任意信源随机和的一类随机Shannon-McMillan定理

采用构造相容分布与非负上鞅的方法研究任意信源随机和相对熵密度的强极限定理,并由此得出若干任意信源,m阶马氏信源,无记忆信源的随机Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广.     

Relative Thermodynamic Stabilities of Isomeric Vinyl Ethers Derived from 2-Acetyland 2-Isobutyryltetrahydrofurans. An Experimental and DFT Study

The relative thermodynamic stabilities of four isomeric vinyl ethers obtained by acid-catalyzed cleavage of MeOH from the dimethyl acetals of both 2-acetyltetrahydrofuran and 2-isobutyryltetrahydrofuran have been determined by chemical equilibration in cyclohexane solution. In addition, the structures and relative energies of many of these compounds have also been studied theoretically by DFT calculations. In each series of compounds, the endocyclic isomers, 5-(1-methoxyethyl)-2,3-dihydrofuran and 5-(1-methoxy-2-methylpropyl)-2,3-dihydrofuran, respectively, show the highest thermodynamic stabilities. This is particularly prominent for the vinyl ethers derived from 2-isobutyryltetrahydrofuran in which the equilibrium mixture consists of 90% of the endocyclic isomer at room temperature. The geometrical (exocyclic) isomers of the latter series of compounds show unexpected relative thermodynamic stabilities, but on the basis of the geometry-optimized structures provided by the DFT calculations, a reasonable explanation can be found.     

Intramolecular Alkylation of Aromatic Compounds XXXVI [1]. Stereoselective Synthesis of C/D-cis-Configured Ergolines

Summary.  The stereoselective synthesis of cis-ergoline is presented. Starting from rac-N-benzoyl tryptophan methyl ester, the key compound indolinylmethylpyridin-3-one was prepared via a seven-step reaction in good yield. Since its cyclization to the desired ergolinone failed, the key compound was reduced to yield the two diastereomeric pyridin-3-ols; only one of them cyclized in trifluoromethanesulfonic acid, affording cis-ergoline. Catalytic hydrogenation of the latter gave N,N′-dimethyldihydroergoline, the X-ray crystallography of which revealed both the correct structure and identical relative configurations at C-5a and C-6a (SS or RR). Hydroboration and subsequent perruthenate oxidation of the Δ⁹-ergoline provided access to the regioisomeric ergolinols and ergolinones. Received December 27, 2001. Accepted January 15, 2002     

一类非线性多重调和方程△~mu=f(|x|,u,|u|)的正整解

本文建立了一类Ｒｎ（ｎ≥３）中非线性多重调和方程△~ｍｕ＝ｆ（|ｘ|，ｕ，|(ｕ|）（ｍ≥２）正 的径向对称整体解的存在性定理，并给出了解的有关性质，推广了文［１］－［４］的有关结果．     

关于James-Stein估计的小样本性质

首先给出了Jam es-S te in估计优于岭估计的充分条件,随后在P itm an准则下给出了Jam es-S te in估计优于最小二乘估计的简短证明.     

Quantifying coherence with dynamical discord

Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.     

Automated and efficient quantum chemical determination and energetic ranking of molecular protonation sites

We present an automated quantum chemical protocol for the determination of preferred protonation sites in organic and organometallic molecules containing up to a few hundred atoms. It is based on the Foster–Boys orbital localization method, whereby we automatically identify lone pairs and π orbitals as possible protonation sites. The method becomes efficient in conjunction with the robust and fast GFN‐xTB semiempirical method proposed recently (Grimme et al ., J. Chem. Theory Comput . 2017, 13 , 1989). The protonated isomers that are found within a few seconds to minutes of computational wall‐time on a standard desktop computer are then energetically refined using density functional theory (DFT), where we use a high‐level double‐hybrid reference method to benchmark GFN‐xTB and low‐cost DFT approaches. The proposed DFT/GFN‐xTB/LMO composite protocol is generally applicable to almost arbitrary molecules including transition metal complexes. Importantly it is found that even in electronically complicated cases, the GFN‐xTB optimized protomer structures are reasonable and can safely be used in single‐point DFT calculations. Corrections from energy to free energy mostly have a small effect on computed protomer populations. The resulting protomer equilibrium is valuable, for example, in the context of electrospray ionization mass spectrometry where it may help identify the ionized species and assist the interpretation of the experiment. © 2017 Wiley Periodicals, Inc.     

不同等级煤与油共炼的转化率差异及残渣分析

选取安徽褐煤、辽宁褐煤和贵州烟煤三种煤为原料,以油溶性环烷酸钼为催化剂,分别与马瑞常渣(MRAR)、克炼常渣(KAR)以及催化裂化油浆(FCCS)在高压釜内模拟悬浮床加氢共炼反应。结果表明,不同的油体系下,两种褐煤都能达到83%以上的转化率,而对于贵州烟煤,转化率最高的FCCS体系与最低的KAR体系分别为67.75%和50.31%,相差很大。采用FT-IR和SEM分析反应后固体残渣,计算了固体残渣中脂肪族和芳香族中各个基团的相对含量,并对比了不同体系反应后固体残渣的微观形貌。结果表明,KAR体系的固体残渣脂肪链较长,支链化程度高,取代度较低。转化率较高的褐煤反应后固体残渣结构松散,分散度高;转化率较低的烟煤固体残渣随着转化率降低,残渣颗粒逐渐变大,表面更加光滑,板结程度加深。     

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.