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	1. Valuation and Optimal Decision for Perpetual American Employee Stock Options under a Constrained Viscosity Solution Framework
	BIAN Baojun,YUAN Quan,HU Shuntai
	Mathematics 06 January 2013
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	Abstract:This paper is concerned with the constrained viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation arising from the valuation of a block of perpetual American employee stock options (ESOs). The exercise process of the employee is described by a fluid model with a capped exercise rate. The value of the ESOs defined as the maximal expectation of the discounted exercise benefits satisfies the HJB equation. The existence and uniqueness of the constrained viscosity solution is obtained after the proof of the associated comparison principal. The limit case with the cap value approaching infinity is also studied followed by a numerical simulation model. The corresponding optimal exercise decision is determined by the value function of this optimization problem.
	TO cite this article:BIAN Baojun,YUAN Quan,HU Shuntai. Valuation and Optimal Decision for Perpetual American Employee Stock Options under a Constrained Viscosity Solution Framework[OL].[ 6 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4511967


	2. Integral Form of the Fractional Schr
	Dong Jianping
	Mathematics 07 September 2012
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	Abstract:The integral form of the 3D space fractional Schr"odinger equationis derived in this paper. Using this integral equation, we study thescattering problems in the fractional quantum mechanics and obtainthe analytical approximate solutions of the wave function and thescattering amplitude using the Born approximation method. The Bornseries, with corrections of every order, is also given. In the end,we discuss the validity of the Born approximation and show thevalidity condition.
	TO cite this article:Dong Jianping. Integral Form of the Fractional Schr[OL].[ 7 September 2012] http://en.paper.edu.cn/en_releasepaper/content/4488917

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	3. Maximum principles for forward-backward doubly stochastic differential equations with jumps
	Xu Shuli,Jiang jun
	Mathematics 30 August 2012
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	Abstract:The forward-backward stochastic differential equations has received considerable research attention in a large of domains, especially in mathematical finance. The subject of stochastic maximum principles for forward-backward stochastic optimal control problems has been discussed by many authors, this paper researchs a stochastic system consisting of a forward-backward doubly stochastic differential equations with jump and obtains a genereal sufficient maximum principle for forward-backward doubly stochastic differential equations with jump.
	TO cite this article:Xu Shuli,Jiang jun. Maximum principles for forward-backward doubly stochastic differential equations with jumps[OL].[30 August 2012] http://en.paper.edu.cn/en_releasepaper/content/4486654


	4. Exponential stability of BAM neural networks with delays via joint periodically intermittent and impulsive control
	HU Jian-Qiang,LIANG Jin-Ling
	Mathematics 05 January 2012
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	Abstract:The exponetial stabilization problem for a class of bidirectional associative memory (BAM) neural networks with discrete delays by the joint periodically intermittent control and impulsive control scheme is investigated, meanwhile the Lipschitzian activation functions in the system do not have to assume their boundedness, monotonicity or differentiability. Some sufficient criteria for global exponential stability are derived by using analysis techniques and Lyapunov function. Finally, a illustrative example is given at the end of this paper to show the effectiveness of our results.
	TO cite this article:HU Jian-Qiang,LIANG Jin-Ling. Exponential stability of BAM neural networks with delays via joint periodically intermittent and impulsive control[OL].[ 5 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4459879


	5. Adaptive Stabilization for Genetic Regulatory Networks with Mixed Delays
	HU Jianqiang,LIANG Jinling
	Mathematics 04 January 2012
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	Abstract:In this paper, the stabilization of a class of mixed delayed genetic regulatory networks (GRNs) is investigated. The adaptive feedback control scheme is used to achieve global asymptotic stability for the GRNs with finite distributed delays and discrete delays. By introducing the integral partitioning technique and delay fractioning approach, a Lyapunov-Krasovskii function (LKF) is constructed, and some sufficient stability criteria in the form of LMIs are established. Finally, a numerical example is given to illustrate the effectiveness of our theoretical results and less conservativeness of the proposed method.
	TO cite this article:HU Jianqiang,LIANG Jinling. Adaptive Stabilization for Genetic Regulatory Networks with Mixed Delays[OL].[ 4 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4459588


