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991.
Jun Cheng Jie Cang Shi-Jun Liao 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):450-478
A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated
by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with
the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil–Jacotin transformation
is used to transfer the original exponentially nonlinear boundary-value problem in an unknown domain into an algebraically
nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude
water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction
is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest,
but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves
and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current
than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves
on a shear current: a train of propagating waves on a shear current breaks as the fiuid velocity at crest equals the wave
phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than
that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve
many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering. 相似文献
992.
We study the limit properties of solutions to one class of systems of differential equations as the number of equations and some parameters tend to infinity. We establish a close connection between solutions to these systems and differential equations with retarded argument. Our convergence theorems provide a new method for approximation of solutions to nonlinear differential equations with retarded argument.Original Russian Text Copyright © 2005 Demidenko G. V. and Likhoshvai V. A.The authors were supported by the Russian Foundation for Basic Research (Grants 03-01-00328, 03-04-48506, 03-04-48829, 03-07-96833, 04-01-00458, 05-04-49068, and 05-07-90274), the Integration Grant of the Siberian Branch of the Russian Academy of Sciences (No. 119 and 148), the Program Development of the Scientific Potential of Higher School of the Ministry for Education of the Russian Federation (Grant 8273), and NSF:FIBR (Grant EF-0330786).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 538–552, May–June, 2005. 相似文献
993.
We find exact solutions of the equations of motion for a closed relativistic string that carries a point mass and moves in the space given by the direct product of Minkowski space and a compact manifold (multidimensional torus). We investigate physical characteristics of the system states described by these solutions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 72–82, January, 2005. 相似文献
994.
Searching for a counterfeit coin with two unreliable weighings 总被引:1,自引:0,他引:1
We provide a worst-case optimal procedure to identify one unknown heavy coin among N identically looking coins when a balance scale is used and at most two weighing results can be erroneous. The exact minimal number of weighings is determined. This solves completely the weighing problem of the case of two unreliable weighings. 相似文献
995.
In the present study, we treat the stochastic homogeneous Gompertz diffusion process (SHGDP) by the approach of the Kolmogorov equation. Firstly, using a transformation in diffusion processes, we show that the probability transition density function of this process has a lognormal time‐dependent distribution, from which the trend and conditional trend functions and the stationary distribution are obtained. Second, the maximum likelihood approach is adapted to the problem of parameters estimation in the drift and the diffusion coefficient using discrete sampling of the process, then the approximated asymptotic confidence intervals of the parameter are obtained. Later, we obtain the corresponding inference of the stochastic homogeneous lognormal diffusion process as limit from the inference of SHGDP when the deceleration factor tends to zero. A statistical methodology, based on the above results, is proposed for trend analysis. Such a methodology is applied to modelling and forecasting vehicle stocks. Finally, an application is given to illustrate the methodology presented using real data, concretely the total vehicle stocks in Spain. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
996.
This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction–correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction–correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms. 相似文献
997.
In this paper, some new results on the exact penalty function method are presented. Simple optimality characterizations are given for the differentiable nonconvex optimization problems with both inequality and equality constraints via exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable invexity assumption. Furthermore, the equivalence between a saddle point in the invex mathematical programming problem and an optimal point in its exact penalized optimization problem is also proved. 相似文献
998.
基于暴雨内涝天气对公交线路运行影响强弱的三种情形,通过实际调查(RP)和意向调查(SP)的调查结果进行效用模型估计和决策变量的敏感性分析,解析暴雨内涝下公交乘客的出行选择行为机理,得到公交乘客出行选择行为的影响因素(由强至弱)是步行时间、票价、车内时间和车内拥挤程度,以及所选出行方式的主要特点(由强至弱)是零换乘、低票价、中途易更改出行意愿和运行稳定.最后根据上述结果,从调度指挥、对信息服务、交管保障三个方面进行了暴雨内涝天气下公交应急预案的探讨. 相似文献
999.
Manuel Ritoré Cé sar Rosales 《Transactions of the American Mathematical Society》2004,356(11):4601-4622
We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.
We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.