Properties of the value function in optimal control problems with infinite horizon

The article investigates properties of the value function of the optimal control problem on infinite horizon with an unlimited integrand index appearing in the quality functional with a discount factor. The estimate is derived for approximating the value function in a problem with the infinite horizon by levels of value functions in problems with lengthening finite horizons. The structure of the value function is identified basing on stationary value functions which depend only on phase variables. The description is given for the asymptotic growth of the value function generated by various types of the quality functional applied in economic and financial modeling: logarithmic, power, exponential, linear functions. The property of continuity is specified for the value function and estimates are deduced for the Holder parameters of continuity. These estimates are needed for the development of grid algorithms designed for construction of the value function in optimal control problems with infinite horizon

The role of mathematics for physics teaching and understanding

That mathematics is the “language of physics” implies that both areas are deeply interconnected, such that often no separation between “pure” mathematics and “pure” physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers’ background and experiences. The results fit well into the derived model of PCK

Numerical methods for construction of value functions in optimal control problems with infinite horizon

The article is devoted to the analysis of optimal control problems with infinite time horizon. These problems arise in economic growth models and in stabilization problems for dynamic systems. The problem peculiarity is a quality functional with an unbounded integrand which is discounted by an exponential index. The problem is reduced to an equivalent optimal control problem with the stationary value function. It is shown that the value function is the generalized minimax solution of the corresponding Hamilton-Jacobi equation. The boundary condition for the stationary value function is replaced by the property of the Hölder continuity and the sublinear growth condition. A backward procedure on infinite time horizon is proposed for construction of the value function. This procedure approximates the value function as the generalized minimax solution of the stationary Hamilton-Jacobi equation. Its convergence is based on the contraction mapping method defined on the family of uniformly bounded and Hölder continuous functions. After the special change of variables the procedure is realized in numerical finite difference schemes on strongly invariant compact sets for optimal control problems and differential games. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND licens

Analysis of Economic Growth Models via Value Function Design

Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals. An example is given to illustrate construction of the value function in economic growth models. © 201

Numerical methods for construction of value functions in optimal control problems on an infinite horizon

This article deals with the optimal control problem on an infinite horizon, the quality functional of which is contained in the integrand index and the discounting factor. A special feature of this formulation of the problem is the assumption of the possible unboundedness of the integrand index. The problem reduces to an equivalent optimal control problem with a stationary value function as a generalized (minimax, viscosity) solution of the Hamilton–Jacobi equation satisfying the Hölder condition and the condition of linear growth. The article describes the backward procedure on an infinite horizon. It is the method of numerical approximation of the generalized solution of the Hamilton–Jacobi equation. The main result of the article is an estimate of the accuracy of approximation of a backward procedure for solving the original problem. Problems of the analyzed type are related to modeling processes of economic growth and to problems of stabilizing dynamic systems. The results obtained can be used to construct numerical finite-difference schemes for calculating the value function of optimal control problems or differential games. © 2019 Udmurt State University. All right reserved

Synthesis by High-Efficiency Liquid-Phase (HELP) Method of Oligonucleotides Conjugated with High-Molecular Weight Polyethylene Glycols (PEGs)

The chemical modification of synthetic oligonucleotides has recently been investigated to improve their pharmacological utilization. In addition to chemical alterations of the backbone and of the heterocyclic bases, their conjugation with amphiphylic moieties, such as the polyethylene glycol has been proposed. The large scale production of these molecules as demanded for commercial purposes is hampered by the heterogeneity of the solid-phase processes and by the low reactivity of high-molecular weight PEGs in solution. A new synthetic procedure based on the recently developed liquid-phase method (HELP), has been set up to overcome these limitations

INFLUENCE OF IRRADIATION TREATMENT MODES OF MILK ON THE PROCESSES OF LIPID PEROXIDATION

Irradiation treatment of milk was performed with a dose range from 1 to 10 kGy in the stream and in the package. In order to estimate the intensity of lipid peroxidation process in irradiated milk the concentration of malonic dialdehyde was evaluated using the spectrophotometric method. The conclusions about the effect of different irradiation treatment modes on intensity of the lipid peroxidation process in milk were formulated.Работа выполнена при финансовой поддержке РФФИ (№ проекта 13-03-01100)

ХИМИЧЕСКИЙ СОСТАВ МЫШЕЧНОЙ ТКАНИ РАЗЛИЧНЫХ ВИДОВ СЕЛЬСКОХОЗЯЙСТВЕННОЙ ПТИЦЫ ПРИ СКАРМЛИВАНИИ МИКРОДОБАВОК СЕЛЕНА И ЙОДА

The article reveals the results on studying how feeding poultry with selenium and iodine microadditives influences the chemical composition of broilers’, turkeys’ and quails’ lean meat. The experiments were carried out on broilers of Smena-2 cross, poults of But-8 cross and quails of Japan cross in the poultry farms of Kemerovo region. Theauthorsarrangedthecontrolgroupandtheexperimentalone, each of themcontained 70 broilers, 30 poults and 17 quails aged 60 days. The researchers defined the concentration of nutrients, minerals and aminoacids in the lean tissue of broilers aged 49 days and turkeys aged 124 days when including organic and non-organic forms of selenium combined with non-organic form of iodine. Chemicalanalysisof leantissueofquails aged 120 days was conducted when feeding them with high amount of organic selenium and organic iodine. The researchers make conclusion that all the factors studied didn’t influence the chemical composition of broilers’, turkeys’ and quails’ meat. Thepaperdeclaresaboutreducingoffatconcentrationon 0.27–3.50 %, increasing of ash concentration on 0.03–0.21 % and increasing of potassium concentration on 0.07–6.32 % in comparison with the control group. Thiscontributestonutritionalqualityofthemeat.Представлены результаты исследований по изучению влияния скармливания микродобавок селена и йода на химический состав мышечной ткани цыплят-бройлеров, индеек и перепелов. Научно-хозяйственные опыты проводили в птицеводческих хозяйствах Кемеровской области на цыплятах-бройлерах кросса Смена-2, индюшатах-бройлерах кросса But-8, перепелах японской породы. Для проведения экспериментов были сформированы контрольная и опытная группы суточных цыплят-бройлеров по 70 голов в каждой, суточных индюшат-бройлеров – по 30 голов, перепелов в возрасте 60 дней – по 17 голов. Содержание основных питательных, минеральных веществ и аминокислот в мышечной ткани цыплят-бройлеров и индеек определяли в возрасте 49 и 124 дней соответственно при включении в рацион птицы в период выращивания органической и неорганической форм селена в сочетании с неорганической формой йода. Химический анализ мышечной ткани перепелов проводили в возрасте 120 дней при скармливании в составе рациона повышенных доз селена и йода в органических формах. Все изучаемые в экспериментах факторы достоверно не повлияли на химический состав мяса цыплят-бройлеров, индеек и перепелов. В целом в мышечной ткани подопытной птицы установлено снижение содержания жира на 0,27–3,50 %, повышение содержания золы – на 0,03–0,21, калия – на 0,07–6,32 % по сравнению с контрольными аналогами, что положительно сказывается на пищевой ценности данного продукта питания