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A method for gyrotron cathode treatment by flow of potassium ions has been developed, and the effect of ion bombardment on the emission characteristics of W-Ba and LaB6 cathodes has been investigated. The influence of cathode surface material, cathode emission activity and ion energy on the result of ion treatment was revealed. It was shown that ion bombardment can be used for the increase of cathode emission uniformity due to the activation of the W-Ba cathode areas with low electron emission and due to the deactivation of the LaB6 cathode areas with high electron emission.

A chaotic piece-wise linear map having arbitrary interchange of linear increasing and decreasing branches is introduced. Polynomial eigenfunctions for associated non-selfadjoint Perron–Frobenius operator are found. Odd eigenvalus of the operator depend on difference between numbers of increasing and decreasing map branches. This situation may determine transition of odd polynomials from set of eigenfunctions to null-space of the operator or lead to nonsimplicity of eigenvalues.

Hundred years ago Albert Einstein’s five important works were published. These works changed significantly our representation about the world around and had huge influence on the development of our civilization.

The concept of spatial deterministic chaos is justified. An attempt to give its settheoretic definition is undertaken. Transition from the ordinary differential equations to discrete maps without use of an approximation of the instantaneous response is realized for mathematical description of spatial deterministic chaos. The developed theoretical theses are applied for deriving a dynamics model in terms of discrete maps of nonlinear phase shift in a ring interferometer.

Families of initial-final maps, bifucation lines, maps of Lyapunov’s characterictic exponents and fractal dimentionality D0 are constructed for a model of nonlinear pphase shift dynamics for ont- and two-frequency field in a ring interferometer. The influence of a spectrum form of two-frequency radiation to a structure of mentioned maps is clarified.Ways of maps quantitative analysis are suggested and realized. Two languages of nonlinear dynamics description in the ring interferometer are compared: with the help of ordinary differential equations and of the discrete map.

A set of the nonlinear equations, approximately describing thermoelectrohydrodynamical convection in circular semiconductor cell, which comes to Lorenz model, is obtained. The dependences of the model parameters of materials and ring size, of affixed electric field and of temperature gradient are investigated.

The influence of a pulse train on the dynamics of unidirectly nonlinearly coupled Hindmarsh-Rose neurons is investigated. The synchronization of the spike-generating neuron by the periodical pulse train is studied. Information and dynamical aspects of burst generation under the action of a pulse train with irregular interpulse intervals are analyzed. It is shown that the backward burst-to-spike transformation by the neuron at rest is possible. Dynamic unreliability during the spike-to-burst transformation is explained qualitatively.

Emission characteristics of autoemitters with a various relief of a Surface are investigated. It is experimentally shown, that reduction of a backlash in microdiod devices inevitably leads to significant growth of macroscopical intensity of an electrostatic field at the set size of an autoemission current.

The possibility of reconstruction of complex unharmonic motion function of subject was investigated using autodyne interference system. Experimental results of parameter determination of complex unharmonic motion of reflector were presented. It was shown that application of manystages digital filtration of autodyne experimental signal allows to decrease influence of noise distortion on reconstruction signal.

Based on the parabolic differential equation solution behaviour of the pulse width at half-height in linear second order dispersion media was analyzed. It was shown that rectangular non-chirped pulse width varies non-monotonously with distance and reaches 50–60% initial width at compression length that is equal to 0.44 dispersive length. This compression was shown to be caused by dispersive pulse-edges perturbations that lead to frequency chirp on pulse top.