A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

Fe2O3-catalyzed Pummerer rearrangement of acyl chlorides and sulfoxides: Facile synthesis of alkylthiomethyl ester

A simple, effective approach for the Pummerer rearrangement of acyl chlorides with sulfoxides by using a low-cost and more abundant Fe catalyst has been described. The alkylthiomethyl ester products were prepared in good to excellent yields for a range of different substrates including asymmetrical sulfoxides and acyl chlorides with a variety of functional groups under mild reaction conditions. The reaction features short reaction time, simple manipulation, cheap reagents and a broad substrate scope. Single crystal X-ray analysis of a representative methylthiomethyl (MTM) group containing product was also reported.     

一类SEI传染病扩散模型及其移动边沿

该文研究一类SEI传染病模型,其中病毒在潜伏期和感染期具有感染性.首先研究固定区域上SEI偏微分方程组,考虑平衡解的局部稳定性和全局稳定性.然后重点研究相应的自由边界问题,其中自由边界表示病毒的移动边沿。给出了该问题解的全局存在性、唯一性,讨论了自由边界的性质,证明了病毒要么蔓延,要么消退.还给出了蔓延和消退的充分条件,结果表明:当有效接触率很小或平均潜伏期较短,且初始染病区域小时,疾病消退;而当有效接触率大或平均潜伏期较长,且初始染病区域大时,疾病蔓延.     

Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.     

Synthesis and Application of N-Tosyl Piperidinyl-Containing α-Aminophosphonates

Abstract

A series of novel (4′-tosyl) piperidin-4-yl containing α-aminophosphonates were synthesized by a one-pot reaction, efficiently catalyzed by magnesium perchlorate, under solvent-free conditions from 1-tosylpiperidin-4-one, substituted aromatic amines, and diethyl phosphite (DEP). The synthesized compounds were characterized by IR, ¹H NMR, ¹³C NMR, ³¹P NMR, and HRMS spectroscopy. A single-crystal X-ray structure of diethyl 4-(2-chlorophenyl) amino-1-(4’-methylbezenesulfonyl) piperidin-4-yl-phosphonate (2a) was obtained, and some of the title compounds displayed insecticidal activities against Plutella xylostella.

Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional figures and tables.