Biharmonic hypersurfaces in Riemannian manifolds

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1}, \cite{CMO2}. We then apply the equation to show that the generalized Chen's conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-parameter) family of conformally flat metrics and a (4-parameter) family of multiply warped product metrics each of which turns the foliation of an upper-half space of \mathhbb{R}^m by parallel hyperplanes into a foliation with each leave a proper biharmonic hypersurface. We also characterize proper biharmonic vertical cylinders in $S^2\times \mathbb{R}$ and $H^2\times \mathbb{R}$.Comment: 16 pages with a correction to Theorem 3.

Deep Reinforcement Learning for Resource Allocation in V2V Communications

In this article, we develop a decentralized resource allocation mechanism for vehicle-to-vehicle (V2V) communication systems based on deep reinforcement learning. Each V2V link is considered as an agent, making its own decisions to find optimal sub-band and power level for transmission. Since the proposed method is decentralized, the global information is not required for each agent to make its decisions, hence the transmission overhead is small. From the simulation results, each agent can learn how to satisfy the V2V constraints while minimizing the interference to vehicle-to-infrastructure (V2I) communications

Sound generated by rubbing objects

In the present paper, we investigate the properties of the sound generated by rubbing two objects. It is clear that the sound is generated because of the rubbing between the contacting rough surfaces of the objects. A model is presented to account for the role played by the surface roughness. The results indicate that tonal features of the sound can be generated due to the finiteness of the rubbing surfaces. In addition, the analysis shows that with increasing rubbing speed, more and more high frequency tones can be excited and the frequency band gets broader and broader, a feature which appears to agree with our intuition or experience.Comment: 3 pages, 2 figure