Dual properties of orthogonal polynomials of discrete variables associated with the quantum algebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">su</Emphasis>(2))

We show that for every set of discrete polynomials y _n (x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials z _k (ξ(t)) of degrees k = s-a and k = b-s-1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative families. This allows us to obtain new expressions for the Clerbsch-Gordan and Racah coefficients of the quantum algebra U _q (su(2)) in terms of various Hahn and Racah q-polynomials. Dedicated to the memory of our teacher and friend Arnold F. Nikiforov (18.11.1930–27.12.2005).     

Multi—mode q—oscillator algebras with q^2（k＋1）=1 and related thermo field dynamics

A type of multi-mode q-oscillator algebra with q^2(k+1)=1 is set up and the associated q_k-thermo field dynamics is constructed for all k=1,2,…,∞ in a unified form. It is demonstrated that these q_k-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima [1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases. As simple applications, the q_k-statistical average of some operators are given.     

Co和稳定元素对Nd3(Fe,Co,M)29(M=Ti,V,Cr) 化合物结构和磁性的影响

利用x射线衍射和磁测量研究了不同稳定元素Co以及Ti,V和Cr替代对Nd₃Fe_29-x-yCo_xM_y(M=Ti,V,Cr)化合物结构和磁性的影响.研究发现:每一个稳定元素都有一替代量极限,在此极限以内所有化合物均为Nd₃(Fe,Ti)₂₉型结构,A2/m空间群.不同稳定元素的溶解极限不同.Co的替代量与稳定元素有关,当以Cr作为稳定元素时,Cr的替代量随着Co含量的提高而提高 关键词： 3(Fe')" href="#">Nd₃(Fe Co 29')" href="#">M)₂₉ 结构 磁性     

Comment on ＂Symbolic Computation and q-Deformed Function Solutions of the （2＋1）-Dimensional Breaking Soliton Equation＂

In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, which are in the form of q-deformed hyperbolic and triangular functions as new solutions. In this comment, we will show that these solutions are just the special cases of some known solutions of the Riccati equation and thus they are not new solutions.     

MgmBn(m=1,2;n=1—4)团簇结构与性质的密度泛函理论研究

用密度泛函理论(DFT)的杂化密度泛函B3LYP方法在6-31G基组水平上对Mg_mB_n(m=1,2;n=1-4)团簇各种可能的构型进行几何结构优化，预测了各团簇的最稳定结构.并对最稳定结构的振动特性、电离势、成键特性、极化率和超极化率等性质进行了理论研究.结果表明，团簇的最稳定结构大多是平面结构，团簇的稳定结构中通常是几个呈负电性的B原子形成一个负电中心，而其他B原子和Mg原子通常处在端位，且显正电性；团簇中通常是B-B键和B-Mg键共存，极少出现Mg-Mg键， 关键词： mB_n(m=1')" href="#">Mg_mB_n(m=1 n=1-4)团簇 密度泛函理论 结构与性质     

甲醛在金红石型TiO2(100)-(1×1)表面的光解离

We have investigated the photoinduced decomposition of formaldehyde (CH₂O) on a rutile TiO₂(100)-(1×1) surface at 355 nm using temperature-programmed desorption. Products, formate (HCOO^-), methyl radical (CH₃·), ethylene (C₂H₄), and methanol (CH₃OH) have been detected. The initial step in the decomposition of CH₂O on the rutile TiO₂(100)-(1×1) surface is the formation of a dioxymethylene intermediate in which the carbonyl O atom of CH₂O is bound to a Ti atom at the five-fold-coordinated Ti⁴⁺ (Ti_5c) site and its carbonyl C atom bound to a nearby bridge-bonded oxygen (O_b) atom, respectively. During 355 nm irradiation, the dioxymethylene intermediate can transfer an H atom to the O_b atom, thus forming HCOO^- directly, which is considered as the main reaction channel. In addition, the dioxymethylene intermediate can also transfer methylene to the O_b row and break the C-O bond, thus leaving the original carbonyl O atom at the Ti_5c site. After the transfer of methylene, several pathways to products are available. Thus, we have found that O_b atoms are intimately involved in the photoinduced decomposition of CH₂O on the rutile TiO₂(100)-(1×1) surface.     

U(1) symmetry in the current algebra and N-fermionic massless Thirring model

Local U(1) symmetry in current algebra constructed by fermions has been found. The symmetry is related to the simplest q-deformation of N-fermions. We give the physical interpretation through the N-fermionic massless Thirring model. The Bethe ansatz wavefunction is also given.     

