is a jump of two holomorphic functions defined on the sides of the hypersurface. In particular, the results can be applied to ℂℙ2 since by removing a point from it we get a line bundle over ℂℙ1.
Roots of Simple Modules
Authors: Külshammer Burkhard
Published: December 2010

We introduce roots of indecomposable modules over group algebras of finite groups, and we investigate some of their properties. This allows us to correct an error in Landrock's book which has to do with roots of simple modules.
Character Degree Graphs of Solvable Groups of Fitting Height 2
Authors: Lewis Mark L.
Published: December 2010

Given a finite group G, we attach to the character degrees of G a graph whose vertex set is the set of primes dividing the degrees of irreducible characters of G, and with an edge between p and q if pq divides the degree of some irreducible character of G. In this paper, we describe which graphs occur when G is a solvable group of Fitting height 2.
The Spectrum and Isometric Embeddings of Surfaces of Revolution
Authors: Engman Martin
Published: December 2010

A sharp upper bound on the first S1 invariant eigenvalue of the Laplacian for S1 invariant metrics on S2 is used to find obstructions to the existence of S1 equivariant isometric embeddings of such metrics in (ℝ3, can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in (ℝ3, can). This leads to generalizations of some classical results in the theory of surfaces.
A Szpilrajn–Marczewski Type Theorem for Concentration Dimension on Polish Space
Authors: Myjak Józef , Szarek Tomasz , Śleçzka Maciej
Published: December 2010

LetXbe a Polish space. We will prove that

where dimLXand dimTXstand for the concentration dimension and the topological dimension ofX, respectively.
A Characterization of Products of Projective Spaces
Authors: Occhetta Gianluca
Published: December 2010

We give a characterization of products of projective spaces using unsplit covering families of rational curves.
On the Modularity of Three Calabi–Yau Threefolds With Bad Reduction at 11
Authors: Schütt Matthias
Published: December 2010

This paper investigates the modularity of three non-rigid Calabi–Yau threefolds with bad reduction at 11. They are constructed as fibre products of rational elliptic surfaces, involving the modular elliptic surface of level 5. Their middle ℓ-adic cohomology groups are shown to split into two-dimensional pieces, all but one of which can be interpreted in terms of elliptic curves. The remaining pieces are associated to newforms of weight 4 and level 22 or 55, respectively. For this purpose, we develop a method by Serre to compare the corresponding two-dimensional 2-adic Galois representations with uneven trace. Eventually this method is also applied to a self fibre product of the Hesse-pencil, relating it to a newform of weight 4 and level 27.
Polygons with Prescribed Gauss Map in Hadamard Spaces and Euclidean Buildings
Authors: Balser Andreas
Published: December 2010

We show that given a stable weighted configuration on the asymptotic boundary of a locally compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration. Moreover, the same result holds for semistable configurations on arbitrary Euclidean buildings.
A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn
Authors: Pacelli Allison M.
Published: December 2010

In this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.
A Note on Detecting Algebraic Cycles
Authors: Ravindra G. V.
Published: December 2010

The purpose of this note is to show that the homologically trivial cycles contructed by Clemens and their generalisations due to Paranjape can be detected by the technique of spreading out. More precisely, we associate to these cycles (and the ambient varieties in which they live) certain families which arise naturally and which are defined over ℂ and show that these cycles, along with their relations, can be detected in the singular cohomology of the total space of these families.
On the Polyak–Viro Vassiliev Invariant of Degree 4
Authors: Stoimenow A.
Published: December 2010

Using the Polyak–Viro Gauss diagram formula for the degree-4 Vassiliev invariant, we extend some previous results on positive knots and the non-triviality of the Jones polynomial of untwisted Whitehead doubles.
Higher Dimensional Spaces of Functions on the Spectrum of a Uniform Algebra
Authors: Basener Richard F.
Published: December 2010

