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     

Analysis of RNA sequence structure maps by exhaustive enumeration I. Neutral networks

Summary Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of allGC andAU sequences with chain lengths up to 30. The computed structural data are evaluated through exhaustive enumeration and used as an exact reference for testing analytical results derived from mathematical models and sampling based on statistical methods. Several new concepts of RNA sequence to secondary structure mappings are investigated, among them that ofneutral networks (being sets of sequences folding into the same structure). Exhaustive enumeration allows to test several previously suggested relations: the number of (minimum free energy) secondary structures as a function of the chain length as well as the frequency distribution of structures at constant chain length (commonly resulting in generalized forms ofZipf's law).

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Analyse der Beziehungen zwischen RNA-Sequenzen und Sekundärstrukturen durch vollständige Faltung, 1. Mitt. Faltung, Neutrale Netzwerke

Zusammenfassung Die globalen Benziehungen zwischen RNA-Sequenzen und Sekundärstrukturen werden als Abbildungen aus einem Raum aller Sequenzen in einen Raum aller Strukturen aufgefaßt. Diese Abbildungen werden durch Falten aller binären Sequenzen desGC-undAU-Alphabets mit Kettenlängen bis zun=30 untersucht. Die berechneten Strukturdaten werden durch vollständiges Abzählen ausgewertet und als eine exakte Referenz zum Überprüfen analytischer Resultate aus mathematischen Modellen sowie zum Testen statistisch erhobener Proben verwendet. Einige neuartige Konzepte zur Beschreibung der Beziehungen zwischen Sequenzen und Strukturen werden eingehend untersucht, unter ihnen der Begriff derneutralen Netzwerke. Ein neutrales Netzwerk besteht aus allen Sequenzen, die eine bestimmte Struktur ausbilden. Vollständiges Abzählen ermöglicht beispielsweise die Bestimmung aller Strukturen minimaler freier Energie in Abhängigkeit von der Kettenlänge ebenso wie die Bestimmung der Häufigkeitsverteilungen der Strukturen bei konstanten Kettenlängen. Die letzteren folgen einer verallgemeinerten FormZipfschen Gesetzes.

     

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.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

IMPACT MODEL RESOLUTION ON PAINLEVE’S PARADOX

Painlevé‘s paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlevé‘s example. The results confirm ““““impact without collision““““ in the inconsistent states of the system. A ““““critical normal force““““ which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical results, a rule of the velocity‘s jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough.     

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.     

运用Poincaré-Miranda定理数值验证变分不等式解的存在性

本文运用Poincaré-Miranda定理数值验证变分不等式问题解的存在性.证明这一新方法相对于已有的方法更具有普遍性,并通过数值例子说明本方法的高效性.