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The nonlinear stability in the {L^p} -norm, p ≥ 1 , of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general m × m systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.

Redundant via insertion is highly recommended for improving chip yield and reliability. In this paper, we study the problem of double via insertion with wire bending (DVI/WB) in a post-routing stage, where a single via can have at most one redundant via inserted next to it. Aside from this, we are allowed to bend existing signal wires for enhancing the insertion rate of double vias. The goal of DVI/WB is to primarily insert as many double vias as possible and to minimize the amount of layout perturbation as the secondary objective. We formulate the DVI/WB problem as that of finding a minimum-weight maximum independent set (mWMIS) on an enhanced conflict graph. We propose algorithms to perform wire bending and to construct the enhanced conflict graph from a given design. Moreover, we also propose a zero-one integer linear program (0-1 ILP) based approach to solve mWMIS. Experimental results show that

Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm ller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichm ller map between Riemann surfaces of finite type are theoretically guaranteed [1]. Recently, a simple iterative algorithm for computing the Teichm ller maps between connected Riemann surfaces with given boundary value was proposed in [11]. Numerical results was reported in the paper to show the effectiveness of the algorithm. The method was successfully applied to landmark-matching registration. The purpose of this paper is to prove the iterative algorithm proposed in [11] indeed converges.