376. CMB 2005 (vol 48 pp. 409)
377. CMB 2005 (vol 48 pp. 340)
 Andruchow, Esteban

Short Geodesics of Unitaries in the $L^2$ Metric
Let $\M$ be a type II$_1$ von Neumann algebra, $\tau$ a trace in $\M$,
and $\l2$ the GNS Hilbert space of $\tau$. We regard the unitary group
$U_\M$ as a subset of $\l2$ and characterize the shortest smooth
curves joining two fixed unitaries in the $L^2$ metric. As a
consequence of this we obtain that $U_\M$, though a complete (metric)
topological group, is not an embedded riemannian submanifold of $\l2$
Keywords:unitary group, short geodesics, infinite dimensional riemannian manifolds. Categories:46L51, 58B10, 58B25 

378. CMB 2005 (vol 48 pp. 161)
379. CMB 2005 (vol 48 pp. 283)
 Thibault, Lionel; Zagrodny, Dariusz

Enlarged Inclusion of Subdifferentials
This paper studies the integration of inclusion of subdifferentials. Under
various verifiable conditions, we obtain that if two proper lower
semicontinuous functions $f$ and $g$ have the subdifferential of $f$
included in the $\gamma$enlargement of the subdifferential of $g$, then
the difference of those functions is $ \gamma$Lipschitz over their
effective domain.
Keywords:subdifferential,, directionally regular function,, approximate convex function,, subdifferentially and directionally stable function Categories:49J52, 46N10, 58C20 

380. CMB 2005 (vol 48 pp. 267)
 Rodman, Leiba; Šemrl, Peter; Sourour, Ahmed R.

Continuous Adjacency Preserving Maps on Real Matrices
It is proved that every adjacency preserving continuous map
on the vector space of real matrices of fixed size, is either a
bijective affine tranformation
of the form $ A \mapsto PAQ+R$, possibly followed by the transposition if
the matrices are of square size, or its range is contained
in a linear subspace consisting of matrices of rank at most one
translated by some matrix $R$. The result
extends previously known
theorems where the map was assumed to be also injective.
Keywords:adjacency of matrices, continuous preservers, affine transformations Categories:15A03, 15A04. 

381. CMB 2005 (vol 48 pp. 260)
382. CMB 2005 (vol 48 pp. 195)
 Daniel, D.; Nikiel, J.; Treybig, L. B.; Tuncali, H. M.; Tymchatyn, E. D.

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 rimmetrizable. Locally
connected Suslinian continua have weight at most $\omega_1$ and under
appropriate settheoretic conditions are metrizable. Nonseparable
locally connected Suslinian continua are rimfinite on some open set.
Keywords:Suslinian continuum, Souslin line, locally connected, rimmetrizable,, perfectly normal, rimfinite Categories:54F15, 54D15, 54F50 

383. CMB 2005 (vol 48 pp. 180)
 Cynk, Sławomir; Meyer, Christian

Geometry and Arithmetic of Certain Double Octic CalabiYau Manifolds
We study CalabiYau manifolds constructed as double coverings of
$\mathbb{P}^3$ branched along an octic surface. We give a list of 87
examples corresponding to arrangements of eight planes defined over
$\mathbb{Q}$. The Hodge numbers are computed for all examples. There are
10 rigid CalabiYau manifolds and 14 families with $h^{1,2}=1$. The
modularity conjecture is verified for all the rigid examples.
Keywords:CalabiYau, double coverings, modular forms Categories:14G10, 14J32 

384. CMB 2005 (vol 48 pp. 147)
 Väänänen, Keijo; Zudilin, Wadim

BakerType 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 nonzero 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\'etype 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 

385. CMB 2005 (vol 48 pp. 121)
386. CMB 2004 (vol 47 pp. 624)
 Zhang, Xi

A Compactness Theorem for YangMills Connections
In this paper, we consider YangMills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of YangMills
connections with the uniformly bounded $L^{\frac{m}{2}}$norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:YangMills connection, vector bundle, gauge transformation Categories:58E20, 53C21 

387. CMB 2004 (vol 47 pp. 530)
 Iranmanesh, A.; Khosravi, B.

A Characterization of $ PSU_{11}(q)$
Order components of a finite simple group were introduced in [4].
It was proved that some nonabelian 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 

388. CMB 2004 (vol 47 pp. 481)
 Bekjan, Turdebek N.

A New Characterization of Hardy Martingale Cotype Space
We give a new characterization of Hardy martingale cotype
property of complex quasiBanach 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 quasiBanach space.
Keywords:Hardy martingale, Hardy martingale cotype,, plurisubharmonic function Categories:46B20, 52A07, 60G44 

389. 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 CWcomplexes 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 2skeleton 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, pseudosimplicial category,, simplicial set, classifying space, homotopy type Categories:18D10, 18G30, 55P15, 55P35, 55U40 

390. 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 lowdimensional manifolds, notions of recurrence Categories:57M50, 37B20 

391. CMB 2004 (vol 47 pp. 417)
392. CMB 2004 (vol 47 pp. 398)
 McKinnon, David

A Reduction of the BatyrevManin Conjecture for Kummer Surfaces
Let $V$ be a $K3$ surface defined over a number field $k$. The
BatyrevManin 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 $UZ_U$ 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 BatyrevManin conjecture for $V$ can be reduced to the
BatyrevManin 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, BatyrevManin conjecture, Kummer, surface, rational curve, abelian surface, height Categories:11G35, 14G05 

393. CMB 2004 (vol 47 pp. 389)
394. 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 nonnil 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 

395. 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 finitedimensional 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 

396. CMB 2004 (vol 47 pp. 237)
 Laubie, François

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:
$$
u_m (\gamma) = i_0 (\gamma) + \frac{i_1 (\gamma)  i_0(\gamma)}{p} +
\cdots + \frac{i_m (\gamma)  i_{m1} (\gamma)}{p^m} , \quad (m \in
\mathbb{N}).
$$
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 

397. 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 semidefinite. We also study some
related geometric and topological properties of the moduli space.
Keywords:hermitian quadratic form, positive definite, positive semidefinite Category:15A63 

398. CMB 2004 (vol 47 pp. 152)
399. CMB 2004 (vol 47 pp. 133)
 Wang, Wei

Embeddability of Some ThreeDimensional Weakly Pseudoconvex ${\rm CR}$ Structures
We prove that a class of perturbations of standard ${\rm CR}$
structure on the boundary of threedimensional 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 

400. 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 
