Fundamental solution of rotating generalized stokes problem in ℝ<Superscript>3</Superscript>

In this paper,the fundamental solution of rotating generalized Stokes problem in R 3 is established.To obtain it,some fundamental solutions of other problems also are established,such as generalized Laplace problem,generalized Stokes problem and rotating Stokes problem.     

一个新的带参数的Hilbert型积分不等式

本文研究Hilbert积分不等式的推广问题.利用引入参数和对数积分核函数,建立了一种新的Hilbert型积分不等式,证明了用Euler数和π来表示的常数因子是最佳的,推广了经典的Hilbert积分不等式.     

Run up flow of an incompressible micropolar fluid between parallel plates – A state space approach

In this paper, we study the run up flow of an incompressible micropolar fluid between two horizontal infinitely long parallel plates. Initially a flow of the fluid is induced by a constant pressure gradient until steady state is reached. After the steady state is reached, the pressure gradient is suddenly withdrawn while the two plates are impulsively started with different velocities in their own plane. Using the Laplace transform technique and adopting the state space approach, we obtain the velocity and microrotation components in Laplace transform domain. A standard numerical inversion procedure is used to find the velocity and microrotation in space-time domain for various values of time, distance, material parameters and pressure gradient. The variation of velocity and microrotation components is studied and the results are illustrated through graphs. It is observed that the micropolarity parameter has a decreasing effect on velocity component. It is also found that as the gyration parameter increases there is a decrease in microrotation component and an increase in velocity component.     

On the expected discounted penalty function for the compound Poisson risk model with delayed claims

In this paper, we consider an extension to the compound Poisson risk model for which the occurrence of the claim may be delayed. Two kinds of dependent claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed with a certain probability. Both the expected discounted penalty functions with zero initial surplus and the Laplace transforms of the expected discounted penalty functions are obtained from an integro-differential equations system. We prove that the expected discounted penalty function satisfies a defective renewal equation. An exact representation for the solution of this equation is derived through an associated compound geometric distribution, and an analytic expression for this quantity is given for when the claim amounts from both classes are exponentially distributed. Moreover, the closed form expressions for the ruin probability and the distribution function of the surplus before ruin are obtained. We prove that the ruin probability for this risk model decreases as the probability of the delay of by-claims increases. Finally, numerical results are also provided to illustrate the applicability of our main result and the impact of the delay of by-claims on the expected discounted penalty functions.     

Extraction of cobalt(Ⅱ) from aqueous solution by N,N'-carbonyl difatty amides

The development of economic and environmentally friendly extractants to recover cobalt metal is required due to the increasing demand for this metal.In this study,solvent extraction of Co(Ⅱ) from aqueous solution using a mixture of N,N’-carbonyl difatty amides(CDFAs) synthesised from palm oil as the extractant was carried out.The effects of various parameters such as acid,contact time,extractant concentration,metal ion concentration and stripping agent and the separation of Co(Ⅱ) from other metal ions such as Fe(Ⅱ),Ni(Ⅱ),Zn(Ⅲ) and Cd(Ⅱ) were investigated.It was found that the extraction of Co(Ⅱ) into the organic phase involved the formation of 1:1 complexes.Co(Ⅱ) was successfully separated from commonly associated metal ions such as Fe(Ⅱ),Ni(Ⅱ),Zn(Ⅲ) and Cd(Ⅱ).Co(Ⅱ) stripping from the loaded organic phase was studied in aqueous solution.These results are useful to recover Co(Ⅱ) from aqueous solution utilising(CDFAs) as an extractant.     

加权Orlicz-Lorentz鞅空间的原子分解及其应用

本文研究加权Orlicz-Lorentz鞅空间的原子分解理论.利用原子分解方法,获得了加权Orlicz-Lorentz鞅空间的内插理论以及鞅变换算子的有界性证明.上述结果推广了Orlicz和Lorentz鞅空间理论相关结果.     

An efficient regioselective sonochemical synthesis of novel 4-aryl-3-methyl-4,5-dihydro-1H-pyrazolo[3,4-b]pyridin-6(7H)-ones

An efficient ultrasound-assisted preparation of a series of novel 4-aryl-3-methyl-4,5-dihydro-l//-pyrazolo[34-b]pyridin-6(7H)ones via the reaction of 5-amino-3-methyl-1H-pyrazole,Meldrum’s acid and various arylaldehydes using one-pot three-component approach is described.This rapid method produced the products in short reaction times(3-4 min) and excellent yields(87-95%).     

1,3,5-三[(4’-乙炔基苯基)乙炔基]苯的合成

设计了多种合成路线制备芳香炔基树枝状化合物中间体1,3,5-三[(4’-乙炔基苯基)乙炔基]苯,通过一系列的合成路线和反应条件的对比,发现多官能团的端基炔化合物与芳基溴化合物之间发生多重Sonogashira反应时,常会生成不同取代程度的极性相似化合物,因而难以分离.采用多官能团的端基炔化合物与芳基碘化合物反应可以避免这种情况.最终确定以1,3,5-三溴苯和2-甲基-3-丁炔-2-醇为原料,制得中间产物1,3,5-三乙炔基苯;再以对碘苯胺和三甲基硅乙炔为原料,经重氮化化、卤代反应制得4-三甲基硅乙炔基碘苯;后者与1,3,5-三乙炔苯经Sonogashira反应、裂解去保护反应,制得化合物1,3,5-三[(4’-乙炔基苯基)乙炔基]苯.用1H NMR,13C NMR,元素分析等表征手段确认了中间体及最终产物的结构.     

Synthesis of 3,4,5-trisubstituted piperidine via SN2’ reaction

Abstract

3,4,5-Trisubstituted piperidine-containing compounds displayed a range of biological activities, are potential drug candidates to treatment of Alzheimer’s disease, sexual dysfunctions or obesity, heart and kidney insufficiency. However, the inherent difficulty in obtaining a variety of 3,4,5-trisubstituted piperidines has greatly hindered their systematic medicinal chemistry studies for them. In this paper, we disclose an efficient synthesis of racemic and chiral 3,4,5-trisubstituted piperidines via S_N2’ reaction.