An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

Influence of the vertical advection on the nonlinear dynamic properties of the upper-mesosphere photochemistry

We study the influence of the vertical advection on the behavior of the mesospheric photochemical system (altitudes from 80 to 90 km), which is initially in the regime of a nonlinear (subharmonic) response to diurnal variations in solar radiation. It is shown that allowance for the atmospheric transport significantly modifies the nonlinear dynamic properties of this system and, depending on the value and speed direction of the mean vertical wind, can lead to either a suppression of nonlinear oscillations of the minor gas constituents of the upper mesosphere or an increased complexity of their behavior under the actual atmospheric conditions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radio.zika, Vol. 49, No. 12, pp. 1043–1050, December 2006.     

Synthesis of N-trinitroethyl derivatives of linear and heterocyclic nitrogen-containing compounds

Earlier unknown N-trinitroethyl derivatives of acetylhydrazine, 4-amino-1,2,4-triazole, and 2,4,6-triamino-1,3,5-triazine, which are potential components for gas-generating formulations, were synthesized. Dedicated to Academician N. K. Kochetkov on the occasion of his 90th birthday. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1306–1309, May, 2005.     

Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant

We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L _k -type distances. In the case of a uniform distribution, we also establish their limit distribution together with that of the supremum distance. It turns out that in the uniform case, the measures of deviation are of greater order and their limit distributions are different.     

Interaction between the components of a five-component cold medicine

The reasons why five-component cold pills, a new complex medicine under development, change their color during shelf life are studied. The oxidation of ascorbic acid (AA) is responsible for the change in color; this process is enhanced in the presence of nitrogen base compounds. The IR spectra of equimolar mixtures of AA with some such compounds signify these changes. The results of this work can be used to eliminate undesired effects.     

Calculation of singularities of an imbedding of a generic algebraic surface in projective space P3

Functional Analysis and Its Applications -     

Electronic structure of transition metals under pressure

Conclusions In this short review we have tried to demonstrate the advances made in the intensive study of the behavior of the electronic structure of metals under pressure in recent years. The alloys of transition metals, including intermetallic ordered compounds, have for the time being proved to lie outside the scope of this review, mainly because of the lack, in practice, of theoretical calculations in this area. Clearly, progress in this field is also being held up by the lack of detailed experimental investigations devoted to the behavior of alloys under pressure. This is due to the complexities involved in carrying out many traditional experimental procedures under high pressures. We should like to emphasize, however, that at the present time theoretical calculations have taken on a predictive power and this gives reason to hope that progress in calculations will in turn stimulate progress in experimentation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 50–62, December, 1982.     

Revision of the theory of symmetric one-step methods for ordinary differential equations

In this paper we develop a new theory of adjoint and symmetric methods in the class of general implicit one-step fixedstepsize methods. These methods arise from simple and natural definitions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for methods having these properties and show, in particular, that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition, we give a very simple test to identify the symmetric methods in practice.