数学分析中的一题多解问题

通过两个积分 (一个是不定积分 ,一个是定积分 )及一个极限 ,说明如何灵活使用积分法解决积分问题 ,方法灵活、巧妙 ,适用范围广 .     

校准电表的一种方法

利用电位差计的高精度，设计出合理的实验电路对C31型电表进行校准，使得电表的准确度等级得以提高。     

Drinfeld algebra deformations, homotopy comodules and the associahedra

The aim of this work is to construct a cohomology theory controlling the deformations of a general Drinfel'd algebra and thus finish the program which began in [13], [14]. The task is accomplished in three steps. The first step, which was taken in the aforementioned articles, is the construction of a modified cobar complex adapted to a non-coassociative comultiplication. The following two steps each involves a new, highly non-trivial, construction. The first construction, essentially combinatorial, defines a differential graded Lie algebra structure on the simplicial chain complex of the associahedra. The second construction, of a more algebraic nature, is the definition of a map of differential graded Lie algebras from the complex defined above to the algebra of derivations on the bar resolution. Using the existence of this map and the acyclicity of the associahedra we can define a so-called homotopy comodule structure (Definition 3.3 below) on the bar resolution of a general Drinfel'd algebra. This in turn allows us to define the desired cohomology theory in terms of a complex which consists, roughly speaking, of the bimodule and bicomodule maps from the bar resolution to the modified cobar resolution. The complex is bigraded but not a bicomplex as in the Gerstenhaber-Schack theory for bialgebra deformations. The new components of the coboundary operator are defined via the constructions mentioned above. The results of the paper were announced in [12].

     

Terpenes in organic synthesis

A seven-step synthesis ofS-(+)-hydroprene (S-1) in 20 % overall yield starting fromS-(+)-3,7-dimethyl-1,6-octadiene (2) of 55+-10 % optical purity is described. The introduction of an optical enhancement step in the synthetic sequence at the stage ofS-(–)-3,7-dimethyl-1-octanol (9) raises the optical purity ofS-1 from 50 % to 80 %.For part 13, see. ref.¹ Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 342–348, February, 1993.     

Quantum Mechanical Calculations of Redox Potentials of the Metal Clusters in Nitrogenase

We have calculated redox potentials of the two metal clusters in Mo-nitrogenase with quantum mechanical (QM) calculations. We employ an approach calibrated for iron–sulfur clusters with 1–4 Fe ions, involving QM-cluster calculations in continuum solvent and large QM systems (400–500 atoms), based on structures from combined QM and molecular mechanics (QM/MM) geometry optimisations. Calculations on the P-cluster show that we can reproduce the experimental redox potentials within 0.33 V. This is similar to the accuracy obtained for the smaller clusters, although two of the redox reactions involve also proton transfer. The calculated P¹⁺/P^N redox potential is nearly the same independently of whether P¹⁺ is protonated or deprotonated, explaining why redox titrations do not show any pH dependence. For the FeMo cluster, the calculations clearly show that the formal oxidation state of the cluster in the resting E₀ state is MoIIIFe3IIFe4III , in agreement with previous experimental studies and QM calculations. Moreover, the redox potentials of the first five E₀–E₄ states are nearly constant, as is expected if the electrons are delivered by the same site (the P-cluster). However, the redox potentials are insensitive to the formal oxidation states of the Fe ion (i.e., whether the added protons bind to sulfide or Fe ions). Finally, we show that the later (E₄–E₈) states of the reaction mechanism have redox potential that are more positive (i.e., more exothermic) than that of the E₀/E₁ couple.     

Unsteady hydromagnetic flow of a reactive variable viscosity third‐grade fluid in a channel with convective cooling

This paper examines the combined effects of a transverse magnetic field and variable viscosity on unsteady flow of a reactive third‐grade electrically conducting fluid and heat transfer in a channel with convective cooling at the surface. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi‐implicit finite‐difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system. It is in general noted that those parameters that increase/decrase one flow quantity (velocity or temperature) also lead to the increase/decrease respectively of the other quantity. Copyright © 2011 John Wiley & Sons, Ltd.     

双（2,2-二硝基丙基）甲缩醛的结构和爆轰性能的量子化学研究

利用B3LYP/6-311＋G（2d,p）方法对一种新型含能增塑剂双（2,2-二硝基丙基）甲缩醛进行几何优化,计算了其红外光谱、生成焓和爆轰特性. 分析了最弱键的键离解能和键级并预测了目标化合物的热稳定性. 结果表明双（2,2-二硝基丙基）甲缩醛中的四个N-NO2键的键离解能都为164.38 kJ/mol. 表明目标化合物是一个热力学性能稳定的化合物. 以凝聚相生成焓和分子密度为基础,采用Kamlet-Jacobs方法预测其爆速和爆压. 目标化合物的晶体结构属于P21空间群.     

Pandemic-Driven Development of a Medical-Grade,Economic and Decentralized Applicable Polyolefin Filament for Additive Fused Filament Fabrication

A polyolefin with certified biocompatibility according to USP class VI was used by our group as feedstock for filament-based 3D printing to meet the highest medical standards in order to print personal protective equipment for our university hospital during the ongoing pandemic. Besides the chemical resistance and durability, as well as the ability to withstand steam sterilization, this polypropylene (PP) copolymer is characterized by its high purity, as achieved by highly efficient and selective catalytic polymerization. As the PP copolymer is suited to be printed with all common printers in fused filament fabrication (FFF), it offers an eco-friendly cost–benefit ratio, even for large-scale production. In addition, a digital workflow was established focusing on common desktop FFF printers in the medical sector. It comprises the simulation-based optimization of personalized print objects, considering the inherent material properties such as warping tendency, through to validation of the process chain by 3D scanning, sterilization, and biocompatibility analysis of the printed part. This combination of digital data processing and 3D printing with a sustainable and medically certified material showed great promise in establishing decentralized additive manufacturing in everyday hospital life to meet peaks in demand, supply bottlenecks, and enhanced personalized patient treatment.     

脑胶质瘤磁共振弥散张量成像定量参数与VEGF、MMP-9表达的相关性

本研究旨在分析脑胶质瘤患者的磁共振弥散张量成像(DTI)参数与病变组织血管内皮生长因子(VEGF)和基质金属蛋白酶-9(MMP-9)表达的相关性,以及DTI参数对脑胶质瘤进行分级诊断的价值.根据病理分级将102例脑胶质瘤患者分为低级别组(47例)和高级别组(55例),均行MRI和DTI检查,定量测定表观弥散系数(ADC...