New Braid Group Representations of C3(D3) and C4(D4) and Their Correspondent Link Polynomials

The new braid group representations of C₃(D₃) and C₄(D₄) are obtained by solving the defining relations of braid groups directly. And by introducing the appropriate diagonal matrices h, the associated link polynomials are derived also.     

单调二次样条插值及其在状态方程计算中的应用

本文证明了如下结果:设a,b,y_a,y_b,y_a',y_b',均为实数,满足aab;y_a'≥0,y_b'≥0;则当y_a'+y_b'≤4(y_b-y_a)/(b-a)时,满足s(a)=y_a,s(b)=y_b,S'(a)=y_a',S'(b)=y_b'的以a,(a+c)/(2),b为插值节点的单调增加二次样条函数S(x)εC'[a,b]存在且唯一,而且当y_a'+y_b'>4((y_b-y_a)/(b-a))时,满足上述要求的二次插值样条函数不存在。根据这个结果讨论了多节点单调二次插值样条函数的存在性,并且给出了在不同区域间状态方程的能量与压强曲面光滑衔接的一个计算方法。     

Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R₃', R₂', and R₁' lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG:Cr³⁺ as well as thermal shifts of GSZFS, R₁ line and R₂ line of ruby have been calculated. The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R₁ line and R₂ line of ruby, several conclusions have also been obtained.     

Initial Phase Dependence of the Soliton Decay Rate for the Nonlinear Schrodinger Equation with a Lossy Term

By using a recursion relation from the x-discrete nonlinear Schrödinger equation with a "lossy" term, we prove that the solitons propagate along the fiber in the decay rate exp -(I+ M₀)Γx if the "initial" input phase (at x = 0) is taken as the form M_oΓt²/2α_l. The same conclusions can also be obtained from the exact numerical calculations.     

Topology change and θ-vacua in 2D Yang-Mills theory

We discuss the existence of θ-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IUR's) of π₁(G) if M is orientable, and with the IUR's of π₁(G)/2π₁(G) if M is non-orientable.     

Effective AC and DC Responses of Nonlinear Composites at Higher Concentration

For higher concentration of inclusions, an effective medium approximation （EMA） method is used to investigate the bulk effective response of weakly nonlinear composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE ＋Xα｜E｜^2 E. As an example of three dimensions, under the external AC and DC electric fields Eapp = Eα（1 ＋ sinωt）, we have derived the general effective nonh＇near response of composites by the EMA method for higher concentration of spherical inclusions. Furthermore, the effective nonlinear responses at harmonics are predicted.     

Hyperfine Constants for Low-Lying States in ^137Ba^＋

Relativistic many-body perturbation calculation is applied to calculate the hyperfine constants for the lowlying states 6S1/2, 6P1/2, 6P3/2, 5D3/2, and 5D5/2 in the alkaline earth ion ^137Ba^＋. The zeroth-order hyperfine constants are calculated with Dirac-Fock wave functions, and the finite basis sets of the Dirac-Fock equation are constructed by B splines. With the finite basis sets, the core polarization and the correlation effect are calculated. The final results for magnetic dipole hyperfine a constants are obtained.     

采用高信噪比电磁诱导透明谱测定~(85)Rb原子5D_(5/2)态的超精细相互作用常数

基于~(85)Rb原子5S1/2-5P3/2-5D_(5/2)阶梯型能级系统(780 nm+776 nm),利用高信噪比的电磁诱导透明谱对~(85)Rb原子5D_(5/2)态超精细分裂进行测量.其中,频率校准是通过位相型电光调制器和共焦法布里-珀罗腔共同实现的.通过测量~(85)Rb原子5D′5/2态(F′=5),(F′′=4)及(F′′=3)之间的超精细分裂,我们确定了~(85)Rb原子5D_(5/2)态的磁偶极超精细相互作用常数(A=-(2.222±0.019)MHz)和电四极超精细相互作用常数(B=(2.664±0.130)MHz).     

Boson Representations of Subalgebra Chain for Quantum Algebra (Cl)q with q a Root of Unity

The method of q-deformed boson realization is extended to the caee that q is a root of unity. By using thb method, many irreducible and indecomposable representations of each su balgebra in a su balgebra chain of the quantum universal enveloping algebra (quan tum algebra) (C_l)_q are obtained on the q-deformed Fock space and its quotient space. AB an example, the representations of (C₃)_q are constructed in explicit forms. Besides, by embedding (A₁)_q = (C_l)_q, into the subalgebra chain, a new realisation of (A₁)_q and its representations are obtained.     

