La(OTf)3 catalyzed synthesis of α-aryl tetrasubstituted pyrroles through [4+1] annulation under microwave irradiation

A La(OTf)₃ catalyzed synthesis of tetrasubstituted pyrroles under microwave irradiation has been developed affording various α-aryl tetrasubstituted pyrroles in acceptable to good yields (36–82% yield) through condensation/alkyne azacyclization/isomerization sequence. Functionalized α-aryl pentasubstituted pyrroles could be prepared from tetrasubstituted pyrroles through easy transformations.     

Ground state solutions and geometrically distinct solutions for generalized quasilinear Schrödinger equation

In this paper, we study the following generalized quasilinear Schrödinger equation where N≥3, is a C¹ even function, g(0) = 1 and g^′(s) > 0 for all s > 0. Under some suitable conditions, we prove that the equation has a ground state solution and infinitely many pairs ±u of geometrically distinct solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR GENERALIZED DRINFELD-SOKOLOV EQUATIONS

Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.     

喹唑啉类衍生物的合成及其抗肿瘤活性

以异香草醛为原料,设计并合成了8个喹唑啉类衍生物(8a～8h),其结构经1H NMR,13C NMR和MS确证。初步抗肿瘤活性测试结果表明,8a～8h对人乳腺癌细胞Bcap-37具有一定程度的体外活性抑制作用。     

K3PO4 promoted dipolar [3+3] cyclization: Direct synthesis of pyrazino[2,1-a]isoquinoline derivatives

A K₃PO₄ promoted dipolar [3+3] cyclization of dihydroisoquinoline imines and arylacyl bromides has been developed. This process realized the direct synthesis of pyrazino[2,1-a]isoquinoline derivatives in 44–69% yields. A head to tail dimerization was proposed as key step for this procedure.     

Multi-objective optimal design of feedback controls for dynamical systems with hybrid simple cell mapping algorithm

This paper presents a study of multi-objective optimal design of full state feedback controls. The goal of the design is to minimize several conflicting performance objective functions at the same time. The simple cell mapping method with a hybrid algorithm is used to find the multi-objective optimal design solutions. The multi-objective optimal design comes in a set of gains representing various compromises of the control system. Examples of regulation and tracking controls are presented to validate the control design.     

A study of stepped acoustic resonator with transfer matrix method

Transfer matrix method was applied in the study of stepped acoustic resonators. Transfer matrix method was more competent in comparison with analytic method to investigate the acoustic properties of stepped acoustic resonator, especially multi-step acoustic resonator. With the help of the numerical solution, the resonance frequencies, the phase angles and the radiation impedances of stepped acoustic resonators which consisted of one to five sub-tubes were studied theoretically and experimentally. The numerical solutions were in excellent agreement with the experimental results.     

关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

利用(G'/G)-展开法求广义的(2+1)维ZK-MEW方程的新精确解

结合齐次平衡法原理并利用(G'/G)-展开法,研究了广义的(2+1)维ZK-MEW方程的精确解,从而得到了广义的(2+1)维ZK-MEW方程的用双曲函数和三角函数表示的通解,当双曲函数通解中常数取特殊值时,便得到广义的(2+1)维ZK-MEW方程的孤立波解,获得了与现有文献不同的新精确解.