Counter-examples of regularity behavior for σ-evolution equations

In this paper, we mainly discuss the infinite loss of regularity and μ-loss for a σ-evolution type model with oscillating in time coefficients. On the one hand, an explicit counter-example has been constructed in the frequency space to show the precise infinite loss of regularity. On the other hand, due to the finite propagation speed property for σ∈(0,1], we construct the counter-example of a sequence of solutions in R by applying state of art techniques.     

Pnictogen-Bonding Catalysis: An Interactive Tool to Uncover Unorthodox Mechanisms in Polyether Cascade Cyclizations

Pnictogen-bonding catalysis and supramolecular σ-hole catalysis in general is currently being introduced as the non-covalent counterpart of covalent Lewis acid catalysis. With access to anti-Baldwin cyclizations identified as unique characteristic, pnictogen-bonding catalysis appeared promising to elucidate one of the hidden enigmas of brevetoxin-type epoxide opening polyether cascade cyclizations, that is the cyclization of certain trans epoxides into cis-fused rings. In principle, a shift from S_N2- to S_N1-type mechanisms could suffice to rationalize this inversion of configuration. However, the same inversion could be explained by a completely different mechanism: Ring opening with C−C bond cleavage into a branched hydroxy-5-enal and the corresponding cyclic hemiacetal, followed by cascade cyclization under conformational control, including stereoselective C−C bond formation. In this report, a pnictogen-bonding supramolecular Sb^V catalyst is used to demonstrate that this unorthodox polyether cascade cyclization mechanism occurs.     

Functionalization of Conductive Poly(thiophenes) and Poly(pyrroles)

New methods for functionalization of conductive poly(thiophenes) and poly(pyrroles) using fused aromatics or crown ethers are discussed.     

Calculations of random fixed point index

In this paper, we prove an important inequality and investigate some new calculating problems of random fixed point index, and generalize famous theorem by means of the theory of random fixed point index.     

单子集映射mτ与标准部分逆映射st-1的同态性

在饱和模型中,讨论了单子集映射m_T及标准部分逆映射st^-1的同态性质.证明了m_T能扩张成一个σ-同态的充要条件是X是可数紧空间.在一定条件下,st^-1是Borelσ-代数上的σ-同态映射,当且仅当X是预Hausdorff的,并给出了一个正则测度的一个Loeb表示.     

论实变函数解题方法

根据多年的教学经验较系统地总结了实变函数的解题方法,这些方法很值得师生学习和应用.     

Butadienyl Diiron Complexes: Nonplanar Metalla-Aromatics Involving σ-Type Orbital Overlap

A new class of nonplanar metalla-aromatics, diiron complexes bridged by a 1,3-butadienyl dianionic ligand, were synthesized in high yields from dilithio reagents and two equivalents of FeBr₂. The complexes consist of two antiferromagnetically coupled high-spin Fe^II centers, as revealed by magnetometry, Mössbauer spectroscopy, and DFT calculations. Furthermore, experimental (X-ray structural analysis) and theoretical analyses (NICS, ICSS, AICD, MOs) suggest that the complexes are aromatic. Remarkably, this nonplanar metalla-aromaticity is achieved by an uncommon σ-type overlap between the ligand p and metal d orbitals, in sharp contrast to the intensively studied planar aromatic systems featuring delocalized π-type bonding. Specifically, the σ-type interaction between the two Fe 3d_xz orbitals and the butadienyl π orbital results in the formation of a six-electron conjugated system and hence enables the aromatic character.     

集值映射空间在紧开拓扑下的N性质(英文)

本文研究了点紧连续集值映射族在紧开拓扑下的N性质.利用cs-σ网方法获得了如下结果:若X是N0空间,Y是N空间,则C_k(X,Y)是N空间.该结论将J.A.Guthrie关于单值连续映射空间的结论推广到了集值映射空间上,并且改进了相关结论.