三角条件等式的证明

在一定条件下才能成立的等式,我们称之为条件等式。一般说来,对于给定的条件可导出一系列的结果,如何才能导出结论等式呢?下面谈谈在这方面的教学体会。一条件转化把条件中出现的量进行变换,变成结论等式中的量,这样,条件中量与量间的相互关系,就是结论中的量与量之间的关系,从而不难推出结论等式。例1 若sin~2Acsc~2B+ccs~2Acos~2C=1,求证tg~2Actg~2B=sin~2C。条件与结论中涉及的量A、B、C这三个角的三角函数,但结论中与条件中出现的各角的三角函数名称却不相同,这时可以把条件中出现的各角的三角函数转化为在结论中出现的函数。因     

不可微B—凸多目标规划

本文利用Ｂｅｃｔｏｒ等人引进的Ｂ－凸函数，在Ｃｌａｒｋｅ广义梯度意义下，针对Ｌｉｐｓｈｉｔｚ函数类，讨论了不可微Ｂ－凸多目标规划的非控解的充分条件及必要条件，而且给出了相应的对偶问题及对偶定理。     

金属腐蚀研究中的椭偏术

本文着重介绍了椭偏术的基本原理及其在腐蚀研究领域中应用的技术问题及解决方法。并应用椭偏仪和电化学测试方法对不锈钢缝隙腐蚀表面膜的动力学规律进行了初步探讨,结果表明,椭偏术原理,计算是复杂的,但操作简便。用于腐蚀金属表面膜的原位测试,则有它独到的优点。     

一类积分行列式及其对群表示论的应用

<正> 大家知道,在Schur L.,Weyl H.等人建立的经典群的表示理论中,所谓“母函数”法是一个重要的方法.所谓“母函数”,是指一些特殊的群的共轭类的函数,这种类函数根据Peter-weyl定理可以表示为群的既约表示的特征的级数,适当选择这些母函数,常常可以得到群的既约表示的完全系,也可以得到两既约表示直积的分解式以及其它关于群表示的重要事实.在本世纪五十年代,华罗庚教授成功地利用这一方法将群表示论系统地应用于多复变典型域的调和分析的研究,这总结在他的名著[1]中.纵观这些研究,其中心     

中等浓度表面活性剂溶液流变特性的实验研究

为研究剪切速率和溶液浓度对中等浓度表面活性剂溶液流变特性的影响,在25℃、1～300s-1剪切速率范围内,对质量分数分别为0.05%、0.07%、0.10%和0.15%的CTAC/NaSal表面活性剂溶液进行稳态模式下的流变测量.研究表明,随着表面活性剂浓度的增大,由剪切诱导转变引起的黏度增稠率依次减小,当浓度达到某一临界饱和值时不再有剪切诱导转变发生,该浓度所对应的黏度-剪切速率流变曲线称为最大黏度线.当浓度低于临界饱和浓度时,在以临界剪切速率为界的两区域内,剪切速率-剪切应力流变曲线分别符合对数模型.从能量的视角分析了剪切诱导结构(SIS)可能的形成机理,指出诱导SIS形成的临界能量值本质上是由胶束结构决定的.从流变的角度指出,对于中等浓度的表面活性剂溶液,SIS不再是产生湍流减阻的必要条件.     

Entanglement for Two-Qubit Extended Werner-Like States： Effect of Non-Markovian Environments

We investigate the sudden birth and sudden death of entanglement of two qubits interacting with uncorrelated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs＇ entanglement sudden birth. Furthermore, under the conditions of different purity and initial entangIement, the revival of qubits＇ entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.     

Entanglement in One-Dimensional Random XY Spin Chain with Dzyaloshinskii--Moriya Interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii-Moriya （DM） interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. （i） For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. （ii） For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings （or magnetic field） play competing roles in enhancing quantum entanglement.     

基于大间距准则的混合核Fisher判别分析

针对KFDA算法中存在的问题,提出了基于大间距准则的混合核Fisher人脸特征提取算法;首先,将原始数据通过非线性映射投影到高维数据空间;然后,引入大间距准则和混合核函数使得同类样本在投影后离得更近,不同类样本在投影后离得更远;在PIE和AR人脸库中的仿真实验验证了算法的有效性和稳定性。     

高纯锗探测器的广泛应用和自主研制进展

以目前国际上极为活跃开展的暗物质探测、无中微子双 衰变研究为例,评述了高纯锗探测器的重要性及其广泛的应用前景。介绍了己开展的高纯锗单晶、探测器制备的关键技术研究进展:合作单位已研制出了用于高纯锗单晶材料制备的区熔炉、单晶炉;并制备出直径为20  50 cm、纯度为12N(< 41011  atoms/cm3)、位错< 5000 atoms/cm2 的锗单晶;掌握了高纯锗探测器(平面型、同轴型)制备的关键技术,用进口高纯锗单晶材料制备出的同轴型高纯锗探测器对射线的能量分辨率及探测效率均达到进口产品指标,使用自制的12N 高纯锗单晶材料己制备出平面型高纯锗探测器。呼吁加速高纯锗研制的自主创新步伐,尽早实现其国产化目标。The article reviews importance and wide applications of HPGe detector, especially the application on the dark matter search experiment and double beta decay experiment. The research progress on the Highpurity germanium single crystal and HPGe detector in China has been introduced. The cooperation partner developed new type zone-refining furnace and single crystal furnace. The ultra-purity germanium single crystal with 20~50 cm, purity up to 12N(net impurity concentration is less than 41011 atoms/cm3), and dislocation less than 5 000 /cm3 was prepared. The key technologies for preparing planar and coaxial HPGe detector were mastered. The coaxial detector, which has been made of imported ultra-purity germanium single crystal has excellent energy resolution and efficiency as the imported commercial detector. The planar detector using selfmade germanium single crystal was also successfully manufactured. The research group appeals for speeding up the pace of independent innovation on the high-purity germanium, and achieving the high-purity germanium localization as soon as possible.