300 results
Search Results
2. Boundary stabilization of an axially moving system of elasticity with an exponentially bounded external disturbance.
- Author
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Aouragh, My Driss and Nahli, Mohamed
- Subjects
HYBRID systems ,SYSTEMS theory ,EXPONENTIAL stability ,ELASTICITY ,CLOSED loop systems ,ADHESIVE tape - Abstract
This paper discusses the stabilization problem of a tape moving axially between two sets of rollers. We propose a modelization which yields a hybrid system accounting for the mass of the left rollers that undergoes an external non-uniformly bounded disturbance. The active disturbance rejection control approach is adopted in this paper; first, an extended state observer with time varying gain of exponential type is designed to estimate the disturbance; then, a feedback controller is proposed in which the approximated disturbance is used to eliminate the effect of the disturbance. We prove the well-posedness of the closed-loop system by the semigroup theory. We employ the Lyapunov method to establish the exponential stability. We conclude by presenting a numerical example to support the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. Fractional optimal control problem for a mathematical modeling of African swine fever virus transmission.
- Author
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Kouidere, Abdelfatah, Balatif, Omar, and Rachik, Mostafa
- Subjects
AFRICAN swine fever virus ,PESTICIDES ,MATHEMATICAL models ,MATHEMATICAL analysis ,COMPUTER simulation - Abstract
To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin's maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. A novel mechanism measurement of predator interference in predator–prey models.
- Author
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Alebraheem, Jawdat and Abu-Hassan, Yahya
- Abstract
A characteristic of ecosystems is the existence of manifold of independencies which are highly complex. Various mathematical models have made considerable contributions in gaining a better understanding of the predator–prey interactions. The main components of any predator–prey models are, firstly, how the different population classes grow and secondly, how the prey and predator interacts. In this paper, the two populations’ growth rates obey the logistic law and the carrying capacity of the predator depends on the available number of prey are considered. Our aim is to clarify the relationship between models and Holling types functional and numerical responses in order to gain insights into predator interferences and to answer an important question how competition is carried out. We consider a predator–prey model and a two-predator one-prey model to explain the idea. The novel approach is explained for the mechanism measurement of predator interference through depending on numerical response. Our approach gives good correspondence between an important real data and computer simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. A Comprehensive Study of Covid 19 in Florida
- Author
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Bennett, Julian, Eriksen, Lauren, and Li, Xingjie Helen
- Subjects
Statistics - Applications ,Quantitative Biology - Populations and Evolution ,93A30 - Abstract
Within the likes of any highly contagious and unpredictable disease, lies a predictable and attainable growth rate that researchers can find in order to make logistical conclusions about that particular disease and its affected regions' counterparts. The foundation that researchers pull from when studying a particular disease and looking for its growth rate is the Susceptible-Infected-Removed (SIR) model, presented by a series of differential equations. The issue with the SIR model lies not in its complexity, but actually its simplicity and lack of a potentially high-finite amount of factors; the limit being bounded by the amount of data available for that particular factor. Our research involves the application of multiple regressions to pinpoint and identify our Covid lockdown periods, followed by the modification of the SIR model. This involved creating new model approximations such as the time-delayed SIR model and the reinfected SIR model in order to take into account factors such as incubation and reinfection, and get the lowest error discrepancy as possible for our infection rate. We were able to conclude that the more factors that we took into account, our error rate became lower and our results became more accurate. We could also identify outlier Metros and draw certain conclusions on performance level and the reasons behind them. We then moved on to find correlations, if any, between the infection rates and outside factors. We looked at demographic and weather data to demonstrate whether correlations appeared. We found that there are a few factors with high correlations, including graduate education and low temperatures.
- Published
- 2024
6. Parameter estimation of modified gray model GM (1, N) and model application.
- Author
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Cheng, Maolin, Li, Jiano, Liu, Yun, and Xiang, Minyin
- Subjects
DIFFERENTIAL equations ,ANALYTICAL solutions ,PREDICTION models - Abstract
The GM (1, N) model is an important prediction model among gray models, but the conventional GM (1, N) model shows big errors sometimes mainly due to the structural inconsistency between the gray differential equation for parameter estimation and the whitening equation for prediction. The paper derives the modified model of conventional gray differential equation based on the whitening equation, and the gray differential equation obtained in this way has the structure basically consistent with the structure of whitening equation. The paper estimates parameters with the gray differential equation of modified GM (1, N) model and gives three parameter estimation methods with different background values. The time response equation for conventional GM (1, N) model generally has no analytical solution, but the paper gives a specific solving method for the time response equation of modified model. The example proves that the modified GM (1, N) model given and the models built with the methods proposed improve the simulation and prediction accuracy significantly compared with the conventional model. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
7. Interplay Between Homophily-Based Appraisal Dynamics and Influence-Based Opinion Dynamics: Modeling and Analysis
- Author
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Liu, Fangzhou, Cui, Shaoxuan, Mei, Wenjun, Dorfler, Florian, and Buss, Martin
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Dynamical Systems ,93A30 - Abstract
In social systems, the evolution of interpersonal appraisals and individual opinions are not independent processes but intertwine with each other. Despite extensive studies on both opinion dynamics and appraisal dynamics separately, no previous work has ever combined these two processes together. In this paper, we propose a novel and intuitive model on the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics. We assume that individuals' opinions are updated via the influence network constructed from their interpersonal appraisals, which are in turn updated based on the individual opinions via the homophily mechanism. By theoretical analysis, we characterize the set of equilibria and some transient behavior of our model. Moreover, we establish the equivalence among the convergence of the appraisal network to social balance, the modulus consensus of individual opinions, and the non-vanishing appraisals. Monte Carlo validations further show that the non-vanishing appraisals condition holds for generic initial conditions. Compared with previous works that explain the emergence of social balance via person-to-person homophily mechanism, our model provides an alternative explanation in terms of the person-to-entity homophily mechanism. In addition, our model also describes how individuals' opinions on multiple irrelevant issues become correlated and converge to modulus consensus over time-varying influence networks.
