Using density function theory （DFT）, the Cu-doped Aln （n=1-15） clusters have been stud- ied. The electron affinity, ionization potential, Mulliken population analysis of Cu, mean polarizability, polarizability ani...Using density function theory （DFT）, the Cu-doped Aln （n=1-15） clusters have been stud- ied. The electron affinity, ionization potential, Mulliken population analysis of Cu, mean polarizability, polarizability anisotropy, dipole moments and HOMO-LUMO gaps have also been calculated on the basis of optimized geometries. The results indicate that there is magic numbers in copper-doped aluminum clusters and electronic characteristic depended on the size of clusters. As n=13, the electron affinity and ionization potential of cluster changed more than 0.3 and 0.6 eV respectively, compared with neighborhood clusters.展开更多
Analyzes the shortcomings of the classic capital market theories based on EMH and discloses the complexity essence of the capital market. Considering the capital market a complicated, interactive and adaptable dynamic...Analyzes the shortcomings of the classic capital market theories based on EMH and discloses the complexity essence of the capital market. Considering the capital market a complicated, interactive and adaptable dynamic system, with complexity science as the method for researching the operation law of the capital market, this paper constructs a nonlinear logical model to analyze the applied realm, focal point and interrelationship of such theories as dissipative structure theory, chaos theory, fractal theory, synergetics theory, catastrophe theory and scale theory, and summarizes and discusses the achievements and problems of each theory. Based on the research, the paper foretells the developing direction of eomplexity science in a capital market.展开更多
Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(...Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.展开更多
The equilibrium geometries, potential energy curves, spectroscopic dissociation energies of the ground and low-lying electronic states of He2, He2^＋ and He2^＋＋ are calculated using symmetry adapted cluster/symmetry...The equilibrium geometries, potential energy curves, spectroscopic dissociation energies of the ground and low-lying electronic states of He2, He2^＋ and He2^＋＋ are calculated using symmetry adapted cluster/symmetry adapted cluster-configuration interaction （SAC/SAC-CI） method with the basis sets CC-PV5Z. The corresponding dissociation limits for all states are derived based on atomic and molecular reaction statics. The analytical potential energy functions of these states are fitted with Murrell-Sorbie potential energy function from our calculation results. The spectroscopic constants Be, αe, ωe, and ωeχe of these states are calculated through the relationship between spectroscopic data and analytical energy function, which are in well agreement with the experimental data. In addition, the origin of the energy barrier in the ground state X^I∑9^＋ of He2^＋＋ energy curve are explained using the avoided crossing rules of valence bond model.展开更多
A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain.In this work, the author gives a complete characterization ...A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain.In this work, the author gives a complete characterization of the recurrent property of this process. The long time behavior of this process such as its p-th moment is also studied. Moreover, the quantitative properties of the regime-switching geometric Brownian motion with two-state switching are investigated to show the difference between geometric Brownian motion with switching and without switching. At last, some estimates of its first passage probability are established.展开更多
The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a n...The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[（p）], It is interesting to see that the [~ （p）[ is symmetric with respect to the axis p = 0 and the number of wave crest of [ （p）[ is equal to n ＋ 1. We also study the variation of ]k（p）l with respect to . The arnplitude of ｜ψ（p）] first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments.展开更多
The equilibrium geometries, relative stabilities, and electronic properties of Ca2Sin （n = 1-11） clusters have been systematically investigated by using the density function theory at the 6-311G （d） level The opti...The equilibrium geometries, relative stabilities, and electronic properties of Ca2Sin （n = 1-11） clusters have been systematically investigated by using the density function theory at the 6-311G （d） level The optimized geometries indicate that the most stable isomers have three-dimensional structures for n = 3-11. The electronic properties of Ca2 Sin （n = 1-11） dusters axe obtained through the analysis of the natural charge population, natural electron configuration, vertical ionization potential, and vertical electron affinity. The results show that the charges in corresponding Ca2Sin clusters transfer from the Ca atoms to the Sin host. Based on the obtained lowest-energy geometries, the size dependence of cluster properties, such as averaged binding energies, fragmentation energies, second-order energy differences, HOMO- LUMO gaps and chemical hardness, are deeply discussed.展开更多
基金The work was supported by the National Natural Science Foundation of China （No.10374036 and No. 10374037） and the Chinese Academic of Engineering Physics （No.51480030105JW1301）.
