scholarly journals Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3013
Author(s):  
Leonid Shaikhet
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Wide Class ◽  
Asymptotic Properties ◽  
Nonlinear Mathematical Model ◽  
Simple Criterion ◽  
Stochastic Perturbations ◽  
Food Engineering ◽  
Nonlinear Mathematical Models

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

INDUSTRIAL POLLUTION AND ASTHMA: A MATHEMATICAL MODEL

2000 ◽  
Vol 08 (04) ◽  
pp. 347-371 ◽  
Author(s):  
MINI GHOSH
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Differential Equations ◽  
Mathematical Models ◽  
Stability Theory ◽  
Industrial Pollution ◽  
Air Pollutant ◽  
Logistic Growth ◽  
Nonlinear Mathematical Models

In this paper, some nonlinear mathematical models are proposed and analyzed to study the spread of asthma due to inhaled pollutants from Industry. The following two types of demographics are considered here; (i) population with constant immigration, (ii) population with logistic growth. In each type of demography, the following three cases have been considered regarding the release of pollutant into the environment; (i) when emission of the pollutant into the environment is constant, (ii) when emission of the pollutant is population dependent, and (iii) when emission of the pollutant is periodic. Using stability theory of differential equations and computer simulation, it is shown that due to an increase in the air pollutant, the asthmatic (diseased) population increases in the region under consideration.

scholarly journals A Mathematical Model of Universal Basic Income and Its Numerical Simulations

Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 331
Author(s):  
Maria Letizia Bertotti
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Real World ◽  
Poverty Alleviation ◽  
The Other ◽  
Nonlinear Ordinary Differential Equations ◽  
Basic Income ◽  
Market Society ◽  
Number Of Individuals

In this paper, an elementary mathematical model describing the introduction of a universal basic income in a closed market society is constructed. The model is formulated in terms of a system of nonlinear ordinary differential equations, each of which gives account of how the number of individuals in a certain income class changes in time. Societies ruled by different fiscal systems (with no taxes, with taxation and redistribution, with a welfare system) are considered and the effect of the presence of a basic income in the various cases is analysed by means of numerical simulations. The main findings are that basic income effectively acts as a tool of poverty alleviation: indeed, in its presence the portion of individuals in the poorest classes and economic inequality diminish. Of course, the issue of a universal basic income in the real world is more complex and involves a variety of aspects. The goal here is simply to show how mathematical models can help in forecasting scenarios resulting from one or the other policy.

EFFECT OF AWARENESS PROGRAMS IN CONTROLLING THE PREVALENCE OF AN EPIDEMIC WITH TIME DELAY

2011 ◽  
Vol 19 (02) ◽  
pp. 389-402 ◽  
Author(s):  
A. K. MISRA ◽  
ANUPAMA SHARMA ◽  
VISHAL SINGH
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Stability Theory ◽  
Direct Contact ◽  
Behavioral Changes ◽  
Nonlinear Mathematical Model ◽  
Awareness Programs

A nonlinear mathematical model with delay to capture the dynamics of effect of awareness programs on the prevalence of any epidemic is proposed and analyzed. It is assumed that pathogens are transmitted via direct contact between susceptibles and infectives. It is assumed further that cumulative density of awareness programs increases at a rate proportional to the number of infectives. It is considered that awareness programs are capable of inducing behavioral changes in susceptibles, which result in the isolation of aware population. The model is analyzed using stability theory of differential equations and numerical simulations. The model analysis shows that, though awareness programs cannot eradicate infection, they help in controlling the prevalence of disease. It is also found that time delay in execution of awareness programs destabilizes the system and periodic solutions may arise through Hopf-bifurcation.

scholarly journals Analysis of modern modeling methods in problems of stabilization of motions of mechatronic systems with differential constraints

2018 ◽  
Vol 7 (2.23) ◽  
pp. 9
Author(s):  
Krasinskiy A.Ya ◽  
Krasinskaya E.M.
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Operating Mode ◽  
Mechatronic Systems ◽  
Natural Behavior ◽  
Holonomic Constraints ◽  
Operating Modes ◽  
Modeling Methods ◽  
Nonlinear Mathematical Models ◽  
Steady Motions

The most important problem of controlling mechatronic systems is the development of methods for the fullest possible application of the properties of our own (without the application of controls) motions of the object for the optimal use of all available resources. The basis of this can be a non-linear mathematical model of the object, which allows to determine the degree of minimally necessary interference in the natural behavior of an object with the purpose of stable implementation of a given operating mode. The operating modes of the vast majority of modern mechatronic systems are realized due to the steady motions (equilibrium positions and stationary motions) of their mechanical components, and often these motions are constrained by connections of various kinds. The paper gives an analysis of methods for obtaining nonlinear mathematical models in stabilization problems of mechanical systems with differential holonomic and non-holonomic constraints. 

