Realization of Vertex Operators of 7-Twisted Affine Lie Algebra sl（3,C）[θ]

In this paper, we construct a new algebra structure 7-twisted atone Lie algebra sl（3,C）[θ] and study its vertex operator representations.     

New Exact Solutions of （1 ＋ 1）-Dimensional Coupled Integrable Dispersionless System

This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed.     

铬蓝黑R负载活性炭对Cr（Ⅲ）和Pb（Ⅱ）的吸附性能

研究了新型吸附材料铬蓝黑R（钙试剂）负载改性的活性炭对样品中Cr（Ⅲ）和Pb（Ⅱ）的固相萃取（SPE）并用电感耦合等离子体-原子发射光谱法（ICP-AES）进行检测.优化了pH值、吸附剂用量、流速等条件以达到定量吸附（≥95％）,同时研究了洗脱剂的最佳洗脱条件以及共存离子干扰等问题.本法测定Cr（Ⅲ）和Pb（Ⅱ）的检出限分别为0.91ng·mL-1和0.65ng·mL-1,将其应用于土壤沉积物、猪肝、黄河水中的Cr（Ⅲ）和Pb（Ⅱ）含量的测定,加标回收率在98％-101％之间;用于测定标准物质中Cr（Ⅲ）和Pb（Ⅱ）的含量,结果与标准物参照值一致.     

Some New Exact Solutions to the Dispersive Long－Wave Equation in（2＋1）－Dimensional Spaces

In this paper, by using a further extended tanh method- and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2 l )-dimensional spaces are obtained.     

动力学椭圆代数Aq,p,π（gln^）的Drinfeld流

从推广的Yang-Baxter关系“RLL＝LLR”出发，利用高秩高斯分解，得到了动力学椭圆代数Aq,p,π（gln^)及其对应的Drinfeld流，其中R，R^*是A(1)n-1面模型对应的谱参数有一关于代数中心平移的动力学R矩阵。     

Growth,defects,and properties of GdCa4O（BO3）3 and Nd：GdCa4O（BO3）3 crystals

Pure and neodymium-doped gadolinium calcium oxoborate crystals of high quality were grown by the Czochralski method.The orientation of crystal was precisely determined,and the samples for measurements were prepared.Through synchrotron x-ray topography and high-resolution x-ray diffractometry,the twin structure was discovered.Some properties such as the figure of merit value,and dielectric,piezoelectric,and elastic constants were meausured along with a discussion of the anisotropy of the laser properties.     

Comment on “Computer Algebra and Solutions to the Karamoto-Sivashinsky Equation” [Commun. Theor. Phys. （Beijing, China） 43 （2005） 39]

In a recent article [Commun. Theor. Phys. （Beijing, China） 43 （2005） 39], Xie et al. improved the extended tanh function method by introducing a generalized Riccati equation and its new solutions. Then they choose the Karamoto-Sivashinsky （KS） equation to illustrate their approach and obtain many exact solutions of the KS equation. So they claim that, by using their method, one not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear evolution equations. In this comment, we will show that the claim is incorrect.     

Symbolic Computation and Construction of Soliton－Like Solutions to the（2＋l）－Dimensional Breaking Soliton Equation

Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions.     

Ln7O6（BO3）（PO4）2：Eu（Ln=Al,Gd,Y）的UVU—UV激发和辐射发光

本文报道了Ln7O6(BO3)(PO4)2:Eu(Ln=La,Gd,Y)在UVU－UV区的激发光谱及Eu^3 在可见区的发射光谱,其激发光谱包括基质在真空紫外区的激发带和激活剂离子在紫外区的Eu^3 -O^2-电荷迁移带,随着La^3 ,Gd^3 ,Y^3 离子半径逐渐减小,Eu^3 -O^2-电荷迁移带的重心位置逐渐向高能量方向移动,Gd7O6(BO3)(PO4)2:Eu和Y7O6（BO3）（PO4）2：Eu在真空紫外区的吸收与Eu^3 -O^2-电荷迁移带位于紫外区的吸收的比值要高于在La7O6(BO3)(PO4)2:Eu中的这个比值,激发能可被基质吸收,传递给激活剂离子,得到Eu^3 的红光发射,在Gd7O6(BO3)(PO4)2:Eu中,^5D0→^7F1的发射强度较强,在Y7O6（BO3）（PO4）2：Eu中,^5D0→^7F2和^5D0→^7F3的跃迁较强。     

New expressions for g—factors of the mixed ground state of 3d^9 ions with a compressional tetragonal symmetry and its application to NaCl：Ni^＋（I）

We deduce new expressions for g-factors of the 3d⁹ ions with a compressional tetragonal symmetry, in which we consider not only the contribution from the spin-orbit coupling of the central transition metal ion but also that of the ligand orbits as well as the admixture of ²B_1g into ²A_1g (ground state). By using the new formulae, the electron paramagnetic resonance g-factors for NaCl:Ni⁺(I) are studied. Thus, the puzzle that the g_‖-shift is positive is reasonably explained.     

