WnNim(n+m=8)团簇轨道能级与芳香性的理论研究

用密度泛函理论(DFT)中的b3lyp方法,在Lanl2dz基组水平上对W_nNi_m(n+m=8)团簇的各种可能构型进行几何参数全优化,得到它们的基态构型;并对基态构型的轨道能级分布、能隙、HOMO、LUMO能级、芳香性和热力学性质进行分析,结果表明:团簇W₅Ni₃和W₆Ni₂的Alpha轨道和Beta轨道是完全简并的,所有电子都是严格两两配对的;团簇W₂Ni₆能隙最小,化学活性最强,组成前线轨道的成分基本相同;W₆Ni₂能隙最大,化学活性最弱;团簇W₁Ni₇,W₅Ni₃,W₆Ni₂,W₇Ni₁具有芳香性,W₂Ni₆具有反芳香性;团簇的生成焓都是负值,为放热反应,热力学上是稳定的.     

基于模糊模型的不同结构的混沌系统同步

针对不同结构的混沌系统广义同步问题，提出了基于T-S 模糊模型的H_∞控制方法，利用Lyapunov方法和线性矩阵不等式技术,给出了误差闭环系统稳定的充分条件.仿真结果表明了方法的有效性. 关键词： H_∞控制')" href="#">H_∞控制 广义同步 混沌系统 模糊控制     

基于二缺位钨多酸化合物的二维相关红外光谱研究

通过水热法合成了一例新颖的稀土钨多酸化合物H₂₆(C₂H₈N₂H₂)K(H₂O)[K(H₂O)Nd₈(H₂O)₂(W₃O₁₂)(SiW₁₀O₃₈)₄]·18H₂O 1。该化合物的不对称单元由两个[SiW₁₀O₃₈]^12-通过一个{Nd₄(H₂O)¹²⁺}结构单元和W₃O₁₂连接而成。化合物1簇阴离子通过K离子连接成一维无限链,再通过氢键连接成二维平面结构。针对该化合物,做了一系列表征,测试了其二维相关红外光谱,并对其作了详细分析,结果说明化合物1簇阴离子振动偶极矩对磁...     

一类NLS-mKdV方程族的扩展可积系统

利用代数变换，构造了与文献［５］中的loop代数₂的子代数等价的loop代数1的一个子 代数₁.再将₁扩展为一个高维的loop代数.利用设计了一个等谱问题 ，结合子代数间的直 和运算和同构关系，得到了NLS_mKdV方程族的一类扩展可积系统.作为约化情形，求得了著 名的Schrdinger方程与mKdV方程的可积耦合系统. 关键词： loop代数 可积系统 等谱问题     

Ti掺杂W$lt;sub$gt;18$lt;/sub$gt;O$lt;sub$gt;49$lt;/sub$gt;纳米线的电子结构与NO$lt;sub$gt;2$lt;/sub$gt;敏感性能的第一性原理研究

采用基于密度泛函理论框架下的第一性原理平面波超软赝势方法,通过理论建模,研究了Ti掺杂的非化学计量比W₁₈O₄₉纳米线的几何与能带结构以及电子态密度,并通过进一步计算NO₂/Ti-W₁₈O₄₉纳米线吸附体系的吸附能、电荷差分密度与电荷布居,分析了Ti掺杂W₁₈O₄₉纳米线的气体吸附与敏感性能. 计算发现,Ti掺杂改变了W₁₈O₄₉纳米线的表面电子结构,引入的额外的杂质态密度和费米能级附近能带结构的显著变化,使掺杂纳米线带隙与费米能级位置改变,纳米线导电性能增强. 吸附在W₁₈O₄₉纳米线表面的NO₂作为电子受体从纳米线导带夺取电子,导致纳米线电导降低,产生气体敏感响应. 与纯相W₁₈O₄₉纳米线相比,NO₂/Ti-W₁₈O₄₉纳米线吸附体系内部存在更多的电子转移,从理论上定量地反映了Ti掺杂对改善W₁₈O₄₉纳米线气敏灵敏度的有效性. 对Ti掺杂纳米线不同气体吸附体系电子布居的进一步计算表明,Ti掺杂纳米线对NO₂气体具有良好的灵敏度和选择性. 关键词： 密度泛函计算 Ti掺杂 18O₄₉纳米线')" href="#">W₁₈O₄₉纳米线 气敏     

