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71.
72.
Qingjie Cao Sergey Piskarev Stefan Siegmund 《Numerical Functional Analysis & Optimization》2013,34(10):1287-1307
This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value problems with exponential bounded solutions on the corresponding subspaces. We show that such a decomposition of the flow persists under rather general approximation schemes, utilizing a uniform condensing property. The main assumption of our results are naturally satisfied, in particular, for operators with compact resolvents and condensing semigroups and can be verified for finite elements as well as finite differences methods. 相似文献
73.
Yunfei Chen 《Wireless Communications and Mobile Computing》2013,13(6):565-576
Collaborative spectrum sensing with user selection is analyzed for correlated shadowing in the practical cases of imperfect power measurements and noisy secondary links. The user selection is performed using the minimum probability of missed opportunity criterion and the random search criterion. Both the Neyman–Pearson rule and the minimum probability of error rule are considered. The sensing performance is examined with respect to different system parameters. Numerical results show that user selection can achieve a large amount of resource saving at little performance loss. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
74.
Sergey Bolotin 《分析论及其应用》2021,37(1):1-23
We prove the existence of trajectories shadowing chains of heteroclinic orbits to a symplectic normally hyperbolic critical manifold of a Hamiltonian system.The results are quite different for real and complex eigenvalues. General results are applied to Hamiltonian systems depending on a parameter which slowly changes with rate ε. If the frozen autonomous system has a hyperbolic equilibrium possessing transverse homoclinic orbits, we construct trajectories shadowing homoclinic chains with energy having quasirandom jumps of order ε and changing with average rate of orderε| ln ε|. This provides a partial multidimensional extension of the results of A. Neishtadt on the destruction of adiabatic invariants for systems with one degree of freedom and a figure 8 separatrix. 相似文献
75.
Microcrystalline silicon (μc-Si:H) thin films with and without boron doping are deposited using the radio-frequency plasma-enhanced chemical vapour deposition method. The surface roughness evolutions of the silicon thin films are investigated using ex situ spectroscopic ellipsometry and an atomic force microscope. It is shown that the growth exponent β and the roughness exponent α are about 0.369 and 0.95 for the undoped thin film, respectively. Whereas, for the boron-doped μc-Si:H thin film, β increases to 0.534 and α decreases to 0.46 due to the shadowing effect. 相似文献
76.
77.
In this paper, the J/ψ nuclear absorption effect is studied at RHIC and LHC energies with the EKS98 shadowing parameterizations. By assuming that the J/ψ absorption cross section, σ abs , increases with the charmonium-nucleon (J/ψ-N) center of mass energy, s J/ψN , it is found that σ abs should depend on x F (or y) at a certain center of mass energy per nucleon pair,s , especially at LHC energies. The theoretical results with the x F (or y)-dependence of the absorption effect are in good agreement with the experiment data from PHENIX in d-Au collisions and the predicted results will be examined by the forthcoming experimental data from LHC in d-Pb collisions. Finally, we also present baseline calculations of cold nuclear matter effects on J/ψ production in nucleus-nucleus (A-A) collisions and find that the x F (or y)-dependence of absorption effect is very small at both RHIC and LHC energies in A-A collisions. 相似文献
78.
79.
We consider three numerical methods – one based on power series, one on the Magnus series and matrix exponentials, and one
a library initial value code – for solving a linear system arising in non‐selfadjoint ODE eigenproblems. We show that in general,
none of these methods has a cost or an accuracy which is uniform in the eigenparameter, but that for certain special types
of problem, the Magnus method does yield eigenparameter‐uniform accuracy. This property of the Magnus method is explained
by a trajectory‐shadowing result which, unfortunately, does not generalize to higher order Magnus type methods such as those
in [11,12].
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
80.
Heinrich Steinlein Hans-Otto Walther 《Journal of Dynamics and Differential Equations》1990,2(3):325-365
In an earlier paper we generalized the notion of a hyperbolic set and proved that the Shadowing Lemma remains valid, for C1-maps which need not be invertible. Here we establish the existence of (generalized) hyperbolic structures along transversal homoclinic trajectories of C1-maps. The hyperbolic structure and shadowing are then used to give a new proof of a result due to Hale and Lin (and ilnikov) on symbolic dynamics forall trajectories sufficiently close to a transversal homoclinic trajectory. The result is applied to a Poincaré map without continuous inverse, which is associated with a periodic orbit of an autonomous differential delay equation. 相似文献