Enhancement of nonlinear optical properties of nanocarbon cluster C60 by aluminum doping

The search for good nonlinear optical (NLO) materials is of utmost importance in laser technology and optical information science, making it a popular research topic in materials science. It is reported that the introduction of alkali metal Li can enhance the NLO properties of nanocarbon materials. Here, metal Al, which exhibits similar electron transfer characteristics to Li, was used for the first time to enhance the NLO properties of nanocarbon cluster C₆₀, which possesses a large delocalized π structure and the highest yield in the fullerene family. Density functional theory calculations in combination with Boltzmann distribution showed that the most thermodynamically stable Al@I_h(1812)-C₆₀ exhibited good second-order NLO properties, which originated from the noncentrosymmetry geometry and one extra delocalized electron on I_h(1812)-C₆₀ from the 3p shell of inner Al. Density of state analysis indicated that the molecular orbitals of Al@I_h(1812)-C₆₀ were primarily formed by I_h(1812)-C₆₀ with minimal Al participation, and the presence of Al always resulted in an antibonding orbital effect. Bond critical point and electron localization function analyses indicated almost no covalent interaction between Al and I_h(1812)-C₆₀. Exohedral functionalization was employed to further stabilize Al@I_h(1812)-C₆₀ with radical character, and the infrared spectrum was also analyzed in detail. This study has promising implications for expanding the potential applications of fullerenes in optical devices.     

Die Reaktion von Tellurhexafluorid mit Trimethylamin,Strukturen der TeF5−- und SeF5−-Anionen

Reaction of Telluriumhexafluoride and Trimethylamine, Structures of the TeF₅^? and SeF₅^? Anions The reaction of TeF₆ and (CH₃)₃N is of the redox kind, resulting in reduction of tellurium: X-ray single crystal analysis reveals the compounds (CH₃)₂N? CH₂? N(CH₃)₂⁺TeF₅^? and [(CH₃)₃NH⁺]₅(TeF₅^?)₃(HF₂^?)₂. By comparison with published data it can be shown that this mixture is identical to previously published [(CH₃)₃N]₂TeF₆. The latter was supposed to be one of the few examples of tellurium in a coordination state of eight. (CH₃)₄N⁺TeF₅^? and (CH₃)₄N⁴SeF₅^? are obtained and their structure is investigated by single crystal x-ray methods also. The anions SF₅^?, SeF₅^? and TeF₅^? are discussed in terms of weak interactions.     

The global weak solution for the shallow water wave model of moderate amplitude

In this paper, we firstly establish the existence theorem of the global weak solutions of the Cauchy problem for the shallow water wave model of moderate amplitude, then following the idea in Xin and Zhang’s work (see Xin and Zhang, 2002), we prove the uniqueness of global weak solutions using the localization analysis in the transport equation theory. Finally, several travelling wave solutions are derived.     

重复采购竞拍中两种卡特尔串谋机制稳定性的边界条件研究

深入研究临界贴现因子和保留价格两种因素对重复采购竞拍中的两种卡特尔串谋机制稳定性的影响。研究表明:(1)当串谋成员的贴现因子超过临界贴现因子时,没有成员会背叛串谋协定;(2)相比简单保留价格和纳什均衡保留价格,本文提出的阻挠串谋的最小保留价格最能有效阻止销售方串谋行为并确保采购方一定收益。研究结果有助于增进对重复采购拍卖下两种卡特尔串谋机制的运作机理的理解,丰富了重复采购环境下竞拍串谋监管机制和策略的理论研究内容。     

GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR GENERALIZED QUANTUM MHD EQUATION

We prove the existence of a weak solution for a generalized quantum MHD equation in a 2-dimensional periodic box for large initial data. The existence of a global weak solution is established through a three-level approximation,energy estimates, and weak convergence for the adiabatic exponent γ 1.     

Limit distributions and one-parameter groups of linear operators on Banach spaces

Let = {U_t: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set (X) of all probability measures on X. By (Q; ) we denote the class of all limit measures of {U_tn(μ₁ * μ₂*…*μ_n)*δ_xn}, where {μ_n}Q, {x_n}X and measures U_tnμ_j (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes L_m( ) as follows: L₀( )= ( (X); ), L_m( )= (L_m−1( ); ) for m=1, 2,… and L_∞( )=_m=0^∞L_m( ). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from L_m( ), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators.     

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Let Ω be a bounded open subset of ℝ ⁿ , n > 2. In Ω we deduce the global differentiability result

A note on -estimates for stable integrals with drift

Let be of the form where is a symmetric stable process of index with . We obtain various -estimates for the process . In particular, for and any measurable, nonnegative function we derive the inequality

As an application of the obtained estimates, we prove the existence of solutions for the stochastic equation for any initial value .

     

Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

半度量空间的刻画

We use the notions of weak base g-functions and pair networks to give some new characterizations of semi-metric spaces.