Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

基于变芯径光纤的光学系统在光造型中的应用

光学系统采用变芯径光纤，可大幅度提高光的传输效率，增加光学子系统柔性。描述了光造型工作原理及其理论依据，在介绍所研制的光的成型系统光学子系统的基础上，阐述了紫外光源的选择与设计，及变芯径光纤的设计、传输、耦合与聚焦等技术。该套基于变芯径光纤的光学子系统成本低、体积小、效率高，巳成功应用于所研制的台式低成本快速成型系统中，为该系统的进一步推广奠定了技术基础。     

Quantitative measurements of Ge surface segregation during SiGe alloy growth

Ge segregation during the growth of Si_{1 − x}Ge_x alloys (x = 5, 10, 20, and 40%) was studied using X-ray photoelectron spectroscopy. The alloys were grown in thicknesses up to 20.0 nm at 500°C to measure quantitatively the amount of segregated surface Ge. The length of alloy needed to reach steady-state growth edge was found to decrease with increasing alloy concentration (4.8, 2.8, 2.4, and 2.0 nm, respectively). It was found that each alloy had a complete monolayer of Ge on the surface and an increasing amount of segregated Ge in the second layer (20, 55, 80, and 95%, respectively) during steady-state growth. An increase in the temperature of alloy growth (400–750°C) resulted in an increase in the leading edge of alloy growth but did not change the amount of segregated Ge during steady-state growth. We propose that film stress is responsible for the amount of Ge segregation.     

Determination of calcium in water by flow injection analysis — inductively coupled plasma (FIA-ICP) emission spectrometry

Summary Using an 11 ml centrifugal type spray chamber, a rapid sample introduction rate of 320 injections per hour may be achieved when interfacing flow injection analysis and inductively coupled plasma emission spectrometric techniques. Calcium was determined in water samples with a relative standard deviation of better than 3.5% over the analytical range of 10 to 200 mg · l^–1 Ca. Mean recovery was 97%.

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Calciumbestimmung im Wasser mit dem Flow-injection-Prinzip kombiniert mit der Induktions-gekoppelten Plasma-Emissions-Spektrometrie (FIA-ICP)