For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for s...For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.展开更多
The van Genuchten model is the most widely used soil water retention curve （SWRC） model. Two undisturbed soils （clay and loam） were used to evaluate the accuracy of the integral method to estimate van Genuchten mo...The van Genuchten model is the most widely used soil water retention curve （SWRC） model. Two undisturbed soils （clay and loam） were used to evaluate the accuracy of the integral method to estimate van Genuchten model parameters and to determine SWRCs of undisturbed soils. SWRCs calculated by the integral method were compared with those measured by a high speed centrifuge technique. The accuracy of the calculated results was evaluated graphically, as well as by root mean square error （RMSE）, normalized root mean square error （NRMSE） and Willmott＇s index of agreement （1）. The results obtained from the integral method were quite similar to those by the centrifuge technique. The RMSEs （4.61 ×10^-5 for Eum-Orthic Anthrosol and 2.74 × 10^-4 for Los-Orthic Entisol） and NRMSEs （1.56 × 10^-4 for Eum- Orthic Anthrosol and 1.45 ×10^-3 for Los-Orthic Entisol） were relatively small. The 1 values were 0.973 and 0.943 for Eum-Orthic Anthrosol and Los-Orthic Entisol, respectively, indicating a good agreement between the integral method values and the centrifuge values. Therefore, the integral method could be used to estimate SWRCs of undisturbed clay and loam soils.展开更多
A new mathematical model to estimate the parameters of the probability-integral method for mining subsidence prediction is proposed.Based on least squares support vector machine(LS-SVM) theory, it is capable of improv...A new mathematical model to estimate the parameters of the probability-integral method for mining subsidence prediction is proposed.Based on least squares support vector machine(LS-SVM) theory, it is capable of improving the precision and reliability of mining subsidence prediction.Many of the geological and mining factors involved are related in a nonlinear way.The new model is based on statistical theory(SLT) and empirical risk minimization(ERM) principles.Typical data collected from observation stations were used for the learning and training samples.The calculated results from the LS-SVM model were compared with the prediction results of a back propagation neural network(BPNN) model.The results show that the parameters were more precisely predicted by the LS-SVM model than by the BPNN model.The LS-SVM model was faster in computation and had better generalized performance.It provides a highly effective method for calculating the predicting parameters of the probability-integral method.展开更多
The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
基金The National Natural Science Foundation of China(No.10972151,11272227)
文摘For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.
基金Project supported by the International Partnership Program for Creative Research Teams of the Chinese Academy of Sciences (CAS) & the State Administration of Foreign Experts Affairs (SAFEA), China, and the Hundreds-Talent Program of the Chinese Academy of Sciences, China (No. 90502006)
文摘The van Genuchten model is the most widely used soil water retention curve （SWRC） model. Two undisturbed soils （clay and loam） were used to evaluate the accuracy of the integral method to estimate van Genuchten model parameters and to determine SWRCs of undisturbed soils. SWRCs calculated by the integral method were compared with those measured by a high speed centrifuge technique. The accuracy of the calculated results was evaluated graphically, as well as by root mean square error （RMSE）, normalized root mean square error （NRMSE） and Willmott＇s index of agreement （1）. The results obtained from the integral method were quite similar to those by the centrifuge technique. The RMSEs （4.61 ×10^-5 for Eum-Orthic Anthrosol and 2.74 × 10^-4 for Los-Orthic Entisol） and NRMSEs （1.56 × 10^-4 for Eum- Orthic Anthrosol and 1.45 ×10^-3 for Los-Orthic Entisol） were relatively small. The 1 values were 0.973 and 0.943 for Eum-Orthic Anthrosol and Los-Orthic Entisol, respectively, indicating a good agreement between the integral method values and the centrifuge values. Therefore, the integral method could be used to estimate SWRCs of undisturbed clay and loam soils.
基金Projects 50774080 supported by the National Natural Science Foundation of China200348 by the Foundation for the National Excellent Doctoral Dis-sertation of China
文摘A new mathematical model to estimate the parameters of the probability-integral method for mining subsidence prediction is proposed.Based on least squares support vector machine(LS-SVM) theory, it is capable of improving the precision and reliability of mining subsidence prediction.Many of the geological and mining factors involved are related in a nonlinear way.The new model is based on statistical theory(SLT) and empirical risk minimization(ERM) principles.Typical data collected from observation stations were used for the learning and training samples.The calculated results from the LS-SVM model were compared with the prediction results of a back propagation neural network(BPNN) model.The results show that the parameters were more precisely predicted by the LS-SVM model than by the BPNN model.The LS-SVM model was faster in computation and had better generalized performance.It provides a highly effective method for calculating the predicting parameters of the probability-integral method.
文摘The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
