Filiform李代数Q_n的Hom-结构

首先证明了有限维Z-阶化李代数上的一个线性算子是Hom-结构的充分必要条件,即它的每个齐次分支也是Hom-结构.然后计算了特征零代数闭域上一类有限维Z-阶化Filiform李代数Qn的齐次Hom-结构,从而决定了Qn的所有Hom-结构.     

Q‐symmetry and conditional Q‐symmetries for Drinfel'd–Sokolov–Wilson system

We study in this paper the Q‐symmetry and conditional Q‐symmetries of Drinfel'd–Sokolov–Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. Copyright © 2014 John Wiley & Sons, Ltd.     

A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters

In a fairly recent paper (2008 American Control Conference, June 11‐13, 1035‐1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal‐value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution. Copyright © 2014 JohnWiley & Sons, Ltd.     

On the structure of split Leibniz triple systems

We study the structure of arbitrary split Leibniz triple systems with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length, the simplicity of the Leibniz triple systems is characterized.     

Determination of sulfonamide residues in cultured sea cucumber by pre-column derivatization capillary electrophoresis with fluorescence detection

A simple and mild method for the separation of sulfonamide residues based on a condensation reaction with O-phthalaldehyde solution (OPA) as labeling reagent with capillary electrophoresis has been developed. A 58.5 cm × 50 μm i.d. (50 cm effective length) untreated fused-silica capillary was used. To optimize the separation conditions, the background electrolyte concentration, pH, column temperature, voltage and other factors were evaluated. The optimal separation conditions were as follows: 20 mmol L^?1 borate buffer; pH 9.1; column temperature 20 °C; separation voltage 18 kV, pressure 50 mbar and injection time 8 s. Under the optimal conditions, 10 kinds of sulfonamide derivatives could be well-separated within 8 min, and the linear ranges were 0.35–100 μg kg^?1. The detection limit (at a signal-to-noise ratio of 3) was in the range of 0.12–0.25 μg kg^?1, and the quantification limit (at a signal-to-noise ratio of 10) was in the range of 0.35–0.70 μg kg^?1. The sulfonamide residues from cultured sea cucumber samples were determined under the optimal conditions with satisfactory results.     

Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras

Using deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case sl(2,C)$\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$, there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter.     

超高效液相色谱-串联质谱法定量分析尿液中色氨酸及其代谢产物

基于超高效液相色谱-串联质谱(UPLC-MS/MS)建立定量分析色氨酸(Trp)及代谢产物3-OH-犬尿氨酸(3-OH-Kyn)、3-OH-邻氨基苯甲酸(3-OH-AA)、黄尿酸(XA)、犬尿氨酸(Kyn)、5-羟基吲哚乙酸(5-HIAA)、犬尿喹啉酸(KA)和5-羟色胺(5-HT)的方法,应用该方法分析其在尿样中的含量,探讨排泄规律。将尿样稀释、离心后,加入丹磺酰氯(DNS-Cl)衍生,经Thermo C₁₈色谱柱(50 mm×3 mm, 2.7 μm)分离和0.1%甲酸和甲醇梯度洗脱后,采用电喷雾电离(ESI)源,在正离子扫描和多反应监测(MRM)模式下检测。以咖啡酸(CA)为内标,定量分析。结果显示,8种目标化合物的线性关系良好,相关系数(R ²)≥0.9740,检测灵敏(LOD为0.005~0.5 ng/mL),回收率高(93.24%~107.65%)。采用本方法检测分析了健康志愿者70个尿液样本,在尿样中检测到Trp原型及其7种代谢产物。结果表明,体内的Trp是通过原型和代谢两种方式排泄:Trp原型的含量为5.22~20.88 μg/mL;尿液中经代谢后排泄的Trp量是原型的124%~268%,即体内的Trp主要经代谢后排出体外。方法主要研究了Trp-5-HT和Trp-Kyn两条途径的代谢产物含量,Trp经Kyn降解生成的3-OH-AA和3-OH-Kyn含量较多,即Trp-Kyn是体内Trp的主要代谢途径。方法通过UPLC-MS/MS实现了尿液中Trp及其代谢产物含量的检测,能为临床检查提供技术和理论支持。     

Infinitesimal supersymmetries over Lie groups and their classification for gl(1,1) and sl(1,1)

Infinitesimal supersymmetries over classical Lie groups that are not necessarily induced by a Lie supergroup are described. They yield a notion of supersymmetry that is less rigid than the assumption of a Lie supergroup action but still implies an underlying action of a Lie group. In contrast to Lie supergroups, the arising representation-theoretical Lie supergroups (RTLSG) occur as families associated to Harish–Chandra superpairs. However morphisms of RTLSGs directly correspond to morphisms of Harish–Chandra superpairs. Particular RTLSGs can be derived from the explicit constructions of Lie supergroups given by Kostant and Koszul. The Lie superalgebras $\mathfrak{g}\mathfrak{l}(1,1)$ or $\mathfrak{s}\mathfrak{l}(1,1)$ appearing also in higher dimensional classical Lie superalgebras, provide interesting first examples of RTLSGs. A classification of RTLSGs associated to real and complex $\mathfrak{g}\mathfrak{l}(1,1)$- and $\mathfrak{s}\mathfrak{l}(1,1)$-Harish–Chandra superpairs is given by parameter spaces and complete sets of invariants. The underlying Lie group is assumed to be connected but possibly not simply connected.     

The minimal dimensions of faithful representations for Heisenberg Lie superalgebras

This paper aims to determine the minimal dimensions and super-dimensions of faithful representations for Heisenberg Lie superalgebras over an algebraically closed field of characteristic zero.