265 research outputs found
Geometric realization and K-theoretic decomposition of C*-algebras
Suppose that A is a separable C*-algebra and that G_* is a (graded) subgroup
of K_*(A). Then there is a natural short exact sequence 0 \to G_* \to K_*(A)
\to K_*(A)/G_* \to 0.
In this note we demonstrate how to geometrically realize this sequence at the
level of C*-algebras. As a result, we KK-theoretically decompose A as 0 \to
A\otimes \Cal K \to A_f \to SA_t \to 0 where K_*(A_t) is the torsion subgroup
of K_*(A) and K_*(A_f) is its torsionfree quotient. Then we further decompose
A_t : it is KK-equivalent to \oplus_p A_p where K_*(A_p) is the p-primary
subgroup of the torsion subgroup of K_*(A). We then apply this realization to
study the Kasparov group K^*(A) and related objects.Comment: 9 pages.To appear in International J. Mat
The fine structure of the Kasparov groups I: continuity of the KK-pairing
In this paper it is demonstrated that the Kasparov pairing is continuous with
respect to the natural topology on the Kasparov groups, so that a
KK-equivalence is an isomorphism of topological groups. In addition, we
demonstrate that the groups have a natural pseudopolonais structure, and we
prove that various KK-structural maps are continuous.Comment: 35 pages. To appear in J. Functional Analysi
The Vortex-Wave equation with a single vortex as the limit of the Euler equation
In this article we consider the physical justification of the Vortex-Wave
equation introduced by Marchioro and Pulvirenti in the case of a single point
vortex moving in an ambient vorticity. We consider a sequence of solutions for
the Euler equation in the plane corresponding to initial data consisting of an
ambient vorticity in and a sequence of concentrated blobs
which approach the Dirac distribution. We introduce a notion of a weak solution
of the Vortex-Wave equation in terms of velocity (or primitive variables) and
then show, for a subsequence of the blobs, the solutions of the Euler equation
converge in velocity to a weak solution of the Vortex-Wave equation.Comment: 24 pages, to appea
Existence of families of spacetimes with a Newtonian limit
J\"urgen Ehlers developed \emph{frame theory} to better understand the
relationship between general relativity and Newtonian gravity. Frame theory
contains a parameter , which can be thought of as , where
is the speed of light. By construction, frame theory is equivalent to general
relativity for , and reduces to Newtonian gravity for .
Moreover, by setting \ep=\sqrt{\lambda}, frame theory provides a framework to
study the Newtonian limit \ep \searrow 0 (i.e. ). A number of
ideas relating to frame theory that were introduced by J\"urgen have
subsequently found important applications to the rigorous study of both the
Newtonian limit and post-Newtonian expansions. In this article, we review frame
theory and discuss, in a non-technical fashion, some of the rigorous results on
the Newtonian limit and post-Newtonian expansions that have followed from
J\"urgen's work
On globally non-trivial almost-commutative manifolds
Within the framework of Connes' noncommutative geometry, we define and study
globally non-trivial (or topologically non-trivial) almost-commutative
manifolds. In particular, we focus on those almost-commutative manifolds that
lead to a description of a (classical) gauge theory on the underlying base
manifold. Such an almost-commutative manifold is described in terms of a
'principal module', which we build from a principal fibre bundle and a finite
spectral triple. We also define the purely algebraic notion of 'gauge modules',
and show that this yields a proper subclass of the principal modules. We
describe how a principal module leads to the description of a gauge theory, and
we provide two basic yet illustrative examples.Comment: 34 pages, minor revision
Standardized Laparoscopic Intracorporeal Right Colectomy for Cancer: Short-Term Outcome in 111 Unselected Patients
Purpose This study was designed to evaluate the impact of a standardized laparoscopic intracorporeal right colectomy on the short-term outcome of patients with neoplasia. Methods Consecutive patients with histologically proven right colon neoplasia underwent a standardized laparoscopic intracorporeal right colectomy with medial to lateral approach encompassing ten sequential steps: 1) ligation of ileocolic vessels, 2) identification of right ureter, 3) dissection along superior mesenteric vein, 4) division of omentum, 5) division of right branch of middle colic vessels, 6) transection of transverse colon, 7) mobilization of right colon, 8) transection of terminal ileum, 9) ileocolic anastomosis, 10) delivery of specimen. Values were medians (ranges). Results From July 2002 to June 2005, 111 laparoscopic intracorporeal right colectomies were attempted with a 5.4 percent conversion rate. There were 57 women and 54 men, aged 64.9 (range, 40–85) years, with body mass index of 33 (range, 20–43), American Society of Anesthesiology score of 2 (range, 2–4), 36.9 percent comorbidities, and 37.8 percent previous abdominal surgery. The indication for surgery was cancer in 109 patients. Operative time was 120 (range, 80–185) minutes. Estimated blood loss was 69 (range, 50–600) ml. Overall length of skin incisions was 66 (range, 60–66) mm; 29 (range, 2–41) lymph nodes were harvested. Length of stay was four (range, 2–30) days. Complication rate was 4.5 percent. Conclusions A standardized laparoscopic intracorporeal right colectomy resulted in a favorable short-term outcome in unselected patients with neoplasia of the right colon
Cosmological post-Newtonian expansions to arbitrary order
We prove the existence of a large class of one parameter families of
solutions to the Einstein-Euler equations that depend on the singular parameter
\ep=v_T/c (0<\ep < \ep_0), where is the speed of light, and is a
typical speed of the gravitating fluid. These solutions are shown to exist on a
common spacetime slab M\cong [0,T)\times \Tbb^3, and converge as \ep
\searrow 0 to a solution of the cosmological Poisson-Euler equations of
Newtonian gravity. Moreover, we establish that these solutions can be expanded
in the parameter \ep to any specified order with expansion coefficients that
satisfy \ep-independent (nonlocal) symmetric hyperbolic equations
Derivation of the Zakharov equations
This paper continues the study of the validity of the Zakharov model
describing Langmuir turbulence. We give an existence theorem for a class of
singular quasilinear equations. This theorem is valid for well-prepared initial
data. We apply this result to the Euler-Maxwell equations describing
laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic
estimate that describes solutions of the Euler-Maxwell equations in terms of
WKB approximate solutions which leading terms are solutions of the Zakharov
equations. Because of transparency properties of the Euler-Maxwell equations,
this study is led in a supercritical (highly nonlinear) regime. In such a
regime, resonances between plasma waves, electromagnetric waves and acoustic
waves could create instabilities in small time. The key of this work is the
control of these resonances. The proof involves the techniques of geometric
optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of
pseudodifferential operators, and a semiclassical, paradifferential calculus
Localisation and colocalisation of KK-theory at sets of primes
Given a set of prime numbers S, we localise equivariant bivariant Kasparov
theory at S and compare this localisation with Kasparov theory by an exact
sequence. More precisely, we define the localisation at S to be KK^G(A,B)
tensored with the ring of S-integers Z[S^-1]. We study the properties of the
resulting variants of Kasparov theory.Comment: 16 page
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