Y2(Fe1-x-y,Coy,Crx)17化合 物的结构及居里温度

通过x射线衍射及磁测量手段研究了Y₂(Fe_1-y-x,Co_y,C r_x)₁₇化合物的结 构及居里温度.研究结果表明Y₂(Fe_1-y-x,Co_y,Crx)₁₇化合物具有六 角相的Th₂Ni₁₇型结构.随着x的增加，Y₂(Fe 关键词： 2(Fe_1-y-x')" href="#">Y₂(Fe_1-y-x y')" href="#">Co_y x)_{1 7}化合物')" href="#">Cr_x)_{1 7}化合物 x射线衍射 居里温度     

R3(Fe1-xCox)29-yCry(R=Gd,Sm)化合物相稳定性研究

在制备出Gd₃(Fe_1-xCo_x)_29-yCr_{y化合物基础上，成功制备出Sm3(Fe1-xCox)29 -yCry化合物，通过x射线衍射和热磁分析对R3(Fe1-x< /sub>Co x)29-yCry 关键词： 3(Fe1-xCox)29-yCry化合物')" href="#">R3(Fe1-xCox)29-yCry化合物 相结构 单轴磁晶各向异性}     

AlxOy(x=1—2,y=1—3)分子几何结构与稳定性的DFT研究

用密度泛函理论(DFT)的B31yp方法在6-311++g^水平上对Al_xO_y(x=1—2,y=2—3)分子的几何构型、电子结构、振动频率等性质进行了理论研究. 通过对基态结构的几何参数分析发现，它们的基态结构趋于直线或平面结构. 对基态结构的绝热电离能讨论表明，金属铝原子数一定时，氧原子数从1增加到3，其气态分子越来越稳定，铝原子数少的分子体系更稳定. 系统给出了该系列分子基态的几何参数、电子结构、光谱性质. Al₂O₃的C_2V三重态是该分子的能量最低结构. 关键词： xO_y分子')" href="#">Al_xO_y分子 密度泛函理论 结构与稳定性     

Theoretical study on the interaction of heptafluoro-iso-butyronitrile decomposition products with Al (1 1 1)

Seeking environmentally friendly gas-insulated medium has become a research hotspot in recent years. At present, C₃F₇CN (Heptafluoro-iso-butyronitrile) is considered to be a potential SF₆ environment-friendly alternative gas and some achievements have been made in the study of its insulation and decomposition characteristics, but there are few reports on the compatibility between its characteristic decomposition products and materials. The investigation of compatibility between gas-insulated medium and material is an important part of evaluating its comprehensive performance. In this paper, we investigated the interaction between C₂F₅CN, CF₃CN, COF₂ and CF₄ with the aluminium widely used in electrical equipment. It was found that the interaction between C₂F₅CN, CF₃CN and Al (1 1 1) surface is strong. There are obvious charge transfer and electron orbital overlap between the C atom, N atom in CN group and Al (1 1 1). The interaction between COF₂, CF₄ and Al (1 1 1) surface is weak and van der Waal’s forces play the major role. Relevant results reveal the characteristics of C₃F₇CN decomposition products and provide theoretical guidance for evaluating the material compatibility between C₃F₇CN decomposition products and aluminium.     

A study of the interaction between perylene and the TiO2(1 1 0)-(1 × 1) surface-based on XPS, UPS and NEXAFS measurements

The interaction between a semi-large aromatic hydrocarbon compound (perylene) and the TiO₂(1 1 0)-(1 × 1) surface under ultra high vacuum conditions has been probed by X-ray photoemission spectroscopy (XPS), ultraviolet photoemission spectroscopy (UPS) and near-edge X-ray absorption fine structure (NEXAFS) methods. UPS measurements of the adsorbate system have been compared with an experimental UPS spectrum of perylene in the gas phase and a calculated spectrum obtained by means of density functional theory (DFT) methods. NEXAFS results of perylene molecules adsorbed on TiO₂(1 1 0)-(1 × 1) were compared with data from an α-phase perylene single crystal. A novel analysis of the valence data has been employed to show that no strong chemical interaction takes place between perylene and the TiO₂(1 1 0)-(1 × 1) surface. Furthermore, angle-dependent NEXAFS measurements and the growth curve results suggest that the perylene molecules are oriented flat down onto the TiO₂ substrate due to weak van der Waals interactions.     

q-Deformation of the Double Complex Ernst Equation

From a known three-dimensional representation of the double quantum algebra su _q ((J)), a nonlinear q-deformed Ernst equation system is obtained. By using a gauge covariant form, the deformation effects are found to generate a torsion in the field and to form a gauge field with source.     

