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。     

挖掘课本习题的智力因素,发展学生探索能力

课本习题在帮助学生理解基础知识、掌握解题技能技巧,以及灵活运用知识解决各种具体问题等方面都有着十分重要的意义。因此重视课本习题,钻研课本习题,挖掘它们的智力因素,充分发挥课本习题的作用是非常必要的。本文举出一例,作为对这个问题的初步探。     

内禀退相干下Tavis-Cummings模型中原子的纠缠演化与贝尔不等式破坏

通过求解系统的Milburn方程，研究了两个二能级原子和单模场相互作用系统中原子间纠缠和贝尔不等式破坏随时间的演化特性，讨论了偶极相互作用、场与原子的失谐量对纠缠度以及贝尔不等式破坏的影响.结果表明：原子间偶极-偶极相互作用对纠缠度和贝尔不等式破坏有显著影响，失谐量增大会使两原子的纠缠度和贝尔不等式破坏变大，并且两原子所能达到稳定的纠缠受偶极相互作用系数与失谐量两者之差的影响.同时还发现两原子的纠缠与贝尔不等式破坏并不是单调的函数关系，很小的纠缠也可以产生贝尔不等式破坏. 关键词： Milburn理论 偶极-偶极相互作用 失谐量 贝尔不等式破坏     

自然循环回路内芯片的强化沸腾换热研究

针对电子器件的高效冷却问题,对自然循环回路系统内表面加工有方柱形微结构的硅片上FC-72的强化沸腾换热性能进行了实验研究.测试了两个芯片,其表面上的方柱形微结构的边长均为30μm,但高度分别为60 μm和200 μm.沸腾介质的过冷度设为10 K、25 K和35 K.随着壁面过热度的增加,微结构表面芯片上的热流密度急剧增加且临界热流密度时芯片的表面温度低于芯片回路正常工作的临界上限温度85℃,这与其在池沸腾换热中的特点一样.但临界热流密度值与池沸腾情况相比有所降低.     

Numerical Simulation of the Elastic Shrinkage Induced by Portevin-Le Chatelier Effect

A new one-dimensional phenomenological model based on the dynamic strain aging mechanism is developed. In order to account for the elastic shrinkage induced by the Portevin-Le Chatelier effect, elastic deformation is considered under the boundary conditions of the present model. The simulated results are found to be in good agreement with the experimental observations.     

Electronic Structures of Wurtzite GaN with Ga and N Vacancies

The electronic band structures of wurtzite GaN with Ga and N vacancy defects are investigated by means of the first-principles total energy calculations in the neutral charge state. Our results show that the band structures can be significantly modified by the Ga and N vacancies in the GaN samples. Generally, the width of the valence band is reduced and the band gap is enlarged. The defect-induced bands can be introduced in the band gap of GMV due to the Ga and N vacancies. Moreover, the GaN with high density of N vacancies becomes an indirect gap semiconductor. Three defect bands due to Ga vacancy defects are created within the band gap and near the top of the valence band. In contrast, the N vacancies introduce four defect bands within the band gap. One is in the vicinity of the top of the valence band, and the others are near the bottom of the conduction band. The physical origin of the defect bands and modification of the band structures due to the Ga and N vacancies are analysed in depth.     

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     

Entanglement control in one-dimensional s= 1/2 random XY spin chain

The entanglement in one-dimensional random XY spin systems where the impurities of exchange couplings and the external magnetic fields are considered as random variables is investigated by solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics near particular locations of the system is also studied when the exchange couplings （or the external magnetic fields） satisfy three different distributions （the Gaussian distribution, double-Gaussian distribution, and bimodal distribution）. We find that the entanglement can be controlled by varying the strength of external magnetic field and the distributions of impurities. Moreover, the entanglement of some nearest-neighbouring qubits can be increased for certain parameter values of the three different distributions.     

Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbouring interactions

By using the method of density-matrix renormalization-group to solve the different spin spin correlation functions, the nearest-neighbouring entanglement （NNE） and the next-nearest-neighbouring entanglement （NNNE） of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearestneighbouring interaction of exchange couplings, external magnetic fields and the next-nearest neighbouring interaction. For a dimerised ferromagnetic spin chain, the NNNE appears only above a critical dimerized interaction, meanwhile, the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring （NNN） interaction on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always reduces the NNE. The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.