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481  Concordance des nœuds de dimension $4$ Blanlœil, Vincent; Saeki, Osamu
We prove that for a simply connected closed
$4$dimensional manifold, its embeddings
into the sphere of dimension $6$ are all
concordant to each other.


486  HigherDimensional Modular\\CalabiYau Manifolds Cynk, S.; Hulek, K.
We construct several examples of higherdimensional CalabiYau manifolds and prove their
modularity.


504  Asymptotic Existence of Resolvable Graph Designs Dukes, Peter; Ling, Alan C. H.
Let $v \ge k \ge 1$ and $\lam \ge 0$ be integers. A block
design $\BD(v,k,\lambda)$ is a collection $\cA$ of $k$subsets of a
$v$set $X$ in which every unordered pair of elements from $X$ is
contained in exactly $\lambda$ elements of $\cA$. More generally, for a
fixed simple graph $G$, a graph design $\GD(v,G,\lambda)$ is a
collection $\cA$ of graphs isomorphic to $G$ with vertices in $X$ such
that every unordered pair of elements from $X$ is an edge of exactly
$\lambda$ elements of $\cA$. A famous result of Wilson says that for a
fixed $G$ and $\lambda$, there exists a $\GD(v,G,\lambda)$ for all
sufficiently large $v$ satisfying certain necessary conditions. A
block (graph) design as above is resolvable if $\cA$ can be
partitioned into partitions of (graphs whose vertex sets partition)
$X$. Lu has shown asymptotic existence in $v$ of resolvable
$\BD(v,k,\lambda)$, yet for over twenty years the analogous problem for
resolvable $\GD(v,G,\lambda)$ has remained open. In this paper, we settle
asymptotic existence of resolvable graph designs.


519  On Axiomatizability of NonCommutative $L_p$Spaces Henson, C. Ward; Raynaud, Yves; Rizzo, Andrew
It is shown that Schatten $p$classes
of operators between Hilbert spaces of different (infinite)
dimensions have ultrapowers which are (completely) isometric to
noncommutative $L_p$spaces. On the other hand, these Schatten
classes are not themselves isomorphic to noncommutative $L_p$
spaces. As a consequence, the class of noncommutative $L_p$spaces
is not axiomatizable in the firstorder language developed by
Henson and Iovino for normed space structures, neither in the
signature of Banach spaces, nor in that of operator spaces. Other
examples of the same phenomenon are presented that belong to the
class of corners of noncommutative $L_p$spaces. For $p=1$ this
last class, which is the same as the class of preduals of ternary
rings of operators, is itself axiomatizable in the signature of
operator spaces.


535  Generalized Descent Algebras Hohlweg, Christophe
If $A$ is a subset of the set of reflections of a finite Coxeter
group $W$, we define a sub$\ZM$module $\DC_A(W)$ of the group
algebra $\ZM W$. We discuss cases where this submodule is a
subalgebra. This family of subalgebras includes strictly the
Solomon descent algebra, the group algebra and, if $W$ is of type
$B$, the MantaciReutenauer algebra.


547  Inverse Laplace Transforms Encountered in Hyperbolic Problems of NonStationary FluidStructure Interaction Iakovlev, Serguei
The paper offers a study of the inverse Laplace
transforms of the functions $I_n(rs)\{sI_n^{'}(s)\}^{1}$ where
$I_n$ is the modified Bessel function of the first kind and $r$ is
a parameter. The present study is a continuation of the author's
previous work %[\textit{Canadian Mathematical Bulletin} 45]
on the
singular behavior of the special case of the functions in
question, $r$=1. The general case of $r \in [0,1]$ is addressed,
and it is shown that the inverse Laplace transforms for such $r$
exhibit significantly more complex behavior than their
predecessors, even though they still only have two different types
of points of discontinuity: singularities and finite
discontinuities. The functions studied originate from
nonstationary fluidstructure interaction, and as such are of
interest to researchers working in the area.


567  Exotic Torsion, Frobenius Splitting and the Slope Spectral Sequence Joshi, Kirti
In this paper we show that any Frobenius split, smooth, projective
threefold over a perfect field of characteristic $p>0$ is
HodgeWitt. This is proved by generalizing to the case of
threefolds a wellknown criterion due to N.~Nygaard for surfaces to be HodgeWitt.
We also show that the second crystalline
cohomology of any smooth, projective Frobenius split variety does
not have any exotic torsion. In the last two sections we include
some applications.


579  $p$Radial Exceptional Sets and Conformal Mappings Kot, Piotr
For $p>0$ and for a given set $E$ of type $G_{\delta}$ in the boundary
of the unit disc $\partial\mathbb D$ we construct a holomorphic function
$f\in\mathbb O(\mathbb D)$ such that
\[
\int_{\mathbb D\setminus[0,1]E}ft^{p}\,d\mathfrak{L}^{2}<\infty\]
and\[
E=E^{p}(f)=\Bigl\{ z\in\partial\mathbb D:\int_{0}^{1}f(tz)^{p}\,dt=\infty\Bigr\} .\]
In particular if a set $E$ has a measure equal to zero, then a function
$f$ is constructed as integrable with power $p$ on the unit disc $\mathbb D$.


