2000年新教材一个高考题的另解

理科天津卷第20题 用总长14．8m的钢条制作一个长方体框架，如果所制作容器的底边的一边比另一边长0．5m，那么高为多少时容器的容积最大?并求出它的最大容积．     

86公式(a~2)~(1/2)=｜a｜=a (a≥0) or -a(a<0)的发现与应用

课题的提出想一想，程序Ⅰ揭示了怎样的数学关系？Ｓ１：（ａ）２＝ａ（ａ≥０）．（公式１）Ｔ：对不对呢？我们来验证一下．分别向公式１中输入数据ａ＝０；ａ＝２；ａ＝１３，输出的结果依次是（０）２＝０；（２）２＝２；（１３）２＝１３．结论与公式１相符，说明Ｓ１同学有较强的观察力，一下就抓住了问题本质．结合程序Ⅰ，请同学们谈谈对公式１的认识．Ｓ２：公式１包含有两种运算，先‘取算术平方根’，后‘平方’．Ｓ３：要使ａ有意义，输入的数据ａ必须是非负实数，输出的数据仍是ａ．Ｔ：认识深刻！下面请同学们在不改变上述两…     

圆形工件正次品检验及再加工模型

针对圆形工件合格性检验问题建立了两个优化模型,运用Matlab软件进行编程求解,确定了圆心的位置,据此判断出工件一为正品,工件二为次品.接下来为判断能否将次品经过再加工使其成为正品,建立了模型三,并指出了对工件二的简单再加工方法.     

STUDIES ON RESPONSE CHARACTERISTICS OF DRUG ISE''''S (Ⅳ) SELECTIVITY OF, DRUG ISE''''S WITH HETERO-POLY ACID ANION SITE TOWARD METAL IONS

The relationship between the selectivity of six drug ion-selective electrodes with anionic species of hetero-poly acid as exchange site and the structural and thermodynamical parameters of the metal ion has been investigated experimentally and theoretically. The electrode selectivity is controlled mainly by the extractibility or hydrophobicity of the metal ion, but not by the ion-association-complex formation process. Linear relationship exists between the pK_(ij) value and the structural parameter z~2/(r + 0.85) and the thermodynamic parameter of hydration (△G_h) of the metal ion. Better correlation is obtained for the pK_(ij)vs. (z~2/r)~(-k) relationship.     

国产SY-01型液相色谱仪气动泵的改进

SY-01型液相色谱仪目前虽已停止生产,但有不少单位购有此种仪器,并仍在使用。该仪器的气动泵易出故障,主要是因为使用的电子元件质量欠佳,使气动泵电气部件失灵。另外气动泵中使用两个交流电磁阀,因交变电流使铁芯振动,易使上阀门橡皮部份损坏而漏气或粘住。我们针对上述两方面的弊病对气动泵进行改进。改进中省去了气动泵电气部件,克服了这部份易出故障的弊病;将气动泵的两个交流电磁阀的     

颗粒超导体中静电效应的非对角项对有序转变的影响

本文用有限温自洽类声子近似,对引入静电能的非对角项后颗粒超导体中相有序转变的影响进行了计算。发现比不考虑非对角项时,其相有序转变温度T_c~*降低,相有序的出现临界值α_c提高。     

Dark blue erenkov second harmonic generation in the two-layer-stacked hexagonal periodically poled MgO:LiNbO_3s

We report the dark blue nonlinearˇCerenkov radiation by the second harmonic generation(SHG)in a two-layer-stacked hexagonal periodically-poled-MgO:LiNbO3s(PPMgOLNs).Based on the direct wafer bonding of two target PPMgOLNs rotating around the axis perpendicular to the plane with an angle of 30°,twelve bright spots as twice of those in a single PPMgOLN are shown at each second-harmonicˇCerenkov ring.The experimental results agree with the theoretical ones and present a promising application in the fabrication of three-dimensional(3D)PPMgOLNs.     

Nonequilibrium thermodynamics and fluctuation relations for small systems

In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti–Cohen fluctuation theorem, and then to the Evans–Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.     

基于柴油机ω型燃烧室缸内激波的活塞破坏研究

以二维数值模拟为基础,研究柴油机ω型燃烧室内的冲击波发展震荡过程,得到作用于活塞不同位置处的超压分布.模拟结果表明:由于燃烧室结构的独特性,导致冲击波能在特定区域进行汇聚,致使该区域超压明显高于其他区域.将该模拟结果与实际破坏失效的活塞进行对比,发现冲击波汇聚区域往往就是活塞被破坏的地方.数值模拟结果和实际破坏结果得到了很好的吻合.这为揭示柴油机活塞因爆震出现而造成的破坏机理以及燃烧室抗爆震结构形状设计提供了理论基础.