课本一题的多种证法

高中数学《必修2》（人教版2007年2月第三版）第73页的第5题,是一道妙题．我们发现其证明的入口宽,思路广,探索后得到多种证明方法．这种发散性思维对于提高我们的思维能力起到了很好的促进作用．     

解两类无理函数最值问题的三角代换法

在学校阅览室中,我读到了文[1]、文[2],文[1]介绍了用a·b≤｜a｜·｜b｜求两类无理函数最值的方法,但该文只考虑了最大值,而没有考虑最小值,为了弥补这一局限,文[2]给出了新的方法——规划法．该法虽然巧妙,但解答过程并不简洁．经过研究我发现,利用三角代换可以很方便地解决这两类无理函数的最值问题,下面我结合原文中的例子予以说明．     

关于2011年CUMCM-D题的一种解法与若干思考

本文系2011年全国大学生数学建模竞赛专科组高教社杯获得者针对本年度竞赛D题的一种解法与若干思考的阐述。首先系统介绍了对此题认识和解题思路,其次提供了一类基于启发式算法求解此问题的参考解法,最后对该问题提出了进一步研究的一个方向。     

《化学通报》网络版(Chemistry Online)2001年4月论文摘要

引用方法 :作者 (多位作者间以逗号隔开 ) .题目 .化学通报 ,年 ,卷 :Ｗ××× (×××为网络版目次中序号的后三位 )[Ｗ 0 1 0 32 ]中性水介质中钙、镁离子对钨酸盐缓蚀机理的影响 Ｃｏｒｒｏｓｉｏｎ ｉｎｈｉｂｉｔｉｏｎＭｅｃｈａｎｉｓｍｏｆＴｕｎｇｓｔａｔｅｉｎＮｅｕｔｒａｌＡｑｕｅｏｕｓＳｏｌｕｔｉｏｎｓ李　燕　　陆　柱 (华东理工大学防腐蚀中心　上海　 2 0 0 2 37)用极化曲线法和Ａｕｇｅｒ能谱研究了中性水介质中Ｃａ2 +、Ｍｇ2 +离子对钨酸盐缓蚀机理的影响。碳钢极化曲线表明 :在含Ｃｌ-和ＷＯ42 -的水中 ,添加Ｃａ…     

Simplified Scheme for Testing Symmetrization Postulate for Photons

We propose a scheme for testing the small violations of the symmetrization postulate （SP） for photons in cavity QED. In the scheme, a degenerate A-type three-level atom is sent through a cavity field initially in a q-deformed coherent state. After an appropriate interaction time, the atom is measured by a state-selective detector. The probability that the atom makes a transition from one of the lower states to the other characterizes the violation of the SP. In the scheme, only one atom is required and classical fields are unnecessary, which is prior to the previous schemes.     

Symmetries of Energy-Momentum Tensor： Some Basic Facts

It has been pointed out by Hall et al. [Gen. Rel. Gray. 28 （1996） 299.] that matter collineations can be defined by using three different methods. But there arises the question whether one studies matter collineations by using LεTab=0, or LεT^ab = 0 or LεT^b a=0. These alternative conditions are, of. course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.     

Three-Mode Cyclic Squeezed States Constructed via EPR Entangled State

We construct the three-mode cyclic squeezed states and analyze its squeezing property by using the technique of integration within an ordered product of operators and the natural representation of the two-mode squeezing operator in the Einstein-Podolsky-Rosen entangled state basis.     

One- and Two-Mode Combination Squeezing Operator for Two Harmonic Oscillators with Coordinate-Momentum Coupling

By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinatemomentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H = p21/2m1 m1ω21x21/2 p22/2m2 m2ω22x22/2 - λx2p1, so its ground state is a one- and two-mode combination squeezed state.Quantum fluctuation in the ground state is calculated.     

Cyclic Heating-Annealing and Boltzmann Distribution of Free Energies in a Spin-Glass System

Ergodicity of a spin-glass is broken at low temperatures; the system is trapped in one of many ergodic configurational domains. Transitions between different ergodic domains are achievable through a heating-annealing procedure. If this experiment is repeated infinite times, all ergodic configurational domains will be visited with frequences that decreasing exponentially with their free energies. The mean free energy density of a spin-glass system on a random graph is calculated based on this free energy Boltzmann distribution in the present work, by means of the cavity approach.     

Multipartite State Representations in Multi-mode Fock Space and Their Squeezing Transformations

We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product （IWOP） technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.