Two new secolignans （1 and 2） were isolated from the roots of Urtica mairei Levi. The structures of these two compounds were determined on the basis of extensive spectroscopic methods including HR-EI-MS, 1D and 2D N...Two new secolignans （1 and 2） were isolated from the roots of Urtica mairei Levi. The structures of these two compounds were determined on the basis of extensive spectroscopic methods including HR-EI-MS, 1D and 2D NMR experiments.展开更多
We study the structure of a metric n-Lie algebra G over the complex field C. Let G = S＋R be the Levi decomposition, where T4 is the radical of G and S is a strong semisimple subalgebra of G. Denote by re（G） the num...We study the structure of a metric n-Lie algebra G over the complex field C. Let G = S＋R be the Levi decomposition, where T4 is the radical of G and S is a strong semisimple subalgebra of G. Denote by re（G） the number of all minimal ideals of an indecomposable metric n-Lie algebra and R^⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R^⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to rn（G） ＋ 1. The centralizer of T4 in G is equal to the sum of all minimal ideals; it is the direct sum of R^⊥and the center of G. Finally, G has no strong semisimple ideals if and only if R^⊥ R.展开更多
Introducing carbon trading into electricity market can convert carbon dioxide into schedulable resources with economic value.However,the randomness of wind power generation puts forward higher requirements for electri...Introducing carbon trading into electricity market can convert carbon dioxide into schedulable resources with economic value.However,the randomness of wind power generation puts forward higher requirements for electricity market transactions.Therefore,the carbon trading market is introduced into the wind power market,and a new form of low-carbon economic dispatch model is developed.First,the economic dispatch goal of wind power is be considered.It is projected to save money and reduce the cost of power generation for the system.The model includes risk operating costs to account for the impact of wind power output variability on the system,as well as wind farm negative efficiency operating costs to account for the loss caused by wind abandonment.The model also employs carbon trading market metrics to achieve the goal of lowering system carbon emissions,and analyze the impact of different carbon trading prices on the system.A low-carbon economic dispatch model for the wind power market is implemented based on the following two goals.Finally,the solution is optimised using the Ant-lion optimisation method,which combines Levi's flight mechanism and golden sine.The proposed model and algorithm's rationality is proven through the use of cases.展开更多
The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.
We study polynomial representations of finite dimensional （R or C） Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle stru...We study polynomial representations of finite dimensional （R or C） Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle structures.展开更多
The authors have recently completed a partial classification of the ten-dimensional real Lie algebras that have the non-trivial Levi decomposition, namely, for such algebras whose semi-simple factor is so(3). In the p...The authors have recently completed a partial classification of the ten-dimensional real Lie algebras that have the non-trivial Levi decomposition, namely, for such algebras whose semi-simple factor is so(3). In the present paper, we obtain a matrix representation for each of these Lie algebras. We are able to find such representations by exploiting properties of the radical, principally, when it has a trivial center, in which case we can obtain such a representation by restricting the adjoint representation. Another important subclass of algebras is where the radical has a codimension one abelian nilradical and for which a representation can readily be found. In general, finding matrix representations for abstract Lie algebras is difficult and there is no algorithmic process, nor is it at all easy to program by computer, even for algebras of low dimension. The present paper represents another step in our efforts to find linear representations for all the low dimensional abstract Lie algebras.展开更多
Through a variable transformation, the Whitham-Broer-Kaup system is transformed into a parameter Levi system. Based on the Lax pair of the parameter Levi system, the N-fold Darboux transformation with multi-parameters...Through a variable transformation, the Whitham-Broer-Kaup system is transformed into a parameter Levi system. Based on the Lax pair of the parameter Levi system, the N-fold Darboux transformation with multi-parameters is constructed. Then some new explicit solutions for the Whitham-Broer-Kaup system are obtained via the given Darboux transformation.展开更多
[ Objective] This study aimed to establish an optimized suspension culture for hairy roots of Aconitum coreanum （Levi.） Raipaics. [ Method ] Hairy root of Aconitum coreanum （ Levl. ） Raipaics A0489 was selected as...[ Objective] This study aimed to establish an optimized suspension culture for hairy roots of Aconitum coreanum （Levi.） Raipaics. [ Method ] Hairy root of Aconitum coreanum （ Levl. ） Raipaics A0489 was selected as experimental material, to screen the optimal medium for suspension culture. [ Result] Aconitum coreanum （Levl.） Raipaics hairy roots showed different growth conditions in various liquid medium; salt concentration, nitrogen content, sugar content, rotation speed and room temperature had great influences on the growth of Aconitum coreanum （Levi.） Raipaics hairy roots. [ Conclusion] The optimal suspension culture system for Aconitum coreanum （ Levi. ） Raipaics hairy roots was established ： B5 was used as basic medium, culture temperature was 20℃ under dark conditions, rotation speed was 140 r/m in the first 15 d and 110 r/m in the latter 15 d.展开更多
