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351. CMB 2004 (vol 47 pp. 417)

Niu, Pengcheng; Han, Yanwu; Han, Junqiang
A Hopf Type Lemma and a CR Type Inversion for the Generalized Greiner Operator
In this paper we establish a Hopf type lemma and a CR type inversion for the generalized Greiner operator. Some nonlinear

Keywords:Hopf type lemma, CR inversion, Liouville type, theorem generalized Greiner operator

352. CMB 2004 (vol 47 pp. 389)

He, Jianxun
An Inversion Formula of the Radon Transform Transform on the Heisenberg Group
In this paper we give an inversion formula of the Radon transform on the Heisenberg group by using the wavelets defined in [3]. In addition, we characterize a space such that the inversion formula of the Radon transform holds in the weak sense.

Keywords:wavelet transform, Radon transform, Heisenberg group
Categories:43A85, 44A15

353. CMB 2004 (vol 47 pp. 343)

Drensky, Vesselin; Hammoudi, Lakhdar
Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. Like all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the considered problem and combinatorics of words.

Keywords:locally nilpotent rings,, nil rings, locally nilpotent semigroups,, semigroup algebras, monomial algebras, infinite words
Categories:16N40, 16S15, 20M05, 20M25, 68R15

354. CMB 2004 (vol 47 pp. 332)

Charette, Virginie; Goldman, William M.; Jones, Catherine A.
Recurrent Geodesics in Flat Lorentz $3$-Manifolds
Let $M$ be a complete flat Lorentz $3$-manifold $M$ with purely hyperbolic holonomy $\Gamma$. Recurrent geodesic rays are completely classified when $\Gamma$ is cyclic. This implies that for any pair of periodic geodesics $\gamma_1$, $\gamma_2$, a unique geodesic forward spirals towards $\gamma_1$ and backward spirals towards $\gamma_2$.

Keywords:geometric structures on low-dimensional manifolds, notions of recurrence
Categories:57M50, 37B20

355. CMB 2004 (vol 47 pp. 321)

Bullejos, M.; Cegarra, A. M.
Classifying Spaces for Monoidal Categories Through Geometric Nerves
The usual constructions of classifying spaces for monoidal categories produce CW-complexes with many cells that, moreover, do not have any proper geometric meaning. However, geometric nerves of monoidal categories are very handy simplicial sets whose simplices have a pleasing geometric description: they are diagrams with the shape of the 2-skeleton of oriented standard simplices. The purpose of this paper is to prove that geometric realizations of geometric nerves are classifying spaces for monoidal categories.

Keywords:monoidal category, pseudo-simplicial category,, simplicial set, classifying space, homotopy type
Categories:18D10, 18G30, 55P15, 55P35, 55U40

356. CMB 2004 (vol 47 pp. 298)

Yahaghi, Bamdad R.
Near Triangularizability Implies Triangularizability
In this paper we consider collections of compact operators on a real or complex Banach space including linear operators on finite-dimensional vector spaces. We show that such a collection is simultaneously triangularizable if and only if it is arbitrarily close to a simultaneously triangularizable collection of compact operators. As an application of these results we obtain an invariant subspace theorem for certain bounded operators. We further prove that in finite dimensions near reducibility implies reducibility whenever the ground field is $\BR$ or $\BC$.

Keywords:Linear transformation, Compact operator,, Triangularizability, Banach space, Hilbert, space
Categories:47A15, 47D03, 20M20

357. CMB 2004 (vol 47 pp. 237)

Laubie, François
Ramification des séries formelles
Let $p$ be a prime number. Let $k$ be a finite field of characteristic $p$. The subset $X+X^2 k[[X]]$ of the ring $k[[X]]$ is a group under the substitution law $\circ $ sometimes called the Nottingham group of $k$; it is denoted by $\mathcal{R}_k$. The ramification of one series $\gamma\in\mathcal{R}_k$ is caracterized by its lower ramification numbers: $i_m(\gamma)=\ord_X \bigl(\gamma^{p^m} (X)/X - 1\bigr)$, as well as its upper ramification numbers: $$ u_m (\gamma) = i_0 (\gamma) + \frac{i_1 (\gamma) - i_0(\gamma)}{p} + \cdots + \frac{i_m (\gamma) - i_{m-1} (\gamma)}{p^m} , \quad (m \in \mathbb{N}). $$ By Sen's theorem, the $u_m(\gamma)$ are integers. In this paper, we determine the sequences of integers $(u_m)$ for which there exists $\gamma\in\mathcal{R}_k$ such that $u_m(\gamma)=u_m$ for all integer $m \geq 0$.

Keywords:ramification, Nottingham group
Categories:11S15, 20E18

358. CMB 2004 (vol 47 pp. 22)

Goto, Yasuhiro
A Note on the Height of the Formal Brauer Group of a $K3$ Surface
Using weighted Delsarte surfaces, we give examples of $K3$ surfaces in positive characteristic whose formal Brauer groups have height equal to $5$, $8$ or $9$. These are among the four values of the height left open in the article of Yui \cite{Y}.