In this paper we introduce a nested family of spaces of continuous functions defined on the spectrum of a uniform algebra. The smallest space in the family is the uniform algebra itself. In the “finite dimensional” case, from some point on the spaces will be the space of all continuous complex-valued functions on the spectrum. These spaces are defined in terms of solutions to the nonlinear Cauchy–Riemann equations as introduced by the author in 1976, so they are not generally linear spaces of functions. However, these spaces do shed light on the higher dimensional properties of a uniform algebra. In particular, these spaces are directly related to the generalized Shilov boundary of the uniform algebra (as defined by the author and, independently, by Sibony in the early 1970s).
Simplicial Cohomology of Some Semigroup Algebras
Authors: Gourdeau F. , Pourabbas A. , White M. C.
Published: December 2010

In this paper, we investigate the higher simplicial cohomology groups of the convolution algebra ℓ1(S) for various semigroupsS. The classes of semigroups considered are semilattices, Clifford semigroups, regular Rees semigroups and the additive semigroups of integers greater thanafor some integera. Our results are of two types: in some cases, we show that some cohomology groups are 0, while in some other cases, we show that some cohomology groups are Banach spaces.
Functoriality of the Coniveau Filtration
Authors: Arapura Donu , Kang Su-Jeong
Published: December 2010

It is shown that the coniveau filtration on the cohomology of smooth projective varieties is preserved up to shift by pushforwards, pullbacks and products.
A Remark on a Modular Analogue of the Sato–Tate Conjecture
Authors: Kuo Wentang
Published: December 2010

The original Sato–Tate Conjecture concerns the angle distribution of the eigenvalues arising from non-CM elliptic curves. In this paper, we formulate amodular analogue of the Sato–Tate Conjecture and prove that the angles arising from non-CM holomorphic Hecke eigenforms with non-trivial central characters are not distributed with respect to the Sate–Tatemeasure for non-CM elliptic curves. Furthermore, under a reasonable conjecture, we prove that the expected distribution is uniform.
Un nouveau point de repère dans la théorie des formes automorphes
Authors: Langlands Robert P.
Published: December 2010

Ceux qui connaissent l’auteur et ses écrits, comme par exemple [L1] et [L2], savent que la notion de fonctorialité et les conjectures rattachées à celle-ci ont été introduites —en suivant ce que Artin avait fait pour un ensemble plus restreint de fonctions— pour aborder le problème de la prolongation analytique générale des fonctions L-automorphes. Ils savent en plus que je suis d’avis que seules les méthodes basées sur la formule des traces pourront aller au fond des problèmes. Il n’en reste pas moins que malgré de récents progrès importants sur le lemme fondamental et la formule des traces nous sommes bien loin de notre but.
Linking Number of Singular Links and the Seifert Matrix
Authors: Hebda James J. , Hsieh Chun-Chung , Tsau Chichen M.
Published: December 2010

We extend the notion of linking number of an ordinary link of two components to that of a singular link with transverse intersections, in which case the linking number is a half-integer. We then apply it to simplify the construction of the Seifert matrix, and therefore the Alexander polynomial, in a natural way.
On the Existence of Asymptotic-lp Structures in Banach Spaces
Authors: Tcaciuc Adi
Published: December 2010

It is shown that if a Banach space is saturated with infinite dimensional subspaces in which all “special” n-tuples of vectors are equivalent with constants independent of n-tuples and of n, then the space contains asymptotic-lp subspaces for some 1 ≤ p ≤ ∞. This extends a result by Figiel, Frankiewicz, Komorowski and Ryll-Nardzewski.
Acetylene C2H2 retrievals from MIPAS data and regions of enhanced upper tropospheric concentrations in August 2003
Authors: Parker R. J. , Remedios J. J. , Moore D. P. , Kanawade V. P.
Published: December 2010

