弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.     

Reaction mechanism and rate constants of the CH+CH4 reaction: a theoretical study

Ab initio and density functional calculations have been performed to elucidate the mechanism of CH radical insertion into methane. The results show that the reaction can be viewed to occur via two stages. On the first stage, the CH radical approaches methane without large structural changes to acquire proper positioning for the subsequent stage, where H-migration occurs from CH₄ to CH, along with a C–C bond formation. Where the first stage ends and the second begins, a tight transition state was located using the B3LYP/6-311G(d,p) and MP4(SDQ)/6-311++G(d,p) methods. Using a rigid rotor – harmonic oscillator approach within transition state theory, we show that at the MP5/6-311++G(d,p)//MP4(SDQ)/6-311++G(d,p) level the calculated rate constants are in a reasonably good agreement with experiment in a broad temperature range of 145–581 K. Even at low temperatures, the insertion reaction bottleneck is found about the location of the tight transition state, rather than at long separations between the CH and CH₄ reactants. In addition, high level CCSD(T)-F12/CBS calculations of the remainder of the C₂H₅ potential energy surface predict the CH+CH₄ reaction to proceed via the initial insertion step to the ethyl radical which then can emit a hydrogen atom to form highly exothermic C₂H₄+H products.     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.     

Zhiber-Shabat方程的多辛几何和多辛隐式格式研究

Zhiber-Shabat方程,描述许多重要的物理现象,是一类重要的非线性方程,有着许多广泛的应用前景.本文给出Zhiber-Shabat方程的多辛几何结构和多辛Fourier拟谱方法.数值算例结果表明多辛离散格式具有较好的长时间的数值稳定性.     

超空间上高阶Teodorescu算子

本文首先由超空间上Cauchy-Pompeiu公式定义了超空间上高阶Teodorescu算子,研究了此类算子的一些基本性质.其次,利用此类算子,我们得到了$k$-超正则函数的Almansi型展开. 最后运用这个展开,我们证明了$k$-超正则函数的Morera型定理、开拓定理和唯一性定理.     

Kinetic Studies of the Thermal cis-to-trans Isomerization of Dioxaphospholanes

By following a previously reported method,¹ the synthesis of r-2-alkoxy-cis-4-cis-5-dimethyl-1,3,2-λ³-dioxaphospholanes ligands (1 and 3) was carried out. The purpose of this work is the kinetic study of the inversion barrier at phosphorus for 1 and 3 and the comparison with the already informed dioxaphospholane 2. The kinetic measurements of the thermal isomerization cis-to-trans were performed by ³¹P NMR spectroscopy, observing a first order kinetics for both compounds. The energy of activation (E_a) for the epimerization of compounds cis-1 and cis-3 was calculated to be 16.0 ± 0.6 and 11.8 ± 0.8 kcal/mol, respectively. The values of the thermodynamic parameters of the transition state (Δ H^≠, Δ S^≠, Δ G^≠) suggest that the inversion at phosphorus not only depends on the spatial requirements of the alkoxy substituent but also on entropic effects. The thermodynamic parameters Δ H°, Δ S°, and Δ G° were also evaluated and they show that the cis isomers are preferred from enthalpic point of view, but entropic effects dominate the equilibrium trans ? cis leading to the entropically favored trans isomers. Furthermore, the results are supported by density functional theory calculations of 1–4 at the B3LYP/6-31G** level.     

Cyclic (ALN)n Compounds as Precursors to Aluminum Nitride: Synthesis and Structure of [(CH3)2AlNH2]3 and the Planar Species [(t-C4H9)2AlNH2]3

Abstract

The crystal and molecular structures of the title compounds, [(CH₃)₂AlNH₂]₃ 1 and [(t-C₄H₉)₂AlNH₂]₃ 2, have been determined in connection with their investigation as possible precursors to aluminum nitride. Both compounds have an (AlN)₃ ring-structure with distorted tetrahedral geometries for the ring Al and N atoms. The distortion from tetrahedral geometry is most pronounced for the N atoms where the endocyclic Al-N-Al bond angles average 125.3 for 1 and 134.2 for 2. The (AlN)₃ ring in 1 is in a skew-boat conformation with no unusual intra- or intermolecular contacts. Compound 2 on the other hand exhibits an unprecedented planar (AlN)₃ ring as required by a crystallographic three-fold symmetry axis. The effects of the Al and N substituents on the (AlN)₃ ring size and conformation, as well as on the endocyclic Al-N-Al bond angles, are discussed in the context of the structural results obtained for these and other (AlN)_n ring compounds.     

Viscosity-Temperature Behavior of Hydroxypropyl Cellulose Solution in Presence of an Electrolyte or a Surfactant: A Convenient Method to Determine the Cloud Point of Polymer Solutions

The viscosity of hydroxypropyl cellulose (HPC) solution with or without an additive has been measured continuously as a function of temperature with the help of a vibro-viscometer. The viscosity of the polymer solution showed a gradual decrease initially with increase in temperature until a particular point beyond which there was a sharp decrease in the viscosity, which coincided with the clouding of the solution. The cloud point temperature (CP) of the polymer solution was determined from the first derivative plot of viscosity vs. temperature. Effect of addition of an electrolyte or a surfactant on the CP of HPC solution has also been studied. While a decrease in CP of HPC solution in presence of fluoride, chloride, or bromide ions was observed, presence of iodide or thiocyanide ions led to an increase in the CP. However, presence of an ionic surfactant initially lowered the CP but beyond a particular surfactant concentration a sharp increase in cloud point was observed due to interaction of the surfactant with the polymer. The results suggest that surfactants with longer hydrophobic tail or more hydrophobic groups have more affinity for HPC.     

Relationship between Reactivity Ratios and Configuration for Donor—Acceptor Type Copolymers

For binary copolymers from an acrylic monomer (acceptor type, M¹) and an aromatic-substituted monomer (donor type, M₂) a linear relation between log (r₂/r¹) and the probability of “coisotactic” alternating addition is observed. This can be a proof for the influence of monomer polarity on the copolymer configuration.