Keywords:formal Brauer groups, $K3$ surfaces in positive, characteristic, weighted Delsarte surfaces
Categories:14L05, 14J28

359. CMB 2004 (vol 47 pp. 152)

Zheng, Jian-Hua
On Uniqueness of Meromorphic Functions with Shared Values in Some Angular Domains
In this paper we investigate the uniqueness of transcendental meromorphic function dealing with the shared values in some angular domains instead of the whole complex plane.

Keywords:Nevanlinna theory, meromorphic function, shared value
Category:30D35

360. CMB 2004 (vol 47 pp. 133)

Wang, Wei
Embeddability of Some Three-Dimensional Weakly Pseudoconvex ${\rm CR}$ Structures
We prove that a class of perturbations of standard ${\rm CR}$ structure on the boundary of three-dimensional complex ellipsoid $E_{p,q}$ can be realized as hypersurfaces on $\mathbb{C}^2$, which generalizes the result of Burns and Epstein on the embeddability of some perturbations of standard ${\rm CR}$ structure on $S^3$.

Keywords:deformations, embeddability, complex ellipsoids
Categories:32V30, 32G07, 32V35

361. CMB 2004 (vol 47 pp. 73)

Li, Ma; Dezhong, Chen
Systems of Hermitian Quadratic Forms
In this paper, we give some conditions to judge when a system of Hermitian quadratic forms has a real linear combination which is positive definite or positive semi-definite. We also study some related geometric and topological properties of the moduli space.

Keywords:hermitian quadratic form, positive definite, positive semi-definite
Category:15A63

362. CMB 2003 (vol 46 pp. 617)

Pak, Hong Kyung
On Harmonic Theory in Flows
Recently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of $H$-harmonic and $H^*$-harmonic spaces associated to a H\"ormander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric.

Keywords:contact structure, geodesible flow, isometric flow, basic cohomology
Categories:53C20, 57R30

363. CMB 2003 (vol 46 pp. 632)

Runde, Volker
The Operator Amenability of Uniform Algebras
We prove a quantized version of a theorem by M.~V.~She\u{\i}nberg: A uniform algebra equipped with its canonical, {\it i.e.}, minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.

Keywords:uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space
Categories:46H20, 46H25, 46J10, 46J40, 47L25

364. CMB 2003 (vol 46 pp. 373)

Laugesen, Richard S.; Pritsker, Igor E.
Potential Theory of the Farthest-Point Distance Function
We study the farthest-point distance function, which measures the distance from $z \in \mathbb{C}$ to the farthest point or points of a given compact set $E$ in the plane. The logarithm of this distance is subharmonic as a function of $z$, and equals the logarithmic potential of a unique probability measure with unbounded support. This measure $\sigma_E$ has many interesting properties that reflect the topology and geometry of the compact set $E$. We prove $\sigma_E(E) \leq \frac12$ for polygons inscribed in a circle, with equality if and only if $E$ is a regular $n$-gon for some odd $n$. Also we show $\sigma_E(E) = \frac12$ for smooth convex sets of constant width. We conjecture $\sigma_E(E) \leq \frac12$ for all~$E$.

Keywords:distance function, farthest points, subharmonic function, representing measure, convex bodies of constant width
Categories:31A05, 52A10, 52A40

365. CMB 2003 (vol 46 pp. 216)

Li, Chi-Kwong; Rodman, Leiba; Šemrl, Peter
Linear Maps on Selfadjoint Operators Preserving Invertibility, Positive Definiteness, Numerical Range
Let $H$ be a complex Hilbert space, and $\HH$ be the real linear space of bounded selfadjoint operators on $H$. We study linear maps $\phi\colon \HH \to \HH$ leaving invariant various properties such as invertibility, positive definiteness, numerical range, {\it etc}. The maps $\phi$ are not assumed {\it a priori\/} continuous. It is shown that under an appropriate surjective or injective assumption $\phi$ has the form $X \mapsto \xi TXT^*$ or $X \mapsto \xi TX^tT^*$, for a suitable invertible or unitary $T$ and $\xi\in\{1, -1\}$, where $X^t$ stands for the transpose of $X$ relative to some orthonormal basis. Examples are given to show that the surjective or injective assumption cannot be relaxed. The results are extended to complex linear maps on the algebra of bounded linear operators on $H$. Similar results are proved for the (real) linear space of (selfadjoint) operators of the form $\alpha I+K$, where $\alpha$ is a scalar and $K$ is compact.

Keywords:linear map, selfadjoint operator, invertible, positive definite, numerical range
Categories:47B15, 47B49

366. CMB 2003 (vol 46 pp. 310)

Wang, Xiaofeng
Second Order Dehn Functions of Asynchronously Automatic Groups
Upper bounds of second order Dehn functions of asynchronously automatic groups are obtained.

