Synthesis and crystal structures of two structurally related kryptoracemates

Kryptoracemates are racemic compounds (pairs of enantiomers) that crystallize in Sohnke space groups (space groups that contain neither inversion centres nor mirror or glide planes nor rotoinversion axes). Thus, the two symmetry‐independent molecules cannot be transformed into one another by any symmetry element present in the crystal structure. Usually, the conformation of the two enantiomers is rather similar if not identical. Sometimes, the two enantiomers are related by a pseudosymmetry element, which is often a pseudocentre of inversion, because inversion symmetry is thought to be favourable for crystal packing. We obtained crystals of two kryptoracemates of two very similar compounds differing in just one residue, namely rac‐N‐[(1S ,2R ,3S )‐2‐methyl‐3‐(5‐methylfuran‐2‐yl)‐1‐phenyl‐3‐(pivalamido)propyl]benzamide, C₂₇H₃₂N₂O₃, (I), and rac‐N‐[(1S ,2S ,3R )‐2‐methyl‐3‐(5‐methylfuran‐2‐yl)‐1‐phenyl‐3‐(propionamido)propyl]benzamide dichloromethane hemisolvate, C₂₅H₂₈N₂O₃·0.5CH₂Cl₂, (II). The crystals of both compounds contain both enantiomers of these chiral molecules. However, since the space groups [P 2₁2₁2₁ for (I) and P 1 for (II)] contain neither inversion centres nor mirror or glide planes nor rotoinversion axes, there are both enantiomers in the asymmetric unit, which is a rather uncommon phenomenon. In addition, it is remarkable that (II) contains two pairs of enantiomers in the asymmetric unit. In the crystal, molecules are connected by intermolecular N—H…O hydrogen bonds to form chains or layered structures.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

氧化石墨阳离子交换容量测定过程中结构的变化

氧化石墨(GO)结构层上的碳羟基(―C―OH)和边缘羧基(―COOH)在水介质中发生质子化反应解离出的H+具有阳离子可交换性。实验采用甲醛缩合法测量了GO的阳离子交换容量(CEC),用X射线衍射(XRD)、傅里叶变换红外(FTIR)光谱和X射线光电子能谱(XPS)分析测试手段对GO阳离子交换过程中间产物的结构变化进行了分析。结果表明,GO的CEC高达541.48 mmol/100 g。NH_4~+和Ca~(2+)交换后的GO,保持稳定的层状结构,c轴方向层间距分别增大了0.1499和0.2905 nm。NH_4+和Ca~(2+)主要以层间可交换阳离子形式存在于层间域中,并与水分子形成可交换水化阳离子层,部分以[NH_4(H_2O)_6]+和[Ca(H_2O)_6]_2+的形式存在于结构层的边缘附近,共同平衡结构层水解产生的负电荷。     

矩阵代数收敛至球面与非交换度量几何

介绍了Rieffel定义的紧致量子度量空间与量子Gromov-Hausdorff距离和近来Latrémolière定义的量子Gromov-Hausdorff邻距,分别讨论了矩阵代数如何在这两种量子距离下收敛至球面.     

解析Sobolev型空间上的算子与算子代数

介绍Hardy-Sobolev空间和Fock空间及其算子与算子代数研究方面所做的工作,包括对这两类空间上几类特殊算子有界性、紧性、Fredholm性、指标理论、谱和本性谱、范数和本性范数、Schatten-p类的讨论,以及由它们所生成的C~*-代数的研究.     

A fast discontinuous finite element discretization for the space‐time fractional diffusion‐wave equation

In this article, we study fast discontinuous Galerkin finite element methods to solve a space‐time fractional diffusion‐wave equation. We introduce a piecewise‐constant discontinuous finite element method for solving this problem and derive optimal error estimates. Importantly, a fast solution technique to accelerate Toeplitz matrix‐vector multiplications which arise from discontinuous Galerkin finite element discretization is developed. This fast solution technique is based on fast Fourier transform and it depends on the special structure of coefficient matrices. In each temporal step, it helps to reduce the computational work from required by the traditional methods to log , where is the size of the coefficient matrices (number of spatial grid points). Moreover, the applicability and accuracy of the method are verified by numerical experiments including both continuous and discontinuous examples to support our theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2043–2061, 2017     

不同权的Bloch型空间之间的加权复合算子再刻画

本文研究了单位圆中从空间β_L到β_α的加权复合算子uC_φ为有界算子和紧算子的条件.利用阶估计等方法,获得了有界性和紧性的简捷充要条件,推广了叶善力的相应结果.     

SL(n+1,R)/S(GL(1,R)×GL(n,R))上线丛的一个超几何方程

本文研究了伪黎曼对称空间SL（n+1,R）/S（GL（1,R）×GL（n,R））线丛上的微分方程.利用李代数方法,即Casimir算子得到这个微分算子.这个微分算子是一个超几何方程,这个结论推广了文献[1,3,5]中的微分方程.     

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

nAbstract Let p 0 and μ be a normal function on [0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ [0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1.