二次域Q（√7）的单位给出的三角数及相关的不定方程问题

研究了二次域Q（√7）中单位Vn＋Un√7）=（8＋3√7）n所给出的两个递归数列{Vn},{Un}中的三角数问题,找到了{Vn},{Un}中的所有的三角数.作为应用,给出了与其相关的两个不定方程的整数解.     

一个三角不等式的推广

文 [1]证明了“若α ,β ,γ为正锐角 ,且ｓｉｎ2 α ｓｉｎ2 β ｓｉｎ2 γ =1,求证 :α β γ <π2 ”后 ,作了本题的上界估计 .若α ,β ,γ为正锐角 ,且ｓｉｎ2 α ｓｉｎ2 β ｓｉｎ2 γ =1,求证α β γ≤ 3ａｒｃｓｉｎ 13.文 [1]未对其进行证明 ,现将该不等式作如下推广 .定理　若α1,α2 ,… ,αｎ(ｎ≥ 3)为正锐角 ,且 ｎｉ=1ｓｉｎ2 αｉ=1,则 ｎｉ=1αｉ≤ｎａｒｃｓｉｎ 1ｎ.引理　若α1,α2 ,… ,αｎ(ｎ≥ 2 )均为正锐角 ,并且它们的两两之和也为正锐角 ,则ｓｉｎ2 1ｎ ｎｉ=1αｎ≤ 1ｎ ｎｉ=1ｓｉｎ2 αｉ.证　 …     

恒成立问题的三角解法

<正>对数学竞赛中的一类恒成立问题,若能抓住题目的特征,恰当地运用三角代换常可使问题获得简易的解答.     

一个新的高维向量Lie代数及其应用

构造了一个新的8维向量Lie代数,通过适当设计等谱问题,利用屠格式和扩展的迹恒等式得到了AKNS族的可积耦合及Hamilton结构.     

谈三角问题中隐含条件的挖掘

隐含条件是指题目中隐而不显、含而未露的固有条件，它通常巧妙地隐藏在题设的背后．常因未能挖掘题设中的隐含条件，使求解陷入困境，或是得出错误的结论．解题时需能揭开其表层面纱，深入挖掘所隐含的信息。并予以充分利用，方可得出正确结果．下面结合实例谈谈三角问题中的隐含条件的挖掘．     

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.     

广义Bianchi恒等式的某些应用

本文给出由非不变性拉氏量导致的广义Bianchi恒等式的若干应用。导出强守恒律,用于某些场论,得到相应的弱守恒律,讨论了非不变拉氏量系统的Dirac约束。     

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.