Area spectrum of the three-dimensional Godel black hole

<正>The aim of this paper is to investigate the area spectrum of the three-dimensional Godel black hole by using two different methods.The result shows that the area spectrum of the black hole is△A = 8πl_p~2,which confirms the initial proposal of Bekenstein that the area spectrum is independent of black hole parameters and the spacing is 8πl_p~2.     

Two New Types of Conserved Quantities Deduced from Noether Symmetry for Nonholonomic Mechanical System

For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.     

Mei Symmetry and Mei Conserved Quantity for a Non-holonomic Systemof Non-Chetaev's Type with Unilateral Constraints in Nielsen Style

Mei symmetry and Mei conserved quantity for a non-holonomic system of non-Chetaev's type with unilateral constraints in the Nielsen style are studied. The differential equations of motion for the system above are established. The definition and the criteria of Mei symmetry, conditions, and expressions of Mei conserved quantity deduced directly from the Mei symmetry are given. An example is given to illustrate the application of the results.     

New Conserved Quantities of Noether--Mei Symmetry for Nonholonomic Mechanical System

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanical system are studied. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained.     

A new type of conserved quantity of Lie symmetry for the Lagrange system

This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an example is given to illustrate the application of the result.     

Weak Noether symmetry for a nonholonomic controllable mechanical system

This paper discusses the weak Noether symmetry for a nonholonomic controllable mechanical system of Chetaev type, and presents expressions of three kinds of conserved quantities obtained by using weak Noether symmetry. Finally, the application of these new results is illustrated by an example.     

EFFECTS OF CONSTRAINTS ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF A BIRKHOFF SYSTEM

After a Birkhoff system is restricted by constraints, the determining equations, the Lie symmetries, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some Lie symmetries will disappear and under certain conditions some Lie symmetries will still remain present. The condition under which Lie symmetries and conserved quantities of the system will remain is given.     

新的耦合mKdV方程族及其Liouville可积的无限维Hamilton结构

根据第Ⅱ屠格式,从一个特征值问题出发,本文推得了一族新的耦合ｍＫｄＶ方程,然后用迹恒等式人出了其无限维Ｈａｍｉｌｔｏｎ结构。最后证明了该Ｈａｍｉｌｔｏｎ方程族是Ｌｉｏｕｖｉｌｌｅ可积的,并且有无穷多个彼此对合的公共守恒密度。     

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained. An example is given to illustrate the application of the results.