scholarly journals Application of the Riccati hereditary mathematical model to the study of the dynamics of radon accumulation in the storage chamber

2021 ◽  
Vol 254 ◽  
pp. 03001
Author(s):  
Dmitryi Tverdyi ◽  
Roman Parovik ◽  
Evgeniy Makarov ◽  
Pavel Firstov ◽  
Nazira Alimova
Keyword(s):  
Mathematical Model ◽  
Riccati Equation ◽  
Model Equation ◽  
Real Data ◽  
Accurate Description ◽  
Variable Order ◽  
Accumulation Process ◽  
Storage Chamber ◽  
Real Curves ◽  
Hereditary Properties

The article proposes a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates. The model equation is the fractional Riccati equation with a derivative of a fractional variable order of the Gerasimov-Caputo type, taking into account heredity, as well as taking into account nonlinearity, which is responsible for the mechanisms of radon entry into the chamber. The obtained model curves of the accumulation process are compared with real data. It is shown that the model described in the work gives a better agreement between the model and real curves of radon accumulation and can be used for a more accurate description of the processes occurring in the chamber.

scholarly journals Research of the process of radon accumulation in the accumulating chamber taking into account the nonlinearity of its entrance

2020 ◽  
Vol 196 ◽  
pp. 02027
Author(s):  
Dmitriy Tverdyi ◽  
Roman Parovik ◽  
Evgeniy Makarov ◽  
Pavel Firstov
Keyword(s):  
Mathematical Model ◽  
Nonlinear Function ◽  
Real Data ◽  
Accurate Description ◽  
Real Curves ◽  
Hereditary Properties

The paper presents a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates, and also uses a nonlinear function that is responsible for the mechanisms of radon entering the chamber. The simulation of accumulation is performed in comparison with real data. It is shown that the model presented in this work gives a better agreement between the model and real curves of radon accumulation and can be used for a more accurate description of the processes occurring in the chamber.

scholarly journals Fractional Riccati equation to model the dynamics of COVID-19 coronovirus infection

2021 ◽  
Vol 2094 (3) ◽  
pp. 032042
Author(s):  
D A Tverdyi ◽  
R I Parovik
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Riccati Equation ◽  
Russian Federation ◽  
Variable Coefficients ◽  
Variable Order ◽  
Modified Newton Method ◽  
Coronavirus Infection ◽  
The Russian Federation ◽  
The Republic

Abstract The article proposes a mathematical model based on the fractional Riccati equation to describe the dynamics of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. The model fractional Riccati equation is an equation with variable coefficients and a derivative of a fractional variable order of the Gerasimov-Caputo type. The solution to the model Riccati equation is given using the modified Newton method. The obtained model curves are compared with the experimental data of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. It is shown that with a suitable choice of parameters in the mathematical model, the calculated curves give results close to real experimental data.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Time Coordination of Periodic Passenger Train Connections in Conditions of Single-Track Lines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Filip Lorenz ◽  
Vit Janos ◽  
Dusan Teichmann ◽  
Michal Dorda
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Real Data ◽  
Real Problem ◽  
Single Track ◽  
Railway Stations ◽  
Optimization Software ◽  
Proposed Model ◽  
The Individual ◽  
The Given

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.

scholarly journals About rats and jackfruit trees: modeling the carrying capacity of a Brazilian Atlantic Forest spiny-rat Trinomys dimidiatus (Günther, 1877) – Rodentia, Echimyidae – population with varying jackfruit tree (Artocarpus heterophyllus L.) abundances

2015 ◽  
Vol 75 (1) ◽  
pp. 208-215 ◽  
Author(s):  
JHF Mello ◽  
TP Moulton ◽  
DSL Raíces ◽  
HG Bergallo
Keyword(s):  
Mathematical Model ◽  
Population Size ◽  
Seed Production ◽  
Atlantic Forest ◽  
Small Mammal ◽  
Carrying Capacity ◽  
Real Data ◽  
Brazilian Atlantic Forest ◽  
Artocarpus Heterophyllus ◽  
Small Mammal Community

We carried out a six-year study aimed at evaluating if and how a Brazilian Atlantic Forest small mammal community responded to the presence of the invasive exotic species Artocarpus heterophyllus, the jackfruit tree. In the surroundings of Vila Dois Rios, Ilha Grande, RJ, 18 grids were established, 10 where the jackfruit tree was present and eight were it was absent. Previous results indicated that the composition and abundance of this small mammal community were altered by the presence and density of A. heterophyllus. One observed effect was the increased population size of the spiny-rat Trinomys dimidiatus within the grids where the jackfruit trees were present. Therefore we decided to create a mathematical model for this species, based on the Verhulst-Pearl logistic equation. Our objectives were i) to calculate the carrying capacity K based on real data of the involved species and the environment; ii) propose and evaluate a mathematical model to estimate the population size of T. dimidiatus based on the monthly seed production of jackfruit tree, Artocarpus heterophyllus and iii) determinate the minimum jackfruit tree seed production to maintain at least two T. dimidiatus individuals in one study grid. Our results indicated that the predicted values by the model for the carrying capacity K were significantly correlated with real data. The best fit was found considering 20~35% energy transfer efficiency between trophic levels. Within the scope of assumed premises, our model showed itself to be an adequate simulator for Trinomys dimidiatus populations where the invasive jackfruit tree is present.

