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This paper proves the nonlinear asymptotic stability of the Lane-Emden solutions for spherically symmetric motions of viscous gaseous stars if the adiabatic constant γ lies in the stability range (4/3, 2). It is shown that for small perturbations of a LaneEmden solution with same mass, there exists a unique global (in time) strong solution to the vacuum free boundary problem of the compressible Navier-Stokes-Poisson system with spherical symmetry for viscous stars, and the solution captures the precise physical behavior that the sound speed is C 1/2 -H¨older continuous across the vacuum boundary provided that γ lies in (4/3, 2). The key is to establish the global-in-time regularity uniformly up to the vacuum boundary, which ensures the large time asymptotic uniform convergence of the evolving vacuum boundary, density and velocity to those of the Lane-Emden solution with detailed convergence rates, and detailed large time behaviors of solutions near the vacuum boundary. In particular, it is shown that every spherical surface moving with the fluid converges to the sphere enclosing the same mass inside the domain of the Lane-Emden solution with a uniform convergence rate and the large time asymptotic states for the vacuum free boundary problem (1.1.2) are determined by the initial mass distribution and the total mass. To overcome the difficulty caused by the degeneracy and singular behavior near the vacuum free boundary and coordinates singularity at the symmetry center, the main ingredients of the analysis consist of combinations of some new weighted nonlinear functionals (involving both lower-order and higher-order derivatives) and space-time weighted energy estimates. The constructions of these weighted nonlinear functionals and space-time weights depend crucially on the structures of the Lane-Emden solution, the balance of pressure and gravitation, and the dissipation. Finally, the uniform boundedness of the acceleration of the vacuum boundary is also proved.

We present a real-time approach for acquiring 3D objects with high fidelity using hand-held consumer-level RGB-D scanning devices. Existing real-time reconstruction methods typically do not take the point of interest into account, and thus might fail to produce clean reconstruction results of desired objects due to distracting objects or backgrounds. In addition, any changes in background during scanning, which can often occur in real scenarios, can easily break up the whole reconstruction process. To address these issues, we incorporate visual saliency into a traditional real-time volumetric fusion pipeline. Salient regions detected from RGB-D frames suggest user-intended objects, and by understanding user intentions our approach can put more emphasis on important targets, and meanwhile, eliminate disturbance of non-important objects. Experimental results on real world scans demonstrate that our system is capable of effectively acquiring geometric information of salient objects in cluttered real-world scenes, even if the backgrounds are changing.