19,489 research outputs found
The Crossed Product by a Partial Endomorphism and the Covariance Algebra
Given a local homeomorphism \sigma:U -> X where U is a clopen subset of an
compact and Hausdorff topological space X, we obtain the possible transfer
operators L_\rho which may occur for \al:C(X) -> C(U) given by \al(f)=f\sigma.
We obtain examples of partial dynamical systems (X_A,\sigma_A) such that the
construction of the covariance algebra C^*(X_A,\sigma_A) and the crossed
product by partial endomorphism O(X_A,\al,L) associated to this system are not
equivalent, in the sense that there does not exists invertible function \rho in
C(U) such that O(X_A,\al,L_\rho)=C^*(X_A,\sigma).Comment: 13 pages, no figure
On the mass formula and Wigner and curvature energy terms
The efficiency of different mass formulas derived from the liquid drop model
including or not the curvature energy, the Wigner term and different powers of
the relative neutron excess has been determined by a least square fitting
procedure to the experimental atomic masses assuming a constant
R/A ratio. The Wigner term and the curvature energy can be
used independently to improve the accuracy of the mass formula. The different
fits lead to a surface energy coefficient of around 17-18 MeV, a relative sharp
charge radius r of 1.22-1.23 fm and a proton form-factor correction to the
Coulomb energy of around 0.9 MeV
Adaptive Clustering through Semidefinite Programming
We analyze the clustering problem through a flexible probabilistic model that
aims to identify an optimal partition on the sample X 1 , ..., X n. We perform
exact clustering with high probability using a convex semidefinite estimator
that interprets as a corrected, relaxed version of K-means. The estimator is
analyzed through a non-asymptotic framework and showed to be optimal or
near-optimal in recovering the partition. Furthermore, its performances are
shown to be adaptive to the problem's effective dimension, as well as to K the
unknown number of groups in this partition. We illustrate the method's
performances in comparison to other classical clustering algorithms with
numerical experiments on simulated data
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