scholarly journals A Decision-Making Algorithm Based on the Average Table and Antitheses Table for Interval-Valued Fuzzy Soft Set

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1131
Author(s):  
Xiuqin Ma ◽  
Yanan Wang ◽  
Hongwu Qin ◽  
Jin Wang
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Real Data ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Data Set ◽  
Realistic Situation ◽  
Effective Decision ◽  
Working Out ◽  
Interval Valued

Interval-valued fuzzy soft set is one efficient mathematical model employed to handle the uncertainty of data. At present, there exist two interval-valued fuzzy soft set-based decision-making algorithms. However, the two existing algorithms are not applicable in some cases. Therefore, for the purpose of working out this problem, we propose a new decision-making algorithm, based on the average table and the antitheses table, for this mathematical model. Here, the antitheses table has symmetry between the objects. At the same time, an example is designed to prove the availability of our algorithm. Later, we compare our proposed algorithm with the two existing decision-making algorithms in several cases. The comparison result shows that only our proposed algorithm can make an effective decision in exceptional cases, and the other two methods cannot make decisions. It is therefore obvious that our algorithm has a stronger decision-making ability, thus further demonstrating the feasibility of our algorithm. In addition, a real data set of the homestays in Siming District, Xiamen is provided to further corroborate the practicability of our algorithm in a realistic situation.

scholarly journals A Mathematical Model for Predicting the Winnowing Efficiency of Bambara Groundnut Sheller

2020 ◽  
Vol 5 (2) ◽  
pp. 225-228
Author(s):  
Inimfon Samuel Ossom ◽  
Akindele Folarin Alonge ◽  
Kingsley Charles Umani ◽  
Edidiong J. Bassey
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Moisture Content ◽  
Model Equation ◽  
Model Simulation ◽  
Least Square Method ◽  
Bambara Groundnut ◽  
Least Square ◽  
Predicted Model ◽  
Experimental Values

A mathematical model for predicting the winnowing efficiency of bambara groundnut sheller was developed. The regression equation for model simulation was developed using Least Square Method. The model was verified and validated by fitting it into established experimental data from winnowing efficiency of already existed Bambara groundnut sheller. The result revealed that the fitted model correlated well with the experimental data with R-square value of 0.99. The winnowing efficiency obtained from the predicted model was approximately the same values with the experimental values. Therefore, the model equation was considered to be reasonably good for predicting the winnowing efficiency of bambara groundnut sheller for known values of moisture content and blower speed.

scholarly journals Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

2019 ◽  
Vol 14 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Matvey Kulakov ◽  
E.Ya. Frisman
Keyword(s):  
Mathematical Model ◽  
Model Equation ◽  
Temporal Dynamics ◽  
Local Population ◽  
Two Dimensional ◽  
Attraction Basin ◽  
Local Populations ◽  
Long Range Interactions ◽  
Spatio Temporal ◽  
Formation Of Groups

The paper proposed a mathematical model for spatio-temporal dynamics of two-age populations coupled by migration living on a two-dimensional areal. The model equation is a system of nonlocal coupled two-dimensional maps. We considered cases when populations are coupled in a certain neighborhood of different form: circle, square or rhombus. Special attention is paid to the situation when the intensity of the migrants flow between the territories decreases with increasing distance between them. For this model we study the conditions for the formation of groups of synchronous populations or clusters that form, in space, typical structures like spots or stripes mixed with solitary states. It is shown that the dynamics, in time, of different clusters may differ significantly and may not be coherent and correspond to several simultaneous multistable regimes or potential states of the local population. Such spatio-temporal regimes are forced and are caused by impacts or perturbations on a single or several populations when their number falls into the attraction basin of another regime. With strong coupling, such clusters are rare and are represented by single outbursts or solitary states. However, the decrease in the coupling strength leads to the fact that these outbursts cause oscillations of their neighbors, and in their neighborhood a cluster of solitary states is formed which is surrounded by subpopulations with a different type of dynamics. It was found that the interaction of different type of clusters leads to the formation of a large number of groups with transitional dynamics that were not described for local populations.

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