Expand all Collapse all | Results 351 - 375 of 440 |
351. CMB 2005 (vol 48 pp. 195)
On Suslinian Continua A continuum is said to be Suslinian if it does not contain uncountably
many mutually exclusive nondegenerate subcontinua. We prove that
Suslinian continua are perfectly normal and rim-metrizable. Locally
connected Suslinian continua have weight at most $\omega_1$ and under
appropriate set-theoretic conditions are metrizable. Non-separable
locally connected Suslinian continua are rim-finite on some open set.
Keywords:Suslinian continuum, Souslin line, locally connected, rim-metrizable,, perfectly normal, rim-finite Categories:54F15, 54D15, 54F50 |
352. CMB 2005 (vol 48 pp. 161)
Hankel Convolution Operators on Spaces of Entire Functions of Finite Order In this paper we study Hankel transforms and Hankel convolution
operators on spaces of entire functions of finite order and their
duals.
Keywords:Hankel transform, convolution, entire functions, finite order Category:46F12 |
353. CMB 2005 (vol 48 pp. 147)
Baker-Type Estimates for Linear Forms in the Values of $q$-Series We obtain lower estimates for the absolute values
of linear forms of the values of generalized Heine
series at non-zero points of an imaginary quadratic field~$\II$,
in particular of the values of $q$-exponential function.
These estimates depend on the individual coefficients,
not only on the maximum of their absolute values.
The proof uses a variant of classical Siegel's method
applied to a system of functional Poincar\'e-type equations
and the connection between the solutions of these functional
equations and the generalized Heine series.
Keywords:measure of linear independence, $q$-series Categories:11J82, 33D15 |
354. CMB 2005 (vol 48 pp. 121)
Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ |
Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ We look at the simple continued fraction expansion of $\sqrt{D}$
for any $D=2^hc $ where $c>1$ is odd with a goal of
determining necessary and
sufficient conditions for the central norm (as determined by
the infrastructure of the underlying real quadratic order therein) to be
$2^h$. At the end of the paper, we also address the case where $D=c$
is odd and the central norm of $\sqrt{D}$ is equal to $2$.
Keywords:quadratic Diophantine equations, simple continued fractions,, norms of ideals, infrastructure of real quadratic fields Categories:11A55, 11D09, 11R11 |
355. CMB 2004 (vol 47 pp. 530)
A Characterization of $ PSU_{11}(q)$ Order components of a finite simple group were introduced in [4].
It was proved that some non-abelian simple groups are uniquely determined
by their order components. As the main result of this paper, we
show that groups $PSU_{11}(q)$ are also uniquely determined by
their order components. As corollaries of this result, the
validity of a conjecture of J. G. Thompson and a conjecture of W.
Shi and J. Bi both on $PSU_{11}(q)$ are obtained.
Keywords:Prime graph, order component, finite group,simple group Categories:20D08, 20D05, 20D60 |
356. CMB 2004 (vol 47 pp. 624)
A Compactness Theorem for Yang-Mills Connections In this paper, we consider Yang-Mills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of Yang-Mills
connections with the uniformly bounded $L^{\frac{m}{2}}$-norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:Yang-Mills connection, vector bundle, gauge transformation Categories:58E20, 53C21 |
357. CMB 2004 (vol 47 pp. 481)
A New Characterization of Hardy Martingale Cotype Space 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.
Keywords:Hardy martingale, Hardy martingale cotype,, plurisubharmonic function Categories:46B20, 52A07, 60G44 |
358. CMB 2004 (vol 47 pp. 398)
A Reduction of the Batyrev-Manin Conjecture for Kummer Surfaces Let $V$ be a $K3$ surface defined over a number field $k$. The
Batyrev-Manin conjecture for $V$ states that for every nonempty open
subset $U$ of $V$, there exists a finite set $Z_U$ of accumulating
rational curves such that the density of rational points on $U-Z_U$ is
strictly less than the density of rational points on $Z_U$. Thus,
the set of rational points of $V$ conjecturally admits a stratification
corresponding to the sets $Z_U$ for successively smaller sets $U$.
In this paper, in the case that $V$ is a Kummer surface, we prove that
the Batyrev-Manin conjecture for $V$ can be reduced to the
Batyrev-Manin conjecture for $V$ modulo the endomorphisms of $V$
induced by multiplication by $m$ on the associated abelian surface
$A$. As an application, we use this to show that given some restrictions
on $A$, the set of rational points of $V$ which lie on rational curves
whose preimages have geometric genus 2 admits a stratification of
Keywords:rational points, Batyrev-Manin conjecture, Kummer, surface, rational curve, abelian surface, height Categories:11G35, 14G05 |
359. CMB 2004 (vol 47 pp. 417)
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 |
360. CMB 2004 (vol 47 pp. 389)
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 |
361. CMB 2004 (vol 47 pp. 343)
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 |
362. CMB 2004 (vol 47 pp. 332)
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 |
363. CMB 2004 (vol 47 pp. 321)
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 |
364. CMB 2004 (vol 47 pp. 298)
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 |
365. CMB 2004 (vol 47 pp. 237)
Ramification des sÃ©ries 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 |
366. CMB 2004 (vol 47 pp. 22)
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 |
367. CMB 2004 (vol 47 pp. 152)
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 |
368. CMB 2004 (vol 47 pp. 133)
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 |
369. CMB 2004 (vol 47 pp. 73)
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 |
370. CMB 2003 (vol 46 pp. 617)
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 |
371. CMB 2003 (vol 46 pp. 632)
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 |
372. CMB 2003 (vol 46 pp. 373)
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 |
373. CMB 2003 (vol 46 pp. 216)
Linear Maps on Selfadjoint Operators Preserving Invertibility, Positive Definiteness, Numerical Range |
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 |
374. CMB 2003 (vol 46 pp. 310)
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 |
375. CMB 2003 (vol 46 pp. 268)
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 |