A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（g...A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.展开更多
In organic chemistry, as defined by Abegg, Kossel, Lewis and Langmuir, compounds are normally represented using structural formulas called Lewis structures. In these structures, the octet rule is used to define the nu...In organic chemistry, as defined by Abegg, Kossel, Lewis and Langmuir, compounds are normally represented using structural formulas called Lewis structures. In these structures, the octet rule is used to define the number of covalent bonds that each atom forms with its neighbors and multiple bonds are frequent. Lewis’ octet rule has unfortunately shown limitations very early when applied to non-organic compounds: most of them remain incompatible with the “rule of eight” and location of charges is uncertain. In an attempt to unify structural formulas of octet and non-octet molecules or single-charge ions, an even-odd rule was recently proposed, together with a procedure to locate charge precisely. This even-odd rule has introduced a charge-dependent effective-valence number calculated for each atom. With this number and the number of covalent bonds of each element, two even numbers are calculated. These numbers are both used to understand and draw structuralformulas of single-covalent-bonded compounds. In the present paper, a procedure is proposed to adjust structural formulas of compounds that are commonly represented with multiple bonds. In order to keep them compatible with the even-odd rule, they will be represented using only single covalent bonds. The procedure will then describe the consequences of bond simplification on charges locations. The newly obtained representations are compared to their conventional structural formulas, i.e. single-bond representation vs. multiple-bond structures. Throughout the comparison process, charges are precisely located and assigned to specific atoms. After discussion of particular cases of compounds, the paper finally concludes that a rule limiting representations of multiplecovalent bonds to single covalent bonds, seems to be suitable for numerous known compounds.展开更多
[目的]筛选罗田苍术[Atractylodes lancea (Thunb.) DC.Subsp.Luotianensis Hu et Feng in ed.]增殖培养的最佳培养基,为罗田苍术种苗工厂化生产提供技术指导。[方法]以罗田苍术的嫩枝为外植体,筛选出最适宜的基本培养基;再利用L9(34)...[目的]筛选罗田苍术[Atractylodes lancea (Thunb.) DC.Subsp.Luotianensis Hu et Feng in ed.]增殖培养的最佳培养基,为罗田苍术种苗工厂化生产提供技术指导。[方法]以罗田苍术的嫩枝为外植体,筛选出最适宜的基本培养基;再利用L9(34)正交试验优化6-BA、KT、NAA和IBA的配比。[结果]N68为罗田苍术最适宜的基本培养基,各植物生长调节剂的最佳浓度为1.0 mg/L6-BA+1.0 mg/LKT+0.5 mg/LNAA+0.2 mg/LIBA。[结论]该试验筛选出了罗田苍术增殖培养的最佳培养配方,为罗田苍术种苗工厂化生产提供了技术指导。展开更多
The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to ...The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.10671142)
文摘A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.
文摘In organic chemistry, as defined by Abegg, Kossel, Lewis and Langmuir, compounds are normally represented using structural formulas called Lewis structures. In these structures, the octet rule is used to define the number of covalent bonds that each atom forms with its neighbors and multiple bonds are frequent. Lewis’ octet rule has unfortunately shown limitations very early when applied to non-organic compounds: most of them remain incompatible with the “rule of eight” and location of charges is uncertain. In an attempt to unify structural formulas of octet and non-octet molecules or single-charge ions, an even-odd rule was recently proposed, together with a procedure to locate charge precisely. This even-odd rule has introduced a charge-dependent effective-valence number calculated for each atom. With this number and the number of covalent bonds of each element, two even numbers are calculated. These numbers are both used to understand and draw structuralformulas of single-covalent-bonded compounds. In the present paper, a procedure is proposed to adjust structural formulas of compounds that are commonly represented with multiple bonds. In order to keep them compatible with the even-odd rule, they will be represented using only single covalent bonds. The procedure will then describe the consequences of bond simplification on charges locations. The newly obtained representations are compared to their conventional structural formulas, i.e. single-bond representation vs. multiple-bond structures. Throughout the comparison process, charges are precisely located and assigned to specific atoms. After discussion of particular cases of compounds, the paper finally concludes that a rule limiting representations of multiplecovalent bonds to single covalent bonds, seems to be suitable for numerous known compounds.
文摘[目的]筛选罗田苍术[Atractylodes lancea (Thunb.) DC.Subsp.Luotianensis Hu et Feng in ed.]增殖培养的最佳培养基,为罗田苍术种苗工厂化生产提供技术指导。[方法]以罗田苍术的嫩枝为外植体,筛选出最适宜的基本培养基;再利用L9(34)正交试验优化6-BA、KT、NAA和IBA的配比。[结果]N68为罗田苍术最适宜的基本培养基,各植物生长调节剂的最佳浓度为1.0 mg/L6-BA+1.0 mg/LKT+0.5 mg/LNAA+0.2 mg/LIBA。[结论]该试验筛选出了罗田苍术增殖培养的最佳培养配方,为罗田苍术种苗工厂化生产提供了技术指导。
基金Acknowledgements The authors would like to show their hearty thanks to Professor Shigeru Kanemitsu for enlightening discussion and encouragement. The second author was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101175, 11371165）, 985 Project, and 211 Project.
文摘The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.
