New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bendin...New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.展开更多
Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the gr...Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.展开更多
目的建立银杏叶片体外溶出度与空间分布均匀度评价方法,探究体外溶出行为对空间分布均匀度的影响,实现银杏叶片质量控制。方法首先,采用《中国药典》2020年版方法完成银杏叶片溶出度测定,并基于模型依赖法对银杏叶片体外溶出特性进行评...目的建立银杏叶片体外溶出度与空间分布均匀度评价方法,探究体外溶出行为对空间分布均匀度的影响,实现银杏叶片质量控制。方法首先,采用《中国药典》2020年版方法完成银杏叶片溶出度测定,并基于模型依赖法对银杏叶片体外溶出特性进行评价;其次,通过对称参数图像分析法(symetry parameterimage analysis,SPIA)和均匀度百分比指数法(percentage of homogeneity,H%)对银杏叶片空间分布均匀度进行评价;最后,建立偏最小二乘(partial least square,PLS)和标准正则变换(standardized normal variate,SVR)模型对银杏叶片体外溶出度与活性药物成分(active pharmaceutical ingredient,API)空间分布均匀度进行关联辨识研究。结果银杏叶片在45 min内完全溶出且累积溶出率大于70%,且不同批次溶出行为存在差异;银杏叶片API空间分布均匀度范围为64.09%~76.54%,其中5个批次银杏叶片质量差异较大;银杏叶片体外溶出度与API空间分布均匀度PLS和SVR模型R^(2)值分别为0.1110和0.2540,两者没有相关性。结论所建方法可客观评价中药固体制剂的溶出度与空间分布均匀度,实现银杏叶片与空间分布均匀度的关联辨识研究,为银杏叶片制造过程质量控制及提升提供了方向。展开更多
In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact sol...In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.展开更多
文摘New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.
基金the State Key Basic Research Program of China under Grant No.2004CB318000
文摘Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.
文摘目的建立银杏叶片体外溶出度与空间分布均匀度评价方法,探究体外溶出行为对空间分布均匀度的影响,实现银杏叶片质量控制。方法首先,采用《中国药典》2020年版方法完成银杏叶片溶出度测定,并基于模型依赖法对银杏叶片体外溶出特性进行评价;其次,通过对称参数图像分析法(symetry parameterimage analysis,SPIA)和均匀度百分比指数法(percentage of homogeneity,H%)对银杏叶片空间分布均匀度进行评价;最后,建立偏最小二乘(partial least square,PLS)和标准正则变换(standardized normal variate,SVR)模型对银杏叶片体外溶出度与活性药物成分(active pharmaceutical ingredient,API)空间分布均匀度进行关联辨识研究。结果银杏叶片在45 min内完全溶出且累积溶出率大于70%,且不同批次溶出行为存在差异;银杏叶片API空间分布均匀度范围为64.09%~76.54%,其中5个批次银杏叶片质量差异较大;银杏叶片体外溶出度与API空间分布均匀度PLS和SVR模型R^(2)值分别为0.1110和0.2540,两者没有相关性。结论所建方法可客观评价中药固体制剂的溶出度与空间分布均匀度,实现银杏叶片与空间分布均匀度的关联辨识研究,为银杏叶片制造过程质量控制及提升提供了方向。
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090the Natural Science Foundation of Shandong Province under Grant No.ZR2015AL008the High-Level Personnel Foundation of Liaocheng University under Grant No.31805
文摘In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.
