scholarly journals NONLINEAR MATHEMATICAL MODEL OF PEDAGOGICAL SYSTEM FUNCTIONING

2020 ◽  
Vol 34 (4) ◽  
pp. 93-98
Author(s):  
Irina V. Konopleva ◽  
◽  
Anna R. Sibireva ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Modeling ◽  
Differential Equations ◽  
Dimensional Space ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Stability Limit ◽  
Point Of View ◽  
Social Phenomena ◽  
System Functioning

The purpose of this article is to study the crisis in pedagogical systems from the point of view of an internal observer. The aim of the work is to build and investigate a mathematical model describing the course of crises in pedagogical systems. When building the model, a synergetic methodology, system and process approaches are used. For the mathematical analysis of various social phenomena, systems of differential equations are used to investigate the dynamics of the process. The paper considers a system of nonlinear differential equations in three-dimensional space that describes the functioning of the pedagogical system during the crisis. Numerical and topological methods of nonlinear dynamics, the method of Lyapunov characteristic exponents and the theory of strange attractors by Lorentz were used to study it. Numerical modeling of system solutions for various sets of control parameters (system coefficients) makes it possible to determine the region of stability (asymptotic stability), limit cycles, bifurcation points, and describe possible trajectories of development of the pedagogical system. Mathematical modeling deepens the knowledge about the essence of crises, the peculiarities of their course, makes it possible to study qualitative and numerical modeling, and also allows predicting possible effective measures to combat crisis phenomena and develop new approaches in the management of pedagogical systems.

scholarly journals On Global Dynamics in Duffing Equation with Quasiperiodic Perturbation

2020 ◽  
Vol 22 (2) ◽  
pp. 164-176
Author(s):  
Timofey N. Dragunov ◽  
Kirill E. Morozov ◽  
Albert D. Morozov
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Nonlinear Differential Equations ◽  
Uniform Mesh ◽  
Global Dynamics ◽  
Nonlinear Operator Equations ◽  
Wide Range ◽  
Perturbations Of Initial Data ◽  
Analysis Of Stability ◽  
Stated Problem

An iterative method for solution of Cauchy problem for one-dimensional nonlinear hyperbolic differential equation is proposed in this paper. The method is based on continuous method for solution of nonlinear operator equations. The keystone idea of the method consists in transition from the original problem to a nonlinear integral equation and its successive solution via construction of an auxiliary system of nonlinear differential equations that can be solved with the help of different numerical methods. The result is presented as a mesh function that consists of approximate values of the solution of stated problem and is constructed on a uniform mesh in a bounded domain of two-dimensional space. The advantages of the method are its simplicity and also its universality in the sense that the method can be applied for solving problems with a wide range of nonlinearities. Finally it should be mentioned that one of the important advantages of the proposed method is its stability to perturbations of initial data that is substantiated by methods for analysis of stability of solutions of systems of ordinary differential equations. Solving several model problems shows effectiveness of the proposed method.

scholarly journals Development of a Mathematical Model for Tracking Movement of a Human Limb in Three-Dimensional Space Using MEMS Sensors

2021 ◽  
Vol 11 (3) ◽  
pp. 74-82
Author(s):  
N.I. Levonovich
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Practical Importance ◽  
Three Dimensional ◽  
Suitable Model ◽  
Mems Sensors ◽  
Model Experiments ◽  
Human Limb ◽  
Tracking Movement ◽  
Three Dimensional Space

This article discusses the development of a mathematical model for a device capable of tracking the movements of a human limb based on the readings of microelectromechanical sensors. For developing and selecting the most suitable model, experiments were conducted based on publicly available components. The result obtained is of practical importance since it can be used to create a device.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

scholarly journals Platonic solids generate their four-dimensional analogues

2013 ◽  
Vol 69 (6) ◽  
pp. 592-602 ◽  
Author(s):  
Pierre-Philippe Dechant
Keyword(s):  
Coxeter Groups ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Root Systems ◽  
Point Of View ◽  
Platonic Solids ◽  
Four Dimensions ◽  
Potential Applications ◽  
Regular Convex ◽  
Quasi Crystals

