At the second order Douglas–Kroll–Hess(DKH2)level,the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute...At the second order Douglas–Kroll–Hess(DKH2)level,the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths,dissociation energies,vertical ionization potentials,and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters(Irn,n≤8).These results are compared with the experimental and theoretical data available in the literature.Our results confirm the theoretical predictions made by Feng et al.about the catalytic activities of the Ir4 and Ir6 clusters.From the optimized geometries,DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out.It is the first time that the polarizabilities of small iridium clusters have been studied.For n≤4,the mean dipole polarizabilities per atom present an odd–even oscillatory behavior,whereas from Ir5 to Ir8,they decrease with the cluster size increasing.The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.展开更多
The reaction mechanisms of Ti（~3F） ＋ CH2C12→CH2=TiCl2 and Ti（~3F） ＋ CHC13→HC÷TiCl3 were investigated with Gaussian 03 program package at the B3PW91/6-311＋＋G（d,p）level.The computational results reveale...The reaction mechanisms of Ti（~3F） ＋ CH2C12→CH2=TiCl2 and Ti（~3F） ＋ CHC13→HC÷TiCl3 were investigated with Gaussian 03 program package at the B3PW91/6-311＋＋G（d,p）level.The computational results revealed that：1） Both reaction systems are initiated by Ti（~3F） atom attacking the C atom of CH2C12 and CHCl3 to activate a C-Cl bond;2） Both reaction systems were carried out via triplet reaction channels;3） CH2=TiCl2 has singlet and triplet isomers,and the singlet one is more stable;4） The HOMO of CH2=TiCl2（S） illustrates a π-bonding interaction between C and Ti;5） Only singlet HC÷TiCl3 was located,and the Mulliken atomic spin densities show that the two single electrons are mostly on the C atom.展开更多
At the Douglas-Kroll-Hess （DKI4） level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and el...At the Douglas-Kroll-Hess （DKI4） level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters （Agn, n ≤ 7）. The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.展开更多
We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.T...We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.展开更多
In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or conv...In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders.展开更多
Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and t...Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.展开更多
基金supported by the CNPq,CAPES,and FAPES(Brazilian Agencies)
文摘At the second order Douglas–Kroll–Hess(DKH2)level,the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths,dissociation energies,vertical ionization potentials,and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters(Irn,n≤8).These results are compared with the experimental and theoretical data available in the literature.Our results confirm the theoretical predictions made by Feng et al.about the catalytic activities of the Ir4 and Ir6 clusters.From the optimized geometries,DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out.It is the first time that the polarizabilities of small iridium clusters have been studied.For n≤4,the mean dipole polarizabilities per atom present an odd–even oscillatory behavior,whereas from Ir5 to Ir8,they decrease with the cluster size increasing.The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.
基金financially supported by the National Natural Science Foundation of China(11174215)Natural Science Foundation of Shandong Province(ZR2012BL10)the University Science and Technology Project of Shandong Province(No.J13LD05)
文摘The reaction mechanisms of Ti（~3F） ＋ CH2C12→CH2=TiCl2 and Ti（~3F） ＋ CHC13→HC÷TiCl3 were investigated with Gaussian 03 program package at the B3PW91/6-311＋＋G（d,p）level.The computational results revealed that：1） Both reaction systems are initiated by Ti（~3F） atom attacking the C atom of CH2C12 and CHCl3 to activate a C-Cl bond;2） Both reaction systems were carried out via triplet reaction channels;3） CH2=TiCl2 has singlet and triplet isomers,and the singlet one is more stable;4） The HOMO of CH2=TiCl2（S） illustrates a π-bonding interaction between C and Ti;5） Only singlet HC÷TiCl3 was located,and the Mulliken atomic spin densities show that the two single electrons are mostly on the C atom.
基金Project supported by CNPq,CAPES,and FAPES(Brazilian Agencies)
文摘At the Douglas-Kroll-Hess （DKI4） level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters （Agn, n ≤ 7）. The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.
基金supported by the National Natural Science Foundation of China (Grant No. 70471071)
文摘We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.
基金supported by National Natural Science Foundation of China (Grant No.10571167)National Basic Research Program of China (973 Program) (Grant No.2007CB814902)Science Fund for Creative Research Groups (Grant No.10721101)
文摘In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders.
基金supported by Guangdong Natural Science Foundation (Grant No.2008276)a grant from the Research Grants Council of Hong Kong,China
文摘Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.
