Finding of Bounded Solutions to Linear Impulsive Systems

The problem of the existence of bounded on the entire real axis solutions to linear nonhomogeneous systems of differential equations undergoing impulsive perturbations at the fixed moments of time is investigated. Sufficient conditions for the hyperbolicity of solutions to the homogeneous multidimensional impulsive system are obtained. The derived conditions are applied to the study of the bounded solutions to the nonhomogeneous impulsive system. Sufficient conditions for the existence of a unique bounded solution to the nonhomogeneous system in the case of weak regularity of the corresponding homogeneous system are formulated. The advantage of such an approach is that the established conditions can be effectively tested for specific classes of impulse-perturbed systems, since they are formulated in terms of coefficients of initial problems. The obtained conditions allow applying classical solution methods of differential equations for the propositions on solvability and continuous dependence of solutions on parameters of the impulsive systems.The theory of systems with impulsive actions has wide possibilities for its application. Many evolution processes in physics, engineering, automatic control, biology, economics are exposed to short-term perturbations during their evolution. For example, processes with abrupt changes are observed in mechanics (spring movement under shock influence, functioning of the clock mechanism, change of rocket speed at separation stages), in radio engineering (generation of impulses of various forms). Similar processes are also observed in biology (heart beat, cell division), biotechnology (growing biocomposites), and control theory (industrial robots).Therefore, qualitative investigation of impulsive systems in this work is a relevant challenge of the modern theory of mathematical modelin

Establishing Conditions for the Existence of Bounded Solutions to the Weakly Nonlinear Pulse Systems

Processes that involve jump-like changes are observed in mechanics (the movement of a spring under an impact; clockwork), in radio engineering (pulse generation), in biology (heart function, cell division). Therefore, high-quality research of pulse systems is a relevant task in the modern theory of mathematical modeling. This paper considers the issue related to the existence of bounded solutions along the entire real axis (semi-axis) of the weakly nonlinear systems of differential equations with pulse perturbation at fixed time moments. A concept of the regular and weakly regular system of equations for the class of the weakly nonlinear pulse systems of differential equations has been introduced. Sufficient conditions for the existence of a bounded solution to the heterogeneous system of differential equations have been established for the case of poorly regularity of the corresponding homogeneous system of equations. The conditions for the existence of singleness of the bounded solution along the entire axis have been defined for the weakly nonlinear pulse systems. The results were applied to study bounded solutions to the systems with pulse action of a more general form. The established conditions make it possible to use the classical methods of differential equations to obtain statements about solvability and the continuous dependence of solutions on the parameters of a pulse system. It has been shown that classical qualitative methods for studying differential equations are mainly naturally transferred to dynamic systems with discontinuous trajectories. However, the presence of a pulse action gives rise to a series of new specific problems. The theory of systems with pulse influence has a wide range of applications. Such systems arise when studying pulsed automatic control systems, in the mathematical modeling of various mechanical, physical, biological, and other processes

Changes in Soluble Protein Profile in Cotton Leaves Indicate Rubisco Damage after Treatment with Sumi-Alpha Insecticide

The cotton plant suffers from many pests and due to its economic importance, the use of efficient but ecologically friendly pesticides is highly desirable. The insecticide Sumi-Alpha with active compound Esfenvalerate is widely used for cotton treatment in Uzbekistan. This insecticide is considered as moderately hazardous for different organisms of ecosystems, while more collected data and relevant research is a necessity for judgement of their safety and/or potential risk. Therefore, a comparative analysis of cotton leaves was performed to study the protein profile changes upon treatment with this insecticide. Our data showed elevated accumulation of fructose bisphosphate aldolase and degradation of RuBisCo in the treated tissue. Besides, a protein belonging to P-loop containing nucleoside triphosphate hydrolases superfamily exerted lower accumulation. Our results indicate that the applied pyrethroid pesticide possibly can affect photosynthesis performance and cause accumulation of simple saccharides which in turn might contribute to enhanced colonisation of sucking insects. Further molecular research on Sumi-Alpha effects on cotton is necessary for its safer use in agricultural practice

Chemical composition and biological activity of seed oil of amaranth varieties

The work is devoted to study of seed oil composition of amaranth varieties: Kharkov, Lera, Andijan and Helios, acclimatized in Uzbekistan. We demonstrated the possibility of using reversed-phase HPLC using a refractometric detector, which allows simultaneous determination of squalene and triacylglycerides in plant seeds and determining the authenticity of amaranth oils. Established seed oiliness ranged from 6.39 to 7.81 % of the initial mass. Amaranth oil samples contained quite large amount of unsaturated fatty acids 72.72 – 73.28 %, 1.17 % of which is omega-3-alpha-linolenic acid. The squalene content in the seeds ranged from 0.35 % to 0.55 %. It was established that the squalene content in oils obtained by extraction is greater than the one obtained by cold pressing. In the triacylglyceride composition of the investigated cold-pressed and extracted oils, no significant differences were found

Investigation of increasing the recovery rate of refi palladium powder from waste solutions

The research methods for extraction of palladium from waste electrolyte solutions with the use of chloronitric extraction are described. The methods of investigation of the purification from harmful impurities by selective precipitation to obtain a refined palladium powder are given, the parameters on the technological processes are defined, use of the new technologies and equipment used are justifie