This paper shows how regular convex 4-polytopes – the analogues of the Platonic solids in four dimensions – can be constructed from three-dimensional considerations concerning the Platonic solids alone.Viathe Cartan–Dieudonné theorem, the reflective symmetries of the Platonic solids generate rotations. In a Clifford algebra framework, the space of spinors generating such three-dimensional rotations has a natural four-dimensional Euclidean structure. The spinors arising from the Platonic solids can thus in turn be interpreted as vertices in four-dimensional space, giving a simple construction of the four-dimensional polytopes 16-cell, 24-cell, theF4root system and the 600-cell. In particular, these polytopes have `mysterious' symmetries, that are almost trivial when seen from the three-dimensional spinorial point of view. In fact, all these induced polytopes are also known to be root systems and thus generate rank-4 Coxeter groups, which can be shown to be a general property of the spinor construction. These considerations thus also apply to other root systems such as A_{1}\oplus I_{2}(n) which induces I_{2}(n)\oplus I_{2}(n), explaining the existence of the grand antiprism and the snub 24-cell, as well as their symmetries. These results are discussed in the wider mathematical context of Arnold's trinities and the McKay correspondence. These results are thus a novel link between the geometries of three and four dimensions, with interesting potential applications on both sides of the correspondence, to real three-dimensional systems with polyhedral symmetries such as (quasi)crystals and viruses, as well as four-dimensional geometries arising for instance in Grand Unified Theories and string and M-theory.

Investigation of Tangential Contact Damping of Rough Surfaces From the Perspective of Viscous Damping Mechanism

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Wujiu Pan ◽  
Hongshuang Li ◽  
Haoyong Qu ◽  
Liangyu Ling ◽  
Linlin Wang
Keyword(s):  
Mathematical Model ◽  
Energy Dissipation ◽  
Dynamic Testing ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Contact Fatigue ◽  
Load Ratio ◽  
Point Of View ◽  
Tangential Contact

Abstract The contact damping between rough surfaces has an important influence on the wear, vibration, contact fatigue, and energy dissipation between interfaces. In this paper, based on contact theory, a tangential damping mathematical model of rough surfaces is established from the point of view of viscous contact damping energy dissipation mechanism of asperities and considering the fractal characteristics of three-dimensional topography of rough surfaces. Through the combination of micro-contact modeling and macro dynamic testing of composite beams, the analysis results show that there are important evolution rules between tangential damping and surface fractal parameters and material parameters. The nonlinear relations between them are as follows: tangential contact damping is positively correlated with normal load, load ratio, and maximum contact area of asperity, and negatively correlated with fractal roughness; tangential contact damping increases first and then decreases with the increase of three-dimensional fractal dimension. The results of computational and experimental modal analysis show that the established mathematical model is feasible for predicting tangential damping. The study of tangential contact damping between surfaces can lay a foundation for improving the performance of assembly interfaces.

scholarly journals Unsteady Three-Dimensional MHD Non-Axisymmetric Homann Stagnation Point Flow of a Hybrid Nanofluid with Stability Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 784 ◽  
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

The hybrid nanofluid under the influence of magnetohydrodynamics (MHD) is a new interest in the industrial sector due to its applications, such as in solar water heating and scraped surface heat exchangers. Thus, the present study accentuates the analysis of an unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid Al2O3-Cu/H2O nanofluid with stability analysis. By employing suitable similarity transformations, the governing mathematical model in the form of the partial differential equations are simplified into a system of ordinary differential equations. The simplified mathematical model is then solved numerically by the Matlab solver bvp4c function. This solving approach was proficient in generating more than one solution when good initial guesses were provided. The numerical results presented significant influences on the rate of heat transfer and fluid flow characteristics of a hybrid nanofluid. The rate of heat transfer and the trend of the skin friction coefficient improve with the increment of the nanoparticles’ concentration and the magnetic parameter; however, they deteriorate when the unsteadiness parameter increases. In contrast, the ratio of the escalation of the ambient fluid strain rate to the plate was able to adjourn the boundary layer separation. The dual solutions (first and second solutions) are obtainable when the surface of the sheet shrunk. A stability analysis is carried out to justify the stability of the dual solutions, and hence the first solution is seen as physically reliable and stable, while the second solution is unstable.

