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21.
Subhashis Nag 《Proceedings Mathematical Sciences》1989,99(2):103-111
We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus.
This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel
upper half-space as well as to the Hodge metric on the Hodge bundle. 相似文献
22.
The basic theory of symplectic algorithm was introduced. A comparison between Runge-Kutta method and symplectic integration method was preformed in the simulation of the long time behavior of H + H2 system on BKMP potential energy surface. Our results reveal a dis-sipative behavior in the integral of ordinary differential equation by the fourth order Runge-Kutta method, which causes incorrect simulation results in QCT calculations. However, when the symplectic integration method is applied, the dissipative behavior is not found in the same system. When the initial state is the same, the energy deviation of fourth order symplectic integral method is almost one percent of that of fourth order Runge-Kutta method in a 60000-step simulation, and that of sixth order symplectic integral method is much less. These results show that the symplectic integral methods are always the better choice in the integral calculation of the long time behavior in maintaining energy conservation. 相似文献
23.
Th.?Monovasilis Z.?Kalogiratou T.E.?SimosEmail author 《Journal of mathematical chemistry》2005,37(3):263-270
The computation of the energy eigenvalues of the one-dimensional time-independent Schrödinger equation is considered. Exponentially fitted and trigonometrically fitted symplectic integrators are obtained, by modification of the first and second order Yoshida symplectic methods. Numerical results are obtained for the one-dimensional harmonic oscillator and Morse potential.AMS subject classification: 65L15Funding by research project 71239 of Prefecture of Western Macedonia and the E.U. is gratefully acknowledged. 相似文献
24.
Gun'ko VM Villiéras F Leboda R Marciniak M Charmas B Skubiszewska-Zi&ecedil;ba J 《Journal of colloid and interface science》2000,230(2):320-327
Adsorbents synthesized by grafting of titania onto mesoporous silica gel surfaces at different temperatures were studied by means of nitrogen adsorption–desorption and water desorption. The pore size distribution f(Rp) of titania/silica gel depends on the titania concentration (CTiO2) and the temperature of titania synthesis. Nonuniformity of TiO2 phase is maximal at a low CTiO2 value (3.2 wt.% anatase deposited at 473 K), and two peaks of the fractal dimension distribution f(D) are observed at such a concentration of titania, but at larger CTiO2 values, only one f(D) peak is seen. More ordered filling of pores and adsorption sites by nitrogen, reflecting in the shape of adsorption energy distributions f(E) at different pressures of adsorbate, is observed for adsorbent with titania (rutile+anatase) grafted on silica gel at a higher temperature (673 K). 相似文献
25.
We show that, when numerically integrating Hamiltonian problems, nondissipative numerical methods do not in general share the advantages possessed by symplectic integrators. Here a numerical method is called nondissipative if, when applied with a small stepsize to the test equationdy/dt = iy, real, has amplification factors of unit modulus. We construct a fourth order, nondissipative, explicit Runge-Kutta-Nyström procedure with small error constants. Numerical experiments show that this scheme does not perform efficiently in the numerical integration of Hamiltonian problems.This research has been supported by project DGICYT PB92-254. 相似文献
26.
Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution
belongs to the range of the operator (T
*
T)
v
, o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India. 相似文献
27.
R. A. Poliquin R. T. Rockafellar 《Transactions of the American Mathematical Society》1996,348(5):1805-1838
The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.
28.
Chunli Zhang Xueshen Liu Peizhu Ding Yueying Qi 《Journal of mathematical chemistry》2006,39(3-4):451-463
Asymptotic boundary condition (ABC) of laser-atom interaction presented recently is applied to transform the initial value problem of the time-dependent Schrödinger equation (TDSE) in infinite space into the initial and boundary value problem in the finite space, and then the TDSE is discretized into linear canonical equations by substituting the symmetry difference quotient for the 2-order partial derivative. The canonical equation is solved by symplectic algorithm. The ground state and the equal weight coherent superposition of the ground state and the first excited state have been taken as the initial conditions, respectively, while we calculate the population of bound states, the evolution of average distance and the high-order harmonic generation (HHG). The conversion efficiency of HHG can be enhanced by initial coherent superposition state and moderate laser intensities 相似文献
29.
30.
Shi-Xing Liu Ya-Qiu Lang Xue-Shen Liu Pei-Zhu Ding Yue-Ying Qi 《Journal of mathematical chemistry》2007,41(2):113-122
The classical dynamics of 1D H2+ in an intense field are discussed. The initial conditions are chosen at random in the field-free case, and then the Hamiltonian
canonical equations of H2+ system in the intense laser field are solved numerically by mean of the symplectic method under these initial conditions.
The probabilities of survival, dissociation, ionization, and Coulomb explosion of H2+ system in the intense laser field are obtained for different laser intensity based on the classical theory. 相似文献