Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

This study investigates the exact controllability problem for a vibrating non-classical Euler–Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur.     

Variational derivation of improved KP-type of equations

The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.     

Homology of Centralizers

Given a group Π, we study the group homology of centralizers Π _g , g ? Π, and of their central quotients Π _g /〈 g〉. This study is motivated by the structure of the Hochschild and the cyclic homology of group algebras, and is based on Quillen's approach to the cyclic homology of algebras via algebra extensions. A method of computing the de Rham complex of a group algebra by means of a Gruenberg resolution is also developed.     

Exact and explicit solutions of Euler-Painlevé equations through generalized Cole-Hopf transformations

More general Euler-Painlevé equations are exactly linearized using generalized Cole-Hopf transform and are shown to admit exact solutions in terms of Kummer functions. The asymptotic behaviours of Euler-Painlevé equations are also derived.     

Banach空间中无限维线性系统的能控性

研究在非自反状态空间和自反控制空间中无限维线性系统x(t)=Ax(t) Bu(t)的精确能控性和精确零能控性.当A生成C-半群时,得到这个系统关于L~p([O,T],U),1相似文献   

N维最弱受约束电子势模型的精确解

精确地求解了N维最弱受约束电子势模型束缚态的Schrodinger方程,得到了其能级和相对应的归一化径向波函数.在此基础上,运用广义拉盖尔多项式的级数展开得到了N维最弱受约束电子势模型径向矩阵元的通项表达式.