588  Cohomological Dimension and Schreier's Formula in Galois Cohomology Labute, John; Lemire, Nicole; Mináč, Ján; Swallow, John
Let $p$ be a prime and $F$ a field containing a primitive $p$th
root of unity. Then for $n\in \N$, the cohomological dimension
of the maximal pro$p$quotient $G$ of the absolute Galois group
of $F$ is at most $n$ if and only if the corestriction maps
$H^n(H,\Fp) \to H^n(G,\Fp)$ are surjective for all open
subgroups $H$ of index $p$. Using this result, we generalize
Schreier's formula for $\dim_{\Fp} H^1(H,\Fp)$ to $\dim_{\Fp}
H^n(H,\Fp)$.


594  Ramification des groupes abéliens d'automorphismes des corps $\mathbb F_q(\!(X)\!)$ Laubie, François
Soit $q$ une puissance d'un nombre premier
$p$. Dans cette note on \'etablit la g\'en\'eralisation suivante
d'un th\'eor\`eme de Wintenberger : tout sousgroupe ab\'elien
ferm\'e du groupe des $\mathbb F_q$auto\morphismes continus du corps
des s\'eries formelles $\mathbb F_q(\!(X)\!)$ muni de sa filtration
de ramification est un groupe filtr\'e isomorphe au groupe de Galois
d'une extension ab\'elienne d'un corps local {\`a} corps
r\'esiduel $\mathbb F_q$, filtr\'e par les groupes de ramification
de l'extension en num\'erotation inf\'erieure.


598  Artinian Local Cohomology Modules Lorestani, Keivan Borna; Sahandi, Parviz; Yassemi, Siamak
Let $R$ be a commutative Noetherian ring, $\fa$ an ideal
of $R$ and $M$ a finitely generated $R$module. Let $t$ be a
nonnegative integer. It is known that if the local cohomology
module $\H^i_\fa(M)$ is finitely generated for all $i<t$, then
$\Hom_R(R/\fa, \H^t_\fa(M))$ is finitely generated. In this paper it
is shown that if $\H^i_\fa(M)$ is Artinian for all $i<t$, then
$\Hom_R(R/\fa, \H^t_\fa(M))$ need not be Artinian, but it has a
finitely generated submodule $N$ such that
$\Hom_R(R/\fa,\H^t_\fa(M))/N$ is Artinian.


603  Construction of Generalized HarishChandra Modules with Arbitrary Minimal $\mathfrak k$Type Penkov, Ivan; Zuckerman, Gregg
Let $\mathfrak g$ be a semisimple complex Lie algebra and $\k\subset\g$ be
any algebraic subalgebra reductive in $\mathfrak g$. For any simple
finite dimensional $\mathfrak k$module $V$, we construct simple
$(\mathfrak g,\mathfrak k)$modules $M$ with finite dimensional $\mathfrak k$isotypic
components such that $V$ is a $\mathfrak k$submodule of $M$ and the Vogan
norm of any simple $\k$submodule $V'\subset M, V'\not\simeq V$, is
greater than the Vogan norm of $V$. The $(\mathfrak g,\mathfrak k)$modules
$M$ are subquotients of the fundamental series of
$(\mathfrak g,\mathfrak k)$modules.


610  On Weak$^*$ KadecKlee Norms Rychtář, Jan; Spurný, Jiří
We present partial positive results supporting a conjecture that
admitting an equivalent Lipschitz (or uniformly) weak$^*$ KadecKlee norm is
a three space property.


619  On the Existence of Asymptotic$l_p$ Structures in Banach Spaces Tcaciuc, Adi
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$l_p$ subspaces
for some $1 \leq p \leq \infty$.
This extends a result by Figiel, Frankiewicz, Komorowski and
RyllNardzewski.


632  Transformations and Colorings of Groups Zelenyuk, Yevhen; Zelenyuk, Yuliya
Let $G$ be a compact topological group and let $f\colon G\to G$ be a
continuous transformation of $G$. Define $f^*\colon G\to G$ by
$f^*(x)=f(x^{1})x$ and let $\mu=\mu_G$ be Haar measure on $G$. Assume
that $H=\Imag f^*$ is a subgroup of $G$ and for every
measurable $C\subseteq H$,
$\mu_G((f^*)^{1}(C))=\mu_H(C)$. Then for every measurable
$C\subseteq G$, there exist $S\subseteq C$ and $g\in G$ such that
$f(Sg^{1})\subseteq Cg^{1}$ and $\mu(S)\ge(\mu(C))^2$.


637  Author Index  Index des auteurs 2007, for 2007  pour
No abstract.
