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过近似
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  over approximation
     The emphasis was put on the convergent approximation methods and the over approximation methods in the model checking. The algorithm adopted in the verification tool CheckMate and its application on a chemical process system was introduced in details.
     重点介绍了模型检验方法中的收敛近似方法和过近似方法,通过一个化工过程系统的验证实例详细介绍了验证工具CheckMate的验证算法。
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     THE APPROXIMATE CALCULATION OF FLOW OVER A SPILLWAY DAM
     坝水流的近似计算
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     Nonlinear Direct Estimation of Exponential Curve through Fixed Point
     定点指数曲线的非线性近似估计
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     APPROXIMATE DISTRIBUTION OF x~m(n)
     x~m(n)的近似分布
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     Characteristics of Approximate Limit
     近似极限的特征
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     Celebrating Lunar New Year in Shandong
     到山东大年
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In this paper we consider the singularly perturbed boundary value problems for a class of quasilinear difference equations. We use the sum of the solution of the degenerated equation and boundary correcter to approach the accurate solution. We also use the perturbed theory of Matrix and principle of invariant points to prove that the error is order under certain conditions. Finally, a numerical example is illustrated.

本文考虑一类拟线性奇异摄动差分方程的数值解法.主要思想是用退化方程的解及边界层校正解之和去渐过近似原方程解,并用矩阵的摄动理论及不动点原理证明了在一定条件下其误差是量级.最后给出了数值例子.

The conception of formal verification of hybrid systems was introduced. The current formal verification methods of hybrid systems and the verification tools were compared according to representations and computational techniques of the reachable sets. The emphasis was put on the convergent approximation methods and the over approximation methods in the model checking. The algorithm adopted in the verification tool CheckMate and its application on a chemical process system was introduced in details. Finally,...

The conception of formal verification of hybrid systems was introduced. The current formal verification methods of hybrid systems and the verification tools were compared according to representations and computational techniques of the reachable sets. The emphasis was put on the convergent approximation methods and the over approximation methods in the model checking. The algorithm adopted in the verification tool CheckMate and its application on a chemical process system was introduced in details. Finally, the open problems and the future research directions were analyzed.

在介绍混合系统形式验证概念的基础上,从可达集表示和可达集计算方法的角度比较了混合系统的各种形式验证方法和验证工具。重点介绍了模型检验方法中的收敛近似方法和过近似方法,通过一个化工过程系统的验证实例详细介绍了验证工具CheckMate的验证算法。最后分析了混合系统形式验证的难点问题和主要研究方向。

 
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