- Published
- 2020
8. A comparative study for mathematical modelling of the contest of CAR-T and tumour cells in solid cancers using fractional- and integer-order derivatives
- Author
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Kumar, Pushpendra and Erturk, Vedat Suat
- Published
- 2024
- Full Text
- View/download PDF
9. New mixed-integer linear programming model for solving the multidimensional multi-way number partitioning problem.
- Author
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Nikolic, Bojan, Djukanovic, Marko, and Matic, Dragan
- Subjects
INTEGER programming ,MIXED integer linear programming - Abstract
The multidimensional multi-way number partitioning problem considers a set of n vectors of a fixed dimension m ≥ 2 as an input. The goal is to find partitioning of the set into k ≥ 2 subsets such that sums per each coordinate in each subset are as nearly equal as possible. The problem has applications in key encryption and multiprocessor scheduling. Prior to this paper, there has been only one mixed-integer model proposed in case of general k ≥ 2 . In this paper, we propose a new mixed-integer programming model for the general case. The obtained results indicate that our model significantly outperforms the model from literature for larger values of k. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
10. Improved methods for parameter estimation of gray model GM(1,1) based on new background value optimization and model application.
- Author
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Cheng, Maolin and Shi, Guojun
- Subjects
CLEAN energy ,ENERGY consumption ,PREDICTION models ,INTERPOLATION ,CURVES ,PARAMETER estimation - Abstract
In the gray prediction, the GM(1,1) model has been applied widely, but the conventional GM(1,1) model prediction shows big errors sometimes. Many researchers improve prediction accuracy by changing the basic structure of model. The paper tries to make improvements in the models parameter estimation on the basis of new background value optimization without changing the models structure, and gives the following four methods: (1) estimating the parameter of gray model GM(1,1) with the optimized value of exponential curve as the background value; (2) estimating the parameter of gray model GM(1,1) with the optimized value of power function curve as the background value; (3) estimating the parameter of gray model GM(1,1) with the optimized value of polynomial curve as the background value; (4) estimating the parameter of gray model GM(1,1) with the optimized value of interpolation function as the background value. The last part of the paper builds the GM(1,1) model of China's total clean energy consumption with the four improved methods. The simulation and prediction results show that these methods all improve the prediction accuracy of model significantly. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
11. Modeling of the chaotic situation in the recruitment processes
- Author
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Verma, Harendra, Mishra, Vishnu Narayan, and Mathur, Pankaj
- Published
- 2023
- Full Text
- View/download PDF
12. Mathematical modeling, analysis and control in soft robotics: a survey
- Author
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Ortigosa-Martínez, Rogelio, Martínez-Frutos, Jesús, Mora-Corral, Carlos, Pedregal, Pablo, and Periago, Francisco
- Published
- 2024
- Full Text
- View/download PDF
13. Shape-Programming in Hyperelasticity Through Differential Growth.
- Author
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Ortigosa-Martínez, Rogelio, Martínez-Frutos, Jesús, Mora-Corral, Carlos, Pedregal, Pablo, and Periago, Francisco
- Abstract
This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well. Boundary conditions and external loads are allowed in the state law, thus extending previous works where the stress-free hypothesis turns out to be essential. A rigorous mathematical analysis is then carried out to prove the well-posedness of the problem. The numerical approximation is performed using gradient-based optimisation algorithms. Our main goal in this part is to show the possibility to apply inverse techniques for the numerical approximation of this problem, which allows us to address more generic situations than those covered by analytical approaches. Several numerical experiments for beam-like and shell-type geometries illustrate the performance of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. A Multi-Drug Pharmacokinectic Optimal Control Approach in Cancer Chemotherapy
- Author
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Rajan, M. P. and Nanditha, C. K.
- Published
- 2022
- Full Text
- View/download PDF
15. Modelling cystic echinococcosis and bovine cysticercosis co-infections with optimal control.
- Author
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Mwasunda, Joshua A., Chacha, Chacha S., Stephano, Mussa A., and Irunde, Jacob I.
