We consider reversible mechanical systems that have the property of space-time symmetry and are distinguished by a linear transformation of the phase space. It is assumed that the system admits a nondegenerate symmetric periodic motion. The problem of stabilizing the oscillations of a controlled reversible mechanical system is solved, controls are found, an attracting cycle is constructed, and an example is given.

Airborne electromagnetic methods are characterized in detail. A classification of airborne electromagnetic systems is presented. Modern active frequency-domain, time-domain and combined electromagnetic systems, and electromagnetic passive systems are discussed. The paper demonstrates specific aspects to be considered in the development and operation of airborne electromagnetic systems. The paper discusses aspects of processing of signals measured onboard, and techniques to improve system susceptibility, mobility and reliability. Survey results are presented. The paper shows what kind of problems can be effectively resolved today using airborne electromagnetic surveys.

The technology of ground-based and airborne helicopter-based electromagnetic survey measurements aimed at the assessment of prospective areas for water is described. For the complex geocryological conditions of Yakutia, the effectiveness of the time-domain and frequency-domain transient electromagnetics in identifying the zones recommended for water-well drilling is demonstrated.

We propose a new controller parameter adaptive law that guarantees the exponentialstability of the classical dynamic model of the tracking error without using its coordinates in theadaptive law and relaxes some classical assumptions and requirements of adaptive control theory(the need to know the sign/value of the control input gain, the need for an experimental choice ofthe adaptive law gain, and the requirement to the tracking error transfer function to be strictlypositive real considering the output feedback control). The applicability of the proposed law toadaptive state and output feedback control problems is shown. The advantages of developedapproach over the existing ones are demonstrated mathematically and experimentally.

In this paper, for a continuous function defined on a closed subset of a Banach space and differentiable on the interior of the domain, the infimum of the norm of the first derivative is estimated through the variation of the function on the boundary of the domain. A similar result is obtained for locally Lipschitz functions. These results generalize the previously known estimates of the infimum of the norm of the derivative in terms of the variation of the function on the entire domain. Under the assumption that the considered function is twice differentiable on the interior of the domain, similar estimates for the infimum of the norm of the first-order derivative and the estimates of the values of the second-order derivative are obtained. The proof of these results is based on the application of the modifications of the Bishop-Phelps variational principle and the Borwein-Preiss smooth variational principle. As applications of these results, we obtain second-order necessary optimality conditions for minimizing sequences. This proposition is proved under an additional assumption on the norm of the Banach space valid for a wide class of function spaces. In addition, some of the described results are generalized for mappings, acting in Banach spaces ordered by pointed closed convex cones.