变质量完整力学系统的Lie对称与守恒量

研究变质量完整系统的Lie对称和守恒量。利用常微分方程在无限小变换下的不变性建立系统Lie对称的确定方程。给出结构方程和守恒量。举例说明结果的应用。     

Lie symmetries and conserved quantities of holonomic variable mass systems

In this paper, the Lie symmetries and the conserved quantities of the holonomic variable mass systems are studied. By using the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations and the conserved quantities are given. And an example is given to illustrate the application of the result. Foundation item: the National Natural Science Foundation of China (19572038)     

灰色随机变量的熵和信息量

在定义灰随机变量的基础上,应用熵和信息量理论,研究了灰随机变量熵和随机量,得到若干公式和运算性质,拓展了胡庆贺在文[3]中对灰数信息量给出的定义和运算法则,揭示了灰随机变量两类不肯定性的特征及其相互关系,为进一步了解某些信息不完全事物的未知信息量提供了理论依据。     

Lie Symmetrical Hojman Conserved Quantity of Relativistic Mechanical System

In this paper, we study the Lie symmetrical Hojman conserved quantity of a relativistic mechanical system under general infinitesimal transformations of groups in which the time parameter is variable. The determining equation of Lie symmetry of the system is established. The theorem of the Lie symmetrical Hojman conserved quantity of the system is presented. The above results are generalization to Hojman's conclusions, in which the time parameter is not variable and the system is non-relativistic. An example is given to illustrate the application of the results in the last.     

相空间中二阶线性非完整系统的形式不变性

研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量的形式，并举例说明结果的应用. 关键词： 相空间 二阶线性非完整系统 形式不变性 守恒量     

Unified symmetry of mechano-electrical systems with nonholonomic constraints

The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results.     

A possible human counterpart of the principle of increasing entropy

It is well-known that the principle of increasing entropy holds for isolated natural systems that contain non-adaptive molecules. Here we present, for the first time, an experimental evidence for a possible human counterpart of the principle in an isolated social system that involves adaptive humans. Our work shows that the human counterpart is valid even though interactions among humans in social systems are distinctly different from those among molecules in natural systems. Thus, it becomes possible to understand social systems from this natural principle, at least to some extent.     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.     

变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量

研究变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量.建立变质量Chetaev型非完整系统的Appell方程和系统的运动微分方程; 给出函数沿系统运动轨道曲线对时间t全导数的表示式,并在群的无限小变换下,给出变质量Chetaev型非完整系统Appell方程Mei对称性的定义和判据;得到用Appell函数表示的Mei对称性的结构方程和Mei守恒量的表达式,并举例说明结果的应用. 关键词： 变质量 非完整系统 Appell方程 Mei守恒量