Dimeric ortho‐palladated homoveratrylamine as an efficient homogeneous catalyst for copper‐free Sonogashira cross‐coupling reaction

The catalytic activity of ortho‐palladated [Pd{C6H2(CH2CH2NH2)‐(OMe)2,3,4}(m‐Br)]2, a complex of homoveratrylamine in the copper‐free Sonogashira coupling reaction has been investigated. This complex is a catalyst that is efficient, stable and non‐sensitive to air and moisture in the Sonogashira reaction. In this homogeneous catalytic system, various aryl halides were efficiently coupled with phenylacetylene in mostly moderate to good yields in N‐methylpyrrolidone at 100 °C under copper‐free conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Internal flow numerical simulation of a cross‐flow fan in refrigerant operating condition using user‐defined functions

In the paper, a cross‐flow fan in refrigerant operating condition is systematically simulated using user‐defined functions. Three‐dimensional simulations are acquired with Navier–Stokes equations coupled with k–ε turbulence model, and internal flow characteristics of an indoor split‐type air conditioner are obtained, which is mainly composed of cross‐flow fan and heat exchanger. It has systematically been simulated in the isothermal flow condition that the performance of cross‐flow fan may be reduced easily with dry or humid air, and in the refrigerant operating condition in which user‐defined functions are applied to the humid air, considered as a mixture of dry air and vapor. A density‐modulated function is adopted to deal with the condensation of the vapor at the heat‐transfer region approximately. The results show flow mechanism of the two gas‐phase flow, including phase‐vary process. The distribution of the parameters is not uniform at the inlet of the machine, the intensity and position of pressure and velocity vary along the axial direction of the fan, the distribution of vapor volume fraction and turbulent intensity in heat‐transfer region is obtained, and the external characteristic data of the indoor machine are obtained and analyzed. Compared with the experimental data, the calculated characteristic curves and designed parameters are on target. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.     

晃荡

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌(不规则波动)的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

A comparison of quantitative nuclear magnetic resonance methods: internal,external, and electronic referencing

The performance of three quantitative NMR methods was compared in terms of short‐term and long‐term precision and accuracy, robustness, linear range, and general applicability. The Internal Reference method employs a reference material co‐dissolved with sample; the External Reference method employs a reference material contained in a separate solution; and the third method, known as Electronic REference To access In vivo Concentrations (ERETIC), employs an externally calibrated digital reference peak. The Internal Reference method results were the most precise and remained stable within 0.1% for at least 4 weeks. The results from the External Reference and ERETIC methods were practically equivalent to each other during this time. These methods exhibited small differences relative to the standard set by the Internal Reference method and slightly lower precision, establishing them as practical alternatives to the Internal Reference method. In contrast to the Internal Reference method, the External Reference and ERETIC methods possess several advantages that address peak overlap, flexibility of calibration, and duration of applicability. The study was designed such that each spectrum contained the information needed to compare the three methods while all other variables were kept constant. Applicability of pulse width compensation is addressed. ERETIC software compensation and minor adjustments to 90° pulse width were concluded to be unnecessary for this system. Although each of the methods was applied here to specifically calculate and compare chemical purity values, this evaluation applies generally to absolute quantitation by NMR. Copyright © 2013 John Wiley & Sons, Ltd.     

A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta

Price's Law states that linear perturbations of a Schwarzschild black hole fall off as t−2?−3 for t→∞ provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their time derivative is zero), then the decay is predicted to be t−2?−4. We give a proof of t−2?−2 decay for general data in the form of weighted L¹ to L^∞ bounds for solutions of the Regge–Wheeler equation. For initially static perturbations we obtain t−2?−3. The proof is based on an integral representation of the solution which follows from self-adjoint spectral theory. We apply two different perturbative arguments in order to construct the corresponding spectral measure and the decay bounds are obtained by appropriate oscillatory integral estimates.     

Solitary wave solutions and kink wave solutions for a generalized KDV-mKDV equation

Bifurcation method of dynamical systems is employed to investigate solitary wave solutions and kink wave solutions of the generalized KDV-mKDV equation. Under some parameter conditions, their explicit expressions are obtained.     

Analytical Hartree–Fock wave functions for the atoms Cs to Lr

 Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet. Received: 6 December 1999 / Accepted: 29 February 2000 / Published online: 12 May 2000     

On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm

In cities, flood waves may propagate over street surfaces below which lie complicated pipe networks used for storm drainage and sewage. The flood and pipe flows can interact at connections between the underground pipes and the street surface. The present paper examines this interaction, using the shallow water equations to model the flood wave hydrodynamics. Sources and sinks in the mass conservation equation are used to model the pipe inflow and outflow conditions at bed connections. We consider the problem reduced to one dimension. The shallow water equations are solved using a Godunov‐type wave propagation scheme. Wave speeds are modified in the wave propagation algorithm to enable flows to be simulated over nearly dry beds and dry states. First, the model is used to simulate vertical flows through finite gaps in the bed. Next, the interaction of the vertical flows with a dam break flow is considered for both dry and wet beds. An efflux number, En, is defined based on the vertical efflux velocity and the gap length. Comparisons are made with numerical predictions from STAR‐CD, a commercial Navier–Stokes solver that models the free‐surface motions, and a parameter study is undertaken to investigate the effect of the one‐dimensional approximation of the present model, for a range of non‐dimensional efflux numbers. It is found that the shallow flow model gives sensible predictions at all time provided En<0.5, and for long durations for En>0.5. Dam break flow over an underground connecting pipe is also considered. Copyright © 2010 John Wiley & Sons, Ltd.     

一类特殊初值柯西问题的简易解法

通过对初始条件为平面波的三维波动方程柯西问题的研究,利用变量变换,将三维波动方程柯西问题转化为一维波动方程柯西问题,以利用达朗贝尔公式来求解,从而避开了使用复杂的泊松公式.