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41.
Serge Tabachnikov 《Geometriae Dedicata》2007,129(1):83-87
We prove a recent theorem by C. Culter every polygonal outer billiard in the affine plane has a periodic trajectory.
相似文献
42.
Transfer matrix approach of vibration isolation analysis of periodic composite structure 总被引:1,自引:0,他引:1
Wang Yong Huang Qibai Zhou Minggang Xu Zhisheng 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(7):461-471
The transmission properties of elastic waves propagating in a three-dimensional composite structure embedded periodically
with spherical inclusions are analyzed by the transfer matrix method in this paper. Firstly, the periodic composite structures
are divided into many layers, the transfer matrix of monolayer structure is deduced by the wave equations, and the transfer
matrix of the entire structure is obtained in the case of boundary conditions of displacement and stress continuity between
layers. Then, the effective impedance of the structure is analyzed to calculate its reflectivity and transmissivity of vibration
isolation. Finally, numerical simulation is carried out; the experiment results validate the accuracy and feasibility of the
method adopted in the paper and some useful conclusions are obtained.
Project (No. 50075029) supported by the National Natural Science Foundation of China. 相似文献
43.
By using the theory of coincidence degree, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with multiple deviating arguments, a new result on the existence of periodic solutions is obtained. 相似文献
44.
Qin Jiang 《Journal of Mathematical Analysis and Applications》2007,328(1):380-389
Some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second-order Hamiltonian systems by the minimax methods in critical point theory. 相似文献
45.
Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes. 相似文献
46.
In general, we will use the numerical differentiation when dealing with the differential equations. Thus the differential equations can be transformed into algebraic equations and then we can get the numerical solutions. But as we all have known, the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, based on the Sinc method we provide a new method using Sinc method incorporated with the double exponential transformation based on the interpolation of the highest derivatives (SIHD) for the differential equations. The error in the approximation of the solution is shown to converge at an exponential rate. The numerical results show that compared with the exiting results, our method is of high accuracy, of good convergence with little computational efforts. It is easy to treat nonhomogeneous mixed boundary condition for our method, which is unlike the traditional Sinc method. 相似文献
47.
Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System 总被引:1,自引:1,他引:0
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This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied. 相似文献
48.
在用单纯形方法解线性规划的问题时,不可避免会出现退化情况,而某些退化情况会导致循环。目前采用的避免循环的方法一共有两类:传统的摄动法(字典序)和Bland方法。本分析了传统摄动法的一些不足,给出了一种新的摄动法。 相似文献
49.
使用参数Dioid模块网络法,把含大量摄动参数的在普通极大代数意义下非线性状态空间模型在参数Dioid意义下线性化,在此基础上研究一类过程摄动系统的无阻塞鲁棒性.给出了有限缓冲串行生产系统在没有缓冲器下无阻塞的充要条件和充分条件. 相似文献
50.
An initial-value method is given for second-order singularly perturbed boundary-value problems with a boundary layer at one endpoint. The idea is to replace the original two-point boundary value problem by two suitable initial-value problems. The method is very easy to use and to implement. Nontrivial text problems are used to show the feasibility of the given method, its versatility, and its performance in solving linear and nonlinear singularly perturbed problems.This work was supported in part by the Consiglio Nazionale delle Ricerche, Contract No. 86.02108.01, and in part by the Ministero della Pubblica Istruzione. 相似文献