Semiclassical approach to the low-lying collective excitations in nuclei

For low-lying collective excitations we derived the inertia within the semiclassical Gutzwiller approach to the onebody Green’s function at lowest orders in h. The excitation energies, reduced probabilities and energy-weighted sum rules are in agreement with main features of the experimental data

Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials

We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table

Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use perturbation theory to obtain their evolution away from the bifurcation points. As an application, we derive an analytical semiclassical trace formula for the density of states in the separable case, using a uniform approximation for the pitchfork bifurcations occurring there, which allows for full semiclassical quantization. For the non-integrable situations, we show that the uniform contribution of the bifurcating period-one orbits to the coarse-grained density of states competes with that of the shortest isolated orbits, but decreases with increasing chaoticity parameter $\alpha$.Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear in J. Phys. A final version 3; error in eq. (33) corrected and note added in prin

Periodic-Orbit Bifurcations and Superdeformed Shell Structure

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.Comment: 4 pages including 3 figure

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain

Computer analysis of flow data for controlling system refusals

Algorithms are o®ered for selecting the principal elements of a system. Fail- ures of principal elements generate an epidemic of refusals. The preventive main- tenance problem of improving the reliability of functioning of a complex control- ling system is considered. The statistical analysis of moments of failures of the principal elements allows to solve this reliability problem

Computer analysis of flow data for controlling system refusals

Algorithms are o®ered for selecting the principal elements of a system. Fail- ures of principal elements generate an epidemic of refusals. The preventive main- tenance problem of improving the reliability of functioning of a complex control- ling system is considered. The statistical analysis of moments of failures of the principal elements allows to solve this reliability problem

Simulation of adaptive control system with conflict flows of non-homogeneous requests

An adaptive control system with conflict flows of non-homogeneous requests is considered in the paper. A mathematical model of the system is a vector Markov sequence with a countable state space. Components of the Markov sequence satisfy certain functional recurrence relations. The main result of the work is a numerical research of the system by simulation. In particular, some sample estimates for the mean sojourn time of a single request from different queues are presentedThe work was performed as the basic part of the states tasks in the sphere of scientific activities on the Task No 2014/134 and supported by RFBR (project No 18-413-520005