Abstract. Acetylene (C2H2) volume mixing ratios (VMRs) have been successfully retrieved from MIPAS Level 1B radiances during August 2003. The data presented here contain most information between 300 hPa and 100 hPa based on the averaging kernels, with information also at lower altitude levels (up to 500 hPa) albeit with some influence from the 300 hPa level. In our C2H2 retrievals, data at altitude levels above 100 hPa must be treated with caution. Systematic errors are less than 10% at the upper levels but can reach higher levels at 300 hPa in the tropics due to water vapour influences. Random errors per point are less than 15% at lower pressure levels and are closer to 30% at 100 hPa. Global distributions of both the absolute C2H2 and ratios to MOPITT 150 hPa retrievals of carbon monoxide (CO) confirm some significant features for this important hydrocarbon in a characteristic summer month (August 2003), showing tight correlations regionally but globally emphasising the differences between sources and lifetimes of CO and C2H2. The ratios to CO are estimated to be accurate to approximately 10%. A strong isolation of C2H2 within the Asian monsoon anticyclone is observed, evidencing convective transport into the upper troposphere, horizontal advection within the anticyclone at 200 hPa, distinct but measurable gradients at the westward edge of the vortex and formation of a secondary dynamical feature over the Asian Pacific. The data for C2H2 strongly support evidence for a strong isolated core to the anticyclone with distinct gradients surrounding this core. Within this region, there is a relatively lower correlation of C2H2 and CO suggesting difference in injection ratios or more likely due to expected chemical processing. A second strong feature to the global distributions is observed in the enhancement and outflow of biomass burning from Africa at 200 hPa, both north-westward and eastward from 10° S. The easterly flow shows high C2H2 ratios to CO which have significantly decayed before reaching Australia. In the biomass burning regions, C2H2 and CO are relatively tightly correlated. C2H2 enhancements are observed to penetrate to lower altitudes in the African biomass outflow in this month compared to uplift observed in the Asian monsoon anticyclone region. Overall, the data show the distinctive nature of C2H2 distributions, confirm in greater detail than previously possible features of hydrocarbon enhancements in the upper troposphere and highlight the future use of MIPAS hydrocarbon data for testing model transport and OH decay regimes in the middle to upper troposphere.
A reanalysis of MODIS fine mode fraction over ocean using OMI and daily GOCART simulations
Authors: Jones T. A. , Christopher S. A.
Published: December 2010

Abstract. Using daily Goddard Chemistry Aerosol Radiation and Transport (GOCART) model simulations and columnar retrievals of 0.55 μm aerosol optical thickness (AOT) and fine mode fraction (FMF) from the Moderate Resolution Imaging Spectroradiometer (MODIS), we estimate the aerosol concentration and particle size over the global oceans between June 2006 and May 2007 due to black carbon (BC), organic carbon (OC), dust (DU), sea-salt (SS), and sulfate (SU) components. Using Aqua-MODIS aerosol properties embedded in the CERES-SSF product, we find that the mean MODIS FMF values are SS: 0.31±0.09, DU: 0.49±0.13, SU: 0.77±0.16, and (BC+OC):0.80±0.16. We further combine information from the ultraviolet spectrum using the Ozone Monitoring Instrument (OMI) onboard the Aura satellite to improve the classification process, since dust and carbonaceous aerosols have positive Aerosol Index (AI) values >0.5 while other aerosol types have near zero values. By combining MODIS and OMI datasets, we were able to identify and remove data in the SU and CC regions that were not associated with those aerosol types. The same methods used to estimate aerosol size characteristics from MODIS data within the CERES-SSF product were also applied to Level 2 (L2) MODIS aerosol data from both Terra and Aqua satellites for the same time period. As expected, FMF estimates from L2 Aqua data agreed well with the CERES-SSF dataset, also from Aqua. However, the FMF estimate for DU from Terra data was significantly lower (0.37 vs. 0.49) indicating that sensor calibration, sampling differences and/or diurnal changes in DU aerosol size characteristics were occurring. Differences for other aerosol types were generally smaller. Sensitivity studies show that a difference of 0.1 in the estimate of the anthropogenic component of FMF produces a corresponding change of 0.2 in the anthropogenic component of AOT (assuming a unit value of AOT). This uncertainty would then be passed along to any satellite-derived estimates of anthropogenic aerosol radiative effects.
High resolution rainfall – runoff measurement setup for green roof experiments in a tropical environment
Authors: Vergroesen T. , Man Joshi U. , van de Giesen N. C. , van de Ven F. H. M.
Published: December 2010

