A note on dynamic Stackelberg games with leaders in turn

Recently, a model of dynamic Stackelberg games with leaders in turn has been proposed, and dynamic Stackelberg games with leaders in turn have been exploited under a feedback information structure. This paper characterizes dynamic Stackelberg games with leaders in turn under other information structures, both closed-loop and open-loop information structures. Explicit solutions are given for linear-quadratic systems under an open-loop information structure for dynamic Stackelberg games with leaders in turn.     

钕的电子拉曼光谱和一种新的拉曼增强机理

拉曼光谱是研究分子体系微观结构的一种有力工具 [1] ,由于拉曼信号弱 ,在一定程定上影响了拉曼光谱的应用 .为解决此问题 ,人们一方面采用各种先进的光谱测试技术 ,另一方面广泛运用各种拉曼增强机理 ,以提高拉曼光谱的灵敏度 .到目前为止 ,公认的拉曼增强机理只有共振拉曼增强和表面拉曼增强两种 .最近 ,文献报道了一种称为聚集增强的拉曼增强机理[2 ] .众所周知 ,f电子使稀土具有极丰富的电子能级结构 ,使得稀土元素在发展各种高性能的功能材料方面具有巨大的潜在价值 [3～ 5] .人们利用稀土的能级结构发展各种探针技术以表征分子体系在…     

Utilizing feed-back neural network approach for solving linear Fredholm integral equations system

This paper intended to offer an architecture of artificial neural networks (NNs) for finding approximate solution of a second kind linear Fredholm integral equations system. For this purpose, first we substitute the N-th truncation of the Taylor expansion for unknown functions in the origin system. By applying the suggested neural network for adjusting the real coefficients of given expansions in resulting system. The proposed NN is a two-layer feed-back neural network such that it can get a initial vector and then calculates it’s corresponding output vector. In continuance, a cost function is defined by using output vector and the target outputs. Consequently, the reported NN using a learning algorithm that based on the gradient descent method, will adjust the coefficients in given Taylor series. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalization and high accuracy. The proposed method is illustrated by several examples with computer simulations.