	6. H∞ CONTROLLER DESIGN FOR NETWORKED CONTROL
	Wang Jihua
	Mathematics 26 May 2009
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	Abstract:A novel discrete time model is proposed for networked control system (NCS) which converts the uncertainty of time-delay into the uncertainty of the parameter matrix. Based on Lyapunov stability theory and LMI approach, we provide a sufficient condition to the asymptotical stability of NCS without disturbance and design a state feedback controller which stabilizes the system. For the NCS with disturbance, we point out a sufficient condition ensuring the system meeting prescribed H∞ performance gamma and a state feedback controller ensuring the system meeting optimal performance index. Numerical examples are given to illustrate the effectiveness of our results via TrueTime toolbox.
	TO cite this article:Wang Jihua. H∞ CONTROLLER DESIGN FOR NETWORKED CONTROL[OL].[26 May 2009] http://en.paper.edu.cn/en_releasepaper/content/32552


	7. Robust State Estimation for Neural Networks with Discontinuous Activations
	xiaoyang liu,jinde cao
	Mathematics 24 April 2009
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	Abstract:Discontinuous dynamical systems, especially neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. In this paper, the robust state estimation problem is investigated for uncertain neural networks with discontinuous activations and time-varying delay, where the neuron-dependent nonlinear disturbance on the network outputs are only assumed to satisfy the local Lipschitz condition. Based on the theory of differential inclusions and nonsmooth analysis, several criteria are presented to guarantee the existence of the desired robust state estimator for the discontinuous neural networks. It is shown that the design of the state estimator for such networks can be achieved by solving two linear matrix inequalities (LMIs), which are dependent on the size of the time derivative of the time-varying delay. Finally, numerical examples are given to illustrate the theoretical results.
	TO cite this article:xiaoyang liu,jinde cao. Robust State Estimation for Neural Networks with Discontinuous Activations[OL].[24 April 2009] http://en.paper.edu.cn/en_releasepaper/content/31699


	8. Mathematical Theory in Sudoku Puzzle
	Guo Changyu ,Wang Zhiqing ,Guo Huimin
	Mathematics 12 March 2009
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	Abstract:Solving a Sudoku is an NP problem. How to solve a Sudoku puzzle effectively is already a complex problem. To generate a validated Sudoku puzzle of desirable difficulty level is more complex. In this paper, an effective generating algorithm and a simple but efficient difficulty level are proposed. Firstly some common Logical Techniques and Brute Force Search Technique are introduced to solve a Sudoku puzzle. After that, demonstrate an generic generating algorithm, which uses a difficulty level based Analytic Hierarchy Process (AHP). This difficulty level is very reasonable by considering various factors. Some intelligent techniques and sub-processes are used to guarantee this generating algorithm efficient and correct. And the method to generate symmetrical Sudoku Puzzles is put forward just follow it. At last , some useful conclusion is obtained.
	TO cite this article:Guo Changyu ,Wang Zhiqing ,Guo Huimin . Mathematical Theory in Sudoku Puzzle[OL].[12 March 2009] http://en.paper.edu.cn/en_releasepaper/content/30187


	9. Homogenization of Monotone Systems of Non-coercive Hamilton-Jacobi Equations
	Wang Junfang,Zhao Peihao
	Mathematics 03 November 2008
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	Abstract:In this article, we study homogenization for a class of monotone systems of first-order time-dependent Hamilton-Jacobi equations in the case of non-coercive Hamiltonians. And we prove the uniform convergence of the solution of oscillating systems to the solution of the homogenized systems.
	TO cite this article:Wang Junfang,Zhao Peihao. Homogenization of Monotone Systems of Non-coercive Hamilton-Jacobi Equations[OL].[ 3 November 2008] http://en.paper.edu.cn/en_releasepaper/content/25334


	10. Application of Combinatorial Predict Method
	Ma Dan,Zhou Shengwu
	Mathematics 10 October 2008
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	Abstract:Seeking for a scientific and reliable enterprise profit predict method is the key point to ensure the enterprise to get a scientific management. After getting the two predict sequences by stochastic partial elasticity theory and BP neural network, a new method is established to solve the combinatorial weighted coefficients by advance the predict accuracy to get a new predict value. Based on many examples, the new combinatorial predict method is proved to be very effective and much more accurate, and it can improve the reliability of enterprise profit prediction.
	TO cite this article:Ma Dan,Zhou Shengwu. Application of Combinatorial Predict Method[OL].[10 October 2008] http://en.paper.edu.cn/en_releasepaper/content/24706

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