ALGEBRAIC METHOD FOR VIBRATIONAL ENERGY SPECTRA OF H 2O AND NO 2

文内提出一种研究Ｈ２Ｏ和ＮＯ２高激发伸缩振动的Ｕ（２）代数模型,在极限条件下,该模型退化为一种非谐和耦合的局域模模型,用该模型的六个可调参数拟合实验数据,算得的标准偏差比相应的非谐和耦合的局域模型算得的偏差要小     

Gauss Decomposition of Dynamical Elliptic Algebra Aq,p,π(gln)

We propose a dynamical elliptic algebra which is based on the relations RLL = LLR^*, where R and R^* are the dynamical R-matrices of A_n-1⁽¹⁾-type face model with the elliptic module shifted by the center of algebra. nom the high-rank Gauss decomposition,h we obtain the Drinfeld currents of dynarnical elliptic algebra .     

Duality for Coloured Quantum Groups

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L ^± functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach.     

Covering and gluing of algebras and differential algebras

Extending work of Budzyński and Kondracki, we investigate coverings and gluings of algebras and differential algebras. We describe in detail the gluing of two quantum discs along their classical subspace, giving a C^*-algebra isomorphic to a certain Podleś sphere, as well as the gluing of U_q^1/2(sl₂)-covariant differential calculi on the discs.     

Weakly o‐Minimal Expansions of Boolean Algebras

We propose a definition of weak o‐minimality for structures expanding a Boolean algebra. We study this notion, in particular we show that there exist weakly o‐minimal non o‐minimal examples in this setting.     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. III

By extending the methodology given in Parts I and II of this series of articles, certain dynamical systems of chemical kinetic equations are analyzed in the setting of the Banach algebra B(ℬ︁) of all bounded operators acting on a Banach space ℬ︁. In this article, we proceed from the general setting of B(ℬ︁), which played a central role in Part II, toward its specific application to the dynamical systems. In our analysis, crucial initial steps are taken by (i) equipping the abstract space ℬ︁ with the “positive quadrant,” which we denote by Γ(ℝ⁺ⁿ), and by (ii) investigating the asymptotic behavior of the solution χ_ϵ(t) of the initial-value problem is suitably specified for our application purposes. The main theorem and its two specialized versions, together with the notions of Γ-semipositive operators and semipositive matrices presented here, serve as fundamental tools for the analysis of a class of dynamical systems of chemical kinetic equations whose examples were illustratively treated in the previous parts of this series of articles. The techniques developed here for an asymptotic analysis of chemical kinetic dynamical systems will be linked and unified with those for the asymptotic analysis of quantum mechanical systems in a forthcoming part of this series of articles. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 149–163, 1997     

Power series with rational coefficients for two-electron atom energies

The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit +∞ is presented for the energies of the helium singlet and triplet ground states. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63 : 1079–1089, 1997