关于《线性代数》教材改革的几点想法

随着现代科学技术的迅猛发展,尤其是计算机技术的广泛应用,我们应当在工科数学课程的教学内容、教学方法和教学手段上积极改革,与时俱进,以改进教学方法,提高教学质量,使得工科学生能借助于计算机,学好本专业所需的数学知识.在这篇短文中,我们想就《线性代数》的教学内容的改革     

Numerical approach for generic three-phase flow based on cut-cell and ghost fluid methods

In this paper, we introduce numerical methods that can simulate complex multiphase flows. The finite volume method, applying Cartesian cut-cell is used in the computational domain, containing fluid and solid, to conserve mass and momentum. With this method, flows in and around any geometry can be simulated without complex and time consuming meshing. For the fluid region, which involves liquid and gas, the ghost fluid method is employed to handle the stiffness of the interface discontinuity problem. The interaction between each phase is treated simply by wall function models or jump conditions of pressure, velocity and shear stress at the interface. The sharp interface method “coupled level set (LS) and volume of fluid (VOF)” is used to represent the interface between the two fluid phases. This approach will combine some advantages of both interface tracking/capturing methods, such as the excellent mass conservation from the VOF method and good accuracy of interface normal computation from the LS function. The first coupled LS and VOF will be generated to reconstruct the interface between solid and the other materials. The second will represent the interface between liquid and gas.     

A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

UV LASER INITIATED STEREOSELECTIVE HOMOGENEOUS CATALYSIS POLYMERIZATION OF PHENYLACETYLENE

In this paper, the stereoselective homogeneous catalysis polymerization of phenylacetylene by using two kinds of catalysts W(CO)_5CH_3I and W(CO)_4I_2 produced from UV laser photolysis of W (CO)_6 in CH_3I, I_2—C_6H_6 and CHI_3—C_6H_6 respectively was studied. The effects of laser energy, laser irradiation time and lifetime of catalyst on the polymerization of phenylacetylene were discussed. The photoproducts of W (CO)_6 in CH_3I, I2—C_6H_6 and CHI_3—C_6I_6 were determined by IR spectra. The structures of polyphenylacetylene obtained by W (CO)_5CH_3I and W (CO)_4I_2 catalysts were characterized by IR spectra and ~1H NMR spectra.     

New ligands and structural insights into the catalytic asymmetric addition of organozinc reagents to ketones

The catalytic asymmetric addition of alkyl groups to ketones has received considerable attention. Outlined herein is the synthesis of two new ligands based on the C₂-symmetric 11,12-diamino-9,10-dihydro-9,10-ethanoanthracene. The scope of the new ligands has been evaluated in the catalytic asymmetric addition of diethylzinc to a variety of ketones. Enantioselectivities as high as 99% have been achieved. The structures of two of these ligands have been determined by X-ray crystallography and are compared with related structures. Additionally, the structure of a titanium complex bound to a bis(sulfonamide) diol ligand is reported.     

A mild and efficient rhenium-catalyzed transfer hydrogenation of terminal olefins using alcoholysis of amine-borane adducts as a reducing system

[ReBr₂(NO)(CH₃CN)(PTA)₂] (PTA = 1, 3, 5-triaza-7-phosphaadamantane) catalyzes the alcoholysis of ammonia-borane and amine-boranes and the catalytic transfer hydrogenations of various terminal olefins. Excellent yields were achieved at 70 °C in isopropanol using tBuOK as a co-catalyst affording TOF values up to 396 h⁻¹.     

2,2′-Bipyridyl-acetylphenolato mixed ligand copper(II) complexes: syntheses,characterizations and catalytic activity in styrene epoxidation

Two copper(II) complexes, [Cu(bipy)(5-Br-2-hap)(ClO₄)]₂ (1) and [Cu(bipy)(2-hap)(ClO₄)] (2) (where bipy?=?2,2′-bipyridine, 5-Br-2-hap?=?5-bromo-2-hydroxyacetophenone, 2-hap?=?2-hydroxyacetophenone), were synthesized and characterized. The crystal structure of 1 was determined by single crystal X-ray diffraction while 2 was reported earlier. Structural characterization reveals that the presence of bromine in 5-Br-2-hap plays a structure-determining role in dimeric 1 in comparison with the mononuclear 2 where 2-hap was used. Studies of the catalytic potential toward styrene epoxidation in homogeneous system using H₂O₂ as oxidant reveal that 1 is more efficient than 2 with respect to epoxide selectivity.     

基于粗糙集模糊神经网络的爆破振动危害预测

为了探索一种能克服单因素预测的局限性、提高爆破振动危害预测精度的方法,基于粗糙集模糊神经网络理论,建立了综合考虑爆破振动幅值、主频率、主频率持续时间及结构动力特性等10个因素的民房破坏程度预测模型;用铜绿山矿爆破振动和民房破坏情况观测数据,对该模型进行了训练和测试,测试结果与现场观测结果具有良好的一致性。研究表明:粗糙集理论可将现场数据进行属性约简,简化输入变量,缩小神经网络的搜索空间,改善爆破振动的预测性能;基于粗糙集模糊神经网络理论的爆破振动危害预测模型,能更好地考虑各种因素对危害程度的综合影响,避免了单因素预测的局限性。     

时一空守恒元解元（CE／SE）方法综述

时一空守恒元解元方法是近年来兴起的一种全新的高分辨率守恒型方程计算方法．它具有物理概念清晰、计算精度高和格式构造简单等优点,是一种具有广阔发展前景的计算方法．本文详细地介绍了cE／ss方法的基本原理、发展历史、应用情况和最新进展、并指出了当前研究的不足和发展方向．     

基于概率语言术语集的服务外包风险评估方法

考虑服务外包风险评估的不确定性,采用概率语言术语集获取FMEA方法所需的专家评价信息,通过给语言集赋予不同的概率以表达偏好的程度。针对传统FMEA方法没有考虑风险间的相互影响关系,风险严重度评估不够准确的问题,采用广义Choquet积分分析风险间的相互影响关系,得到修正后的风险严重度。考虑严重度、发生度和难检度直接相乘准确性低的问题,采用概率语言VIKOR方法对风险的三个因子进行综合评估。最后以公共体育场馆服务外包风险评估为例,验证了所提方法的有效性。