Beurling-Nevanlinna inequality for subfunctions of the stationary Schrödinger operator

The classical Beurling-Nevanlinna upper bound for subharmonic functions is extended to subsolutions of the stationary Schrödinger equation.

     

扭转弯曲定理和它的一个应用

本文对解析映射证明了一个不动点定理(称为扭转弯曲定理),其中弯曲条件取代了经典扭转定理(参考Ding W.Y.,A generalization of the Poincare-Birkhoff theorem,Proc.Amer.Soc.,1983,88:341-346)中的保面积条件;然后用本文的扭转弯曲定理证明了一类耗散的Duffing方程拥有高阶的次调和解.     

Harnack and mean value inequalities on graphs

We prove a Harnack inequality for positive harmonic functions on graphs which is similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean value inequality of nonnegative subharmonic functions on graphs.     

Quasiprobabilities based on squeezed states

We introduce quasiprobabilities based on the so-called squeezed states to represent the density operator of an oscillator. Such representations become especially useful for oscillators designed to display, strong excitation notwithstanding, pronounced quantum features such as squeezing of the quantum fluctuations of certain observables below the limit characteristic of coherent states.     

Cooperative study teams in mathematics classrooms

This article describes a general instructional strategy designed to help students in the learning process from textbooks and to furnish opportunities for practice in critical reading. Students participate in cooperative learning by breaking the class up into small groups—the Study Teams—and providing them with worksheets and reading organizers, which organize the material into small items that reflect the major concepts in the reading material on which the study is focused. Some of the benefits that this type of instruction with Study Teams can produce are described.     

Some Questions of the Nevanlinna Theory for the Complex Half-Plane

In this paper we give variants of the logarithmic derivative lemma and the second main theorem for the complex half-plane. Here the second main theorem is a special case of a theorem concerning polynomial functions of the coordinates of a holomorphic curve f : C ₊ P ⁿ . This theorem is a variant for C ₊ of a theorem of A. Eremenko and M. Sodin, who considered an entire curve f : C ₊ P ⁿ . The proofs are realized because of the introduction of natural classes of subharmonic, -subharmonic, holomorphic, meromorphic functions in C ₊ . Such functions we shall call just functions.     

杜芬方程的1／3纯亚谐解及其过渡过程

通过谐波平衡法和数值积分法研究了杜芬方程的1／3纯亚谐解,对参数变化的过渡过程的敏感性和扰动初始值的过滤进行了研究,同时,还对谐波平衡法和数值积分法的精度进行了比较,也考虑了亚谐波成分的渐近稳定性。     

1/3 subharmonic solution of elliptical sandwich plates

IntroductionInrecentyears,withtheessentialadvantageoflightweightandhighrigidity ,sandwichplatesandshellshavebeenusedasanimportantpatternofstructuralelementsinaeronautical,astronauticalandnavalengineering .However,nonlinearproblemsforsandwichplatesandshellsareonlyinvestigatedbyafewbecauseofthedifficultiesofnonlinearmathematicalproblems.LiuRen_huaiandXuJia_chu[1,2 ]andothershavemadesomeinvestigationsinthisfield .Bifurcationofnonlinearvibrationforsandwichplateshasnotyetbeeninvestigated .Inthisp…     

Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators

Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly nonlinear damped oscillators isinvestigated. Special attention is paid to the excitation of a nonlinearnormal mode while the energy is initially stored in other modes of thesystem. The transition proceeds via the mechanism of subharmonicresonance which is possible because of the strong nonlinearity of thesystem. The conditions of the energy transition to NNM being effectiveare revealed and guidelines to design such a systems are formulatedin detail.     

非线性转子-密封系统1∶2亚谐共振分岔研究

研究了转子-密封系统在气流激振力作用下的低频振动——1∶2亚谐共振现象．利用流体计算动力学（CFD）方法对转子-密封系统进行了流场模拟计算,辨识出适用于气流流场的Muszynska模型参数,并建立了转子-密封系统动力学方程．采用多尺度方法将系统进行3次截断,并得到系统响应．采用奇异性理论研究了系统的1∶2亚谐共振,进一步得到系统亚谐共振的分岔方程和转迁集,根据转迁集给出了在不同奇异性参数空间内的分岔图．同时,由分岔方程得到了亚谐共振非零解存在的条件．其分析结果对抑制转子-密封系统的亚谐振动有重要的工程意义．