Motivated by applications in nuclear magnetic resonance (NMR) spectroscopy, we introduce a novel blind source separation (BSS) approach to treat nonnegative and correlated data. We consider the (over)-determined case where n sources are to be separated from n linear mixtures (n). Among the n source signals, there are n partially overlapping (Po) sources and one positive everywhere (Pe) source. This condition is applicable for many real-world signals such as NMR spectra of urine and blood serum for metabolic fingerprinting and disease diagnosis. The geometric properties of the mixture matrix and the sparseness structure of the source signals (in a transformed domain) are crucial to the identification of the mixing matrix and the sources. The method first identifies the mixing coefficients of the Pe source by exploiting geometry in data clustering. Then subsequent elimination of variables leads to a sub

This paper is concerned with the Cauchy problem on the VlasovPoissonBoltzmann system for hard potentials in the whole space. When the initial data is a small perturbation of a global Maxwellian, a satisfactory global existence theory of classical solutions to this problem, together with the corresponding temporal decay estimates on the global solutions, is established. Our analysis is based on time-decay properties of solutions and a new timevelocity weight function which is designed to control the large-velocity growth in the nonlinear term for the case of non-hard-sphere interactions.

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We study the limit of quasilocal mass defined in [4] and [5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted slice of the Schwarzchild solution is computed explicitly and shown to give the expected energymomentum four-vector