A new mathematical model of the behaviour of a four-axle freight wagon with UIC single-link suspension

2011 ◽  
Vol 225 (6) ◽  
pp. 637-647 ◽  
Author(s):  
J Matej
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Dynamic Stability ◽  
Dry Friction ◽  
Dynamic Behaviour ◽  
Single Link ◽  
Freight Wagons

This paper analyses the lateral dynamic behaviour of a four-axle freight wagon with Union Internationale des Chemins de fer (UIC) single-link suspension where dry friction is used to damp oscillations. Mathematical models of the standard UIC single-link suspension have been prepared elsewhere according to non-smooth mechanics assumptions and implemented into established MBS programs. Numerical simulations of the motion of the four-axle freight wagon with a 200 kN static axleload have been performed on straight track according to methods appropriate for predicting the dynamic stability of freight wagons.

scholarly journals Analysis of a Mathematical Model. Opportunities for the Training of Food Engineering Students

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1339
Author(s):  
Edwin Sepúlveda ◽  
Difariney González-Gómez ◽  
Jhony Alexander Villa-Ochoa
Keyword(s):  
Mathematical Model ◽  
Qualitative Study ◽  
Mathematical Models ◽  
Mathematics Teaching ◽  
Engineering Students ◽  
Teaching Experiment ◽  
Model Function ◽  
Pedagogical Approach ◽  
Food Engineering ◽  
Food Dryer

International research has revealed different roles of mathematics in the practices of engineers and some implications of mathematics teaching for engineering students. Modeling and mathematical models have proven to be valuable tools for their professional work and for their teaching process. This study identifies opportunities offered by a process of analysis of a mathematical model in the training of engineers. For this analysis, an interpretation of mathematical models as an object–user–representation triad was used; mathematical models were also considered a pedagogical approach to mathematics teaching. Based on this approach, a qualitative study was developed. A teaching experiment was designed, in which, through a set of tasks, the analysis of a model describing the percentage of moisture removed in a radial airflow food dryer is considered. Results show that students evidenced a comprehension of the model function as a covariation relationship and implemented strategies for understanding it through the graphs in the model. The situated character of students’ reasoning and their experience with professional practices of engineers are also highlighted.

scholarly journals Analytical and Approximate Solutions of a Novel Nervous Stomach Mathematical Model

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Yolanda Guerrero Sánchez ◽  
Zulqurnain Sabir ◽  
Hatıra Günerhan ◽  
Haci Mehmet Baskonus
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Death Rate ◽  
Approximate Solutions ◽  
Mathematical Form ◽  
Nonlinear Mathematical Model ◽  
Transformation Technique ◽  
Differential Transformation ◽  
Sleep Factor

The stomach is usually considered as a hollow muscular sac, which initiates the second segment of digestion. It is the most sophisticated endocrine structure having unique biochemistry, physiology, microbiology, and immunology. The pivotal aim of the present study is to propose the nonlinear mathematical model of the nervous stomach system based on three compartments namely, tension (T), food (F), and medicine (M). The detailed description of each compartment is provided along with the mathematical form and different rates/factors, such as sleep factor, food rate, tension rate, medicine term, and death rate. The solution of the designed model is presented numerically by using the well-known differential transformation technique. The behavior of the obtained solution has been captured with respect to time as well as presentations of the numerical simulations.

scholarly journals Predicting the age and weight at puberty of Ongole Grade cattle using nonlinear mathematical model in Kebumen Farmer Association

2017 ◽  
Vol 42 (4) ◽  
pp. 233
Author(s):  
D. Maharani ◽  
A. H. K. Amrullah ◽  
D. T. Widayati ◽  
S. Sumadi ◽  
A. Fathoni ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Logistic Model ◽  
Follicular Phase ◽  
Nonlinear Mathematical Model ◽  
Mature Weight

This research is aimed to evaluate the nonlinear mathematical model in predicting the age and weight of Kebumen Ongole Grade (PO) cattle at puberty. The data used in this research was weight recordings of (768) PO cattle, ranging from calf (< 1 month) to adult (60 months), collected by Kebumen PO cattle Breeder Association (ASPOKEB) from 2013 to 2015. These cattle were reared by a group of farmers located in six sub-districts: Mirit, Lembu Purwo, Ambal, Puring, Petanahan, and Klirong in Kebumen district, Jawa Tengah Province. Brody, Bertalanfy, Logistic and Gompertz mathematical models were used to analyze the data. The analysis showed that the R2of the four models classify high in the category (R2 >0.70). Mature weight (A) of PO cattle predicted by Logistic (349 kg) and Gompertz (358 kg) were most appropriate. Out of the four models, the Logistic model was the most accurate in predicting the weight at puberty (174 kg) of PO cattle, but all observed cattle are still in the follicular phase.

A RESOURCE-DEPENDENT COMPETITION MODEL: EFFECTS OF POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

2012 ◽  
Vol 03 (02) ◽  
pp. 1250003 ◽  
Author(s):  
MANJU AGARWAL ◽  
SAPNA DEVI
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Numerical Simulations ◽  
Carrying Capacity ◽  
Rate Coefficient ◽  
Population Pressure ◽  
Equilibrium Density ◽  
Nonlinear Mathematical Model ◽  
Competing Species ◽  
Increase With Increase

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource. It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass. Further, it is assumed that the resource biomass too is growing logistically in the environment and its carrying capacity decreases with the increase in densities of competing species and industrialization. The growth rate of population pressure is assumed to be proportional to the densities of competing species. Stabilities of all equilibria and conditions which influence the permanence of the system are carried out using theory of differential equations. Numerical simulations are performed to accomplish our analytical findings. It is shown that the equilibrium density of resource biomass decreases as (i) the growth rate coefficient of population pressure increases (ii) the growth rate coefficient of industrialization due to population pressure increases and (iii) the growth rate coefficient of industrialization due to resource biomass increases. It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure. Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

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