A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and...A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.展开更多
A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1....A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.展开更多
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-...A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies.展开更多
A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential f...A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.展开更多
A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A （2＋1）-dimensional multi-component DLW integrable hierarchy is obtained by using a （2＋1）-dimensional zero curvature...A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A （2＋1）-dimensional multi-component DLW integrable hierarchy is obtained by using a （2＋1）-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.展开更多
Objective To investigate the integral dissolution model based on biological potency in order to evaluate the dissolution of Compound Chinese materia medica（CCMM） in vitro. Methods The contents of paeoniflorin, phill...Objective To investigate the integral dissolution model based on biological potency in order to evaluate the dissolution of Compound Chinese materia medica（CCMM） in vitro. Methods The contents of paeoniflorin, phillyrin, ginsenoside Rg1, and adenosine of ten batches of Compound Biejia Ruangan Tablet（CBRT） were determined at different times. The self-defined weighting coefficient based on the contents has been created to establish the integral dissolution model. In addition, the biological potency of CBRT was measured by MTT assay. Then, the f2 similar factor was used to evaluate the similarity of the batches. Results Compared with batch a, some batches’ f2 values of paeoniflorin and adenosine were less than 50, while f2 values of ginsenoside Rg1, phillyrin, and integral component were more than 50. Likewise, ginsenoside Rg1, phillyrin, and integral component were all in good correlation with biological dissolution. Conclusion The results of the integral dissolution based on biological test of CBRT demonstrate that the bioassay method may be a promising supplement for its quality evaluation.展开更多
Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy...Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.展开更多
Voriconazole(VZL)is a second-generation and broad-spectrum triazole against fungal infections.Being a BCS(biopharmaceutics classification system)class II compound,the poor aqueous solubility has limited its bioavailab...Voriconazole(VZL)is a second-generation and broad-spectrum triazole against fungal infections.Being a BCS(biopharmaceutics classification system)class II compound,the poor aqueous solubility has limited its bioavailability and clinical efficacy.Aims to overcome this disadvantage,a cocrystallization strategy based on crystal engineering principles has resulted in five new multi-component crystals of VZL with maleic acid,L-tartaric,protocatechuic,gallic,and 3,5-dinitrobenzoic acids.Structure analysis revealed that the hydroxyl/carboxylic acid···triazole N_(3)hydrogen bonding interaction appears as a main supramolecular heterosynthon in the VZL multi-component crystals with organic acids.And VZL molecule has a flexible conformation in each of the five multi-component structures.The newly synthesized multi-component crystals showed impressive solubility improvement compared to that of the raw material of VZL.Molecular electrostatic potential surfaces(MEPS)analysis based on density functional(DFT)calculations revealed that hydrogen bond interactions in cocrystals mainly involved pairwise interactions in the global maxima and minima sites,but this rule is not always followed.This study indicates the potential of cocrystals to improve the solubility and dissolution rate of VZL.展开更多
文摘A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.
基金中国科学院资助项目，the Science Foundation of Liuhui Center of Tianjin University and Nankai University，辽宁省自然科学基金
文摘A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.
基金the National Natural Science Foundation of China under，南开大学-天津大学合作项目，天津大学校科研和教改项目，the Educational Committee of Liaoning Province of China under Gant
文摘A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies.
基金The project supported by National Natural Science Foundation of China under.Grant No. 10371070
文摘A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.
文摘A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A （2＋1）-dimensional multi-component DLW integrable hierarchy is obtained by using a （2＋1）-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.
基金Major Scientific and Technological Specialized Project for Significant New.Formulation of New Drugs(No.2011ZX09201-201-14)National Natural Science Foundation of China(No.81073069)
文摘Objective To investigate the integral dissolution model based on biological potency in order to evaluate the dissolution of Compound Chinese materia medica（CCMM） in vitro. Methods The contents of paeoniflorin, phillyrin, ginsenoside Rg1, and adenosine of ten batches of Compound Biejia Ruangan Tablet（CBRT） were determined at different times. The self-defined weighting coefficient based on the contents has been created to establish the integral dissolution model. In addition, the biological potency of CBRT was measured by MTT assay. Then, the f2 similar factor was used to evaluate the similarity of the batches. Results Compared with batch a, some batches’ f2 values of paeoniflorin and adenosine were less than 50, while f2 values of ginsenoside Rg1, phillyrin, and integral component were more than 50. Likewise, ginsenoside Rg1, phillyrin, and integral component were all in good correlation with biological dissolution. Conclusion The results of the integral dissolution based on biological test of CBRT demonstrate that the bioassay method may be a promising supplement for its quality evaluation.
基金The authors are very grateful to professor Yu-Feng Zhang for his ardent guidance and help.
文摘Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.
基金supported by Beijing Natural Science Foundation(No.7222261)Key R&D Program of Shan Dong Province(No.2021ZDSYS26)+2 种基金the Fundamental Research Funds for the Central Universities(No.2021-RW350-001)the Xinjiang Uygur Autonomous Region Innovation Environment Construction Special FundTechnology Innovation Base Construction Key Laboratory Open Project(No.2022D04016)。
文摘Voriconazole(VZL)is a second-generation and broad-spectrum triazole against fungal infections.Being a BCS(biopharmaceutics classification system)class II compound,the poor aqueous solubility has limited its bioavailability and clinical efficacy.Aims to overcome this disadvantage,a cocrystallization strategy based on crystal engineering principles has resulted in five new multi-component crystals of VZL with maleic acid,L-tartaric,protocatechuic,gallic,and 3,5-dinitrobenzoic acids.Structure analysis revealed that the hydroxyl/carboxylic acid···triazole N_(3)hydrogen bonding interaction appears as a main supramolecular heterosynthon in the VZL multi-component crystals with organic acids.And VZL molecule has a flexible conformation in each of the five multi-component structures.The newly synthesized multi-component crystals showed impressive solubility improvement compared to that of the raw material of VZL.Molecular electrostatic potential surfaces(MEPS)analysis based on density functional(DFT)calculations revealed that hydrogen bond interactions in cocrystals mainly involved pairwise interactions in the global maxima and minima sites,but this rule is not always followed.This study indicates the potential of cocrystals to improve the solubility and dissolution rate of VZL.
