次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

N‐Heterocyclic Silylenes in Boron Chemistry: Facile Formation of Silylboranes and Silaborinines

Reaction of a N‐heterocyclic silylene (NHSi) with PhBX₂ (X=Cl, Br) readily afforded six‐membered silaborinines through an insertion/ring expansion sequence. Increasing the sterics of the borane from phenyl to duryl enabled the selective generation and isolation of the highly colored silylborane intermediates. Theoretical studies on the mechanism and energetics of the silaborinine formation were fully consistent with the experimental observations.     

One-Pot Palladium-Catalyzed Ligand- and Metal-Oxidant-Free Aerobic Oxidative Isocyanide Insertion Leading to 2-Amino-substituted-4(3H)-quinazolinones

An efficient, ligand- and metal-oxidant-free, one-pot, cascade aerobic oxidative, palladium-catalyzed, multicomponent reaction has been developed through isocyanide insertion of less active secondary amide and aromatic amine, which leads to 2-amino-substituted-4(3H)-quinazolinones. This approach proves to be one of the simplest methods for the synthesis of this class of valuable bioactive heterocyclic scaffolds.     

Theoretical Studies on the Mechanistic Insertions of Singlet Methylene and Halomethylene into Polar S‒H Bonds of Methanethiol,Ethanethiol, 1-Propanethiol and 2-Propanethiol

Abstract

The insertion of ¹CH₂, ¹CHF, ¹CF₂,¹CHCl, and ¹CCl₂ into primary and secondary polar S?H bonds of methanethiol, ethanethiol, 1-propanethiol, and 2-propanethiol have been investigated at HF (Hartree–Fock), MP2 (Møller–Plesset Perturbation Theory), and DFT (density functional theory) levels using 6-31G (d, p) basis set. The insertions follow a two-step mechanism. The potential energy surface exploration identifies ylide-like structures undergoing the 1,2-sigmatropic hydrogen shift concertedly giving the thioether product. But ¹CF₂ forms weak complexes involving 1,2-hydrogen shift. The barrier height in the concerted mechanism varies with the type of carbene moiety and S?H bond. The initial interaction seems to be a function of HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energies of thiols and carbenes, respectively. The natural bond orbital charge analysis showing a net charge flow from the substrate thiol to the reagent carbene at the transition states corroborates this fact.     

On finiteness and continuity of shot noise processes

For a rather general class of stochastic processes induced by time-stationary and by event-stationary random marked point processes, respectively, conditions are given for the almost sure finiteness of these processes and for their continuous dependence on the underlying random marked point process.     

Measure and integration: The basic extension and representation theorems in terms of new inner and outer envelopes

The work of the author in measure and integration is based on new inner and outer envelope formations, which replace the traditional Carathéodory outer measure and certain simple suprema and infima. The new formations lead to essential improvements in both the extent and the adequacy of the basic results. However, they did not find an entrance into the recent textbook literature. The present paper seeks to demonstrate their power with the examples of the basic inner and outer extension and representation theorems for set functions and functionals.     

Pd–phosphinesulfonate bravely battles the “vinyl halide insertion copolymerization” barricade

This overview provides insights into the current state‐of‐the‐art solutions to insertion copolymerization of functional olefinic monomers. The challenges in insertion copolymerization of functional olefinic monomers, with a special emphasis on vinyl halides, are highlighted. The crucial design of the Pd–phosphinesulfonate [Pd(PO)] enables up to 3.6 mol % incorporation of vinyl fluoride (VF) in an ethylene–VF copolymerization reaction. In a significant development, insertion copolymerization of industrially relevant functional olefin, that is, vinyl chloride (VC), was unambiguously ascertained, and a detectable amount of VC (0.4 mol %) was incorporated (at the chain end). In a detailed investigation, the in situ existence of (PO)Pd? H species during the polymerization was revealed, and it was demonstrated that these are indeed responsible for VC incorporation. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1–6