相空间中单面非Chataev型非完整系统的Lie对称性与守恒量

研究相空间中单面非Ｃｈｅｔａｅｖ型非完整系统的Ｌｉｅ对称性与守恒量．首先根据微分方程在无限小变换下的不变性建立Ｌｉｅ对称性所满足的确定方程和限制方程,给出结构方程和守恒量;其次讨论系统的Ｌｉｅ对称性逆问题;最后举一实例说明结果的应用．     

Lie Symmetrical Non-Noether Conserved Quantities of Poincarè-Chetaev Equations

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincarè-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.     

Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage

Based on the first linearized Boussinesq equation,the analytical solution of the transient groundwater model,which is used for describing phreatic flow in a semi- infinite aquifer bounded by a linear stream and subjected to time-dependent vertical seepage,is derived out by Laplace transform and the convolution integral.According to the mathematical characteristics of the solution,different methods for estimating aquifer parameters are constructed to satisfy different hydrological conditions.Then,the equation for estimating water exchange between stream and aquifer is proposed,and a recursion equation or estimating the intensity of phreatic evaporation is also proposed.A phreatic aquifer stream system located in Hualbei Plain,Anhui Province,China,is taken as an example to demonstrate the estimation process of the methods stated herein.     

A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied. The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.     

Symmetry and Hojman Conserved Quantity of Tzénoff Equations for Unilateral Holonomic System

Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformations of groups is investigated. Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoff equations are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetry in the condition of special Mei symmetry respectively is obtained.     

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.     

A new type of conserved quantity of Mei symmetry for Lagrange system

This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.     

Unified symmetry of the nonholonomic system of non-Chetaev type with unilateral constraints in event space

This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equations of motion of the system. Secondly, it obtains the definition and the criterion of the unified symmetry for the system. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints. Finally, an example is given to illustrate the application of the results.     

同位素稀释高分辨气相色谱-高分辨质谱法测定土壤样品中二恶英类化合物的等价毒性当量不确定度的评定

采用同位素稀释高分辨气相色谱-高分辨质谱法（isotope dilution high resolution gas chromatography and high resolution mass spectrometry,ID-HRGC-HRMS）测定土壤样品中二恶英类化合物（polychlorinated dibenzo-p-dioxins and dibenzofurans,PCDD/Fs）的等价毒性当量（toxic equivalent quantity,TEQ）。讨论并确定了测定土壤样品中二恶英类化合物2,3,7,8位异构体不确定度的来源并合成了各异构体的相对标准不确定度;在此基础上,计算了3种等价毒性当量因子（toxic equivalent factor,TEF）框架下土壤样品中PCDD/Fs的TEQ浓度及其合成不确定度和扩展不确定度。     

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.