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901.
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
902.
Vitalij A. Chatyrko 《Topology and its Applications》2007,154(7):1314-1320
In [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993], Aarts and Nishiura investigated several types of dimensions modulo a class P of spaces. These dimension functions have natural transfinite extensions. The small transfinite compactness degree trcmp is such transfinite dimension function extending the small compactness degree cmp. We shall prove that there is no upper bound for trcmp in the class of metrizable spaces, i.e. for each ordinal number α there exists a metrizable space Xα such that trcmpXα=α. We also give a characterization of the dimension dim of a separable (compact) metrizable space in terms of the function cmp of the product of this space with a nowhere locally compact zero-dimensional factor. 相似文献
903.
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
904.
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
905.
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
906.
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
907.
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
908.
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
909.
Parasteh Pirasteh Ali Soltani Lazhar Haji Nicolas Errien 《Applied Surface Science》2006,253(4):1999-2002
In order to understand the optical loss mechanisms in porous silicon based waveguides, structural and optical studies have been performed. Scanning and transmission electron microscopic observations of porous silicon layers are obtained before and after an oxidation process at high temperature in wet O2. Pore size and shape of heavily p-type doped Si wafers are estimated and correlated to the optical properties of the material before and after oxidation. The refractive index was measured and compared to that determined by the Bruggeman model. 相似文献
910.
用TSC程序模拟了EAST装置等离子体放电的全过程。模拟中考虑了自举电流,并加入了离子回旋共振加热ICRH和快波电流驱动FWCD,得到了中心电子温度4.5keV、中心离子温度3.8keV、中心电子密度1.2×1020m–3的D形截面的等离子体。根据模拟结果对EAST装置进行了伏秒数分析,并研究了不同等离子体电流上升时间、有效电荷数Zeff对放电的影响。 相似文献