We propose an approach to mathematical modeling for a system on the basis of comparing scalar products in spaces of real functions integrable on the segment. This approach may be used in discrete and continuous measurement systems and some combinatorial systems, in which comparison problem of function exists in the process of synthesis and optimal choice of their parameters. In theory, such problems are characteristic of boundary value problems for equations of mathematical physics, in particular for multi-point problems that describe oscillatory processes in mechanisms. We have found th
The development of technology for production of metal-filled hydrogels based on copolymers of 2-hydroxyethyl methacrylate (HEMA) with polyvinylpyrrolidone (PVP) by polymerization with simultaneous chemical reduction of metal ions suggests the grounding and determination of optimal technological parameters for its realization. The diverse influence of the initial polymer-monomer composition (PMС) formula on the main parameters of the exotherm of the copolymerization of HEMA with PVP, which constitute the technological mode of chemical deposition of metals, was experimentally proved.
Aim. The research aims to develop a method of optimal PI-controller tuning, which allows to take into account the constraints and to minimize the undesirable indicators of the automatic control quality. Method. In order to carry out the investigation, the problem of optimal PI-controller tuning was stated in a general form. The analysis of the elements of the problem has been conducted. It allowed substituting the elements to the requirements of individual minimization criteria.
The directions of energy and resource saving remain a priority in building science. This is especially concerns to the structural elements of mass production. These elements include large concrete blocks of basement walls (foundation blocks), theirs bearing capacity, even in high-rise building, is used only for 30–50 %. Therefore, starting with the widespread establishment in construction, various ways to improve their constructive forms were proposed to reduce their own weight and optimization. One of the most effective ways is cavity formation.
Features of vending cyber physical systems performance after durable exploitation have been examined. Ready-made means of cyber physical systems scaling have been analyzed. Main advantages and disadvantages of a ready system switchover to a third-party developer’s platform have been defined. Means of large databases optimization have been offered. Analytical data that led to the decision to optimize the existing database have been produced. The elements of vending cyber physical system and possible changes in its structure due to the switchover to different platforms have been covered.
In the presented study, the significant operating variables regarding biosynthesis of citric acid process were assessed and their effects on the process yield were analysed. These variables, namely, initial sucrose concentration, methanol concentration, inoculum density, initial medium pH, spore age, stirrer speed, incubation period, fermentation temperature, particle size distribution, oxygen flow rate, and moisture content have significant influence on bioprocess of citric acid production.
The yield of Shea butter extracted in an unbaffled vessel equipped with an impeller was optimized by varying kneading time, kneading temperature and kneading speed using response surface method (RSM). Helical shaped impeller was mounted on a variable speed Tecmix TM 1100 kneader to knead the Shea paste. Minitab 16.1 software was used for the design and optimization of the process variables. The study indicated that the temperature and speed were highly significant on Shea butter oil yield with p-values of 0.001 and 0.002, respectively.
In the paper, based on the Fokker--Planck--Kolmogorov equation and the statistical control theory, a mathematical model for the operative synthesis of optimal controlling influences for stabilization of the electric mode of an electric arc furnace in a two-contour structure with a high-speed electric circuit for regulating the arc currents is suggested.
Problems of determination of optimal geometric and constructive parameters of long-length structures are presented. For example, a longitudinal profile of a complicated section is adopted, its components of the stress state and its own oscillation frequencies are determined. The choice of optimal profile parameters is made for the implementation of structures with minimum equivalent stresses, as well as for ensuring maximum dynamic stiffness.
The problem of optimal processing tasks in the nodes of a distributed information system on the basis of a mathematical model belonging to a class of two-clustering problems, for which an optimization problem with a fractional linear target function is formulated, was investigated.