- Subjects
CYSTICERCOSIS ,PONTRYAGIN'S minimum principle ,ECHINOCOCCOSIS ,MIXED infections ,BASIC reproduction number - Abstract
Cystic echinococcosis and bovine cysticercosis are diseases of economic importance especially to rural communities that earn their incomes from livestock. In this paper, a mathematical model for cystic echinococcosis and bovine cysticercosis co-infections is formulated and analyzed to determine parameters that drive the diseases and design the optimal control strategy. The basic reproduction number R 0 that governs the dynamics of cystic echinococcosis and bovine cysticercosis is computed by the next-generation matrix method, and the normalized forward sensitivity index is used to derive the sensitivity indices of model parameters. Sensitivity analysis shows that co-infections of cattle with cystic echinococcosis and bovine cysticercosis, open defecation rate by humans who are infected with taeniasis and the rate of slaughtering co-infected cattle play a significant role in the persistence of cystic echinococcosis and bovine cysticercosis. Sobol sensitivity analysis has been carried out to study global sensitivity of model parameters to state variables. The results show that the rate at which exposed dogs progress to infectious class, the rate at which humans who are exposed to taeniasis progress to infectious stage, the rate at which dogs are recruited, cattle per capita natural death rate, cattle recruitment rate and tapeworm eggs' natural death rate are the most sensitive parameters to exposed dogs, humans who are exposed to taeniasis, infectious dogs, infectious cattle, exposed cattle and tapeworm eggs in the environment respectively. The control strategies, such as cattle indoor keeping, meat inspection, and improved hygiene and sanitation are implemented in combination to determine the possibility of controlling the spread of cystic echinococcosis and bovine cysticercosis. The Pontryagin's maximum principle is applied to determine diseases' optimal control strategy. Results show that cattle indoor keeping and meat inspection are more effective in disease control when they are concurrently implemented. Rural communities that earn income from livestock can control cystic echinococcosis and bovine cysticercosis by reducing the number of cattle that are kept in free range system, inspect meat from cattle and improve hygiene and sanitation. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
16. Partial Realization Theory and System Identification Redux
- Author
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Lindquist, Anders
- Subjects
Mathematics - Optimization and Control ,93A30 - Abstract
Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that the nonstandard matrix Riccati equation is universal in the sense that it can be used to solve more general analytic interpolation problems by only changing certain parameters. Such interpolation problems are ubiquitous in systems and control. In this context we also discuss a question posed by R.E. Kalman in beginning of the 1970s.
- Published
- 2017
17. Wind Energy in the United Kingdom: Modelling the Effect of Increases in Installed Capacity on Generation Efficiency
- Author
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Stephens, Anthony D and Walwyn, David R
- Subjects
Physics - Physics and Society ,93A30 - Abstract
The decision by the United Kingdom (UK) government in 2007 that the country should build a 33GW wind fleet, capable of generating 25 percent of the UK electricity requirement, was controversial. Proponents argued that it was the most attractive means of lowering the UK greenhouse gas emissions, whereas opponents noted that it would result in an unnecessary and burdensome additional expense to industry and households. Subsequently there have been calls for the wind fleet target to be further increased to perhaps 50 percent of demand. Although the National Grid has had little difficulty in accommodating the current output of about 10 percent of the total demand on the grid, this will not be the case for a substantially larger wind fleet. When the wind blows strongly, turbines shed wind which is surplus to demand, leading to significant reductions in generating efficiency. The purpose of the research described in this paper has been to develop a method for investigating the likely performance of future large wind fleets. The method relies on the use of mathematical models based on National Grid records for 2013 to 2015, each year being separately analysed. It was found that the incremental load factor of the wind fleet will be reduced to 63 percent of its current level should the wind fleet increase from its current size of 14GW to 35GW, assuming a base load of 15GW, Comment: 24 pages, 15 figures, 4 tables
- Published
- 2016
18. Continuous and discrete modeling of HIV-1 decline on therapy.
- Author
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Akın, Elvan, Yeni, Gülşah, and Perelson, Alan S.
