简议“图形数列”问题

<正>随着新课标的全面展开,"图形数列"问题已经深入高考试题、高考模拟试题以及课本之中,此类问题集趣味性、创新性、探究性于一体.现就近几年高考试题、高考模拟试题以及课本中出现的部分"图形数列"问题简议如下:     

三角级数属于Ba空间的充分必要条件

该文给出了正弦级数和余弦级数在系数满足NBV条件时属于Ba空间的充分必要条件,所得结论 为Ba空间中的首个此类结果,同时也是对L_p空间中已有结论的本质性推广.     

Extended Bose-Hubbard model with pair hopping on triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.     

Quantum phase transitions of fermionic atoms in an anisotropic triangular optical lattice

The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte–Carlo algorithm.The quantum phase diagrams which reflect the temperature–interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system.Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value.The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect.A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed,in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.     

借助二次曲线求三角函数的值域（最值）

有很多三角函数的值域（最值）问题，利用单纯的三角知识难以解出，可考虑借助二次曲线，把函数的值域（最值）问题转化为直线的斜率或截距的范围问题，结合几何图形解答，简单直观．下面举例说明．     

用等值宽度法测量fs脉冲宽度

本文提出利用等值宽度测量fs光脉冲持续时间的方法.给出了脉冲形状为sech~2 (t/T)、exp(-2t~2/T~2)和exp(-2|t|/T)的干涉相关曲线上包络与相应二阶强度相关曲线半宽度等值的位置,它们分别是3.984、4.875和4.928.定义了两种相关测量的临界延迟速度.理论分析与实验结果符合得很好.所得结果表明,该测量方法可将常规超短脉冲相关测量的时间分辨率提高几倍至几十倍.     

二次域Q(√3)的单位给出的两个递归数列中的三角数问题

对二次域Q(√3)中单位Vn Un√3=(2 √3)n所给出的两个递归数列{Vn},{Un}中的三角数问题进行研究,给出了完整的结果.作为应用,解决了与其相关的两个不定方程问题.     

Ni~(2+):CsMgCl_3的光学吸收谱和EPR的研究

应用三角晶场中d2 (d8)电子组态包括静电相互作用和自旋 轨道耦合作用的强场能量矩阵 ,采用完全对角化方法 ,精确地计算了具有D3d 对称的Ni2 + :CsMgCl3 的光学吸收谱和EPR谱。理论结果与实验值符合得很好。     

非线性增益和波导结构对半导体激光器的谱线宽度的作用

本文采用半经典理论研究了非线性增益和波导结构对量子相位噪声引起的模式谱线增宽过程的作用,得出谱线宽度不但与线性增益而且与三阶增益有关,并且都受到波导结构的制书。从而提出新的谱线增宽因子和与功率无关的线宽的新机制。 关键词：