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.     

Influence of quantum degeneracy on the performance of a gas Stirling engine cycle

Based on the state equation of an ideal quantum gas, the regenerative loss of a Stirling engine cycle working with an ideal quantum gas is calculated. Thermal efficiency of the cycle is derived. Furthermore, under the condition of quantum degeneracy, several special thermal efficiencies are discussed. Ratios of thermal efficiencies versus the temperature ratio and volume ratio of the cycle are made. It is found that the thermal efficiency of the cycle not only depends on high and low temperatures but also on maximum and minimum volumes. In a classical gas state the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal quantum gas state the thermal efficiency of the cycle is smaller than that of the Carnot cycle. This will be significant for deeper understanding of the gas Stirling engine cycle.     

Evolution of Bond-Order-Wave Phase in One-Dimensional Mott Insulators

In this paper, by using the level spectroscopy method and bosonization theory, we discuss the evolution of the bond-order-wave （BOW） phase in a one-dimensional half-filled extended Hubbard model wlth the on-site Coulomb repulsion U as well as the inter-site Coulomb repulsion V and antiferromagnetic exchange J. After clarifying the generic phase diagrams in three limiting cases with one of the parameters being fixed at zero individually, we find that the BOW phase in the U-V phase diagram is initially enlarged as J increases from zero but is eventually suppressed as J increases further in the strong-coupling regime. A three-dimensional phase diagram is suggested where the BOW phase exists in an extended region separated from the spin-density-wave and charge-density-wave phases.     

Perturbation to Lie Symmetry and Hojman Exact and Adiabatic Invariants of Generalized Raitzin Canonical Equation of Motion

In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.     

Two Types of New Conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space

In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the results.     

Mei Symmetry and Noether Symmetry of the Relativistic Variable Mass System

The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained. An example is given to illustrate the application of the result.     

Study of the Lie symmetries of a relativistic variable mass system

The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result.     

低维量子磁性和量子海森伯反铁磁体之有效场论

文章对低维量子磁性的基本问题和相关研究进展作了简单评述，强调了量子非线性Sigma模型在研究量子海森伯反铁磁体的低能物理方面所起的作用以及理论本身存在的疑难问题，并简单介绍了作者最近提出的克服这些疑难问题的一个新建议．     

Determination of six aromatic compounds by using target factor analysis-UV spectrometry

The UV-spectra solutions containing mixtures of 1-naphthylamine(NAA), 1-naphthol(NAP), 2,7-dihydroxynaphthalene(DHN), 2,4-dimethoxybenzaldehyde(DMO), methyl salicylate(MSA) and dibutyl phthalate (DBP), have been measured. The numbers, identities and concentrations of the aromatic compounds in the mixtures have been determined successfully using Target Factor Analysis. Some sample mixtures have been analyzed successfully. The average recoveries are 99% for NAP, 102% for NAA, 102% for DHN, 103% for DMO, 102% for MSA, 101% for DBP.     

红外光谱数据的小波压缩和重建

介绍了小波变换及多分辨分析理论，并利用Ｄａｕｂｅｃｈｉｅｓ的正交紧支集小波基和Ｍａｌｌａｔ算法实现了对红外光谱数据的压缩和重建。计算表明，即使对原始数据压缩５倍，仍能很好地重建原有图谱，重建光谱数据与原始光谱数据之间的均方差为０．２６０。这为光谱数据的存储、检索和处理带来了方便。