K,Na掺杂Cu-S纳米晶的水热合成及对结构、性能的影响

利用水热合成技术, 分别以CuCl₂·2H₂O, 硫粉为铜源和硫源, 以KOH或NaOH为矿化剂, 成功合成了Cu₂S纳米晶体和碱金属离子掺杂的KCu₇S₄纳米线和NaCu₅S₃ 微纳米球. 通过X射线衍射(XRD)、电子能谱(EDS)、扫描电镜(SEM)、透射电镜(TEM)和高分辨率透射电镜 (HRTEM) 对产物的结构和形貌进行了表征和分析. 结果显示: KOH含量低于1g或NaOH低于2g时, 产物为斜方辉铜矿Cu₂S; 高碱含量 (不低于3g) 时, K或Na离子成功掺入产物结构中, K掺杂产物为纯净的四方相KCu₇S₄, 单晶结构, 尺寸均匀, 长度可达几十微米的纳米线; Na掺杂未改变产物的形貌, 形成六方晶系结构的NaCu₅S₃. 产物的形成和生长与反应温度、反应时间和矿化剂密切相关. 并讨论了Cu₂S纳米晶及其掺杂纳米晶的形成机理及掺杂机理. 最后研究了碱金属离子掺杂对产物的光学性能的影响, 漫反射光谱显示Cu₂S, KCu₇S₄和NaCu₅S₃纳米晶的光学带隙分别为1.21eV, 0.49eV和0.42eV, K⁺和Na⁺的掺杂, 极大的改变了产物的光学特性. 关键词： 7S₄')" href="#">KCu₇S₄ 5S₃')" href="#">NaCu₅S₃ 水热法 掺杂     

Sieving of H2 and D2 Through End-to-End Nanotubes

We study the quantum molecular sieving of H₂ and D₂ through two nanotubes placed end-to-end. An analytic treatment, assuming that the particles have classical motion along the axis of the nanotube and are confined in a potential well in the radial direction, is considered. Using this idealistic model, and under certain conditions, it is found that this device can act as a complete sieve, allowing chemically pure deuterium to be isolated from an isotope mixture. We also consider a more realistic model of two carbon nanotubes and carry out molecular dynamics simulations using a Feynman-Hibbs potential to model the quantum effects on the dynamics of H₂ and D₂. Sieving is also observed in this case, but is caused by a different process.     

Semileptonic Decays of Bc Meson to a P—Wave Charmonium State χc or hc

The semileptonic decays of meson Bc to a P-wave charmonium state χc(3PJ) or hc(1P1)are computed.The results show that the decays are sizable so they are accessible in Tevatron and LHC,especially,with the detectors LHCB and BTeV in the foreseeable future,and of them,the one to the 1P1 charmonium state potentially offers us a novel window to see the unconfirmed hc particle.In addition,it is pointed out that since the two charmonium radiative decays χc (3P1,2)→J/ψ γ have sizable branching ratios,the cascade decays of the concerned decays and the charmonium radiative decays may affect the result of observing Bc meson through the semileptonic decays Bc→J/ψ l vl substantially.     

Spinor Representations of and Quantum Boson-Fermion Correspondence

This is an extension of quantum spinor construction in [DF2]. We define quantum affine Clifford algebras based on the tensor product of a finite dimensional representation and an infinite highest weight representation of and the solutions of q-KZ equations, construct quantum spinor representations of and explain classical and quantum boson-fermion correspondence. Received: 22 November 1995 / Accepted: 21 July 1998     

Ar-H2(D2, T2)碰撞体系的振转相互作用势及散射截面的理论计算

用量子力学从头算的耦合族CCSD(T)方法, 使用相关一致基组aug-cc-pV5Z并加3s3p2d1f1g高斯键函数计算了Ar原子与H₂分子的振转相互作用和电荷分布, 采用Boys和Bernardi提出的均衡法消除了基组重叠误差(BSSE). 然后用Tang-Toennies势能函数拟合得到Ar-H₂体系相互作用势的解析表达式. 在该相互作用势下, 用密耦方法计算了Ar原子入射能量为83 meV时, Ar-H₂(D₂, T₂)碰撞体系的散射截面. 计算Ar-D₂体系的微分截面与实验值比较符合很好. 计算结果及分析表明, 在长程吸引势的散射中, 色散能起主要作用; 在短程排斥势的散射中, 交换能起重要作用. 当碰撞参数在0.27 nm至0.47 nm的范围时, Ar-H₂(D₂, T₂)碰撞体系的径向偶极发生两次转向.     