- Subjects
REVERSE transcriptase inhibitors ,CONTINUOUS time systems ,REAL numbers ,PROTEASE inhibitors ,MATHEMATICAL models ,DISCRETE systems - Abstract
Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. One of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
19. Worldlines and social networks
- Author
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Jenkovszky, Laszlo
- Subjects
Physics - Physics and Society ,Physics - Popular Physics ,93A30 - Abstract
Familiar laws of physics are applied to study human relations, modelled by their world lines (worldlines, WLs) combined with social networks. We focus upon the simplest, basic element of any society: a married couple, stable due to the dynamic balance between attraction and repulsion. By building worldlines/worldsheets, we arrive at a two-level coordinate systems: one describing the behaviour of a string-like binary system (here, a married couple), the other one, external, corresponding to the motion of this couple in the medium, in which the worldline is embedded, sweeping there a string-like sheet or brane. The approach is illustrated by simple examples (semi-quantitative toy models) of worldlines/sheets, open to further extension, perfections and generalization. World lines (WLs) are combined with social networks (SN). Our innovation is in the application of basic physical laws, attraction and repulsion to human behaviour. Simple illustrative examples with empirical inputs taken from intuition and/or observation are appended. This is an initial attempt, open to unlimited applications., Comment: 16 pages, 11 figures
- Published
- 2021
- Full Text
- View/download PDF
20. Impulsive Stochastic Volterra Integral Equations Driven by Lévy Noise
- Author
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Khalaf, Anas Dheyab, Tesfay, Almaz, and Wang, Xiangjun
- Published
- 2021
- Full Text
- View/download PDF
21. Aggregated Demand Modelling Including Distributed Generation, Storage and Demand Response
- Author
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Marzooghi, Hesamoddin, Hill, David J., and Verbic, Gregor
- Subjects
Mathematics - Optimization and Control ,93A30 - Abstract
It is anticipated that penetration of renewable energy sources (RESs) in power systems will increase further in the next decades mainly due to environmental issues. In the long term of several decades, which we refer to in terms of the future grid (FG), balancing between supply and demand will become dependent on demand actions including demand response (DR) and energy storage. So far, FG feasibility studies have not considered these new demand-side developments for modelling future demand. In Australia, installed rooftop photovoltaic (PV) generation has been increasing significantly in recent years, and this is increasingly influence the nett load profile for FG feasibility studies. This paper proposes an aggregate nett load or demand model to be used at higher voltage levels considering the effect of rooftop PV, energy storage and DR for FG scenarios, which is inspired by the smart home concept. The proposed model is formulated as an optimization problem aiming at minimizing the electricity cost. As a case study, the effect of the load model is studied on the load profile, balancing and loadability of the Australian National Electricity Market in 2020 with the increased penetration of wind and solar generation., Comment: 11 pages, 6 figures, 3 Tables, submitted to IET Generation, Transmission & Distribution
- Published
- 2014
22. A model for the lifetime of a reactive filter.
- Author
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Kiradjiev, Kristian B., Breward, Christopher J. W., and M. Griffiths, Ian
- Abstract
In many industrial applications, reactive filters, which remove toxic substances using chemical reactions, prove very efficient and versatile. One such example is the removal of sulphur dioxide from flue gas by converting it into liquid sulphuric acid. In this paper, we extend a model developed in Kiradjiev et al. (SIAM J Appl Math 82:591–619, 2021) for the operation of a reactive filter to consider the long-time behaviour and determine how the filter becomes clogged with liquid and becomes inefficient. We explore how the parameters that govern the operation of the filter affect its efficiency and discuss optimal filtration strategies. We also consider a distinguished asymptotic limit in terms of the key dimensionless parameters and obtain an explicit solution that compares well with the numerical solution to the full problem. Finally, we compare the results of our model with those from a simplified model for a reactive filter considered in Breward and Kiradjiev (J Eng Math, 129(14):1–28, 2021). [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
23. A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control
- Author
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Kouidere, Abdelfatah, Khajji, Bouchaib, Balatif, Omar, and Rachik, Mostafa
- Published
- 2021
- Full Text
- View/download PDF
24. The Multidimensional Moment Problem with Complexity Constraint.
- Author
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Karlsson, Johan, Lindquist, Anders, and Ringh, Axel
- Abstract
A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the solution set in terms of a bounded finite number of parameters is required. In this paper we provide a complete solution of the multidimensional moment problem with a complexity constraint also allowing for solutions that require a singular measure added to the rational, absolutely continuous one. Such solutions occur on the boundary of a certain convex cone of solutions. In this paper we provide complete parameterizations of all such solutions. We also provide errata for a previous paper in this journal coauthored by one of the authors of the present paper. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
25. Qualitative analysis of physical factors that determine activity coefficients of electrolytes. III. Mixtures of electrolytes.
- Author
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Tikhonov, Nikolay and Tokmachev, Mikhail
- Subjects
QUALITATIVE chemical analysis ,ACTIVITY coefficients ,ELECTROLYTES ,ELECTRIC potential ,NUMERICAL analysis ,MATHEMATICAL models - Abstract
In the paper we propose a model describing interaction characteristics of hydrated ions in the mixtures of uni-univalent electrolytes with a common ion. The main factor taken into consideration is a variation of the hydrate shell size in the mixture from its value in the binary solution. Account of this factor gives a possibility to calculate the corresponding variation of the potential describing the mutual ions interaction. The potential is the sum of the electrostatic potential of ions and potential resulted from deformation of approaching hydrated shells. On this basis it is possible to explain the behavior of curves describing the activity coefficients in the mixtures of electrolytes in the range of concentrations from zero to several moles per liter. The results obtained by a numerical modelling are verified by comparing with the available experimental data. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
26. Balancing Personal Privacy and Public Safety during COVID-19: The Case of South Korea
- Author
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Ahn, Na Young, Park, Jun Eun, Lee, Dong Hoon, and Hong, Paul C.
