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拉格朗日中值定理的另一种证法
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作者 廖学余 《恩施师专学报》 1982年第2期51-52,共2页
拉格朗日中值定理 设f(X)在[a,b]上连续,在(a,b)内可导,则至少存在一点ξ∈(a,b),使得f(b)-f(a)=f′(ξ)(b-a) 在证明中值定理的过程中,要用到 罗尔定理 设F(x)在[a,b]上连续,在(a,b)内可导,且F(b)=F(a),则至少存在一点ξ∈(a,b),使得F... 拉格朗日中值定理 设f(X)在[a,b]上连续,在(a,b)内可导,则至少存在一点ξ∈(a,b),使得f(b)-f(a)=f′(ξ)(b-a) 在证明中值定理的过程中,要用到 罗尔定理 设F(x)在[a,b]上连续,在(a,b)内可导,且F(b)=F(a),则至少存在一点ξ∈(a,b),使得F′(ξ)=O。(每一种数学分析书都有证明) 展开更多
关键词 拉格朗日中值定理 证法 罗尔定理 上连续 辅助函数 传统证法 法线式 种数 对应函数 数学分析
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Connecting parameters optimization on unsymmetrical twin-tower structure linked by sky-bridge 被引量:1
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作者 孙黄胜 刘默涵 朱宏平 《Journal of Central South University》 SCIE EI CAS 2014年第6期2460-2468,共9页
Based on a simplified 3-DOF model of twin-tower structure linked by a sky-bridge,the frequency response functions,the displacement power spectral density(PSD)functions,and the time-averaged total vibration energy were... Based on a simplified 3-DOF model of twin-tower structure linked by a sky-bridge,the frequency response functions,the displacement power spectral density(PSD)functions,and the time-averaged total vibration energy were derived,by assuming the white noise as the earthquake excitation.The effects of connecting parameters,such as linking stiffness ratio and linking damping ratio,on the structural vibration responses were then studied,and the optimal connecting parameters were obtained to minimize the vibration energy of either the independent monomer tower or the integral structure.The influences of sky-bridge elevation position on the optimal connecting parameters were also discussed.Finally,the distribution characteristics of the top displacement PSD and the structural responses,excited by El Centro,Taft and artificial waves,were compared in both frequency and time domain.It is found that the connecting parameters at either end of connection interactively affect the responses of the towers.The optimal connecting parameters can greatly improve the damping connections on their seismic reduction effectiveness,but are unable to reduce the seismic responses of the towers to the best extent simultaneously.It is also indicated that the optimal connecting parameters derived from the simplified 3-DOF model are applicable for two multi-story structures linked by a sky-bridge with dampers.The seismic reduction effectiveness obtained varies from 0.3 to 1.0 with different sky-bridge mass ratio.The displacement responses of the example structures are reduced by approximately 22% with sky-bridge connections. 展开更多
关键词 twin-tower connected structure sky-bridge connecting parameter optimization seismic response
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