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897  The Ground State Problem for a Quantum Hamiltonian Model Describing Friction Bruneau, Laurent
In this paper, we consider the quantum version of a Hamiltonian model
describing friction.
This model consists of
a particle which interacts with a bosonic reservoir representing a
homogeneous medium through which the particle moves. We show that if
the particle is confined, then the Hamiltonian admits a ground state
if and only if a suitable infrared condition is satisfied. The latter
is violated in the case of linear friction, but satisfied when the
friction force is proportional to a higher power of the particle
speed.


917  Admissibility for a Class of Quasiregular Representations Currey, Bradley N.
Given a semidirect product $G = N \rtimes H$ where $N$ is%%
nilpotent, connected, simply connected and normal in $G$ and where
$H$ is a vector group for which $\ad(\h)$ is completely reducible and
$\mathbf R$split, let $\tau$ denote the quasiregular representation of
$G$ in $L^2(N)$. An element $\psi \in L^2(N)$ is said to be admissible
if the wavelet transform $f \mapsto \langle f, \tau(\cdot)\psi\rangle$
defines an isometry from $L^2(N)$ into $L^2(G)$. In this paper we give
an explicit construction of admissible vectors in the case where $G$
is not unimodular and the stabilizers in $H$ of its action on $\hat N$
are almost everywhere trivial. In this situation we prove
orthogonality relations and we construct an explicit decomposition of
$L^2(G)$ into $G$invariant, multiplicityfree subspaces each of which
is the image of a wavelet transform . We also show that, with the
assumption of (almosteverywhere) trivial stabilizers,
nonunimodularity is necessary for the existence of admissible
vectors.


943  A Weighted $L^2$Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds Finster, Felix; Kraus, Margarita
We derive a weighted $L^2$estimate of the Witten spinor in
a complete Riemannian spin manifold~$(M^n, g)$ of nonnegative scalar curvature
which is asymptotically Schwarzschild.
The interior geometry of~$M$ enters this estimate only
via the lowest eigenvalue of the square of the Dirac
operator on a conformal compactification of $M$.


966  Operator Amenability of the Fourier Algebra in the $\cb$Multiplier Norm Forrest, Brian E.; Runde, Volker; Spronk, Nico
Let $G$ be a locally compact group, and let $A_{\cb}(G)$ denote the
closure of $A(G)$, the Fourier algebra of $G$, in the space of completely
bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group
such that $\cstar(G)$ is residually finitedimensional, we show that
$A_{\cb}(G)$ is operator amenable. In particular,
$A_{\cb}(\free_2)$ is operator amenable even though $\free_2$, the free
group in two generators, is not an amenable group. Moreover, we show that
if $G$ is a discrete group such that $A_{\cb}(G)$ is operator amenable,
a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$
if and only if it has an approximate identity bounded in the $\cb$multiplier
norm.


981  The ChenRuan Cohomology of Weighted Projective Spaces Jiang, Yunfeng
In this paper we study the ChenRuan cohomology ring of weighted
projective spaces. Given a weighted projective space ${\bf
P}^{n}_{q_{0}, \dots, q_{n}}$, we determine all of its twisted
sectors and the corresponding degree shifting numbers. The main
result of this paper is that the obstruction bundle over any
3\nobreakdashmulti\sector is a direct sum of line bundles which we use to
compute the orbifold cup product. Finally we compute the
ChenRuan cohomology ring of weighted projective space ${\bf
P}^{5}_{1,2,2,3,3,3}$.


1008  Ideas from Zariski Topology in the Study of Cubical Homology Kaczynski, Tomasz; Mrozek, Marian; Trahan, Anik
Cubical sets and their homology have been
used in dynamical systems as well as in digital imaging. We take a
fresh look at this topic, following Zariski ideas from
algebraic geometry. The cubical topology is defined to be a
topology in $\R^d$ in which a set is closed if and only if it is
cubical. This concept is a convenient frame for describing a
variety of important features of cubical sets. Separation axioms
which, in general, are not satisfied here, characterize exactly
those pairs of points which we want to distinguish. The noetherian
property guarantees the correctness of the algorithms. Moreover, maps
between cubical sets which are continuous and closed with respect
to the cubical topology are precisely those for whom the homology
map can be defined and computed without grid subdivisions. A
combinatorial version of the VietorisBegle theorem is derived. This theorem
plays the central role in an algorithm computing homology
of maps which are continuous
with respect to the Euclidean topology.


1029  The Geometry of $L_0$ Kalton, N. J.; Koldobsky, A.; Yaskin, V.; Yaskina, M.
Suppose that we have the unit Euclidean ball in
$\R^n$ and construct new bodies using three operations  linear
transformations, closure in the radial metric, and multiplicative
summation defined by $\x\_{K+_0L} = \sqrt{\x\_K\x\_L}.$ We prove
that in dimension $3$ this procedure gives all originsymmetric convex
bodies, while this is no longer true in dimensions $4$ and higher. We
introduce the concept of embedding of a normed space in $L_0$ that
naturally extends the corresponding properties of $L_p$spaces with
$p\ne0$, and show that the procedure described above gives exactly the
unit balls of subspaces of $L_0$ in every dimension. We provide
Fourier analytic and geometric characterizations of spaces embedding
in $L_0$, and prove several facts confirming the place of $L_0$ in the
scale of $L_p$spaces.


1050  On the Restriction to $\D^* \times \D^*$ of Representations of $p$Adic $\GL_2(\D)$ Raghuram, A.
Let $\mathcal{D}$ be a division algebra
over a nonarchimedean local field. Given
an irreducible representation $\pi$ of $\GL_2(\mathcal{D})$, we
describe its restriction to the diagonal subgroup $\mathcal{D}^* \times
\mathcal{D}^*$. The description is in terms of the structure of the
twisted Jacquet module of the representation $\pi$. The proof
involves Kirillov theory that we have developed earlier in joint work
with Dipendra Prasad. The main result on restriction also shows that
$\pi$ is $\mathcal{D}^* \times \mathcal{D}^*$distinguished if and only if
$\pi$ admits a Shalika model. We further prove that if $\mathcal{D}$
is a quaternion division algebra then the twisted Jacquet module
is multiplicityfree by proving an appropriate theorem on invariant
distributions; this then proves a multiplicityone theorem on the
restriction to $\mathcal{D}^* \times \mathcal{D}^*$ in the quaternionic
case.


1069  Quotients jacobiens : une approche algĂ©brique Reydy, Carine
Le diagramme d'Eisenbud et Neumann d'un germe est un arbre qui
repr\'esente ce germe et permet d'en calculer les invariants. On donne
une d\'emonstration alg\'ebrique d'un r\'esultat caract\'erisant
l'ensemble des quotients jacobiens d'un germe d'application $(f,g)$
\`a partir du diagramme d'Eisenbud et Neumann de $fg$.


1098  Ruled Exceptional Surfaces and the Poles of Motivic Zeta Functions Rodrigues, B.
In this paper we study ruled surfaces which appear as an exceptional
surface in a succession of blowingups. In particular we prove
that the $e$invariant of such a ruled exceptional surface $E$ is
strictly positive whenever its intersection with the other
exceptional surfaces does not contain a fiber (of $E$). This fact
immediately enables us to resolve an open problem concerning an
intersection configuration on such a ruled exceptional surface
consisting of three nonintersecting sections. In the second part
of the paper we apply the nonvanishing of $e$ to the study of the
poles of the wellknown topological, Hodge and motivic zeta
functions.
