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141.
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
142.
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
143.
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally, we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory. 相似文献
144.
Yevhen Zelenyuk 《Topology and its Applications》2007,154(2):339-357
A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents. 相似文献
145.
The non-resonant third-order non-linear optical properties of amorphous Ge20As25Se55 films were studied experimentally by the method of the femtosecond optical heterodyne detection of optical Kerr effect. The real and imaginary parts of complex third-order optical non-linearity could be effectively separated and their values and signs could be also determined, which were 6.6 × 10−12 and −2.4 × 10−12 esu, respectively. Amorphous Ge20As25Se55 films showed a very fast response in the range of 200 fs under ultrafast excitation. The ultrafast response and large third-order non-linearity are attributed to the ultrafast distortion of the electron orbitals surrounding the average positions of the nucleus of Ge, As and Se atoms. The high third-order susceptibility and a fast response time of amorphous Ge20As25Se55 films makes it a promising material for application in advanced techniques especially in optical switching. 相似文献
146.
Ryuichi Tanaka 《Topology and its Applications》2007,154(15):2849-2855
We describe a finite complex B as I-trivial if there does not exist a Z2-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP2 is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0. 相似文献
147.
Csaba Sándor 《Periodica Mathematica Hungarica》1996,33(2):121-134
148.
Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in 1H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between 1H spins is strong. 29Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the 29Si relaxation of relatively pure samples under static and slow-spinning conditions. 27Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between 27Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated. 相似文献
149.
Tim Bedford 《Constructive Approximation》1989,5(1):33-48
We consider some self-affine fractal functions previously studied by Barnsleyet al. The graphs of these functions are invariant under certain affine scalings, and we extend their definition to allow the use of nonlinear scalings. The Hölder exponent,h, for these fractal functions is calculated and we show that there is a larger Hölder exponent,h
, defined at almost every point (with respect to Lebesgue measure). For a class of such functions defined using linear affinities these exponents are related to the box dimensionD
B of the graph byh2–D
Bh
.Communicated by Michael F. Barnsley. 相似文献
150.
LetS
(1)
(n, Q) denote the maximum module of exponential sums for polynomials of degree n over the Galois fieldF
Q
. In a previous paper the transition to the multiple exponential sums allowed us to obtain a good lower bound of the valueS
(1)
(n, Q), which coincides with Weil's bound whenn = q
(m-1)/2 + 1, whereq, m are odd andm 3. Here the same approach is used for the estimation of the valueS
(d)
(n, Q), which corresponds to polynomials(x
d
) overF
Q
, whered is any divisor ofq – 1. 相似文献