In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^...In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},展开更多
Let （g, [p]） be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of ＂higher＂ reduced enveloping algebras {uxs （g） I s ∈ N} with X running over g＊ ma...Let （g, [p]） be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of ＂higher＂ reduced enveloping algebras {uxs （g） I s ∈ N} with X running over g＊ make representations of g split into different ＂blocks＂. In this paper, we study such an infinite- dimensional algebra Ax （g） ：=lim Uxs （g） for a given X C g＊. A module category equivalence is built between subcategories of U（g）-rnod and Ax（g）-mod. In the case of reductive Lie algebras, （quasi） generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized x-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity.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 new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structur...A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented. As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper.展开更多
A new lignan glycoside, named （7S,8R,8＇R）-（-）-lariciresinol-9-O-a-L-rhamnopyranosyl （1-2） 13-D-glucopyranoside （1）,was isolated from the ethanol extract ofPilea cavaleriei Levi subsp, cavaleriei, together wit...A new lignan glycoside, named （7S,8R,8＇R）-（-）-lariciresinol-9-O-a-L-rhamnopyranosyl （1-2） 13-D-glucopyranoside （1）,was isolated from the ethanol extract ofPilea cavaleriei Levi subsp, cavaleriei, together with 17 known lignans （2-18）. The structuresof these compounds were elucidated by extensive spectroscopic analysis, including 1D NMR, 2D NMR and HR-ESI-MS.All the compounds were obtained from the genus Pilea for the first time.展开更多
We study the Leibniz n-algebra U_(n)(L),whose multiplication is defined via the bracket of a Leibniz algebra L as[x1,…,xn]=[x1,[…,[xn−2,[xn−1,xn]]…]].We show that U_(n)(L)is simple if and only if L is a simple Lie ...We study the Leibniz n-algebra U_(n)(L),whose multiplication is defined via the bracket of a Leibniz algebra L as[x1,…,xn]=[x1,[…,[xn−2,[xn−1,xn]]…]].We show that U_(n)(L)is simple if and only if L is a simple Lie algebra.An analog of Levi's theorem for Leibniz algebras in U_(n)(Lb)is established and it is proven that the Leibniz n-kernel of U_(n)(L)for any semisimple Leibniz algebra L is the n-algebra U_(n)(L).展开更多
Let M be a smooth pseudoconvex hypersurface in ℂ^(n+1) whose Levi form has at most one degenerate eigenvalue. For any tangent vector field L of type (1, 0), we prove the equality of the commutator type and the Levi fo...Let M be a smooth pseudoconvex hypersurface in ℂ^(n+1) whose Levi form has at most one degenerate eigenvalue. For any tangent vector field L of type (1, 0), we prove the equality of the commutator type and the Levi form type associated to L. We also show that the regular contact type, the commutator type and the Levi form type of the real hypersurface are the same.展开更多
基金the NSFC project(No.30572317)research project of the Educational Department of Liaoning Province(No.2004F114)for the financial supports.
文摘Two new secolignans （1 and 2） were isolated from the roots of Urtica mairei Levi. The structures of these two compounds were determined on the basis of extensive spectroscopic methods including HR-EI-MS, 1D and 2D NMR experiments.
基金Supported by National Natural Science Foundation of China (Grant No. 10871192)Natural Science Foundation of Hebei Province, China (Grant No. A2010000194)
文摘We study the structure of a metric n-Lie algebra G over the complex field C. Let G = S＋R be the Levi decomposition, where T4 is the radical of G and S is a strong semisimple subalgebra of G. Denote by re（G） the number of all minimal ideals of an indecomposable metric n-Lie algebra and R^⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R^⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to rn（G） ＋ 1. The centralizer of T4 in G is equal to the sum of all minimal ideals; it is the direct sum of R^⊥and the center of G. Finally, G has no strong semisimple ideals if and only if R^⊥ R.
基金National Natural Science Foundation of China,Grant/Award Number:51677059。
文摘Introducing carbon trading into electricity market can convert carbon dioxide into schedulable resources with economic value.However,the randomness of wind power generation puts forward higher requirements for electricity market transactions.Therefore,the carbon trading market is introduced into the wind power market,and a new form of low-carbon economic dispatch model is developed.First,the economic dispatch goal of wind power is be considered.It is projected to save money and reduce the cost of power generation for the system.The model includes risk operating costs to account for the impact of wind power output variability on the system,as well as wind farm negative efficiency operating costs to account for the loss caused by wind abandonment.The model also employs carbon trading market metrics to achieve the goal of lowering system carbon emissions,and analyze the impact of different carbon trading prices on the system.A low-carbon economic dispatch model for the wind power market is implemented based on the following two goals.Finally,the solution is optimised using the Ant-lion optimisation method,which combines Levi's flight mechanism and golden sine.The proposed model and algorithm's rationality is proven through the use of cases.
