Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

一类广义Liénard系统解的有界性

研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .     

一类具时滞的Liénard型方程的周期解

考虑一类具时滞的 Liénard型方程x+f[x(t) ]x(t) +g[t,x(t-τ(t) ) ]=p(t) =p(t+T) ,利用重合度理论 ,获得了此方程至少存在一个 T周期解的充分条件     

Identification and screening of active components from Ziziphora clinopodioides Lam. in regulating autophagy

This study investigated the flavonoid constituents of a traditional Chinese medical plant Ziziphora clinopodioides Lam. by using ultra-performance liquid chromatography coupled with quadruple time-of-flight mass spectrometry and screened the active components in regulating autophagy.Normal rat kidney (NRK) cells transfected with green fluorescent protein- microtubule-associated protein 1 light Chain 3(GFP-LC3) were treated with Z. clinopodioides flavonoids and its chemical compositions. After 4 h of treatment, the auto-phagy spot aggregation in NRK cells was photographed and observed by laser scanning confocal microscopy. The following 10 flavonoid components of Z. clinopodioides were identified: baicalein(1), quercetin(2), hyperoside(3), quercetin3-O-β-d-glucopyranoside(4), apigenin(5), kaempferol(6), chrysin(7), diosimin(8), linarin(9) and rutin(10). Among these flavonoids, chrysin, apigenin and quercetin were identified as the active principles in activating autophagy. This research may provide a reference for further developing and utilizing Z. clinopodioides.     

The Discrete Approximation of Continuous-state Nonlinear Branching Processes in Lévy Random Environments北大核心CSCD

In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

L~p空间中的Fejér和Hermite-Hadamard型不等式

给出了二阶导数属于Lp空间时Fejér和Hermite-Hadamard型不等式的推广,得到两个新结果.     

Enantioselective Aromatic Amination?

The atroposelective formation of C−N bonds has recently emerged within the field of amination reactions. On first sight, it may seem quite surprising that such an ancient class of organic coupling reactions (Gabriel, Ullmann, Goldberg, Buchwald, Hartwig and many others) has so few enantioselective solutions, and this in spite of asymmetric synthesis being now a mature concept and field. Why should enantioselective C−N bond formation be so difficult? This question and some of the first examples that promise an imminent change of paradigm are herein discussed.     

A mild and efficient copper-catalyzed N-arylation of unprotected sulfonimidamides using boronic acids

An efficient and low cost copper catalyzed system for N-arylation of sulfonimidamides has been developed. The reaction proceeds at room temperature under base free conditions. Various N-aryl, N-heteroaryl, and N-cyclopropyl sulfonimidamides were obtained in good to excellent yields.