1,721,114 research outputs found
Generalized Dirac operators on lorentzian manifolds and propagation of singularities
No full textWe survey the correct definition of a generalized Dirac operator on a Space-Time and the classical result about propagation of singularities. This says that light travels along light-like geodesics. Finally we show this is also true for generalized Dirac operators
The Atiyah Patodi Singer Signature formula for measured foliations
No full textGiven a compact manifold with boundary endowed with a foliation
transverse to the boundary, and which
admits a holonomy invariant transverse measure ,
%Let be the corresponding manifold with
% cylindrical ends and extended foliation with equivalence relation . In the paper \cite{io} we proved a formula for the - index of a
% longitudinal
% Dirac-type operator on in the spirit of Alain Connes' non commutative geometry \cite{Cos}.
%Here is a holonomy invariant transverse measure,
% is the measured eta invariant of the boundary operator defined by Ramachandran \cite{???},
%and the --dimension of the space of extended solution is defined using square integrable representations of the equivalence relation with values in the weighted spaces of the leaves.
we define three types of signature for the pair (foliation, boundary foliation): the analytic signature, denoted
, is the leafwise --index of the signature operator on the extended manifold obtained attaching cylindrical ends to the boundary;
the Hodge signature
\noindent is defined using the natural representation of the Borel groupoid of on the field of square integrable harmonic forms on the leaves; and
the de Rham signature, , defined using the natural representation
of the Borel groupoid of on the field of the relative de Rham spaces of the leaves.
We prove that
these three signatures coincide
As a consequence of the index formula we proved in \cite{io}, we finally obtain the main result of this work,
the Atiyah-Patodi-Singer
signature formula for measured foliations:
We give also, in the appendix, an account of noncommutative integration theory
Boundary integral for the Ramachandran index
Full text linkThe computation for the Ramachandran index for Galois coverings and foliations is reduced to a solely boundary computation. This is a reminescence of the classical theory
A late episode of Ferrar magmatism? Geochemistry and preliminary 40Ar/39Ar results of high Fe (SPCT) tholeiites fron Southern Victoria Land, Antarctica
No full text
Quasilinear elliptic inequalities on complete Riemannian manifolds
No full textWe prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some related boundary value problems are presented
The Baum-Connes conjecture localised at the unit element of a discrete group
Full text linkWe construct a Baum-Connes assembly map localised at the unit element of a discrete group. This morphism, called, is defined in -theory with coefficients in by means of the action of the idempotent canonically associated to the group trace of. We show that the corresponding -Baum-Connes conjecture is weaker than the classical version, but still implies the strong Novikov conjecture. The right-hand side of is functorial with respect to the group
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Learning control of mobile robots using a multiprocessor system
No full textA real-time multiprocessor system is proposed for the solution of the tracking problem of mobile robots operating in a real context with environmental disturbances and parameter uncertainties. The proposed control scheme utilizes multiple models of the robot for its identification in an adaptive and learning control framework. Radial Basis Function Networks (RBFNs) are considered for the multiple models in order to exploit the net non-linear approximation capabilities for modeling the kinematic behavior of the vehicle and for reducing unmodeled contributions to tracking errors. The training of the nets and the tests of the achieved control performance have been done in a real experimental setup. The proposed control architecture improves the robot tracking performance achieving fast and accurate control actions in presence of large and time-varying uncertainties in dynamical environments. The experimental results are satisfactory in terms of tracking errors and computational efforts
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