Self-Diffraction of Bessel Light Beams in a Nonlinear Medium

The phenomenon of self-diffraction of Bessel light beams (BLB) in a nonlinear liquid medium has been studied experimentally and theoretically for the first time. Diffraction maxima which do not correspond to integer orders for an induced periodic structure have been registered. It has been shown that the appearance of these maxima is due to the initial BLB modulation, which can be caused by the departure of the axicon refracting surface from the ideal conical surface, as well as by the imperfection of the form of the Gaussian beam incident on the axicon.     

一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

Submicrometric Displacement and Vibration Measurement Using Optical Feedback in a Fiber Laser

A very simple and efficient technique for the remote sensing of a noncooperative target is presented. This technique is based on the frequency-shifted reinjection of light in a class B laser. Ytterbium- and erbium-doped fiber lasers have both been used to measure displacements with a submicrometric resolution and the vibration power spectrum of an object.     

Synthesis,characterization and properties of methylaminocellulose

Homogeneously prepared tosylcelluloses (TC) with degrees of substitution (DS) of DS_Tos 0.1–1.8 were used as intermediates for the synthesis of methylaminocelluloses (MAC) by nucleophilic substitution with methylamine. TC with DS_Tos up to 1.1 were shown to be valuable intermediates for selective synthesis of MAC with DS_MA varying from 0.1 to approximately 1. No nucleophilic substitution was observed at higher DS_Tos. At the chosen reaction conditions (60 °C, 48 h) residual tosyl moieties remained unchanged and little hydrolysis took place. The samples obtained were characterized by means of elemental analysis, FTIR and ¹³C CP/MAS NMR spectroscopy. ¹³C CP/MAS NMR spectroscopy was found to be an efficient tool for quantification of DS_MA. Furthermore, the swelling behaviour in water was investigated and preliminary tests concerning the bilirubin adsorption capacity of MAC were carried out.     

Nonlinear Energy Transfer over the Wave Spectrum in Water Covered by Solid Ice

On the basis of the hydrodynamic equations for nonlinear elastic-gravity waves beneath a solid ice cover and their Hamiltonian representation, a three-wave kinetic equation for the time evolution of the wave spectrum is formulated. The properties of the kernel of the kinetic integral describing the nonlinear interactions between wave triplets are investigated. An algorithm for numerically calculating the kinetic integral is developed. The rate of nonlinear energy transfer over the wave spectrum is estimated quantitatively and its most important characteristics are found.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Microsolvation of phthalocyanines in superfluid helium droplets.

Experimental and theoretical investigations of the spectroscopy of molecules in superfluid helium droplets provide evidence for the key role of the first helium layer surrounding the dopant molecule in determining the molecule's spectroscopic features. Recent investigations of emission spectra of phthalocyanine in helium droplets revealed a doubling of all transitions. Herein, we present the emission spectra of Mg-phthalocyanine and of phthalocyanine-argon clusters in helium droplets, which confirm the splitting as a general effect of the helium environment. A scheme of levels is deduced from the emission spectra and attributed to quantized states of the first helium layer surrounding the dopant molecule.     

Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization

This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of Itô calculus. Further, it is noted that these relations are very useful within the framework of an equivalent statistical non-linearization technique to build approximate solutions for arbitrary non-linear systems.     

A system-theoretic framework for a wide class of systems I: Applications to numerical analysis

A system-theoretic framework is proposed, which allows the study of hybrid uncertain systems, which do not satisfy the so-called “semigroup property.” Characterizations of the notion of robust global asymptotic output stability (RGAOS) are given. Based on the provided characterizations, the qualitative behavior of hybrid systems obtained by time-discretization of systems of ordinary differential equations with a globally asymptotically stable equilibrium point, is studied.