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In recent years, mathematical modeling has played a key role in many life applications such as computer science, physics, chemistry, and genetics. Actually, in this paper, our focus is on the classifications and the importance of mathematical programming and its applications in health problems especially the Mathematical Modeling of COVID_19. According to the era of the Corona pandemic, it has been using mathematical equations to employ mathematical programming in epidemics and the mechanism of spreading in urban areas. The solution of the problem is presented in two directions; the first was by graphic representation and the other by using computational software via the Python language. [ABSTRACT FROM AUTHOR]

In this paper we consider a controlled dynamical system consisting of two objects in the presence of external perturbations. The dynamics of the first object (the main object of the system) and the second object (the auxiliary object of the system) are described respectively by linear and nonlinear discrete-time recurrent vector equations. In the system under consideration there are two levels of control: basic level (the level I) that is dominant level and auxiliary level (the level II) that is subordinate level. The quality of the control process on every level of the control system is estimated by corresponding convex terminal functional. Both the control levels have different informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control the final state of phase vectors of the objects in the presence of external perturbations. For this problem we propose a mathematical formalization of two-level hierarchical minimax program control the final state of the dynamical system in the presence of external perturbations and incomplete information. In this paper for solving of the investigated problem is proposed the algorithm that has a form of a recurrent procedure of solving a linear and a convex mathematical programming problems, and a finite optimization problems. [ABSTRACT FROM AUTHOR]

In this paper we initiate quasi-dissociate and parallelepiped sets on locally compact hypergroups and study their properties. Also we find quasi-dissociate and parallelepiped subsets of some important class of hypergroups. [ABSTRACT FROM AUTHOR]

Nowadays, with the popularity of the computers, various industries and fields are widely applying computer information technology, which brings about huge demand for a variety of application software. In order to develop software meeting various needs with most economical cost and best quality, programmers must design efficient algorithms. A superior algorithm can not only soul up one thing, but also maximize the benefits and generate the smallest overhead. As one of the common algorithms, dynamic programming algorithms are used to solving problems with some sort of optimal properties. When solving problems with a large amount of sub-problems that needs repetitive calculations, the ordinary sub-recursive method requires to consume exponential time, and dynamic programming algorithm can reduce the time complexity of the algorithm to the polynomial level, according to which we can conclude that dynamic programming algorithm is a very efficient compared to other algorithms reducing the computational complexity and enriching the computational results. In this paper, we expound the concept, basic elements, properties, core, solving steps and difficulties of the dynamic programming algorithm besides, establish the dynamic programming model of the production planning problem [ABSTRACT FROM AUTHOR]

This paper presents a programming code to provide numerical solution of elastohydrodynamic lubrication problem in line contacts which is modeled through an infinite cylinder on a plane to represent the application of roller bearing. In this simulation, vegetable oils will be used as bio-based lubricants. Temperature is assumed to be constant at 40°C. The results show that the EHL pressure for all vegetable oils was increasing from inlet flow until the center, then decrease a bit and rise to the peak pressure. The shapes of EHL film thickness for all tested vegetable oils are almost flat at contact region. [ABSTRACT FROM AUTHOR]

This paper analyzes the effectiveness of various monotonic discretizations of an ODE in a parameter range reduction algorithm by considering the resulting ranges for the parameter λ obtained from the simple model x′ = λx. [ABSTRACT FROM AUTHOR]

In this paper, a new nonlinear interval-based programming (NIP) method based on Radial basis function (RBF) approximation models and RBF global search technique method is proposed. In NIP, searching for the extreme responses of objective and constraints are integrated with the main optimization, which leads to extremely low efficiency. Approximation models are commonly used to promote the computational efficiency. Consequently, two inevitable problems are encountered. The first one is how to obtain the global minimum and maximum in the sub-optimizations. The second one is how to diminish the approximation errors on the response bounds of system. The present method combined with RBF global search technique shows a good feature to overcome these problems. High accuracy and low computational cost can be achieved simultaneously. Two numerical examples are used to test the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

The developed method of iterative optimization of interplanetary missions with the low thrust, using sequence of movement specified mathematical models and design shape spacecraft, is realized. The new articular analytical decision describing planar movement of spacecraft with solar electric propulsion is described, allowing to construct initial approach in the iterative scheme of optimization. Developed a method of modelling and optimization of interplanetary missions ballistic schemes, based on a combination of Pontryagin's maximum principle formalism conditions of transversality and methods of the mathematical programming, allowing to consider restrictions characteristic for concrete interplanetary missions. Recommendations for choice design-ballistic parameters of the interplanetary missions spacecraft, received taking into account features nuclear and solar power plant for missions on delivery of a payload to orbits of Mars, expeditions the Earth-Mars-Earth are received. [ABSTRACT FROM AUTHOR]

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed. [ABSTRACT FROM AUTHOR]

This work is presented a mathematical model of the electromagnetic and heating processes in cylindrical body placed in the inductor and is developed controller, which provide mode of metal hardening. Here, is a simplified version of the problem we shall try to prescribe a given isothermal line to be distinguished at a given final time. The mathematical model includes solving the electromagnetic and heating problems. With the finite elements method the mathematical model is lead to the linear system ODEs. This allows to be used the predictive control system theory and develop a controller which provides a mode of metal hardening. [ABSTRACT FROM AUTHOR]

When we consider and analyze physical events with the purpose of creating corresponding mathematical models we often assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of infinitely small and infinitely large numbers in arithmetic and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature (physics, genetics). We have introduced a new concept of “Observer's Mathematics—Mathematics of Relativity” (see references). Observer's mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. The concept of a quantum arises automatically from the human thought process, rather than from physics. From this point of view classical mechanics is brought closer to quantum mechanics. [ABSTRACT FROM AUTHOR]