An introduction to Wu's method for mechanical theorem proving in geometry

Wu's algebraic method for mechanically proving geometry theorems is presented at a level as elementary as possible with sufficient examples for further understanding the complete method.The work reported here was supported by NSF Grant DCR-8503498.     

论校园文化和德育目标的一致性

中系统介绍了校园化和德育目标的关系，并找准两之间的结合点，通过分析两的一致性和辩证统一关系，达到育人目的。     

The Problem of Estimating the Uncertainty of the Fixed Point Temperature Due to the Presence of Impurities

The main problems in estimating the uncertainty due to the presence of impurities in the material: the absence in the documents of a unique definition of the quantity being measured – the fixed point temperature, the lack of agreed methods of realizing the fixed points and the insufficient justification of the equations used for the estimate, are analyzed. The results of a measurement of the melting point of gallium are presented, which differ in the conditions in which they were realized – with one and two liquid-solid interfaces and different solidification conditions, are presented. The reasons for the considerable difference between the values of the temperatures obtained in these experiments are discussed.     

铜铟铋硫对Sn-Ag基无铅焊料性能的影响

研究了Cu、In、Bi、S元素对Sn-Ag基无铅焊料熔点和铺展性的影响。结果表明:Sn-Ag-Cu三元合金成分为95.5%Sn3.5%Ag1%Cu时具有较低熔点(215℃)和好的铺展性;加入适量的In可降低Sn-Ag合金的熔点和改善铺展性能;随w(Bi)的增加Sn-Ag-Bi三元合金的熔点降低、铺展性变好;Sn-Ag合金的熔点随w(S)的增加而升高,加入少量S能改善Sn-Ag合金的铺展性。     

工业层析洗梯液回收套用的一种方法

以生产甲胺基阿维菌素苯甲酸盐精品的工艺——工业层析产生的洗梯液回收套用的过程为例，说明利用二元恒沸物的组成随压力的变化而变化的规律，对生产洗梯液进行有效、简洁、合理分离及套用的方法。     

Strain waves in colliding bars having nonparallel faces

The paper reports the experimental investigation data for the effect that nonparallel faces of bars under impact exert on the parameters of longitudinal and bending strain waves generated in the bars. The changes in stress magnitudes in the bar under impact with growing angle of the impact faces offset are described. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 6, pp. 73–78, November–December, 2006.     

Partitioning multiple objective optimal solutions with applications in radiotherapy design

The optimal partition for linear programming is induced by any strictly complementary solution, and this partition is important because it characterizes the optimal set. However, constructing a strictly complementary solution in the presence of degeneracy was not practical until interior point algorithms became viable alternatives to the simplex algorithm. We develop analogs of the optimal partition for linear programming in the case of multiple objectives and show that these new partitions provide insight into the optimal set (both pareto optimality and lexicographic ordering are considered). Techniques to produce these optimal partitions are provided, and examples from the design of radiotherapy plans show that these new partitions are useful. A. Holder. Research conducted at Trinity University, TX, and The University of Mississippi, MS. This research was partially supported by ONR Grant N00014-01-1-0917.     

Comparison of the toughening behavior of nylon 6 versus an amorphous polyamide using various maleated elastomers

The toughening effect of two types of elastomers based on ethylene/α-olefin copolymers, viz, an ethylene/propylene copolymer (EPR) with its maleated version, EPR-g-MA, and an ethylene/1-octene copolymer (EOR) with its maleated versions, EOR-g-MA-X% (X=0.35, 1.6, 2.5), for two classes of polyamides: semi-crystalline nylon 6 versus an amorphous polyamide (Zytel 330 from DuPont), designated as a-PA, was explored. The results are compared with those reported earlier based on a styrenic triblock copolymer having a hydrogenated midblock, SEBS, and its maleated version, SEBS-g-MA, elastomer system. Izod impact strength was examined as a function of rubber content, rubber particle size and temperature. All three factors influence the impact behavior considerably for the two polyamide matrices. The a-PA is found to require a somewhat lower content of rubber for toughening than nylon 6. Very similar optimum ranges of rubber particle sizes were observed for ternary blends of EOR-g-MA/EOR with each of the two polyamides while blends based on mixtures of EPR-g-MA/EPR and SEBS-g-MA/SEBS (where the total rubber content is 20% by weight) show only an upper limit for a-PA but an optimum range of particle sizes for nylon 6 for effective toughening. Higher EPR-g-MA contents lead to lower ductile-brittle transition temperatures (T_db) as expected; however, a-PA binary blends with EPR-g-MA have a much lower T_db than do nylon 6 blends when the content of the maleated elastomer is not high. A minimum in plots of ductile-brittle transition temperature versus particle size appears for ternary blends of each of the matrices with EOR-g-MA/EOR; blends based on SEBS-g-MA/SEBS, in most cases, show higher ductile-brittle transition temperatures, regardless of the matrix. However, blends with EPR-g-MA/EPR show comparable T_db with those based on EOR-g-MA/EOR for the amorphous polyamide but show the lowest ductile-brittle transition temperatures for nylon 6 within the range of particle sizes examined. For the blends with a bimodal size distribution, the global weight average rubber particle size is inappropriate for correlating the Izod impact strength and ductile-brittle transition temperature. In general, trends for this amorphous polyamide are rather similar to those of semi-crystalline nylon 6.     

Dynamic responses and damages of water-filled pre-pressurized metal tube impacted by mass

An account is given of some principal observations made from a series of experiments in which three-span pipe beams were subjected to central impact by indenters with different nose shapes. These pipes were filled and pre-pressurized with water in order to identify the main effects produced by the fluid–structure interaction. In comparison, the impact experiments of the pipes with no water were also carried out. The perforation failure modes and corresponding critical impact energies were obtained in different test conditions. The experimental results indicated that the critical perforation energy and the deformation of the wall of the pipe were significantly influenced by the presence of the water and the pressure.     

Preparation and properties of silicone‐containing poly(methyl methacrylate) gels

Poly(methyl methacrylate) (PMMA) gels with varying amounts of silicone and solvent and constant amounts of crosslinker were prepared by solution free radical crosslinking copolymerization of methyl methacrylate (MMA), ethylene glycol dimethacrylate (EGDM), tetraethoxysilane (TEOS) and vinyltriethoxysilane (VTES) comonomer systems. They were then studied in benzene at a total monomer concentration of 3.5 mol L^?1 and 70 °C. The conversion of monomer, volume swelling ratio, weight fraction and gel point were measured as a function of the reaction time, silicone concentration and benzene content up to the onset of macrogelation. Structural characteristics of the gels were examined by using equilibrium swelling in benzene, gel fraction and Fourier‐transform infrared (FTIR) analysis. The morphology of the copolymers was also investigated by SEM. Based on the obtained results, it was concluded that the FTIR data did not have the capacity to show the presence of the VTES or TEOS moiety in these kinds of copolymers. On the other hand, the variation of weight fraction of gel, W_g, and its equilibrium volume swelling ratio in benzene, q_v, exhibited the same behaviour as that of MMA/EGDM copolymers. Also, the dilution of the monomer mixture resulted in an increase in the gel point and swelling degree and a decrease in the percent of conversion and gel fraction. Finally, TEOS is not an ideal silicone compound for reaction in the MMA/EGDM copolymerization system, whereas VTES is a suitable silicone comonomer for this system and it has been proved useful. Copyright © 2005 Society of Chemical Industry