- Subjects
Computer Science - Computers and Society ,Computer Science - Cryptography and Security ,93A30 ,C.0 ,H.0 - Abstract
There has been vigorous debate on how different countries responded to the COVID-19 pandemic. To secure public safety, South Korea actively used personal information at the risk of personal privacy whereas France encouraged voluntary cooperation at the risk of public safety. In this article, after a brief comparison of contextual differences with France, we focus on South Korea's approaches to epidemiological investigations. To evaluate the issues pertaining to personal privacy and public health, we examine the usage patterns of original data, de-identification data, and encrypted data. Our specific proposal discusses the COVID index, which considers collective infection, outbreak intensity, availability of medical infrastructure, and the death rate. Finally, we summarize the findings and lessons for future research and the policy implications., Comment: 11pages
- Published
- 2020
- Full Text
- View/download PDF
27. Modeling the impact of awareness programmes on the sustainable use of water resources
- Author
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Verma, Ahana, Shukla, J. B., and Arora, Maninder Singh
- Published
- 2023
- Full Text
- View/download PDF
28. Deterministic modelling of optimal control strategies for dengue fever transmission in two interconnected patches
- Author
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Abidemi, Afeez, Aziz, Nur Arina Bazilah, and Pindza, Edson
- Published
- 2023
- Full Text
- View/download PDF
29. Delayed Model for HIV Infection with Drug Effects.
- Author
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Sahani, Saroj Kumar and Yashi
- Abstract
Delayed models are a better representation of the nature of HIV. In the present paper, a multi-delayed model of HIV with combination drug therapy has been analysed. Effect of the immune response in the form of effector cell response has also been included to make the model more justified. The threshold properties related with the basic reproduction number R0
have been discussed. The local and global properties of the model have been analysed. Extensive numerical simulations have been performed to show the impact of highly effective drug on the concentration of virus. The numerical simulations and the result proved has led to the conclusion that a highly effective drug when combined with a less effective drug, can very efficiently bring down the viral load to undetectable levels. [ABSTRACT FROM AUTHOR] - Published
- 2018
- Full Text
- View/download PDF
30. Nonexistence results of Caputo-type fractional problem.
- Author
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Kassim, Mohammed D., Ali, Saeed M., Abdo, Mohammed S., and Jarad, Fahd
- Subjects
FRACTIONAL integrals ,CAPUTO fractional derivatives - Abstract
In this paper, we deal with Caputo-type fractional differential inequality where there is a low-order fractional derivative with the term polynomial source. We investigate the nonexistence of nontrivial global solutions in a suitable space via the test function technique and some properties of fractional integrals. Finally, we demonstrate three examples to illustrate our results. The presented results are more general than those in the literature, which can be obtained as particular cases. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
31. A mathematical model for fall armyworm management on maize biomass.
- Author
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Daudi, Salamida, Luboobi, Livingstone, Kgosimore, Moatlhodi, Kuznetsov, Dmitry, and Mushayabasa, Steady
- Subjects
FALL armyworm ,BASIC reproduction number ,MATHEMATICAL models ,BIOMASS ,AGRICULTURAL pests ,CORN - Abstract
Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
32. Impulsive differential equation model in methanol poisoning detoxification: Efficacy of activated charcoal antidote in combating methanol poisoning
- Author
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Ghosh, P. and Peters, J. F.
- Published
- 2020
- Full Text
- View/download PDF
33. State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries.
- Author
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Wang, YaNan, Chen, YangQuan, and Liao, XiaoZhong
- Subjects
PARAMETER identification ,KALMAN filtering ,ALGORITHMS - Abstract
This paper presents a state-of-art survey of the research on fractional-order (FO) modeling with parameter identification, and FO estimation methods for state of charge (SOC), state of health (SOH), and remaining usage life (RUL) of lithium-ion batteries (LIBs) mainly in recent five years. FO electrochemical models and six different types of FO equivalent circuit models (ECMs) are introduced in detail. Then, the corresponding tuning algorithm for parameters of these FO models are also provided in brief. Moreover, FO estimation methods for SOC are listed and analyzed, mainly including FO observers, and FO Kalman filters (FO-KFs). SOH and RUL estimation is another vital aspect for LIBs ageing and degradation monitoring, thus FO estimation methods proposed in recent research within five years are all listed. Finally, some suggestions that may be helpful for further research are proposed in conclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
34. Isolating patterns in a reaction-diffusion system with Smith population growth
- Author
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Guin, Lakshmi Narayan, Das, Sukanya, Mandal, Gourav, Dutta, Swagata, and Chakravarty, Santabrata
