Immobilized palladium on surface-modified Fe3O4/SiO2 nanoparticles: as a magnetically separable and stable recyclable high-performance catalyst for Suzuki and Heck cross-coupling reactions

A palladium-based catalyst (Fe₃O₄/SiO₂/HPG–OPPh₂–PNP) supported on chlorodiphenylphosphine-functionalized magnetic nanoparticles was successfully prepared from Fe₃O₄/SiO₂ with sequential attachment of glycerol and chlorodiphenylphosphine, followed by treatment of an ethanolic solution of palladium chloride with hydrazine. The as-prepared catalyst was characterized by ICP-AES, FTIR, XRD, SEM, and TEM. The Fe₃O₄/SiO₂/HPG–OPPh₂–PNP was found as a magnetically separable and highly active catalyst for Suzuki coupling reactions of aryl iodides, bromides, and chlorides as well as Heck reactions of aryl iodides and bromides. Under appropriate conditions, all reactions afforded the desired products in moderate to excellent yields. Moreover, this catalyst can be easily recovered by using a magnetic field and directly reused for at least six cycles without significant loss of its activity.     

REPRESENTATIONS OF THE TWO PARAMETER DEFORMATION OF THE VIRASORO ALGEBRA

This paper constructs a class of Harish-Chandra modules with multiplicity ≤1 of the two parameter deformation of Virasoro algebra and proves a classification theorem.     

Quantum Euler-Poisson System: Local Existence of Solutions

The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects. The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity, where the pressure-density is general (can be non-convex or non-monotone).     

钾原子中多种受激辐射参与的混频过程

当双原子共振激发钾原子于６Ｓ能级时,由光泵受激辐射和电离复合受激辐射参与的六波或四波混频,产生了位于紫外和紫区的诸多相干辐射、文中对多种混频机制进行了分析和讨论,并对所测得的相干辐射线进行了标识．     

有消费或投资的华氏宏观经济模型

本文对华罗庚教授的宏观经济模型进行了推广 ,在原来模型的基础上 ,分别增加了消费、投资 ,得到两种不同的模型 ,并对模型具有经济意义的解进行了研究