Facile and Rapid Synthesis of 9H-Carbazole-9-Carboxylic Acids Under Microwave Irradiation

The reaction of halogenated 9H-carbazoles or carbazole with bromoesters in DMF under microwave irradiation readily affords a series of 9H-carbazoles-9-hydroxylic acids.     

金催化炔基膦酸酯水合反应合成β-羰基膦酸酯

β-羰基膦酸酯是一类重要的有机化合物和反应中间体,在有机合成及药物化学中发挥着重要的作用.提供了一种高原子经济性、高选择性、温和的炔基膦酸酯水合反应体系.实验结果表明:在阳离子金催化剂(2.5 mol%)的催化作用下,以1,2-二氯乙烷(1 m L)为溶剂,室温下炔基膦酸酯(1 mmol)与水(3 mmol)发生水合反应,高收率、高区域选择性地得到β-羰基膦酸酯化合物(收率≥92%).该方法具有底物适用范围广、反应条件温和、环境友好等优点,为含β-羰基膦酸酯结构单元的天然产物及复杂药物分子的合成提供了一种新途径.     

A numerical and experimental hybrid approach for the investigation of aerodynamic forces on stay cables suffering from rain-wind induced vibration

The aerodynamic forces on a stay cable under a rain-wind induced vibration (RWIV) are difficult to measure directly in a wind tunnel test. This paper presents a hybrid approach that combines an experiment with computational fluid dynamics (CFD) for the investigation on aerodynamic forces of a stay cable under a RWIV. The stay cable and flow field were considered as two substructures of the system. The oscillation of the stay cable was first measured by using a wind tunnel test of a RWIV under an artificial rainfall condition. The oscillation of the cable was treated as a previously known moving boundary condition and applied to the flow field. Only the flow field with the known moving cable boundary was then numerically simulated by using a CFD method (such as Fluent 6.3). The transient aerodynamic forces of the stay cable with a predetermined cable oscillation were obtained from numerical calculations. The characteristics of the aerodynamic forces in the time domain and frequency domain were then analysed for various cases. To verify the feasibility and accuracy of the proposed hybrid approach, the transient aerodynamic forces were applied to a single-degree-of-freedom model (SDOF) of the stay cable to calculate the RWIV of the cable. A comparison was performed between the oscillation responses of the stay cable obtained from the calculated (SDOF model) and experimental results, and the results indicate that the hybrid approach accurately simulates the transient aerodynamic forces of the stay cable. The equivalent damping ratios induced by the aerodynamic forces were obtained for various wind speeds. Furthermore, a nonlinear model of the aerodynamic force is proposed based on the calculation results, and the coefficients in the model were identified by a nonlinear least-squares technique.     

The unusual physicochemical properties of azulene and azulene-based compounds

This review shows the unusual physicochemical properties and wide application of azulene and its derivatives. The recent synthesis strategies of kinds of substituted azulene are also listed.     

ε－次可微多目标规划的最优性条件

本文主要从多目标规划相应的加权问题出发，讨论了在ε－次可微的条件下，凸多目标规划问题η－有效解存在的必要条件与充分条件．     

Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

A metastable flame-front interface and Carrier''s problem

Metastable dynamics for a nonlocal PDE modeling the upwards propagation of a flame-front interface in a vertical channel is analyzed in the one-dimensional case where the channel cross-section is taken to be the slab -1<x<1. In a certain asymptotic limit, the interface assumes a roughly concave parabolic shape, and the tip of the parabola drifts asymptotically exponentially slowly towards the boundary of the domain. In contrast to previous analyses that studied this behavior by transforming the governing nonlocal PDE to a convection–diffusion equation, a novel nonlinear transformation is introduced that transforms the problem to a singularly perturbed quasilinear PDE. The steady-state problem for this transformed PDE, for which the parabolic interface shape maps onto a one-spike solution, is closely related to a class of two-point boundary value problems with seemingly spurious solutions studied initially by G. Carrier in 1968. Rigorous and formal asymptotic results for a one-spike solution to this transformed PDE are obtained together with a formal metastability analysis of certain time-dependent solutions.