On the string interpretation of M(atrix) theory

It has been proposed recently that, in the framework of M(atrix) theory, = 8 supersymmetric U(N) Yang-Mills theory in 1 + 1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM_{1 + 1} gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2,Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.     

失碳倍半萜内酯晶体结构测定

失碳倍半萜内酯的分子式为C₁₄H₂₀O₃,属正交晶系,空间群为D₂⁴-P2₁ 2₁ 2₁。晶胞参数为α=7.526(3)?,b=24.642(10)?,c=6.887(2)?。晶胞内分子数z=4,计算密度D_x=1.23(g·cm^-3。用RASA-IIS四圆衍射仪收集衍射强度数据。用直接法(MULTAN-80)测定晶体结构时曾遭遇失败,改善了起始套衍射点的指标分布后,才获得正确结构解。用准对角矩阵最小二乘法修正了结构参数,对全部独立可观察点,R=0.059。由差值Fouruer综合获得了全部氢原子坐标。最后就原起始套失败的原因和新选起始套的依据作了必要的分析。 关键词：     

铯原子里德伯态精细结构测量

里德伯态光谱是测量里德伯态能级结构和中性原子间相互作用的常用技术手段,特别是高精度的里德伯光谱,可以测量室温原子气室中由偶极相互作用等导致的原子能级频移.在实验中利用反向的852 nm激光和509 nm激光实现了室温原子气室中铯原子6S_(1/2)—6P_(3/2)—57S(D)跃迁的级联双光子激发,实现了里德伯态原子的制备.基于阶梯型电磁诱导透明获得了铯原子里德伯态的高分辨光谱.实验中,基于速度选择的射频边带调制技术,对光谱信号进行了频率标定,测量了铯原子里德伯态57D_(3/2)和57D_(5/2)的精细分裂,分裂间隔为(354.7±2.5)MHz,与理论计算结果基本一致.速度选择的射频调制光谱可以实现里德伯态原子的能级分裂测量,其测量精度对于单光子跃迁的绝对激光频率不敏感;实验中影响57D_(3/2)和57D_(5/2)精细分裂间隔测量精度的主要因素是功率加宽导致的电磁感应透明信号的展宽和509 nm激光频率扫描的非线性.     

Oxygen atom-induced D2 and D2O desorption on D/Si(1 1 1) surfaces

We studied reaction of oxygen atoms with D-terminated Si(1 1 1) surfaces from a desorption point of view. As the D (1 ML)/Si(1 1 1) surface was exposed to O atoms D₂ and D₂O molecules were found to desorb from the surface. The desorption kinetics of D₂ and D₂O molecules exhibited a feature characterized with a quick rate jump at the very beginning of O exposure, which was followed by a gradual increase with a delayed maximum and then by an exponential decrease. The O-induced D₂ desorption spectra as a function of T_s appeared to be very similar to the H-induced D₂ desorption spectrum from the D/Si(1 1 1) surfaces. Possible mechanisms for the O-induced desorption reactions were discussed.     

First-Principles Calculations of the AS,, Electronic Structures

The changes in the GaAs electronic structure due to the arsenic-antisite defect have been calculated by using LDF-LMTO-ASA method to a D_2d-symmetry-supercell ( Ga₁₅As₁₇□₃₂)c,o ntains 15 gallium atoms, 17 arsenic atoms and 32 empty spheres. The results show that the central AsGa atom is antibonding with its nearest neighbor arsenic atoms and therefore induces gap states in GaAs. The gap states are composed of A₁-like state and T₂-like state. The bonding properties of gap states have been analyzed in detail by using density of states (DOS) and combined coefficients of wavefunctions. Our results of E_A1 =E_v+0.70 eV and= E_T2+1.07eV are in good agreement with experiments as well as previous calculation results obtained by other self-consistent methods.     

Localization of the Poincare Group in the Spinor Space

A more general representation of the Poincare group where translation generators are generalized by P_μ= i∂_μ+kγ_μ[(l+γ₅)/2] is discussed. The corresponding spinor gauge field is studied in detail. It is shown that the Lagrangian of fermion keeps its form invariant under the above translation. An additional hidden symmetry of the Dirac field leads to a prediction of existence of an intrinsic energy-momentum for the fernlion.