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71.
72.
Elena Cordero Karlheinz Grö chenig 《Proceedings of the American Mathematical Society》2005,133(12):3573-3579
We study time-frequency localization operators of the form , where is the symbol of the operator and are the analysis and synthesis windows, respectively. It is shown in an earlier paper by the authors that a sufficient condition for , the Schatten class of order , is that belongs to the modulation space and the window functions to the modulation space . Here we prove a partial converse: if for every pair of window functions with a uniform norm estimate, then the corresponding symbol must belong to the modulation space . In this sense, modulation spaces are optimal for the study of localization operators. The main ingredients in our proofs are frame theory and Gabor frames. For and , we recapture earlier results, which were obtained by different methods.
73.
74.
Ewa M. Bednarczuk Enrico Miglierina Elena Molho 《Set-Valued and Variational Analysis》2011,19(4):569-587
The mountain pass theorem for scalar functionals is a fundamental result of the minimax methods in variational analysis. In this work we extend this theorem to the class of \(\mathcal{C}^{1}\) functions \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}\), where the image space is ordered by the nonnegative orthant \(\mathbb{R}_{+}^{m}\). Under suitable geometrical assumptions, we prove the existence of a critical point of f and we localize this point as a solution of a minimax problem. We remark that the considered minimax problem consists of an inner vector maximization problem and of an outer set-valued minimization problem. To deal with the outer set-valued problem we use an ordering relation among subsets of \(\mathbb{R}^{m}\) introduced by Kuroiwa. In order to prove our result, we develop an Ekeland-type principle for set-valued maps and we extensively use the notion of vector pseudogradient. 相似文献
75.
An analytical protocol consisting of X‐ray fluorescence spectroscopy, optical microscopy and Fourier transform infrared spectroscopy was used to study the origin and the nature of the materials (pigments, binders and coating preparation) of the Fundenii Doamnei church mural paint from Bucharest. The main interest of the present study consisted in the original votive paint from narthex, painted in 1757 in a secco technique. During analysis, an unexpected pigment in the votive paint could be detected by the combined analytical techniques: ultramarine blue. Along with this pigment, the presence of gypsum binder based on egg and flax seed oil could also be evidenced. These results demonstrated a secco execution technique of the votive paint and also the presence of a restoration treatment. Moreover, during the present study, the components of the preparation layer and the constitutive pigments from both 1699 and 1757 years mural paints have been analyzed. Hence, the following pigments could be identified: vermilion, azurite, cinnabar, lead white, ochre, natural umber and gold, by using the combination of the analytical techniques. The novelty of our results consists in detecting the composition of the materials used in this church painting (fresco and a secco) during these 254 years since its first restoration. The results of these investigations pointed to the suitability of the non‐destructive and semi‐destructive analytical techniques in the complex characterization of the paints realized in different techniques, at different periods. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
76.
Elena Bosetto Enrico Serra 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2000,17(6):673
We prove that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics. The approach is based on the construction of multibump type heteroclinic solutions to periodic orbits by the use of global variational methods. 相似文献
77.
Arnas Tamaevi
ius Elena Tamaevi
it Tatjana Pyragien Gytis Mykolaitis Skaidra Bumelien 《Communications in Nonlinear Science & Numerical Simulation》2009,14(12):4273-4279
An improvement of the recently described resonant chaos control method is suggested. Negative feedback loop containing a notch-rejection filter, tuned to the main harmonic of the unstable periodic orbit, is supplemented with a set of notch filters tuned to the higher harmonics. The extended method is applied to an electrical circuit representing the Duffing–Holmes type non-autonomous two-well chaotic oscillator. Stabilization of the period-1 orbit is achieved with very small control force. The residual control signal is about 1% compared to the main variable. Mathematical model based on a two-well piecewise parabolic potential is presented and numerical simulation is performed. Numerical results are confirmed by hardware experiments. 相似文献
78.
An investigation is reported of coherent resonance in the degenerate two-level system of the (Fg = 2 --> Fe = 1) transition of the 87Rb D1 line by means of a Hanle effect configuration. In a coherent population trapping experiment, a very narrow (approximately 1-kHz) resonance superimposed upon a broader resonance (approximately 100 kHz) was observed. The dependence of the width and the amplitude of the coherent resonance on the laser power density, on additional constant magnetic fields, on the laser frequency position along the fluorescence profile, and on Rb cells with different dimensions was investigated. 相似文献
79.
Petr A. Obraztsov Anatoliy. A. Sirotkin Elena D. Obraztsova Yuri P. Svirko Sergey V. Garnov 《Optical Review》2010,17(3):290-293
We demonstrate the passive mode-locking of a diode-pumped Nd+3:YAG (central wavelength: 1.32 μm; pulse duration: 50 ps; output energy: up to 70 μJ) laser using a polymer film containing
single-wall carbon nanotubes. The mode-locking regime is stable at a pump repetition rate of up to 1 kHz. We also investigate
the temporal evolution of the light-induced absorption change of the polymer film containing carbon nanotubes in the spectral
range of 1.3–1.5 μm by femtosecond time-resolved pump-probe measurements. The measurements reveal that light-induced transmission
exhibits fast and slow components that last 280 fs and more than 10 ps, respectively. The third-order susceptibility of the
polymer film containing single wall carbon nanotubes is as high as 10−11 esu. 相似文献
80.
In this paper we consider discrete-time positive switched systems, switching among autonomous subsystems, characterized either by monomial matrices or by circulant matrices. Necessary and sufficient conditions are provided guaranteeing either (global uniform) asymptotic stability or stabilizability (i.e. the possibility of driving to zero the state trajectory corresponding to any initial state by resorting to some switching sequence). Such conditions lead to simple algorithms that allow to easily detect, under suitable conditions, whether a given positive switched system is not stabilizable. 相似文献