Site preference of Ti and Nb in L12-ordered Co-Al-W phase and their effect on the properties of the alloy: first-principles study

In this work,the equilibrium structure,electronic and elastic properties of L1₂-ordered Co-Al-W and Co-Al-W-X(X=Ti and Nb)phase were calculated,using first-principles calculations.Among six nonequivalent sites(Al₁,Al₂,Co₃,Co₄,W₅,W₆),Ti and Nb prefer to occupy the W₆site,since the formation enthalpy of the system is lowest when Ti and Nb occupy the W。site.Both Ti and Nb most affect the density of states of Al atoms.Compared with the Al₂ site,which is the sub-preference site of Ti and Nb,the density of states of Al atoms is higher with the addition of Ti and Nb in the W₆site,which means that the latter system is more stable.According to the bulk modulus B,shear modulus G,Young's modulus E,hardness Hv and Poisson's ratioσ,for Co₃(AI,W)alloy,the addition of Ti and Nb in the W₆site decreases its hardness hut increases its duetility.This work cnnfirms that Ti and Nh can stahilize the Cag(Al,W)alloy and have a positive effect in solving the relatively poor ductility of this alloy,which has important implications for the development of cobalt.based alloys.     

时变不确定时滞连续系统的鲁棒H∞保成本控制

针对一类同时具有状态时滞和输入时滞的时变不确定连续系统,研究了H_∞保成本状态反馈控制器的设计,假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件.通过构造广义Lyapunov函数和线性矩阵不等式(LMI)方法,给出了系统可H_∞鲁棒镇定同时满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到鲁棒H_∞保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界,并经过迭代,通过求解凸优化问题得到最优鲁棒H_∞保性能控制器.最后用示例说明了该方法的有效性. 关键词： 连续系统 时滞 H_∞鲁棒控制')" href="#">H_∞鲁棒控制 保成本控制     

动力学对称群方法对三原子分子高激发振动态的理论研究

利用动力学对称群方法研究了弯曲三原子分子的振动高激发态能谱-该方法显示：三原子分子的动力学对称性为U₁(4)U₂(4),则三原子分子的Hamiltonian量可写成代数的各元素之和,通过李代数处理而求得分子代数Hamiltonian量的本征值,进而得到分子的振动能谱-并具体计算了O₃分子- 关键词：     

一类带扰动的Sine-Gordon方程的谱方法

研究一类具扰动的Sine-Gordon方程u_tt-u_xx+αsinu-βu_xxt=g(u),t>0,-∞< x< ∞的周期初值问题,提出了谱方法,并用先验估计方法作了误差估计,证明了近似方法的收敛性,并得到了该问题广义解的存在、唯一性。     

钒掺杂W18O49纳米线的室温p型电导与NO2敏感性能

钨氧化物纳米线在高灵敏度低功耗气体传感器中极具应用潜力, 且通过掺杂改性可进一步显著改善其敏感性能. 本文以WCl₆为钨源, NH₄VO₃为掺杂剂, 采用溶剂热法合成了钒掺杂的W₁₈O₄₉纳米线. 利用扫描电镜、透射电镜、X射线衍射、X射线光电子能谱仪表征了纳米线的微结构, 并利用静态气敏性能测试系统评价了掺杂纳米线的NO₂敏感性能. 研究结果表明: 五价钒离子受主掺杂进入氧化钨晶格结构, 抑制了纳米线沿轴向的生长并导致了纳米线束的二次集聚; 室温下, 钒掺杂W₁₈O₄₉纳米线接触NO₂气体后表现出反常的p型响应特性; 随工作温度逐渐升高至约110 ℃时, 发生从p型到n型的电导特性转变; 该掺杂纳米线气敏元件对浓度低至80 ppb (1 ppb=10^-9) 的NO₂气体具有明显的室温敏感响应和良好的响应稳定性. 分析并探讨了钒掺杂W₁₈O₄₉纳米线的高室温敏感特性及其p-n电导转型机理, 认为钒掺杂W₁₈O₄₉纳米线在室温下的良好敏感响应及反常p型导电性与掺杂纳米线表面高密度非稳表面态诱导的低温气体强吸附有关. 关键词： 氧化钨 纳米线 气体传感器 室温灵敏度     