Spin Number Coherent States and the Problem of Two Coupled Oscillators

From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.     

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

利用SU（2）_（q，s）量子代数的两参数变形振子实现讨论SU（2）_（q，s）相干态

利用ＳＵ（２）ｑ，ｓ量子代数的两参数变形振子实现构造出与Ｐｅｒｅｌｏｍｏｖ相干态形式不同的ＳＵ（２）ｑ，ｓ相干态．证明了ＳＵ（２）ｑ，ｓ，量子代数的表示基是正交的，并讨论了它的相干态的归一性和完备性．指出ＳＵ（２）ｑ，ｓ相干态的相干性受参数ｑ，ｓ的影响，它比单参数变形ＳＵ（２）ｑ相干态更具一般性．     

Algebra Solutions of Antiferromagnet-Antiferromagnet-Ferromagnet Quantum Heisenberg Chains Related to Sp(6,R) Lie Algebra

Antiferromagnet-antiferromagnet-ferromagnet (AF-AF-F) quantum Heisenberg chains in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure, and its algebra solutions related to the Sp(6,R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(6,R)⊃U(1,2).     

Lie Symmetry Analysis,Bäcklund Transformations and Exact Solutions to (2+1)-Dimensional Burgers' Types of Equations

This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations. All of the geometic vector fields of the equations are obtained, an optimal system of the equation is presented. Especially, the Bäcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry. Then, all of the symmetry reductions are provided in terms of the optimal system method, and the exact explicit solutions are investigated by the symmetry reductions and Bäcklund transformations.     

Ca9R(VO4)7 : Eu3+ 发光粉的发光特性

采用高温固相法制备了Eu³⁺离子激活的Ca₉R(VO₄)₇(R = Y, La, Gd)红色发光粉,并利用荧光光谱对发光粉的特性进行研究。激发光谱中,Ca₉Y(VO₄)₇ : Eu³⁺ , Ca₉La(VO₄)₇ : Eu³⁺和Ca₉Gd(VO₄)₇ : Eu³⁺都有两个宽的VO^3-₄激发带和Eu³⁺的特征激发峰。发射光谱中,在Ca₉Y(VO₄)₇ : Eu³⁺ 和Ca₉La(VO₄)₇ : Eu³⁺中的350~550 nm范围内出现VO^3-₄的发射带,而在Ca₉Gd(VO₄)₇ : Eu³⁺中却没有观察到VO^3-₄的发射。在这三种发光粉中,Ca₉Gd(VO₄)₇ : Eu³⁺的发光强度远远高于其它两种,这是由于Gd³⁺的存在有效地使能量通过Gd³⁺ →VO^3-₄ → Eu³⁺及Gd³⁺ → Eu³⁺的两种方式进行能量传递,从而提高了Eu³⁺发光效率。     

Plane Symmetric Solutions in f(R,T) Gravity

The main purpose of this paper is to investigate the exact solutions of plane symmetric spacetime in the context of f(R,T)gravity[Phys.Rev.D 84(2011)024020],where f(R,T)is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T.We explore the exact solutions for two different classes of f(R,T)models.The first class f(R,T)=R+2f(T)yields a solution which corresponds to Taub's metric while the second class f(R,T)=f_1(R)+f_2(T)provides two additional solutions which include the well known anti-deSitter spacetime.The energy densities and corresponding functions for f(R,T)models are evaluated in each case.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU（2） Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation descr/bing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some ttamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

Statistical Physics on the Space (x, v) for Dissipative Systems and Study of an Ensemble of Harmonic Oscillators in a Weak Linear Dissipative Medium

We use the phase space position-velocity (x, v) to deal with the statistical properties of velocity dependent dynamical systems, like dissipative ones. Within this approach, we study the statistical properties of an ensemble of harmonic oscillators in a linear weak dissipative media. Using the Debye model of a crystal, we calculate at first order in the dissipative parameter the entropy, free energy, internal energy, equation of state and specific heat using the classical and quantum approaches. For the classical approach we found that the entropy, the equation of state, and the free energy depend on the dissipative parameter, but the internal energy and specific heat do not depend of it. For the quantum case, we found that all the thermodynamical quantities depend on this parameter. PACS: 05.20.Gg, 05.30.Ch, 05.20.-y, 05.30.-d