Malliavin and Dirichlet structures for independent random variables

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron–Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of $U$-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

One‐pot green synthesis of Cu/bone nanocomposite and its catalytic activity in the synthesis of 1‐substituted 1H‐1,2,3,4‐tetrazoles and reduction of hazardous pollutants

In this work, a simple and green method is reported for the biosynthesis of Cu/bone nanocomposite using Cordyline fruticosa extract as a stabilizer and reductant. Animal bone was used as a natural support to prevent the accumulation of Cu nanoparticles. The catalytic activity of Cu/bone nanocomposite was assessed in the synthesis of 1‐substituted 1H‐1,2,3,4‐tetrazoles and reduction of various organic dyes, including 4‐nitrophenol (4‐NP), nigrosin (NS), congo red (CR) and methylene blue (MB). The best catalytic performance in the synthesis of 1‐substituted tetrazoles was achieved using 0.05 g of Cu/bone nanocomposite at 120°C. In addition, under optimal conditions, the absorption bands corresponding to 4‐NP, CR, NS and MB completely disappeared after about 6 min, 3 min, 50 s and 7 s, respectively. The biosynthesis protocol used in the preparation of Cu/bone nanocomposite offers a very attractive area for further research.     

In situ green synthesis of Cu‐Ni bimetallic nanoparticles supported on reduced graphene oxide as an effective and recyclable catalyst for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles

In the present work, for the first time we have designed a novel approach for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles using reduced graphene oxide (rGO) decorated with Cu‐Ni bimetallic nanoparticles (NPs). In situ synthesis of Cu/Ni/rGO nanocomposite was performed by a cost efficient, surfactant‐free and environmentally benign method using Crataegus azarolus var. aronia L. leaf extract as a stabilizing and reducing agent. Phytochemicals present in the extract can be used to reduce Cu²⁺ and Ni²⁺ ions and GO to Cu NPs, Ni NPs and rGO, respectively. Analyses by means of FT‐IR, UV–Vis, EDS, TEM, FESEM, XRD and elemental mapping confirmed the Cu/Ni/rGO formation and also FT‐IR, NMR, and mass spectroscopy as well as elemental analysis were used to characterize the tetrazoles. The Cu/Ni/rGO nanocomposite showed the superior catalytic activity for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles within a short reaction time and high yields. Furthermore, this protocol eliminates the need to handle HN₃.     

Direct C−H Borylation of Arenes Catalyzed by Saturated Hydride-Boryl-Iridium-POP Complexes: Kinetic Analysis of the Elemental Steps

The saturated trihydride IrH₃{κ³-P,O,P-[xant(PiPr₂)₂]} ( 1 ; xant(PiPr₂)₂=9,9-dimethyl-4,5-bis(diisopropylphosphino)xanthene) activates the B−H bond of two molecules of pinacolborane (HBpin) to give H₂, the hydride-boryl derivatives IrH₂(Bpin){κ³-P,O,P-[xant(PiPr₂)₂]} ( 2 ) and IrH(Bpin)₂{κ³-P,O,P-[xant(PiPr₂)₂]} ( 3 ) in a sequential manner. Complex 3 activates a C−H bond of two molecules of benzene to form PhBpin and regenerates 2 and 1 , also in a sequential manner. Thus, complexes 1 , 2 , and 3 define two cycles for the catalytic direct C−H borylation of arenes with HBpin, which have dihydride 2 as a common intermediate. C−H bond activation of the arenes is the rate-determining step of both cycles, as the C−H oxidative addition to 3 is faster than to 2 . The results from a kinetic study of the reactions of 1 and 2 with HBpin support a cooperative function of the hydride ligands in the B−H bond activation. The addition of the boron atom of the borane to a hydride facilitates the coordination of the B−H bond through the formation of κ¹- and κ²-dihydrideborate intermediates.     

Copper‐Catalyzed Reaction Cascade of Thiophenol Hydroxylation and S‐Arylation through Disulfide‐Directed C−H Activation

Copper‐catalyzed thiophenol C?H activation is described. Through an initial attempt to conduct C‐arylation with arylboronic acid, a rather surprising sequential C?H activation and S‐arylation was discovered. Mechanistic investigation revealed the disulfide intermediate as the key component in directing C?H oxidation. The overall reaction proceeded under mild conditions with molecular oxygen as the oxidant. Discovery of disulfide as the directing group provides a potential new direction for catalytic C?H functionalization under mild conditions.     

Rhodium(III) catalyzed synthesis of isoquinolone fused azabicycles through C–H activation of N-pivaloyloxy benzamides

Herein we describe an efficient one pot strategy toward highly functionalized isoquinolone fused azabicycles having great synthetic potential via C–H activation of N-pivaloyloxy benzamides under very mild conditions. The reaction is accomplished at room temperature within one hour in good to excellent yields and is found to be compatible with a range of diazabicyclic olefins and benzamides. The present strategy offers an easy route for the synthesis of biologically relevant compounds which possess multiple points for divergent synthesis. N–N bond cleavage of synthesized compounds may enable their significant role as effective precursors for the preparation of diaminocyclopentane fused isoquinolones.     

甲型H1N1流感的死亡率高吗——Bayes计量分析框架下的建模与估算

在全球甲型H1N1流感大流行背景下,本文在充分考虑各国甲流感死亡率可能存在个体混合效应、独立效应、相关效应及空间相关效应基础上,运用Bayes计量分析框架下的模型选择标准确定描述各国甲流感死亡率的最优模型,并基于该模型对不同国家甲流感死亡率进行估算。结果显示:个体独立、空间相关效应模型能很好拟合各国甲流感疫情统计数据,利用该模型估算的全球甲流感平均死亡率为0.577%。     

Highly Efficient C?H Hydroxylation of Carbonyl Compounds with Oxygen under Mild Conditions

A transition‐metal‐free Cs₂CO₃‐catalyzed α‐hydroxylation of carbonyl compounds with O₂ as the oxygen source is described. This reaction provides an efficient approach to tertiary α‐hydroxycarbonyl compounds, which are highly valued chemicals and widely used in the chemical and pharmaceutical industry. The simple conditions and the use of molecular oxygen as both the oxidant and the oxygen source make this protocol very environmentally friendly and practical. This transformation is highly efficient and highly selective for tertiary C(sp³) H bond cleavage.