We give a survey on Mœglin's construction of representations in the Arthur packets for p-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing Mœglin's parametrization of elements in the Arthur packets with that of Arthur.

Computational techniques derived from digital signal processing are playing a significant role in the security and digital copyrights of audio, video, and visual arts. In light of the quantum computing, the corresponding algorithms are becoming a new research direction in today’s high-technology world. The nature of quantum computer guarantees the security of quantum data, so a safe and effective quantum watermarking algorithm is in demand. Quantum watermarking is the technique that embeds the invisible quantum signal into quantum multimedia data for copyright protection. This research presents a quantum watermarking algorithm in discrete M-band wavelet domain. Different from most traditional algorithms, we propose a new algorithm which applies quantum watermarking in M-band wavelet domain. Assured by the Heisenberg uncertainty principle and quantum no-cloning theorem, the security of quantum watermark can reach a very high-level standard. In other words, this watermarking algorithm can defeat nearly all attackers, no matter using classical computer or quantum computer.

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We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are weakly mean convex. In contrast, the statement is no longer true if the scalar curvature is replaced by the kth mean curvature, for k greater than 2, as we construct the counterexamples for all k greater than 2. Our proof relies on a new geometric argument which relates the scalar curvature and mean curvature of a hypersurface to the mean curvature of the level sets of a height function. By extending the argument, we show that complete noncompact asymptotically flat hypersurfaces with nonnegative scalar curvature are weakly mean convex and prove the positive mass theorem for such hypersurfaces in all dimensions.

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