Monodentate phosphites with carbohydrate substituents and their application in rhodium catalysed asymmetric hydrosilylation reactions

Several monodentate phosphites derived from d-glucofuranose were prepared and examined as ligands in the rhodium catalysed enantioselective hydrosilylation of acetophenone. A substantial variation in the e.e. values, from racemic to 58% e.e., was seen depending on the nature of the phosphite ligand used and the ligand to metal ratio. The reactivity of the selected phosphite P(DAG)₃ towards [Rh(μ-Cl)(COD)]₂ and [Rh(μ-Cl)(C₂H₄)₂]₂ (DAG=(1:2;5:6)-di(O-isopropylidene)-d-glucofuranosyl) allowed the synthesis of monosubstitued Rh(Cl)(COD)P(dag)₃ and [Rh(μ-Cl)(C₂H₄)P(dag)₃]₂ complexes, and the disubstituted Rh(Cl)(P(dag)₃)₂ and Rh(Cl)(C₂H₄)(P(dag)₃)₂ complexes. This study indicated that the disubstituted compounds offer better enantioselectivities than the monosubstituted ones.     

Multisoliton Solutions of the (2+1)-Dimensional KdV Equation

Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2+1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations.     

Exact Solutions of the Coupled KdV system via a Formally Variable Separation Approach

Most of the nonlinear physics systems are essentially nonintegrable.There in no very doog analytical approach to solve nonintegrable system.The variable separation approach is a powerful method in linear physics.In this letter,the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation.The method is valid not only for integrable models but also for nonintegrable models.Taking a nonintegrable coupled KdV equation system as a simple example,abundant solitary wave solutions and conoid wave solutions are revealed.     

Integrable sigma-models and Drinfeld–Sokolov hierarchies

Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the Drinfeld–Sokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld–Sokolov construction can be used to deduce the existence of commuting charges in these and in wider classes of sigma-models, including those whose target manifolds are exceptional groups or symmetric spaces. This establishes a direct link between commuting quantities in integrable sigma-models and in affine Toda field theories.     

基于FTIR的苔藓植物表征关系除趋势对应分析

苔藓植物是一类重要高等植物。但是,苔藓植物体型小,可供鉴别性状少。应用OMNI采样器-傅里叶变换红外光谱直接测定法鉴别植物样品具有简便、快速和准确的优点。应用傅里叶变换红外光谱直接测定法测定了苔藓植物26种30个样品的红外光谱,以波数-吸光度为指标来表征吸收峰,以红外光谱图为对象,应用除趋势对应分析(Detrended Correspondence Analysis, DCA)比较了30个样品在红外光谱图上的差异程度。结果发现,基于傅里叶变换红外光谱的除趋势对应分析反映出苔藓植物红外光谱的差异与它们分类关系有较好的对应性。因此,应用傅里叶变换红外光谱直接测定法能够鉴别药用苔藓植物。     

New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schrödinger Equation

Some new exact travelling wave and period solutions of discrete nonlinear Schrödinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.     

Bäcklund transformations,kink soliton,breather- and travelling-wave solutions for a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

In this paper, we investigate a (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation in fluid dynamics. Based on the Hirota method, we give a bilinear auto-Bäcklund transformation. Via the truncated Painlevé expansion, we get a Painlevé-type auto-Bäcklund transformation. With the aid of the symbolic computation, we derive some one- and two-kink soliton solutions. We present the oblique and parallel elastic interactions between the two-kink solitons. Via the extended homoclinic test technique, we construct some breather-wave solutions. Besides, we derive some lump solutions with the periods of the breather-wave solutions to the infinity. We observe that the shapes of a breather wave and a lump remain unchanged during the propagation. Based on the polynomial-expansion method, travelling-wave solutions are constructed.     

Convergence criterion of Newton's method for singular systems with constant rank derivatives

The present paper is concerned with the convergence problem of Newton's method to solve singular systems of equations with constant rank derivatives. Under the hypothesis that the derivatives satisfy a type of weak Lipschitz condition, a convergence criterion based on the information around the initial point is established for Newton's method for singular systems of equations with constant rank derivatives. Applications to two special and important cases: the classical Lipschitz condition and the Smale's assumption, are provided; the latter, in particular, extends and improves the corresponding result due to Dedieu and Kim in [J.P. Dedieu, M. Kim, Newton's method for analytic systems of equations with constant rank derivatives, J. Complexity 18 (2002) 187-209].     

Organocatalytic and direct asymmetric vinylogous Michael addition of 3-cyano-4-methylcoumarins to α,β-unsaturated ketones

The first highly regio-, chemo-, and enantio-selective direct vinylogous Michael addition of 3-cyano-4-methylcoumarin derivatives to α,β-unsaturated ketones is described, employing readily available 9-amino-9-deoxy-epiquinine as the iminium organocatalyst.     

关于一个典型函数Fourier级数的Gibbs现象

In this paper,we point out that the Fourier series of a classical function∑∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get:supn≥1‖n∑k=1sin kx/k‖∫x0sin x/xdx=1.85194,which is better than that in[1].