Lipschitz–Volume rigidity in Alexandrov geometry

We prove a Lipschitz–Volume rigidity theorem in Alexandrov geometry, that is, if a 1-Lipschitz map f:X=?_X?→Y$f:X=?X_{?}\to Y$ between Alexandrov spaces preserves volume, then it is a path isometry and an isometry when restricted to the interior of X. We furthermore characterize the metric structure on Y with respect to X when f is also onto. This implies the converse of Petrunin's Gluing Theorem: if a gluing of two Alexandrov spaces via a bijection between their boundaries produces an Alexandrov space, then the bijection must be an isometry.     

Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion‐driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion‐driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.     

二维柱坐标系辐射输运方程保球对称的离散纵标格式

 离散纵标格式是计算辐射输运方程的常用格式之一. 但是, 传统的离散纵标格式求解二维柱坐标系辐射输运方程模拟一维球对称问题时, 会出现明显的非对称现象, 球对称性被破坏. 针对该问题, 本文分析了传统离散纵标格式不能够保持球对称性的原因, 提出了空间基于柱坐标系、方向基于球坐标系的辐射输运方程, 并对该方程设计了新的离散纵标格式, 从理论上证明了当空间网格取球对称剖分时该离散格式能够保持一维球对称性的充分必要条件. 通过对真空球区域辐射输运、与物质耦合辐射输运等球对称算例的数值模拟, 验证了该格式的保球对称性, 球对称误差能够达到机器精度. 非对称辐射驱动模型以及非对称网格剖分条件下的数值模拟等算例也取得了较好的结果.     

Survey study and experimental investigation on the local behavior of pedestrian groups

Current research on pedestrian dynamics mainly focuses on the interactions among isolated individuals, the impact of the presence of groups is not fully considered. In recent 5 years, researchers have started to investigate pedestrian group movement. The aim of this work is to explore the local behavior of pedestrian groups by questionnaires and field observation. Survey study focused on pedestrians' psychology when walking in groups, which included five parts: group size, interpersonal distance, spatial relationship among group members, speed adjustment of group members, information transmission, and acid action among group members. Meantime a field observation was carried out to study group movement characteristics, which contained speed, step frequency, offset angle and interpersonal distance. The survey results show that group members have a closer interpersonal distance, faster information transmission and plenty of acid action. Conversely, group walking has a negative influence on pedestrian's speed, step frequency by comparing with the way isolated pedestrian walks. In addition, it is found that for a certain group, the group members are able to keep movement consistent. Also there exists obvious movement diversity among different group types (male dyads, female dyads, couple groups, and ordinary‐friend groups) because of different gender and social relationship. Ultimately the results will be more promising for helping to model the movement of pedestrian groups. © 2014 Wiley Periodicals, Inc. Complexity 20: 87–97, 2015     

Transition metal-free synthesis of primary amides from aldehydes and hydroxylamine hydrochloride

Primary aromatic amides can be synthesized from aldehydes and hydroxylamine hydrochloride in the presence of Cs₂CO₃. Various aromatic aldehydes (include some heteroaromatic aldehydes) are able to generate the corresponding aromatic amides in moderate to excellent yields.     

Synthesis of aryloxyazetidine derivatives by CuI/l-proline catalyzed coupling reaction of arylboronic acid with 1-Boc-3-iodoazetidine

A novel CuI/l-proline catalyzed coupling reaction of 1-Boc-3-iodoazetidine with various arylboronic acids which produced aryloxyazetidine derivatives in moderate to good yields was investigated.     

Concise synthesis of aromatic tertiary amines via a double Petasis–borono Mannich reaction of aromatic amines,formaldehyde, and organoboronic acids

A simple and efficient strategy to construct aromatic tertiary amines via a double Petasis–borono Mannich reaction of aromatic amines, formaldehyde, and organoboronic acids has been developed. The transformation provides a useful method for the synthesis of amine derivatives.     

Synthesis and application of moisture-stable methallylsilanated phosphorylcholine as a surface modifier

New methallylsilanated phosphorylcholine (MASPCs) were synthesized via a copper-catalyzed ‘click’ reaction and demonstrated excellent moisture stability. Hydroxylated silicon compounds, silanol, and silica were grafted or modified by MASPCs in the presence of triflic acid (TfOH) and they possessed a good grafting efficiency and high loading rate.     

Three New Coordination Compounds with Neodymium Based on Tetrazole Containing Carboxylic Acid Ligands

Reactions of three tetrazole containing carboxylic acid ligands, namely, Hpztza, Htzpya, and Hpytza [Hpztza = 5‐(2‐pyrazinyl)tetrazole‐2‐acetic acid, Htzpya = 3‐(5‐tetrazolyl)pyridine‐1‐acetic acid, Hpytza = 5‐(3‐pyridyl)tetrazole‐2‐acetic acid] with NdCl₃ · 6H₂O under hydrothermal conditions, afforded the complexes [Nd(pztza)₂(H₂O)₆] · pztza · 3H₂O ( 1 ), [Nd₂(tzpya)₂(H₂O)₁₂]Cl₄ · 2H₂O ( 2 ), and [Nd(pytza)₂Cl(H₂O)₂] ( 3 ). The compounds were structurally characterized by elemental analysis, IR spectroscopy and single‐crystal X‐ray diffraction. X‐ray diffraction analyses revealed that compound 1 displays a mononuclear structure, 2 shows a dinuclear structure, and 3 features a 1D polymeric chain structure via pytza as linker. Furthermore, the luminescent properties investigated at room temperature in the solid state show that compound 2 has an obvious decrease in its luminescence, when compared to the ligand.