The algebra of differential operators on the circle and W KP (q)

Radul has recently introduced a map from the Lie algebra of differential operators on the circle of W _n . In this Letter, we extend this map to W _KP ^(q) , a recently introduced one-parameter deformation of W_KP - the second Hamiltonian structure of the KP hierarchy. We use this to give a short proof that W is the algebra of additional symmetries of the KP equation.     

Symmetries and generalizedW∞ algebra of the modified KP equation

The infinitely many symmetries with arbitrary functions of timet for the potential modified Kadomtsev-Petviashvilli equation are obtained by using a simple direct method. These symmetries constitute a generalization of the well-knownW algebra.     

W-hairs of the black holes in three-dimensional spacetime

In a previous publication, we claimed that a black hole can be considered as a topological insulator. A direct consequence of this claim is that their symmetries should be related. In this paper, we give a representation of the near-horizon symmetry algebra of the BTZ black hole using the W1+∞ symmetry algebra of the topological insulator in three-dimensional spacetime. Based on the W1+∞ algebra, we count the number of the microstates of the BTZ black holes and obtain the Bekenstein-Hawking entropy.     

Quantum Torus Symmetry of the KP,KdV and BKP Hierarchies

In this paper, we construct the quantum torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum torus Lie algebra in the KP system by acting on its tau function. Comparing to the W _∞ symmetry, this quantum torus symmetry has a nice algebraic structure with double indices. Further by reduction, we also construct the quantum torus symmetries of the KdV and BKP hierarchies and further derive the quantum torus constraints on their tau functions. These quantum torus constraints might have applications in the quantum field theory, supersymmetric gauge theory and so on.     

Additional symmetries and string equations of the noncommutative B and C type KP hierarchies

In this paper, we construct the noncommutative B and C type KP hierarchies using pseudo-differential operators and reducing conditions. Further a series of additional flows of the noncommutative B and C type KP hierarchies will be defined and the additional symmetries constitute the B and C type infinite dimensional Lie algebra W_1+∞. In addition, the generating function of the additional symmetries can also be proved to have a nice form in terms of wave functions. Further, the string equations of the noncommutative B and C type KP hierarchies are derived.     

Additional Symmetries and String Equation of the CKP Hierarchy

Based on the Orlov and Shulman’s M operator, the additional symmetries and the string equation of the CKP hierarchy are established, and then the higher order constraints on L ^l are obtained. In addition, the generating function and some properties are also given. In particular, the additional symmetry flows form a new infinite dimensional algebra , which is a subalgebra of W _1+∞.      

Additional symmetries of supersymmetric KP hierarchies

We investigate the additional symmetries of several supersymmetric KP ierarchiess: the SKP hierarcy of Manin and Radul, the SKP₂ hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries is isomorphic to the algebra of supperdifferential operators, or equivalentlySW ₁₊. These results seem to suggest that despite their realization depending on the dynamics, the additional symmetries are kinematical in nature.     

The relation between quantumW algebras and Lie algebras

By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrarysl ₂ embeddings we show that a large set of quantumW algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set contains many knownW algebras such asW _N andW ₃ ⁽²⁾ . Our formalism yields a completely algorithmic method for calculating theW algebra generators and their operator product expansions, replacing the cumbersome construction ofW algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that anyW algebra in can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Thereforeany realization of this semisimple affine Lie algebra leads to a realization of theW algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolusions for all algebras in. Some examples are explicitly worked out.