A MATHEMATICAL MODEL OF DRUG ADMINISTRATION BY PHAGOCYTOSIS OF LOADED ERYTHROCYTES

1995 ◽  
Vol 03 (02) ◽  
pp. 447-455
Author(s):  
FORTUNATA SOLIMANO
Keyword(s):  
Mathematical Model ◽  
Drug Delivery ◽  
Time Delay ◽  
Differential Equations ◽  
Red Blood Cells ◽  
Therapeutic Effect ◽  
Discrete Time ◽  
Blood Cells ◽  
Nonlinear Differential Equations ◽  
Discrete Time Delay

A mathematical model for the drug delivery to macrophages of the tissues by using a preassigned cohort of red blood cells loaded with a drug is presented. This model is a system of three nonlinear differential equations, with a discrete time delay and an input depending on the time. The input should be controlled in order to obtain the longest duration of the therapeutic effect.

Railroad track modeling based on the results of mobile laser scanning

2018 ◽  
pp. 408-413
Author(s):  
Elena Lenchenkova
Keyword(s):  
Mathematical Model ◽  
Laser Scanning ◽  
Dimensional Space ◽  
Practical Importance ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Railroad Track ◽  
Railway Line ◽  
Type Data

Objective: To develop a mathematical model of the railroad track based on the initial progressive-type data (laser scanning) in railroad design. Methods: Regression analysis (least-square method), as well as coordinate methods of calculating point position in space were applied. Results: The mathematical model, which could describe the position of the railroad track in three-dimensional space by means of mathematical relations, was obtained. Applicability of approximating models was established. The models make it possible to provide smoothing of laser survey data. Regularization and globalization algorithms of initial data were developed. Practical importance: The introduced model is universal when describing the position of the track at all stages of life cycle of the railway line. It is reasonable to apply the presented model in design engineering in order to balance survey errors, maintain the track in coordinates, as well as to calculate design and profile parameters.

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

scholarly journals MILITARY-HISTORICAL RECONSTRUCTION AS A SOCIAL AND CULTURAL PHENOMENON AND A MEANS OF PATRIOTIC UPBRINGING OF STUDENT YOUTH

2018 ◽  
pp. 104-114
Author(s):  
Сергей Максимов ◽  
Sergei Maksimov ◽  
Елена Степина ◽  
Elena Stepina
Keyword(s):  
Three Dimensional ◽  
Local History ◽  
Point Of View ◽  
Historical Reconstruction ◽  
Native Land ◽  
System Functioning ◽  
Moral Qualities ◽  
Ethnic And Cultural Identity ◽  
Three Dimensional Models ◽  
The Military

The article discusses the military-historical reconstruction as a form of tourist study of local lore and a means of Patriotic upbringing of students. This social phenomenon has a significant potential from the point of view of spiritual and moral development of a student’s personality, because it brings together the most significant components of these processes: cognitive, moral, spiritual, emotional and activity components, corresponding to selected stages, which are selected by authors, of formation of Patriotic consciousness of the student youth as spiritually-moral qualities of students’ personality. Historical reconstruction, which is researched in the context of a tourist study of local lore, expands the boundaries of tourism as object of activity and science. The object of the research in tourist study of local lore is the native land, with its geographical, economic, historical and cultural characteristics through the lens of the tourist identity. In the process of participation in the historical reconstruction as a form of regional activities students produce and accumulate knowledge of the history and culture of their native land; this activity contributes to the formation of such basic values as love for the native land, interest in its history and culture, which ultimately contributes to young people's ethnic and cultural identity, Patriotic consciousness and desire to know their native land. Military-historical reconstruction is the form of tourist study of local lore, which reflects the characteristics of local history as an integral system functioning in the world of three-dimensional models generated by space components, time and society

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