On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Infinitely many coexisting conservative flows in a 4D conservative system inspired by LC circuit

Nonlinear Dynamics - Conservative chaotic flows, a category of incompressible chaos, are usually generated from dynamical systems without dissipation. The existing results on conservative chaos are...     

In‐Depth Understanding of the Chemical Properties of Rarely Explored Carbide Cluster Metallofullerenes: A Case Study of Sc2C2@C3v(8)‐C82 that Reveals a General Rule

The chemical properties of carbide‐cluster metallofullerenes (CCMFs) remain largely unexplored, although several new members of CCMFs have been discovered recently. Herein, we report the reaction between Sc₂C₂@C_3v(8)‐C₈₂, which is viewed as a prototypical CCMF because of its high abundance, and 3‐triphenylmethyl‐5‐oxazolidinone ( 1 ) to afford the corresponding pyrrolidino derivative Sc₂C₂@C_3v(8)‐C₈₂(CH₂)₂NTrt ( 2 ; Trt=triphenylmethyl). Single‐crystal X‐ray crystallography studies of 2 revealed that the reaction takes place at a [6,6]‐bond junction, which is directly over the encapsulated C₂ unit and is far from either of the two scandium atoms. On the basis of theoretical calculations and by considering previously reports, we have found that a hexagonal carbon ring on the cage of Sc₂C₂@C_3v(8)‐C₈₂ is highly reactive toward different reagents due to the overlap of high p‐orbital axis vector (POAV) angles and large LUMO coefficients. We propose that this highly concentrated area of reactivity is generated by the encapsulation of the Sc₂C₂ cluster because this region is absent from the empty fullerene C_3v(8)‐C₈₂. Moreover, the absorption and electrochemical results confirm that derivative 2 is more stable than pristine Sc₂C₂@C_3v(8)‐C₈₂, thus illuminating its potential applications.     

Free volume characteristics of 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole-co-tetrafluoroethylene copolymers: Effect of composition and molecular weight

2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole-co-tetrafluoroethylene (PDD-TFE) copolymer is a good candidate to prepare gas separation membranes with excellent permeability due to its free volume characteristics. However, the influence of PDD-TFE copolymer structure on its free volume characteristics is less studied. In this paper, PDD-TFE copolymers with different compositions and molecular weights were synthesized, and their free volume characteristics were analyzed by positron annihilation lifetime spectroscopy and a molecular dynamics simulation. It indicated that the molar fraction of PDD in copolymers had a significant effect on free volume characteristics, while the molecular weight of copolymers exerted a slight influence on free volume when the molecular weight exceeded a critical region (intrinsic viscosity [η] > 68 ml g⁻¹). PDD-TFE copolymers with greater PDD molar fractions (i.e., 72% and 84%) showed bimodal distributions in positron lifetime and free volume size distributions, while PDD-TFE copolymers with lower PDD molar fractions (i.e., 27% and 35%) exhibited a single peak. The long-lifetime parameter τ₃ was assigned to micro-cavities formed by [-(TFE)_y-PDD-] segments and τ₄ was attributed to micro-cavities formed by [-(PDD)_x-TFE-] segments. The cis and trans transitions of PDD led to a local multilayer spiral structure with a 2.6–4.3 Å layer spacing, which would also increase the free volume of copolymers.     

CdS/沸石分子筛复合光催化剂的制备及光催化性能

以煤矸石为原料,经Na2CO3碱熔活化和水热合成获得了沸石分子筛;利用Cd2+对沸石分子筛进行离子交换并通过沉淀过程制得了CdS/沸石分子筛复合粉体.采用X射线粉末衍射(XRD)和扫描电子显微镜(SEM)对所得样品进行表征,并以模拟太阳光为光源,罗丹明B (RhB)为目标降解物,对其光催化活性进行了研究.结果显示:沸石分子筛上负载的CdS的晶相为立方相,制得的CdS/沸石分子筛复合粉体具有较好的光催化活性,且三次循环利用后仍具有较好的催化活性,在模拟太阳光辐照下,CdS/zeolite(0.5 M)复合粉体重复利用3次后,处理260 min对RhB的降解率仍可达91.3;.所得粉体对RhB的光催化过程符合一级动力学方程式,光催化过程中,RhB 紫外可见光谱的蓝移现象揭示所得CdS/沸石分子筛可通过脱乙基-共轭显色基团断裂途径降解RhB.     

Synthesis and Photophysical Properties of a Sc3N@C80‐Corrole Electron Donor–Acceptor Conjugate

Embedding endohdedral metallofullerenes (EMFs) into electron donor–acceptor systems is still a challenging task owing to their limited quantities and their still largely unexplored chemical properties. In this study, we have performed a 1,3‐dipolar cycloaddition reaction of a corrole‐based precursor with Sc₃N@C₈₀ to regioselectively form a [5,6]‐adduct ( 1 ). The successful attachment of the corrole moiety was confirmed by mass spectrometry. In the electronic ground state, absorption spectra suggest sizeable electronic communications between the electron acceptor and the electron donor. Moreover, the addition pattern occurring at a [5,6]‐bond junction is firmly proven by NMR spectroscopy and electrochemical investigations performed with 1 . In the electronically excited state, which is probed in photophysical assays with 1 , a fast electron‐transfer yields the radical ion pair state consisting of the one‐electron‐reduced Sc₃N@C₈₀ and of the one‐electron‐oxidized corrole upon its exclusive photoexcitation. As such, our results shed new light on the practical work utilizing EMFs as building blocks in photovoltaics.