文摘Using density function theory （DFT）, the Cu-doped Aln （n=1-15） clusters have been stud- ied. The electron affinity, ionization potential, Mulliken population analysis of Cu, mean polarizability, polarizability anisotropy, dipole moments and HOMO-LUMO gaps have also been calculated on the basis of optimized geometries. The results indicate that there is magic numbers in copper-doped aluminum clusters and electronic characteristic depended on the size of clusters. As n=13, the electron affinity and ionization potential of cluster changed more than 0.3 and 0.6 eV respectively, compared with neighborhood clusters.
文摘Analyzes the shortcomings of the classic capital market theories based on EMH and discloses the complexity essence of the capital market. Considering the capital market a complicated, interactive and adaptable dynamic system, with complexity science as the method for researching the operation law of the capital market, this paper constructs a nonlinear logical model to analyze the applied realm, focal point and interrelationship of such theories as dissipative structure theory, chaos theory, fractal theory, synergetics theory, catastrophe theory and scale theory, and summarizes and discusses the achievements and problems of each theory. Based on the research, the paper foretells the developing direction of eomplexity science in a capital market.
基金Project supported by the National Natural Science Foundation of China (No.10271107) the 973 Project of the Ministry of Science and Technology of China (No.G1999075105) the Zhejiang Provincial Natural Science Foundation of China (No.RC97017).
文摘Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.
基金Supported by the Natural Science Foundation of Shaanxi Province of China under Grant No. 2009JM1007
文摘The equilibrium geometries, potential energy curves, spectroscopic dissociation energies of the ground and low-lying electronic states of He2, He2^＋ and He2^＋＋ are calculated using symmetry adapted cluster/symmetry adapted cluster-configuration interaction （SAC/SAC-CI） method with the basis sets CC-PV5Z. The corresponding dissociation limits for all states are derived based on atomic and molecular reaction statics. The analytical potential energy functions of these states are fitted with Murrell-Sorbie potential energy function from our calculation results. The spectroscopic constants Be, αe, ωe, and ωeχe of these states are calculated through the relationship between spectroscopic data and analytical energy function, which are in well agreement with the experimental data. In addition, the origin of the energy barrier in the ground state X^I∑9^＋ of He2^＋＋ energy curve are explained using the avoided crossing rules of valence bond model.
基金supported by the National Natural Science Foundation of China(Nos.11301030,11431014)
文摘A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain.In this work, the author gives a complete characterization of the recurrent property of this process. The long time behavior of this process such as its p-th moment is also studied. Moreover, the quantitative properties of the regime-switching geometric Brownian motion with two-state switching are investigated to show the difference between geometric Brownian motion with switching and without switching. At last, some estimates of its first passage probability are established.
基金Supported partially by 20120876-SIP-IPN, COFAA-IPN, Mexico
文摘The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[（p）], It is interesting to see that the [~ （p）[ is symmetric with respect to the axis p = 0 and the number of wave crest of [ （p）[ is equal to n ＋ 1. We also study the variation of ]k（p）l with respect to . The arnplitude of ｜ψ（p）] first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11304167 and 51374132Postdoctoral Science Foundation of China under Grant No.20110491317Natural Science Foundation of Henan Province under Grant Nos.2011B140015,132300410209,and 132300410290
文摘The equilibrium geometries, relative stabilities, and electronic properties of Ca2Sin （n = 1-11） clusters have been systematically investigated by using the density function theory at the 6-311G （d） level The optimized geometries indicate that the most stable isomers have three-dimensional structures for n = 3-11. The electronic properties of Ca2 Sin （n = 1-11） dusters axe obtained through the analysis of the natural charge population, natural electron configuration, vertical ionization potential, and vertical electron affinity. The results show that the charges in corresponding Ca2Sin clusters transfer from the Ca atoms to the Sin host. Based on the obtained lowest-energy geometries, the size dependence of cluster properties, such as averaged binding energies, fragmentation energies, second-order energy differences, HOMO- LUMO gaps and chemical hardness, are deeply discussed.
