摘要：In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov＇s projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.

摘要：In this note, a robust adaptive control scheme is proposed for a class of nonlinear systems that have unknown multi-plicative terms. Unlike previous results, except for the unknown control directions, we do not require a priori bounds on the unknown parameters. We also allow the unknown parameters to be time-varying provided that they are bounded. Our proposed robust adaptive controller is designed to identify on-line the unknown control directions and is a switching type controller, in which the controller parameters are tuned in a switching manner via a switching logic. Global stability of the closed-loop systems have been proved.

摘要：A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.

摘要：探讨了内蒙古地区太阳总辐射月均值与日照百分率的关系,基于5个气象站1996—1998年连续3 a的月日照时数(n)和太阳总辐射值(R_s)。计算得到Angstrom方程的系数a和b,与和清华等拟合得到的中国西部太阳总辐射公式中的a=0.185,b=0.595,比较一致。同时,R_s和n之间的直接线性关系,R与月平均温度(T)之间的直接线性关系也能用来估算太阳总辐射月均值,总均方根误差约为80 MJ·m^(-2)/month,总百分比误差约为18%。