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91.
Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding
to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the
expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r
2〉 − 〈r〉2]1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket
in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order,
the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic
classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic
quantal system, in general. 相似文献
92.
A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
93.
Bai-suo JIN~ 《中国科学A辑(英文版)》2007,50(9):1303-1315
In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted. 相似文献
94.
Tetsushi Nishida Kokichi Sugihara Masato Kimura 《Journal of Computational and Applied Mathematics》2007
The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points. 相似文献
95.
In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps. 相似文献
96.
Numerical analysis for stochastic age-dependent population equations with Poisson jumps 总被引:1,自引:0,他引:1
In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution. 相似文献
97.
We consider a single machine scheduling problem with two min-sum objective functions: the sum of completion times and the sum of weighted completion times. We propose a simple polynomial time (1+(1/γ),1+γ)-approximation algorithm, and show that for γ>1, there is no (x,y)-approximation with 1<x<1+(1/γ) and 1<y<1+(γ-1)/(2+γ). 相似文献
98.
Karl Sigman 《Operations Research Letters》2007,35(5):581-583
In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments. 相似文献
99.
D. Abouelaoualim 《Pramana》2006,66(2):455-465
We develop a theoretical model to the scattering time due to the electron-confined LO-phonon in GaAs-AlxGa1-xAs superlattice taking into account the sub-band parabolicity. Using the new analytic wave function of electron miniband conduction
of superlattice and a reformulation slab model for the confined LO-phonon modes, an expression for the electron-confined LO-phonon
scattering time is obtained. In solving numerically a partial differential equation for the phonon generation rate, our results
show that forx = 0.45, the LO-phonon in superlattice changes from a bulk-like propagating mode to a confined mode. The dispersion of the
relaxation time due to the emission of confined LO-phonons depends strongly on the total energy. 相似文献
100.
500.8 nmNd∶YAG青光激光器光学薄膜的设计与制备 总被引:5,自引:2,他引:3
从双波长激光运转及和频的机理出发,对LD泵浦Nd∶YAG,LBO腔内和频500.8 nm〖JP2〗青光激光器所使用的光学薄膜进行了设计和制备.在激光反射镜的设计上,为了达到最佳的和频输出,对膜系要求进行了深入分析.采用对谐振腔一端面反射率固定不变并通过对另一腔镜基频光的透射率进行调谐的方法, 在给出合理初始结构后,利用计算机对膜厚进行了优化.并采用双离子束溅射沉积的方法,通过时间监控膜厚法成功制备出青光激光器所使用的全介质激光反射膜, 在室温下实现946 nm和1064 nm双波长连续运转,并通过Ⅰ类临界相位匹配LBO晶体腔内和频在国内首次实现500.8 nm青色激光连续输出.当泵浦注入功率为1.4 W时和频青光最大输出达20 mW. 相似文献