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141.
On noise reduction methods for chaotic data 总被引:1,自引:0,他引:1
Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters. 相似文献
142.
Thomas R. Love 《International Journal of Theoretical Physics》1993,32(1):63-88
The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number. 相似文献
143.
144.
Let be a singular cardinal of regular uncountable cofinality. Let {(): < } be a continuous increasing sequence withlimit , and let =()+(), < be regular cardinals. Let I be a normal ideal on , and assume that the reduced product</I admits a cofinal -scale of ordinal functions. Then +, where =||||I is the I-norm of . 相似文献
145.
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain
Thomas M. Fischer 《Numerische Mathematik》1993,66(1):159-179
Summary The convergence of a Galerkin approximation of the Orr-Sommerfeld eigenvalue problem, which is defined in a semi-infinite domain, is studied theoretically. In case the system of trial functions is based on a composite of Jacobi polynomials and an exponential transform of the semi-infinite domain, the error of the Galerkin approximation is estimated in terms of the transformation parametera and the numberN of trial functions. Finite or infinite-order convergence of the spectral Galerkin method is obtained depending on how the transformation parameter is chosen. If the transformation parameter is fixed, then convergence is of finite order only. However, ifa is varied proportional to 1/N
with an exponent 0<<1, then the approximate eigenvalue converges faster than any finite power of 1/N asN. Some numerical examles are given. 相似文献
146.
Thomas M. Lewis 《Journal of Theoretical Probability》1993,6(2):209-230
LetX, X i ,i≥1, be a sequence of independent and identically distributed ? d -valued random vectors. LetS o=0 and \(S_n = \sum\nolimits_{i = 1}^n {X_i } \) forn≤1. Furthermore letY, Y(α), α∈? d , be independent and identically distributed ?-valued random variables, which are independent of theX i . Let \(Z_n = \sum\nolimits_{i = 0}^n {Y(S_i )} \) . We will call (Z n ) arandom walk in random scenery. In this paper, we consider the law of the iterated logarithm for random walk in random scenery where deterministic normalizers are utilized. For example, we show that if (S n ) is simple, symmetric random walk in the plane,E[Y]=0 andE[Y 2]=1, then $$\mathop {\overline {\lim } }\limits_{n \to \infty } \frac{{Z_n }}{{\sqrt {2n\log (n)\log (\log (n))} }} = \sqrt {\frac{2}{\pi }} a.s.$$ 相似文献
147.
This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic
manifoldN with tamed almost complex structure. (These are the objects used by Gromov to define his symplectic invariants.) The paper
begins by developing some analytic facts about such maps, including a simple new isoperimetric inequality and a new removable
singularity theorem.
The main technique is a general procedure for renormalizing sequences of maps to obtain “bubbles on bubbles.” This is a significant
step beyond the standard renormalization procedure of Sacks and Uhlenbeck. The renormalized maps give rise to a sequence of
maps from a “bubble tree”—a map from a wedge Σ V S2 V S2 V ... →N. The main result is that the images of these renormalized maps converge in L1,2 ∪C° to the image of a limiting pseudo-holomorphic map from the bubble tree. This implies several important properties of the
bubble tree. In particular, the images of consecutive bubbles in the bubble tree intersect, and if a sequence of maps represents
a homology class then the limiting map represents this class. 相似文献
148.
149.
150.
Cai H Chen T Wang X Schultz AJ Koetzle TF Xue Z 《Chemical communications (Cambridge, England)》2002,(3):230-231
Reactions of Ta(NMe2)5 with D2SiR'Ph (R' = Me, Ph) were found to give a dideuteride eta 2-imine complex (Me2N)3Ta(mu-D)2(mu-N-eta 2-N,C-CH2NMe)Ta(NMe2)3(1-d2) through C-H activation of an amide ligand via beta-H abstraction, and the structure of 1 was confirmed by single crystal neutron and X-ray diffraction. 相似文献