密度泛函理论研究ScnO(n=1—9)团簇的结构、稳定性与电子性质

采用基于密度泛函理论的BP86/CEP-121G （O原子采用6-311G^**基组）方法,对Sc_nO （n=1—9）团簇的几何结构、能量与稳定性、电子结构性质及其随团簇尺寸的变化趋势进行了研究.随着团簇原子个数的增加,O原子从位于Sc_n团簇结构的边缘转变为占据团簇的内部位置.O原子的掺入增加了Sc_n团簇的稳定性,使其能隙升高,并改变了其稳定性及电子结构性质随团簇尺寸变化的规律;含有偶数个Sc原子的氧化物团簇比其周围邻近的含有奇数个Sc原子的氧化物团簇具有相对较高的稳定性.Sc_nO团簇电离势的理论计算值与实验值符合得较好,而其电子亲和势呈现振荡交替上升的变化趋势;用最大化学硬度规律等方法表征了Sc_nO氧化物团簇的稳定性和电子结构性质. 关键词： nO团簇')" href="#">Sc_nO团簇 几何结构 电子性质 密度泛函理论     

Density Functional Theory Study on Electronic and Magnetic Properties of Mn-doped (MgO)n (n=2～10) Clusters

利用密度泛函理论方法优化了纯的和M_n原子掺杂的(MgO)_n (n=2～10)团簇的几何结构. 在Mn原子掺杂的氧化镁结构中, 获得了一系列的同分异构体和与之相对应的总能量.MnMg_n-1O_n(n=2～10)的几何构型显示Mn原子优先取代低配位的Mg原子. 结构稳定性分析表明,除了(MgO)₁₀团簇外,其它纯的和掺杂结构的平均结合能均随着团簇的增大而增强. MnMg_n-1O_n团簇的二阶能量差结果表明MnMg₅O₆和MnMg₈O₉比相邻的团簇表现出更高的相对稳定性. 除了MnMgO₂团簇的磁矩为3.00 μB外,其它掺杂结构的磁矩均为5 μB左右. 它们的磁性主要受电荷转移大小、原子在结构中的位置以及结构尺寸所影响.     

熔体旋甩法合成n型(Bi_(0.85)Sb_(0.15))_2(Te_(1-x)Se_x)_3化合物的微结构及热电性能

采用熔体旋甩结合放电等离子烧结(MS-SPS)技术制备了单相n型四元(Bi0.85Sb0.15)2(Te1-xSex)3(x=0.15,0.17,0.19,0.21)化合物,并对所得样品的微结构和热电传输性能进行了系统研究.样品自由断裂面的场发射扫描电子显微镜及抛光面的背散射电子成分分析表明:块体材料晶粒细小,晶粒排列紧密,成分分布均匀且相结构单一,样品中存在大量10—100nm的层状结构.随着Se含量x的增加,样品的电导率和热导率逐渐增加,而Seebeck系数逐渐降低.相比商业应用的区熔材料,MS-SPS方法合成的高Se组成的样品均在425K后表现出更高的ZT值,其中(Bi0.85Sb0.15)2(Te0.83Se0.17)3样品具有最高的ZT值,在360K可达到0.96,并在320—500K均保持较高的ZT值,500K时其ZT值相比区熔材料提高了48%.此外,通过调节Se的含量,可以有效地调控材料的ZT峰值出现的温度段,这对多级或梯度热电器件的制备具有重要意义.     

Hyperpolarized He diffusion MRI and histology of secreted frizzled related protein-1 (SFRP1) deficient lungs in a Murine model

Secreted frizzled related protein-1 (SFRP1) plays a key role in many diverse processes, including embryogenesis, tissue repair, bone formation, and tumor genesis. Previous studies have shown the effects of the SFRP1 gene on lung development using the SFRP1 knockout mouse model via histological and physiological studies. In this study, the feasibility of ADC (acquired via HP ³He) to detect altered lung structure in the SFRP1 knockout (SFRP1^−/−) mice was investigated, and compared to analysis by histology. This study consisted of two groups, the wild-type (WT) mice and the knockout (KO) mice with n = 6 mice for each group. ³He ADC MRI and histology were performed on all of the animals. The global L_m values of WT and KO mice were 35.0 ± 0.8 μm and 38.4 ± 3.8 μm, respectively, which translated to an increase of 9.58% in the L_m of KO mice. The mean global ADCs for the WT and KO mice were 0.12 ± 0.01 cm²/s and 0.13 ± 0.01 cm²/s, respectively, which equated to a relative increase of 8.0% in the KO mice compared to the WT mice. In the sub-analysis of the anterior, medial and posterior lung regions, L_m increased by 10.50%, 6.66% and 11.84% in the KO mice, respectively, whereas the differences in ADC between the two groups in the anterior, medial, and posterior regions were 7.3%, 8.3%, and 4.6%, respectively. These results suggest that HP MRI measurements can be used as a suitable substitute for histology to obtain valuable information about lung geometry non-invasively. This technique is also advantageous as regional measurements can be performed, which can identify lung destruction more precisely. Most importantly, this approach extends far beyond the specific pathology analyzed in this study, as it can be applied to many other pathological conditions in the lung tissue, as well to many other embryonic studies.     

Analytical potential energy function for the electronic states 2^∏1/2 and 2^∏3/2 of O^x2 （x=＋1, -1）

The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.