In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equa...In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.展开更多
文摘结合对称性破损(BS)方法,采用不同的密度泛函理论(DFT)对反铁磁性μ-1,3-N3-Ni(II)叠氮配合物[LNi2(N3)](Cl O4)2(L=pyrazolate)的磁特性进行了研究.结果显示,杂化密度泛函理论(HDFT)的计算结果与实验数据非常吻合,能够准确描述配合物的磁特性.磁轨道研究结果表明,配合物表现出较大的单占据轨道能量劈裂(0.93-0.99 e V),显示配合物的单占据轨道去简并化程度较大,且配合物中的2个磁通道(叠氮基、配体pyrazolate)中都分别存在有氮原子之间的p轨道重叠,这些都使得体系表现为反铁磁耦合作用.另外,配合物的磁性与叠氮桥和两金属离子间形成的二面角(τ,Ni-N-N-N-Ni)密切相关,τ从-55.38°逐渐变化到-1.5°的过程中,其反铁磁性逐渐增强,交换耦合常数(Jab)的绝对值逐渐增大,并在-11.95°处达到最大值(Jab=-151.02 cm-1).在此过程中,配合物中叠氮桥及其所连接的2个Ni离子与pyrazolate基配体L-中的2个桥原子N(4)、N(5)形成的七元环共平面性不断增强,即共平面性会诱导增强体系的反铁磁相互作用.
文摘In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.