- Published
- 2023
- Full Text
- View/download PDF
35. A new expert system in prediction of lung cancer disease based on fuzzy soft sets.
- Author
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Khalil, Ahmed Mostafa, Li, Sheng-Gang, Lin, Yong, Li, Hong-Xia, and Ma, Sheng-Guan
- Subjects
SOFT sets ,FUZZY expert systems ,EXPERT systems ,LUNG cancer ,LUNG diseases ,CORONARY vasospasm ,FUZZY systems ,LATENT class analysis (Statistics) - Abstract
Every year, millions of people worldwide (including a major portion in China) are suffering from lung cancer disease (Chinese report of Smoking and Health 2017). The aim of this paper is to develop a new fuzzy soft expert system which can be used to predict lung cancer disease. A prediction process using this fuzzy soft expert system is composed of four main steps: (1) Transform real-valued inputs into fuzzy numbers. (2) Transform fuzzy numbers of data into fuzzy soft sets. (3) Reduce, using normal parameter reduction method, the obtained family of fuzzy soft sets into a new family of fuzzy soft sets. (4) Use the proposed algorithm to get the output data. An experiment is conducted on forty five patients (thirty males, fifteen females, all are cigarette smokers) who endure treatment in the Respiratory Department of Nanjing Chest Hospital, China. The number of training data taken was 55 records, and the remaining 45 records were used for the testing process in our system by using weight loss, shortness of breath, chest pain, persistence a cough, blood in sputum, and age of patients. The quantized accuracies of the proposed system were found to be 100 % . In this work, we developed a fuzzy soft expert system based on fuzzy soft sets; we used a fuzzy membership functions and an algorithm to predict those patients who may suffer lung cancer. In this way, it is possible to conclude that the use of fuzzy soft expert system can produce valuable results for lung cancer detection. It is found that the fuzzy soft expert system developed is useful to the expert doctor to decide if a patient has lung cancer or not. Finally, we introduce comparison diagnosed between our proposed system and the fuzzy inference system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
36. Periodic Solutions of the N-Preys and M-Predators Model with Variable Rates on Time Scales.
- Author
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Negi, Shekhar Singh, Abbas, Syed, and Malik, Muslim
- Abstract
In this paper, we establish the existence of periodic solution of a delayed predator-prey model with M -predators and N -preys over the time scales. We derive sufficient conditions for the existence of a periodic solution with the help of continuation theorem of coincidence degree theory. At the end, we give an example with numerical simulations to illustrate our analytical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
37. Variational Networks: An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration.
- Author
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Effland, Alexander, Kobler, Erich, Kunisch, Karl, and Pock, Thomas
- Abstract
We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox originates from a tradeoff between optimization and modeling errors of the underlying variational model and holds true even if deep learning methods are used to learn highly expressive regularizers from data. In this paper, we take advantage of this paradox and introduce an optimal stopping time into the gradient flow process, which in turn is learned from data by means of an optimal control approach. After a time discretization, we obtain variational networks, which can be interpreted as a particular type of recurrent neural networks. The learned variational networks achieve competitive results for image denoising and image deblurring on a standard benchmark data set. One of the key theoretical results is the development of first- and second-order conditions to verify optimal stopping time. A nonlinear spectral analysis of the gradient of the learned regularizer gives enlightening insights into the different regularization properties. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
38. Designing a Simulink model for a mixed model stochastic assembly line : A case study using a water bottling plant.
- Author
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Kuriakose, Rangith Baby and Vermaak, Herman Jacobus
- Subjects
- *
ASSEMBLY line methods , *PLANT-water relationships , *ASSEMBLY line balancing , *STOCHASTIC models , *BOTTLED water - Abstract
As the world is moving into the 4th Industrial revolution, commonly referred to as Industry 4.0, mass production is giving way to mass customization. This shift necessitates a change in the design of the assembly line with flexibility and multi variant manufacturing taking precedence. These kind of assembly lines that can manufacture multiple models without a predetermined manufacturing time are referred to as mixed model stochastic assembly lines. This paper looks at how such a mixed model stochastic assembly line can be modelled. This is done by taking the case study of a water bottling plant that is being developed at the university where this research is conducted. The water bottling plant needs to produce 500 ml and 750 ml bottles of clean drinking water which can be used within the university or be sold externally. The primary aim of this paper is to develop a MATLAB model for the water bottling plant and study the results from the simulations. These results will shed light on how the model can be optimized thereby contribute to the niche area of Mixed Model Stochastic Assembly Line Balancing. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
39. A mathematical model for control strategies of COVID-19.
- Author
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Somathilake, L. W.
- Subjects
- *
BASIC reproduction number , *MATHEMATICAL models , *COVID-19 , *SOCIAL distancing , *COMMUNICABLE diseases , *INFECTIOUS disease transmission - Abstract
Until finding medicines or vaccines for newly outbreaking infectious diseases, the mostly applying control strategies are maintaining social distancing, quarantining suspected exposures, and isolating infectious people. This paper proposes a mathematical model for control strategies of COVID-19, considering population sub-classes susceptible (S), Exposed (E), Quarantined (Q), Infected (I), Isolated (J), and Recovered (R). Mathematical models consisting of these sub-classes are called SEQIJR type models. The basic reproduction number of the proposed mathematical model is derived based on the next-generation matrix. Based on the basic reproduction number of the model, the disease dies out and the disease persists parameter spaces are determined. The effects of the rates and applying stages of the control strategies on the spread of the disease are explained. Outcomes of the proposed model are helpful to identify suitable stages and strengths of the control strategies to control the disease, considering available health care capacity. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
40. On the steady state optimization of the biogas production in a two-stage anaerobic digestion model
- Author
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Bayen, Térence and Gajardo, Pedro
