Homogeneous lagrangian systems

The relationship between parameter-independent and parameter-dependent variational problems, and hence between homogeneous and inhomogeneous Lagrangian systems, may be used to explain some aspects of the Cartan form in field theory.     

矩形域上分形插值研究

该文给出了矩形域上分形插值数学模型, 分形插值曲面的计算公式, 证明了分形插值曲面迭代函数系唯一性定理, 导出了分形插值曲面的维数定理,并应用实际数据进行了分形插值曲面的实例研究. 为工程中长期寻求的粗糙表面模拟提供了理论基础和实用方法.     

Ruin probability for correlated negative risk sums model with Erlang processes

This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.     

鲤鱼尾鳍实时三维姿态测量及运动特性分析

为了实现鱼鳍三维运动特性的精确测量, 研究尾鳍的动态瞬时特性, 定量分析其连续变化过程, 建立了基于栅线投影和高速摄像的测量系统和与之对应的分析方法. 以自主游动的鲤鱼为实验对象, 将一组正弦光栅投射在其尾鳍表面, 产生包含三维信息的光栅条纹并由高速摄像机实时采集尾鳍摆动过程的序列图像; 对其中的每一帧图像作二维傅里叶变换、频谱滤波、逆傅里叶变换及三维位相展开等处理后, 重建尾鳍的瞬时三维形态, 再现尾鳍的连续运动过程; 据此测量结果分析研究尾鳍的运动特征及运动学参数. 结果表明, 鲤鱼游速为0.5L/s时, 尾鳍的摆动频率为1.42Hz; 鲤鱼巡游过程中尾鳍的主要运动为侧向摆动, 尾鳍的形状周期性地循环外展和内收, 且尾鳍上叶叶尖的平均摆幅比尾鳍下叶叶尖的平均摆幅约大15.6%.      

Methods of reduction for Lagrange systems on time scales with nabla derivatives

The Routh and Whittaker methods of reduction for Lagrange system on time scales with nabla derivatives are studied.The equations of motion for Lagrange system on time scales are established, and their cyclic integrals and generalized energy integrals are given. The Routh functions and Whittaker functions of Lagrange system are constructed, and the order of differential equations of motion for the system are reduced by using the cyclic integrals or the generalized energy integrals with nabla derivatives. The results show that the reduced Routh equations and Whittaker equations hold the form of Lagrnage equations with nabla derivatives. Finally, two examples are given to illustrate the application of the results.     

基质固相分散-反相液相色谱法测定蔬菜中二甲戊乐灵农药残留

应用基质固相分散-反相液相色谱技术建立了提取、检测蔬菜中二甲戊乐灵农药残留的分析方法。研究了提取及测定条件对检测二甲戊乐灵的影响,确定了最佳提取条件:萃取吸附剂为弗罗里硅土,样品与弗罗里硅土吸附剂的比例为1∶4,洗脱剂为20 mL乙酸乙酯。二甲戊乐灵的测定线性范围为0.02~2.0 mg/L、r0.999。应用此方法测定了某些蔬菜样品中二甲戊乐灵农药残留,测定相对标准偏差为2.2%~5.2%。在几种蔬菜中的加标回收率为85%~93%,当样品为0.5 g时,方法检出限在5.5~10 ng范围内。     

常数分红下相依理赔量的Erlang(2)模型

该文考虑了常数障碍分红策略下的Erlang(2)模型,研究了Gerber-Shiu折现罚金函数和期望折现分红,导出了它们所满足的积分微分方程,并分析了它们的解.     

Banach空间中L-Lipschitzian映射对的公共不动点逼近定理

研究Banach空间中L-Lipschitzian映射对的公共不动点逼近问题.设E表示实Banach空间,K是E中的非空闭凸子集,T,S：K→K是L-Lipschitzian映射,{xn].是带平均误差项的迭代序列,我们给出了{xn）强收敛于T和S的一个公共不动点的充分必要条件,这一结果推广了Banach空间不动点逼近定理.     

Conservation laws of nonconservative nonholonomic system based on Herglotz variational problem

The generalized variational principle of Herglotz type provides a variational method for describing nonconservative or dissipative processes. The purpose of this letter is to extend this variational principle to a first order linear nonholonomic system and study the conservation laws of the nonconservative nonholonomic system based on Herglotz variational problem. A new differential variational principle of the nonconservative nonholonomic system is proposed, which is based on Herglotz variational problem. And the differential equations of motion of the system are also obtained. Then, according to the condition for the invariance of the differential variational principle, the conservation theorem based on Herglotz variational problem for the nonconservative nonholonomic system are obtained. The theorem contains the conservation theorem of the nonconservative holonomic system as its special case, which can be reduced to the first Noether's theorem based on Herglotz variational problem under proper conditions. The inverse theorem of the conservation theorem is also provided and proved. An example is given to illustrate the application at the end of this letter.     

Nonlinear bandgap properties in a nonlocal piezoelectric phononic crystal nanobeam

Applying nonlocal elasticity theory, von Kármán type nonlinear strain-displacement relation and plane wave expansion (PWE) method to Euler-Bernoulli beam, the calculation method of band structure of a nonlinear nonlocal piezoelectric phononic crystal (PC) nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, band gaps of first four orders are picked, and the corresponding influence rules of electro-mechanical coupling fields, nonlocal effect and geometric parameters on band gaps are studied. During the researches, external electrical voltage and axial force are chosen as the influencing parameters related to electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to nonlocal effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the influence rules are compared to those in linear nanobeam. The results are expected to be of help for the design of micro and nano devices based on piezoelectric periodic nanobeam.