基金National Natural Science Foundation of China under Grant Nos.10871165 and 10671121
文摘The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.
文摘We study polynomial representations of finite dimensional （R or C） Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle structures.
文摘The authors have recently completed a partial classification of the ten-dimensional real Lie algebras that have the non-trivial Levi decomposition, namely, for such algebras whose semi-simple factor is so(3). In the present paper, we obtain a matrix representation for each of these Lie algebras. We are able to find such representations by exploiting properties of the radical, principally, when it has a trivial center, in which case we can obtain such a representation by restricting the adjoint representation. Another important subclass of algebras is where the radical has a codimension one abelian nilradical and for which a representation can readily be found. In general, finding matrix representations for abstract Lie algebras is difficult and there is no algorithmic process, nor is it at all easy to program by computer, even for algebras of low dimension. The present paper represents another step in our efforts to find linear representations for all the low dimensional abstract Lie algebras.
文摘Through a variable transformation, the Whitham-Broer-Kaup system is transformed into a parameter Levi system. Based on the Lax pair of the parameter Levi system, the N-fold Darboux transformation with multi-parameters is constructed. Then some new explicit solutions for the Whitham-Broer-Kaup system are obtained via the given Darboux transformation.
基金Supported by Project of Applied Basic Research from the Institute of Special Wild Economic Animal and Plant Science,Chinese Academy of Agricultural Sciences(tcs2004-08)Project of Jilin Science and Technology Bureau(201222306)
文摘[ Objective] This study aimed to establish an optimized suspension culture for hairy roots of Aconitum coreanum （Levi.） Raipaics. [ Method ] Hairy root of Aconitum coreanum （ Levl. ） Raipaics A0489 was selected as experimental material, to screen the optimal medium for suspension culture. [ Result] Aconitum coreanum （Levl.） Raipaics hairy roots showed different growth conditions in various liquid medium; salt concentration, nitrogen content, sugar content, rotation speed and room temperature had great influences on the growth of Aconitum coreanum （Levi.） Raipaics hairy roots. [ Conclusion] The optimal suspension culture system for Aconitum coreanum （ Levi. ） Raipaics hairy roots was established ： B5 was used as basic medium, culture temperature was 20℃ under dark conditions, rotation speed was 140 r/m in the first 15 d and 110 r/m in the latter 15 d.
基金Project supported by the National Natural Science Foundation of China
文摘In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},
基金Supported by National Natural Science Foundation of China (Grant Nos. 11126062,11201293 and 11271130)the Innovation Program of Shanghai Municipal Education Commission (Grant Nos. 12ZZ038 and 13YZ077)
文摘Let （g, [p]） be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of ＂higher＂ reduced enveloping algebras {uxs （g） I s ∈ N} with X running over g＊ make representations of g split into different ＂blocks＂. In this paper, we study such an infinite- dimensional algebra Ax （g） ：=lim Uxs （g） for a given X C g＊. A module category equivalence is built between subcategories of U（g）-rnod and Ax（g）-mod. In the case of reductive Lie algebras, （quasi） generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized x-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity.
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.
文摘A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented. As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper.
文摘A new lignan glycoside, named （7S,8R,8＇R）-（-）-lariciresinol-9-O-a-L-rhamnopyranosyl （1-2） 13-D-glucopyranoside （1）,was isolated from the ethanol extract ofPilea cavaleriei Levi subsp, cavaleriei, together with 17 known lignans （2-18）. The structuresof these compounds were elucidated by extensive spectroscopic analysis, including 1D NMR, 2D NMR and HR-ESI-MS.All the compounds were obtained from the genus Pilea for the first time.
基金The first author was supported by the National Science Foundation(grant number 1658672),USA.
文摘We study the Leibniz n-algebra U_(n)(L),whose multiplication is defined via the bracket of a Leibniz algebra L as[x1,…,xn]=[x1,[…,[xn−2,[xn−1,xn]]…]].We show that U_(n)(L)is simple if and only if L is a simple Lie algebra.An analog of Levi's theorem for Leibniz algebras in U_(n)(Lb)is established and it is proven that the Leibniz n-kernel of U_(n)(L)for any semisimple Leibniz algebra L is the n-algebra U_(n)(L).
基金The third author was supported in part by NSFC(12171372).
文摘Let M be a smooth pseudoconvex hypersurface in ℂ^(n+1) whose Levi form has at most one degenerate eigenvalue. For any tangent vector field L of type (1, 0), we prove the equality of the commutator type and the Levi form type associated to L. We also show that the regular contact type, the commutator type and the Levi form type of the real hypersurface are the same.