- Published
- 2019
- Full Text
- View/download PDF
41. On understanding price-QoS war for competitive market and confused consumers.
- Author
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Ait Omar, Driss, Outanoute, M'Hamed, Baslam, Mohamed, Fakir, Mohamed, and Bouikhalene, Belaid
- Subjects
PRICING ,NASH equilibrium ,BOUNDED rationality ,TELECOMMUNICATION systems ,TELECOMMUNICATIONS services ,EQUILIBRIUM - Abstract
How will bounded rationality influence telecommunication network fluctuations? Recently, there has been an increased research interest in telecommunication network pricing, which leads to many proposals for new pricing schemes motivated by different objectives namely: to maximize service provider's revenue, to guarantee fairness among users and to satisfy quality of service (QoS) requirements for differentiated network services. In the present paper, we consider a system with N rational service providers (SPs) that offer homogeneous telecommunication services to bounded rational costumers. All SPs offer the same services and seek to persuade more customers in the same system, we model this conflict as a noncooperative game. On the one hand, each SP decide his policies of price and QoS in order to maximize his profit. One the other hand, we assume that the customers are boundedly rational and make their subscription decisions probabilistically, according to Luce choice probabilities. Furthermore, the customers decide to which SP to subscribe, each one may migrate to another SP or alternatively switch to "no subscription state" depending on the observed price/QoS. In this work, we have proved through a detailed analysis the existence and uniqueness of Nash equilibrium. We evaluate the impact of user's bounded rationality on the equilibrium of game. Using the price of anarchy, we examine the performance and efficiency of equilibrium. We have shown that the SPs have an interest in confusing customers, which means more than the customers are irrational, the SPs earn more. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
42. From Staphylococcus aureus gene regulation to its pattern formation.
- Author
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Oelker, A., Horger, T., and Kuttler, C.
- Subjects
GENETIC regulation ,STAPHYLOCOCCUS aureus ,QUORUM sensing ,PATTERN formation (Biology) ,ORDINARY differential equations ,PARTIAL differential equations ,EVOLUTION equations - Abstract
The focus of this paper is to develop a new partial differential equation model for the pattern formation of the human pathogen Staphylococcus aureus, starting from a newly developed model of selected gene regulation mechanisms. In our model, we do not only account for the bacteria densities and nutrient concentrations, but also for the quorum sensing and biofilm components, since they enable bacteria to coordinate their behavior and provide the environment in which the colony grows. To this end, we model the relevant gene regulation systems using ordinary differential equations and therefrom derive our evolution equations for quorum sensing and biofilm environment by time-scale arguments. Furthermore, we compare and validate our model and the corresponding simulation results with biological real data observations of Staphylococcus aureus mutant colony growth in the laboratory. We show that we are able to adequately display the qualitative biological features of pattern formation in selected mutants, using the parameter changes indicated by the gene regulation mechanisms. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
43. Three Dimensional Intruder Closest Point of Approach Estimation Based-on Monocular Image Parameters in Aircraft Sense and Avoid.
- Author
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Bauer, Peter, Hiba, Antal, Bokor, Jozsef, and Zarandy, Akos
- Abstract
The paper deals with monocular image-based sense and avoid assuming constant aircraft velocities and straight flight paths. From very limited two dimensional image information it finally characterizes the whole three dimensional collision situation by estimating the time to closest point of approach, the horizontal relative distance and its direction and the vertical relative distance also. The distances are relative to the intruder aircraft horizontal and vertical sizes. The overall estimated relative distance is the closest between the two aircraft in three dimension. So finally, every important information can be extracted to be used in a collision decision. The applicability of the developed method is presented in software-in-the-loop simulation test runs. Several intruder size and speed values are considered together with trajectories covering the whole three dimensional space. The horizontal intruder flight directions relative to the own aircraft cover 360
∘ and the intruder can come from below ar above also. Detailed evaluation and discussion of the results is also included. Finally, the missed detection rate results to be superior (below 3% in every test scenario) though the false alarm rate results a bit high between 7-14%. [ABSTRACT FROM AUTHOR]- Published
