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The problem of control of the process described by the nonlinear differential equation with partial derivatives of the first order, with conditions at t 0 and in a sequence n of points x1 < x2 ... < xn is solved. The criterion of quality of control is the integrated quadratic functional, which depends on a final state of system and set n of controlling parameters. The method of increment of functional is applied to reception of conditions of optimality, and the method of additional argument (MAA) is applied for the decision of the nonlinear equations with partial derivatives.
Let φ={φk}k=−∞∞ denote the extended Takenaka–Malmquist system on unit circle T and let σn,φ(f), f∈L1(T), be the Fejér-type operator based on φ, introduced by V. N. Rusak. We give the convergence criteria for σn,φ(f) in Banach space C(T). Also we prove the Voronovskaya-type theorem for σn,φ(f) on class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
Keywords: Holomorphic functions; Takenaka–Malmquist system; Fejér type operator; Blaschke product; Frostman condition
The natural methods of uniform topology for construction of Wallman compactifications and Wallman realcompactifications are developed. Results on partial order and relations of dimensions in the lattice of compactifications are presented. The construction of the maximal compactification among compactifications of X with fixed realcompactification is given. -
MSC 54E15; 54D35; 54D60; 54F45 . -
Keywords: Uniformity; (Wallman, β-like) compactification; (Wallman) realcompactification; Normal base; Dimension
The problem of minimization of atmosphere pollution by fractions of harmful admixtures is studied. It is supposed that a controlled object is described by non-stationary integral–differential transfer equation with special boundary conditions and control parameters, which are included in the right part of equation as delta-functions. Minimized integral quadratic functional characterizes energy expenditure for control and depends on the average squared deflection of fraction concentration from the desired final state. Optimal conditions are obtained with the help of Pontryagin’s maximum princip ...More
Ethnopharmacological relevance: In their centuries-old nomadic life, since their livestock was the backbone of their lives, the Kyrgyz people used a variety of wild medicinal plants for ethnoveterinary practices. However, the plants used for the treatment of livestock ailments never have been recorded, except rarely in local publications. In this study, we present the HSHR (homemade single species herbal remedy reports), their methods of preparation and application, and the livestock ailments for which these remedies were used.Aims: The collect data from the five different high-altitude valley ...More
The various types of ultrafilter-completeness on zero-sets of uniformly continuous functions are introduced, their properties are studied and characterizations in the category are given.
Extreme microorganism has gained interest because of their special contribution to the environmental and industrial biotechnology, particularly psychrophilic microorganisms which can live and thrive at lower temperatures. They produce enzymes with great potential to adapt to extreme conditions. In this study, a novel psychrophilic bacterial strain designated as TaeBurcu001 grew (optimally at 5.C) on a chemically defined medium containing dalapon (refer to as 2,2-dichloropropionic acid, 2,2-DCP) as the sole carbon source. TaeBurcu001 was isolated from Galindez Island, Antarctica. Phylogenetic a ...More
For a Tychonoff space X, the Dieudonne tau-completion of X, denoted by mu TX, is investigated. The space mu TX is defined as the completion of X with respect to the uniformity uTX, where uTX is generated by all continuous mappings of X to metric spaces of weight