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991.
Emilio Freire Armengol Gasull Antoni Guillamon 《Bulletin des Sciences Mathématiques》2007,131(6):501-517
Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail. 相似文献
992.
We characterize δ-I-sets, discuss the relation between δ-sets, δ-I-sets and I
δ-sets and generalize some of the results. 相似文献
993.
Frank Natterer Olga Klyubina 《计算数学(英文版)》2007,25(3):368-373
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging. 相似文献
994.
利用变温X射线衍射技术,在预烧过程中分析了Nd掺杂Bi4Ti3O12后生成Bi3.15Nd0.85Ti3O12(BNT)相的形成过程以及微结构的变化.实验观察到以30℃/min的升温速率,BNT相在700℃时开始形成,其衍射峰强度随温度的继续升高而增强,衍射峰半高宽随烧结时间延长而减小.X射线衍射分析结果表明,在900℃恒温条件下,烧结约2h,可形成单一的BNT相. 相似文献
995.
In this paper we use the upper semifinite topology in hyperspaces to get results in normal Hausdorff topology. The advantage of this point of view is that the upper semifinite topology, although highly non-Hausdorff, is very easy to handle. By this way we treat different topics and relate topological properties on spaces with some topological properties in hyperspaces. This hyperspace is, of course, determined by the base space. We prove here some reciprocals which are not true for the usual Vietoris topology. We also point out that this framework is a very adequate one to construct the ?ech-Stone compactification of a normal space. We also describe compactness in terms of the second countability axiom and of the fixed point property. As a summary we relate non-Hausdorff topology with some facts in the core of normal Hausdorff topology. In some sense, we reinforce the unity of the subject. 相似文献
996.
半正二阶三点边值问题的解和正解 总被引:8,自引:0,他引:8
考察了非线性二阶三点边值问题的n个解和正解的存在性,其中允许非线性项有一个负的下界并且n是一个任意的自然数.主要结论表明该问题可以具有n个解或者正解,只要非线性项在某些有界集上的“高度”是适当的. 相似文献
997.
Yue Liu Masahito Ohta Grozdena Todorova 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2007
We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave's frequency or the wave's speed of propagation and on the nonlinearity. 相似文献
998.
An element σ of An, the Alternating group of degree n, is extendible in Sn, the Symmetric group of degree n, if there exists a subgroup H of Sn but not An whose intersection with An is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of An to be extendible in Sn is given here. 相似文献
999.
Kullback-Leibler divergence and the Neyman-Pearson lemma are two fundamental concepts in statistics. Both are about likelihood ratios: Kullback-Leibler divergence is the expected log-likelihood ratio, and the Neyman-Pearson lemma is about error rates of likelihood ratio tests. Exploring this connection gives another statistical interpretation of the Kullback-Leibler divergence in terms of the loss of power of the likelihood ratio test when the wrong distribution is used for one of the hypotheses. In this interpretation, the standard non-negativity property of the Kullback-Leibler divergence is essentially a restatement of the optimal property of likelihood ratios established by the Neyman-Pearson lemma. The asymmetry of Kullback-Leibler divergence is overviewed in information geometry. 相似文献
1000.
P. Kh. Atanasova T. L. Bojadjiev S. N. Dimova 《Computational Mathematics and Mathematical Physics》2006,46(4):666-679
Partial critical dependences of the form current-magnetic field in a two-layered symmetric Josephson junction are modeled. A numerical experiment shows that, for the zero interaction coefficient between the layers of the junction, jumps of the critical currents corresponding to different distributions of the magnetic fluxes in the layers may appear on the critical curves. This fact allows a mathematical interpretation of the results of some recent experimental results for two-layered junctions as a consequence of discontinuities of partial critical curves. 相似文献