- 2019
- Full Text
- View/download PDF
44. The model and construction of weak IMFs.
- Author
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Yang, Lijun, Huang, Chao, and Yang, Zhihua
- Subjects
MATHEMATICAL models ,MATHEMATICAL functions ,HILBERT-Huang transform ,PROBLEM solving ,SIGNAL processing - Abstract
The empirical mode decomposition is a powerful tool for analyzing nonstationary signals. It decomposes a signal into a few intrinsic mode functions (IMFs) adaptively. As an empirical model for the so-called monocomponent or narrow-band signals, the IMF lacks rigorous mathematical definition. It is an open theoretic problem to establish a rigorous mathematical model for IMFs. In this paper, we model the IMF as the form $$\rho (t)\cos \theta (t)$$ and study the conditions on $$\rho (t)$$ and $$\theta (t)$$ such that $$\rho (t)\cos \theta (t)$$ is a weak IMF. Some useful sufficient conditions are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
45. Parameter estimation of lithium ion polymer battery mathematical model using genetic algorithm.
- Author
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Fatima Brondani, Marcia de, Sausen, Airam Teresa Zago Romcy, Sausen, Paulo Sérgio, and Binelo, Manuel Osório
- Subjects
GENETIC algorithms ,PARAMETER estimation ,LITHIUM-ion batteries ,METHODOLOGY ,STORAGE batteries - Abstract
The accurate prediction of the rechargeable battery lifetime is of paramount importance for mobile device use optimization. The parameter estimation of battery models utilizes experimental methods that are expensive, require high computational effort, and are time-consuming. This paper presents both the proposition of a methodology based on Genetic Algorithm (GA) for the parameter estimation and the mathematical modeling of Lithium Ion Polymer (LiPo) battery lifetime, model PL383562-2C, using the battery model. The proposed GA method is compared with other empirical methodology that is generally applied to this estimation problem. It stands that the GA employed to estimate these parameters turned the estimation into a more systematic and less subjective process. The model validation is performed based on the comparison between the lifetimes simulated by the battery model and the average experimental lifetimes obtained from a test platform. The results demonstrate both the effectiveness of the battery model to predict the LiPo battery lifetime and the efficiency of GA in its parameter estimation. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
46. Mathematical models for tumours with cancer stem cells.
- Author
-
Meacci, Luca and Primicerio, Mario
- Subjects
TUMOR treatment ,CANCER stem cells ,MATHEMATICAL models ,COMPUTER simulation ,CANCER-related mortality - Abstract
The paper deals with mathematical modelling of the growth of tumours characterized by the presence of cancer stem cells (CSC). These cells are assumed to be immortal and multi-potent, in the sense that they can generate either CSC or ordinary cancer cells (CC). We present a synthetic review of some models that have been proposed in the literature and we report the development of new original models, to open a complete multi-approach window on modellization of the problem. The mathematical models are presented without technical details, but numerical simulations are displayed that exhibit the so-called "tumour growth paradox" that consists in the fact that tumours with a larger death rate for the CC may grow faster than tumours with a lower death rate for the same class of cells. The occurrence of this paradox has important consequences also on the strategy of treatment of tumours. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
47. Existence of fractional order semianalytical results for enzyme kinetics model
- Author
-
Alrabaiah, Hussam, Ali, Amjad, Haq, Fazal, and Shah, Kamal
- Published
- 2020
- Full Text
- View/download PDF
48. Active and Reactive Energy Balance Equations in Active and Reactive Time
- Author
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Jeltsema, Dimitri and Kaiser, Gerald
- Subjects
Mathematics - Dynamical Systems ,93A30 - Abstract
Electrical networks, and physical systems in general, are known to satisfy a power balance equation which states that the rate of change of the energy in time equals the power at the port of the network minus the power dissipated. However, when complex power is considered, there does not seem to exist a similar statement for the imaginary power, either in the time-domain or the frequency-domain. Recently, in the context of electromagnetic fields, it has been shown by complexifying the time to t+js and interpreting s as reactive time, that it is possible to set up an imaginary power balance in terms of the rate of change of reactive energy in reactive time. Here these ideas are specialized to linear and time-invariant RLC networks. For non-sinusoidal waveforms it is shown that the rate of change of reactive energy in reactive time contains all the essential properties and features of the commonly accepted definition of reactive power under sinusoidal conditions. We believe that this provides an unambiguous and physically motivated resolution to the longstanding debate on how to generalize reactive power to non-sinusoidal waveforms., Comment: 6 pages and 2 figures
- Published
- 2016
49. Dynamics of a two predator-one prey system.
- Author
-
Alebraheem, Jawdat and Hasan, Yahya
- Subjects
ECOLOGICAL models ,PREDATION ,LIMIT cycles ,MATHEMATICAL complexes ,LAGRANGIAN points ,MATHEMATICAL models - Abstract
Various ecological models have contributed much to gaining a better understanding of prey-predator interactions. In this paper, an extension of the basic model involving two predators competing on one prey is introduced. The equilibrium points and stability of the points are discussed. The existence of limit cycle and consequent complex dynamical behaviors are shown through a new procedure recently introduced. The persistence and extinction of predators are presented in different forms as steady state, limit cycle, and complex dynamical behaviors. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
50. Analytical Expressions to Counterparty Credit Risk Exposures for Interest Rate Derivatives
- Author
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Li, Shuang, Peng, Cheng, Bao, Ying, Zhao, Yan-long, and Cao, Zhen
- Published
- 2022
- Full Text
- View/download PDF
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