An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

脲醛呋喃树脂中氮含量的测定

脲醛呋喃树脂中的含氮量,一般采用克氏定氮法,方法繁琐,费时较长,不利于快速分析的要求,本文利用气相色谱法对脲醛呋喃树脂中的氮含量进行分析测定,并建立了测定方法.方法简捷、快速、重现性好,加标回收率在100.8～109.0之间,准确度较高,可很好的满足工业生产中快速分析的要求.     

Protecting the infrastructure with thermal spray coatings—Technical note

Thermal sprayed aluminum and zinc provide long-term (> 20 years to first maintenance) corrosion control coatings. However, this application is usually more expensive than painting or galvanizing if thermal spraying (metallizing) is not integrated into the design and fabrication phases of new construction and repair projects. Aluminum and zinc metallized coatings are tough enough to withstand fabrication, transportation, and assembly operations. The improved capabilities and productivity of metallizing equipment for aluminum and zinc spraying are a major factor in their current cost competitiveness. The net result is that the cost difference between metallizing, paint, and galvanizing is getting closer every day. Even though the initial application cost of metallizing may be higher, the life cycle cost (LCC) and average equivalent annual costs (AEAC) are lower than paint coating systems. Metallizing LCCs, when properly engineered into the construction schedule, are equal to or less than paint coating LCCs. This article summarizes some metallizing considerations for installing improved corrosion control coating systems in new construction and in maintenance and repair of infrastructure. Editor’s Note: The following constants have been used to convert between English and Metric dimensions: 1ft²-0.0929 m²; 1lb/ft²-4.89 kg/m²; 1 mil=0.025mm. Presented at the 5th National Thermal Spray Conference (NTSC-93), Infrastructure Maintenance and Repair Session, 10 June 1993, Anaheim, CA.     

生产线试运行过程工艺分析软件的应用

介绍了生产线试运行过程中，用工艺分析软件解决所遇到的工艺问题，为工艺分析软件开拓了一个新的应用领域。     

热压变形对灰口铸铁石墨形态的影响

研究了灰口铸铁(HTl50)在900℃大压下量塑性变形后石墨的分布形态，结果表明：随着压下量的增加，石墨片逐渐趋于平行分布；变形过程中发生了碳的回溶，同时伴随着石墨片的断裂；石墨片体积分数及片间距随压下量的增加而逐渐减少。     

金属及合金中钛的光度分析近况

综述了金属及合金中钛的光度测定方法新近进展情况。     

混凝土小砌块与普通砖混住宅楼造价分析

指出混凝土小型空心砌块是一种节能型的新型墙体材料。本文从经济角度对该种材料和粘土砖材料进行了实例分析、比较,得出了这种新型材料值得推广使用的结论。     

The Structure of the Irreversibly Bound Adhesion Promoter-Substrate Interfacial Layer of γ-Aminopropylsilanetriol on Crystalline Si, as Measured by XPS and FTIR

The irreversibly bound interfacial layer deposited by the γ-aminopropysilanetriol adhesion promoter onto a crystalline silicon substrate, which remains even after profuse washing, was found by XPS to have resulted from the fragmentation and rearrangement of the original γ-aminopropylsilanetriol molecule. A mechanism is proposed, involving the homolytic scission of the terminal N-C bond. One of the subsequent reactions is believed to involve hydrogen loss by abstraction and the formation of a terminal vinyl group, which bonds to the substrate. Support for this mechanism is found in IR spectroscopy of this layer.     

Structural analysis of Au/Mg(OH)2 during deactivation by Debye function analysis

Using a Debye function analysis, the presence of icosahedral and face centered cuboctahedral gold in a 1 1 ratio has been found in freshly prepared Au/Mg(OH)₂ catalyst. The results support earlier studies which suggest the icosahedral form to be more stable at small nanometer sizes. Interactions between the gold and the Mg(OH)₂ support appear to be weak, with the gold rapidly coagulating over a period of three months. Re-analysis of the aged sample shows the gold to be mainly in the form of truncated decahedra.