Weak Convergence Theorems for Nonself Mappings

Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {k(i)n}  [1, ∞)(i = 1, 2), and F := F(T1)∩F(T2) = . An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Fr′echet differentiable norm or its dual E*has Kadec-Klee property, then weak convergence theorems are obtained.     

Carbon‐bridged Tri(cyclopentadiene): Synthesis and Coordination with Ytterbium

Reaction of a mixture of 1,1‐bis(cyclopentadienyl)cyclohexane and pentamethylenefulvene with metallic sodium in THF led to a mixture of cyclohexylidene‐bridged bis(cyclopentadienyl) sodium and two‐cyclohexylidene‐bridged tri(cyclopentadienyl) sodium. Reaction of the salt solutions with anhydrous YbCl₃ in THF afforded a ytterbium complex mixed‐ligated by bridged bis(cyclopentadienide) and bridged tri(cyclopentadienide).     

Synthesis of 6‐Alkylidene‐5,6‐dihydro‐4H‐1,3‐thiazine Derivatives via the Cyclization of N‐3‐Bromo‐3‐alkenylthioamides

By the treatment of N‐3‐bromo‐3‐alkenylthioamides with sodium hydroxide in DMF‐H₂O in the presence of tetra‐butylammonium bromide, series of 6‐alkylidene‐5,6‐dihydro‐4H‐1,3‐thiazine derivatives were prepared in moderate to good yields. The cyclization is supposed to proceed via both the intramolecular vinylic nucleophilic substitution and the elimination‐addition mechanisms (formation of acetylenic intermediates) in a competitive manner.     

On the low-temperature properties of TmCo2Ge2

In this paper low-temperature magnetic properties of TmCo₂Ge₂ are reported. The compound was investigated by means of magnetic, electrical transport, heat capacity and neutron diffraction measurements. Clear anomalies were found in all of the bulk characteristics at the onset of antiferomagnetically ordered state below 2.4 K. According to neutron diffraction data, Tm magnetic moments are aligned along the c-axis, forming the AFI-type magnetic structure. In the paramagnetic state, the specific heat reveals a distinct Schottky contribution with the total crystal field splitting of about 150 K.     

Banach 空间中多值非单调算子的相补问题

应用H-空间中的Park极大元定理,在Banach空间中证明了多值非单调算子的相补问题的解的存在性定理．     

Convergence theorems of fixed points for asymptotically hemi-pseudocontractive mappings

In this paper, the concept of asymptotically hemi-pseudocontractive mapping in Banach space, which is a proper generalization of asymptotically pseudocontractive mapping with nonempty fixed point set as shown by an example, is introduced. Some sufficient and necessary conditions on the strong convergence of the modified Ishikawa and the modified Mann iteration sequences with mean errors for uniformly L-Lipshitzian asymptotically hemi-pseudocontractive mappings are presented.     

Dynamics of entanglement in one-dimensional Ising chains with two- and three-body interactions

The evolution of entanglement in a one-dimensional Ising chain with both two-body and three-body interactions, under two types of initial states, is numerically simulated. We analyse three problems concerning the dynamics of pairwise entanglement: (i) the possibility of generating large entanglement from an initial separable state by the use of a selective irradiation scheme; (ii) the effect of three-body interaction on the generation of entanglement from an initial separable state; (iii) the effect of three-body interaction on the decay of the entanglement from a state with only (m,n)-pair maximal entangled, and the rest in product form. It is shown that a large pairwise concurrence C_mn can be obtained when the resonant, transverse radio-frequency fields are selectively switched on from the mth to nth spins. Three-body interaction will decrease the oscillation amplitude of the nearest neighbour concurrence, while the oscillation amplitude of remote pairwise concurrence will be greatly increased with the consideration of three-body interactions. For an initial (m,n)-pair maximal entangled state, a slow decay of the pairwise concurrence C_mn is found with the introduction of three-body interactions.     

等效零折射率材料微腔中均匀化腔场作用下的简正模劈裂现象

研究了零折射率材料微腔中人造原子与腔模的相干耦合现象.首先通过数值模拟的方法研究了在二维光子晶体微腔中填充阻抗匹配的零折射率材料后腔模的场分布.结果表明零折射率材料的引入使得原本以驻波场形式存在的腔模分布在整个微腔中变得近似均匀且值最大.其次,将人造原子放入腔中的不同位置并与腔模耦合,结果从频谱上观察到腔模的劈裂与人造原子在腔中的位置无关.最后,利用微波实验,通过开口谐振环等效的人造原子与一维复合左右手传输线等效的零折射率材料微腔之间的耦合验证了仿真结果的准确性.该结果为腔量子电动力学中量子点对位难的问题提供了新的方案,同时零折射率材料微腔也为今后研究原子与光子之间的相互作用提供了一个新的平台.     

9，10-二杂环取代蒽衍生物制备与三线态-三线态湮灭上转换性能研究

弱光上转换是基于三线态-三线态湮灭机制将低能量(长波长)的光转换为高能量(短波长)光的一种现象,是通过光敏剂与发光剂之间能量转移实现的。针对当前上转换体系中的光敏剂研究备受关注,而对于同等重要作用的发光剂的研究甚少的现状,利用Suzuki偶联反应制备了两个新的杂环取代蒽衍生物：9,10-二(3-呋喃)蒽(DFA)和9,10-二(3-噻吩)蒽(DTA)并通过结构表征;以9,10-二杂环取代蒽为发光剂、四苯基卟啉钯衍生物(PdTPPMe和PdTPPCOOH)为三线态光敏剂,研究所构成的光敏剂/发光剂双组分体系中,三线态-三线态能量转移效率(k_Q)、发光剂的延迟荧光寿命(τ_DF)及发光剂荧光量子产率(Φ_f)等因素对上转换效率(Φ_UC)的影响。结果表明,高效三线态-三线态能量效率(Φ_TTT)、快速延迟荧光寿命和大荧光量子产率将有利于提高上转换效率。进一步研究发现,含氧发光剂(DFA)与含羧基的光敏剂(PdTPPCOOH)之间可借助氢键发生有效耦合,有利于光敏剂与发光剂之间的三线态能量转移,导致弱光上转换效率显著提高。在半导体激光器(532 nm,70 mW·cm-2)激发下获得强的绿-转-蓝上转换效率最大可达10.11%。所获得的绿-转-蓝上转换荧光可使Pt/WO₃复合半导体受激;产生氧自由基并可促使香豆素转化为7-羟基香豆素。     

Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators北大核心CSCD

Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.