By using Cauchy's integral formula of analytical complex function and the third order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a...By using Cauchy's integral formula of analytical complex function and the third order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a 2D semi infinite body is presented in this paper. The pressure coefficients obtained by the present method agree well with those given by Acrivous, showing the validity of our method.展开更多
Geometrical optimization and electrostatic potential calculations have been performed for a series of halogenated hydrocarbons at the HF/Gen-6d level. A number of electrostatic potentials and the statistically based s...Geometrical optimization and electrostatic potential calculations have been performed for a series of halogenated hydrocarbons at the HF/Gen-6d level. A number of electrostatic potentials and the statistically based structural descriptors derived from these electrostatic potentials have been obtained. Multiple linear regression analysis and artificial neural network are employed simultaneously in this paper. The result shows that the parameters derived from electrostatic 2 potentials σtot^2, V s and ∑ Vs^＋, together with the molecular volume （Vine） can be used to express the quantitative structure-infinite dilution activity coefficients （γ^∞） relationship of halogenated hydrocarbons in water. The result also demonstrates that the model obtained by using BFGS quasiNewton neural network method has much better predictive capability than that from multiple linear regression. The goodness of the model has been validated through exploring the predictive power for the external test set. The model obtained via neural network may be applied to predict γ^∞ of other halogenated hydrocarbons not present in the data set.展开更多
Based on QSPR of alcohol and ether organic compounds in water,geometrical optimization and electrostatic potential calculations were performed at the HF/6-31G＊ level for 73 alcohol and ether organic compounds.Linear ...Based on QSPR of alcohol and ether organic compounds in water,geometrical optimization and electrostatic potential calculations were performed at the HF/6-31G＊ level for 73 alcohol and ether organic compounds.Linear relationships between infinite dilution activity coef-ficient（lnγ∞） of alcohols and ethers in water and theoretical descriptors of the molecular structure were established by multiple regression method.The result shows that the parameters derived from molecular electrostatic potential together with molecular surface area can be preferably used to express the quantitative structure-lnγ∞ relationship of alcohols and ethers in water.This reveals that this model has good predictive capabilities（RCV=0.969）.The molecular electrostatic potential has also been proved to have the general applicability in QSPR model of alcohol and ether organic compounds about γ∞ in water.The QSPR model established may provide a new powerful method for predicting γ∞ of organic compounds in aqueous systems.展开更多
The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless sing...The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless singular boundary method (SBM) to solve infinite domain potential problems.The SBM is mathematically simple, easy-to-program, meshless and integration-free.To guar-antee the uniqueness of numerical solutions, this article adds a constant term into the SBM approximate representation.The effi-ciency and accuracy of the proposed technique are tested to the three infinite domain potential problems.展开更多
In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the ...In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the existence and regularity of multiple nontrivial solutions have been proved.展开更多
文摘By using Cauchy's integral formula of analytical complex function and the third order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a 2D semi infinite body is presented in this paper. The pressure coefficients obtained by the present method agree well with those given by Acrivous, showing the validity of our method.
文摘Geometrical optimization and electrostatic potential calculations have been performed for a series of halogenated hydrocarbons at the HF/Gen-6d level. A number of electrostatic potentials and the statistically based structural descriptors derived from these electrostatic potentials have been obtained. Multiple linear regression analysis and artificial neural network are employed simultaneously in this paper. The result shows that the parameters derived from electrostatic 2 potentials σtot^2, V s and ∑ Vs^＋, together with the molecular volume （Vine） can be used to express the quantitative structure-infinite dilution activity coefficients （γ^∞） relationship of halogenated hydrocarbons in water. The result also demonstrates that the model obtained by using BFGS quasiNewton neural network method has much better predictive capability than that from multiple linear regression. The goodness of the model has been validated through exploring the predictive power for the external test set. The model obtained via neural network may be applied to predict γ^∞ of other halogenated hydrocarbons not present in the data set.
文摘Based on QSPR of alcohol and ether organic compounds in water,geometrical optimization and electrostatic potential calculations were performed at the HF/6-31G＊ level for 73 alcohol and ether organic compounds.Linear relationships between infinite dilution activity coef-ficient（lnγ∞） of alcohols and ethers in water and theoretical descriptors of the molecular structure were established by multiple regression method.The result shows that the parameters derived from molecular electrostatic potential together with molecular surface area can be preferably used to express the quantitative structure-lnγ∞ relationship of alcohols and ethers in water.This reveals that this model has good predictive capabilities（RCV=0.969）.The molecular electrostatic potential has also been proved to have the general applicability in QSPR model of alcohol and ether organic compounds about γ∞ in water.The QSPR model established may provide a new powerful method for predicting γ∞ of organic compounds in aqueous systems.
基金supported by the National Natural Science Foundation of China (10672051)Natural Science Foundation of Hohai University (409251)
文摘The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless singular boundary method (SBM) to solve infinite domain potential problems.The SBM is mathematically simple, easy-to-program, meshless and integration-free.To guar-antee the uniqueness of numerical solutions, this article adds a constant term into the SBM approximate representation.The effi-ciency and accuracy of the proposed technique are tested to the three infinite domain potential problems.
基金supported by National Natural Science Foundation of China (Grant No.11131005)PHD Programs Foundation of Ministry of Education of China (Grant No. 20090141110003)the Fundamental Research Funds for the Central Universities (Grant No. 2012201020202)
文摘In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the existence and regularity of multiple nontrivial solutions have been proved.