Abstract. This article describes the measurement setup that is used for green roof experiments in a tropical environment, the required data treatment to obtain reliable values of rainfall, runoff and evapotranspiration, and how to deal with external disturbances that can influence the experiment results. High resolution rainfall runoff measurements to identify, understand and properly model the relevant runoff processes in a green roof require both tailored equipment and data treatment. A tipping bucket rain gauge is calibrated for and installed to measure minute based rain intensities. A runoff measuring setup is developed that can accurately quantify the runoff up to 6 l/min, and has a high resolution in both time and volume. Two different measuring setups are used to verify the evapotranspiration that is derived from the rainfall and runoff measurements.
An attempt to model the relationship between MMI attenuation and engineering ground-motion parameters using artificial neural networks and genetic algorithms
Authors: Tselentis G-A. , Vladutu L.
Published: December 2010

Abstract. Complex application domains involve difficult pattern classification problems. This paper introduces a model of MMI attenuation and its dependence on engineering ground motion parameters based on artificial neural networks (ANNs) and genetic algorithms (GAs). The ultimate goal of this investigation is to evaluate the target-region applicability of ground-motion attenuation relations developed for a host region based on training an ANN using the seismic patterns of the host region. This ANN learning is based on supervised learning using existing data from past earthquakes. The combination of these two learning procedures (that is, GA and ANN) allows us to introduce a new method for pattern recognition in the context of seismological applications. The performance of this new GA-ANN regression method has been evaluated using a Greek seismological database with satisfactory results.
A Novel Buffering Technique for Aqueous Processing of Zinc Oxide Nanostructures and Interfaces, and Corresponding Improvement of Electrodeposited ZnO‐Cu2O Photovoltaics
Authors: Musselman Kevin P. , Marin Andrew , Wisnet Andreas , Scheu Christina , MacManus‐Driscoll Judith L. , Schmidt‐Mende Lukas
Published: December 2010

A novel buffering method is presented to improve the stability of zinc oxide processed in aqueous solutions. By buffering the aqueous solution with a suitable quantity of sacrificial zinc species, the dissolution of functional zinc oxide structures and the formation of unwanted impurities can be prevented. The method is demonstrated for ZnO films and nanowires processed in aqueous solutions used for the selective etching of mesoporous anodic alumina templates and the electrochemical deposition of Cu2O. In both cases, improved ZnO stability is observed with the buffering method. ZnO‐Cu2O heterojunction solar cells (bilayer and nanowire cells) synthesized using both traditional and buffered deposition methods are characterized by impedance spectroscopy and solar simulation measurements. Buffering the Cu2O deposition solution is found to reduce unwanted recombination at the heterojunction and improve the photovoltaic performance.
Inter‐ and Intramolecular Hydroamination of Unactivated Alkenes Catalysed by a Combination of Copper and Silver Salts: The Unveiling of a Brønstedt Acid Catalysis
Authors: Michon Christophe , Medina Florian , Capet Frédéric , Roussel Pascal , Agbossou‐Niedercorn Francine
Published: December 2010

The combined use of a copper halide, a silver salt and a phosphane ligand was applied for the catalysis of inter‐ and intramolecular hydroamination of alkenes. The reactions of unactivated olefins with nitrogen substrates were investigated. Mechanistic investigations demonstrated that the catalytic system generated a Brønsted acid which appeared to be the prominent catalytic species.
Lewis Acid‐Catalyzed CH Functionalization for Synthesis of Isoindolinones and Isoindolines
Authors: Qian Bo , Guo Shengmei , Xia Chungu , Huang Hanmin
Published: December 2010

The Lewis acid‐catalyzed CH functionalization of 2‐substituted azaarenes with N‐sulfonylaldimines has been developed, which provides a rapid and efficient approach for synthesis of heterocycle‐containing isoindolinones and isoindolines.
Chiral Amino Diol Derivatives as New Modular Organocatalysts for the Enantioselective α‐Chlorination of Cyclic β‐Keto Esters
Authors: Etayo Pablo , Badorrey Ramón , Díaz‐de‐Villegas María D. , Gálvez José A.
Published: December 2010

Highly modular chiral amino diol derivatives have been used as organocatalysts in the enantioselective α‐chlorination of cyclic β‐keto esters. Optimization of the catalyst structure and the reaction conditions has allowed the synthesis of optically active α‐chlorinated products with high enantioselectivities (up to 96% ee) using inexpensive commercially available N‐chlorosuccinimide (NCS) as the chlorine source under mild conditions.