Keywords:second order Dehn function, combing, asynchronously automatic group
Categories:20E06, 20F05, 57M05

367. CMB 2003 (vol 46 pp. 268)

Puls, Michael J.
Group Cohomology and $L^p$-Cohomology of Finitely Generated Groups
Let $G$ be a finitely generated, infinite group, let $p>1$, and let $L^p(G)$ denote the Banach space $\{ \sum_{x\in G} a_xx \mid \sum_{x\in G} |a_x |^p < \infty \}$. In this paper we will study the first cohomology group of $G$ with coefficients in $L^p(G)$, and the first reduced $L^p$-cohomology space of $G$. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

Keywords:group cohomology, $L^p$-cohomology, central element of infinite order, harmonic function, continuous linear functional
Categories:43A15, 20F65, 20F18

368. CMB 2003 (vol 46 pp. 265)

Oh, Seungsang
Reducing Spheres and Klein Bottles after Dehn Fillings
Let $M$ be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.

Keywords:Dehn filling, reducible, Klein bottle
Category:57M50

369. CMB 2003 (vol 46 pp. 95)

Gauthier, P. M.
Cercles de remplissage for the Riemann Zeta Function
The celebrated theorem of Picard asserts that each non-constant entire function assumes every value infinitely often, with at most one exception. The Riemann zeta function has this Picard behaviour in a sequence of discs lying in the critical band and whose diameters tend to zero. According to the Riemann hypothesis, the value zero would be this (unique) exceptional value.

Keywords:cercles de remplissage, Riemann zeta function
Category:30

370. CMB 2003 (vol 46 pp. 130)

Petersen, Peter; Wilhelm, Frederick
On Frankel's Theorem
In this paper we show that two minimal hypersurfaces in a manifold with positive Ricci curvature must intersect. This is then generalized to show that in manifolds with positive Ricci curvature in the integral sense two minimal hypersurfaces must be close to each other. We also show what happens if a manifold with nonnegative Ricci curvature admits two nonintersecting minimal hypersurfaces.

Keywords:Frankel's Theorem
Category:53C20

371. CMB 2003 (vol 46 pp. 122)

Moon, Myoungho
On Certain Finitely Generated Subgroups of Groups Which Split
Define a group $G$ to be in the class $\mathcal{S}$ if for any finitely generated subgroup $K$ of $G$ having the property that there is a positive integer $n$ such that $g^n \in K$ for all $g\in G$, $K$ has finite index in $G$. We show that a free product with amalgamation $A*_C B$ and an $\HNN$ group $A *_C$ belong to $\mathcal{S}$, if $C$ is in $\mathcal{S}$ and every subgroup of $C$ is finitely generated.

Keywords:free product with amalgamation, $\HNN$ group, graph of groups, fundamental group
Categories:20E06, 20E08, 57M07

372. CMB 2002 (vol 45 pp. 483)

Baake, Michael
Diffraction of Weighted Lattice Subsets
A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice $\varGamma$ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice $\varGamma^*$ as lattice of periods. This statement remains true in the setting of a locally compact Abelian group whose topology has a countable base.

Keywords:diffraction, Dirac combs, lattice subsets, homometric sets
Categories:52C07, 43A25, 52C23, 43A05

373. CMB 2002 (vol 45 pp. 428)

Mollin, R. A.
Criteria for Simultaneous Solutions of $X^2 - DY^2 = c$ and $x^2 - Dy^2 = -c$
The purpose of this article is to provide criteria for the simultaneous solvability of the Diophantine equations $X^2 - DY^2 = c$ and $x^2 - Dy^2 = -c$ when $c \in \mathbb{Z}$, and $D \in \mathbb{N}$ is not a perfect square. This continues work in \cite{me}--\cite{alfnme}.

Keywords:continued fractions, Diophantine equations, fundamental units, simultaneous solutions
Categories:11A55, 11R11, 11D09

374. CMB 2002 (vol 45 pp. 337)

Chen, Imin
Surjectivity of $\mod\ell$ Representations Attached to Elliptic Curves and Congruence Primes
For a modular elliptic curve $E/\mathbb{Q}$, we show a number of links between the primes $\ell$ for which the mod $\ell$ representation of $E/\mathbb{Q}$ has projective dihedral image and congruence primes for the newform associated to $E/\mathbb{Q}$.

Keywords:torsion points of elliptic curves, Galois representations, congruence primes, Serre tori, grossencharacters, non-split Cartan
Categories:11G05, 11F80

375. CMB 2002 (vol 45 pp. 378)

Fernández-López, Manuel; García-Río, Eduardo; Kupeli, Demir N.
The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry
A partial differential equation, the local M\"obius 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 M\"obius equation and an additional partial differential equation.

Keywords:submersion, Möbius equation, twisted product, warped product, product Riemannian manifolds
Categories:53C12, 58J99
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