Mathematics

35 pages, 13595 KiB

Open AccessEditor’s ChoiceReview

Trends in Vehicle Re-Identification Past, Present, and Future: A Comprehensive Review

by Zakria, Jianhua Deng, Yang Hao, Muhammad Saddam Khokhar, Rajesh Kumar, Jingye Cai, Jay Kumar and Muhammad Umar Aftab

Mathematics 2021, 9(24), 3162; https://doi.org/10.3390/math9243162 - 08 Dec 2021

Cited by 18 | Viewed by 5812

Abstract

Vehicle Re-identification (re-id) over surveillance camera network with non-overlapping field of view is an exciting and challenging task in intelligent transportation systems (ITS). Due to its versatile applicability in metropolitan cities, it gained significant attention. Vehicle re-id matches targeted vehicle over non-overlapping views [...] Read more.

Vehicle Re-identification (re-id) over surveillance camera network with non-overlapping field of view is an exciting and challenging task in intelligent transportation systems (ITS). Due to its versatile applicability in metropolitan cities, it gained significant attention. Vehicle re-id matches targeted vehicle over non-overlapping views in multiple camera network. However, it becomes more difficult due to inter-class similarity, intra-class variability, viewpoint changes, and spatio-temporal uncertainty. In order to draw a detailed picture of vehicle re-id research, this paper gives a comprehensive description of the various vehicle re-id technologies, applicability, datasets, and a brief comparison of different methodologies. Our paper specifically focuses on vision-based vehicle re-id approaches, including vehicle appearance, license plate, and spatio-temporal characteristics. In addition, we explore the main challenges as well as a variety of applications in different domains. Lastly, a detailed comparison of current state-of-the-art methods performances over VeRi-776 and VehicleID datasets is summarized with future directions. We aim to facilitate future research by reviewing the work being done on vehicle re-id till to date. Full article

(This article belongs to the Special Issue Advancement of Mathematical Methods in Feature Representation Learning for Artificial Intelligence, Data Mining and Robotics)

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12 pages, 259 KiB

Open AccessEditor’s ChoiceArticle

Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

by Slavko Simić and Vesna Todorčević

Mathematics 2021, 9(23), 3104; https://doi.org/10.3390/math9233104 - 01 Dec 2021

Cited by 6 | Viewed by 1503

Abstract

In this article, we give sharp two-sided bounds for the generalized Jensen functional

J_{n} (f, g, h;

p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean [...] Read more.

In this article, we give sharp two-sided bounds for the generalized Jensen functional

J_{n} (f, g, h;

p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean

A_{n} (h;

p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained. Full article

(This article belongs to the Special Issue Recent Trends in Convex Analysis and Mathematical Inequalities)

14 pages, 423 KiB

Open AccessEditor’s ChoiceArticle

A New Attractive Method in Solving Families of Fractional Differential Equations by a New Transform

by Ahmad Qazza, Aliaa Burqan and Rania Saadeh

Mathematics 2021, 9(23), 3039; https://doi.org/10.3390/math9233039 - 26 Nov 2021

Cited by 25 | Viewed by 2264

Abstract

In this paper, we use the ARA transform to solve families of fractional differential equations. New formulas about the ARA transform are presented and implemented in solving some applications. New results related to the ARA integral transform of the Riemann-Liouville fractional integral and [...] Read more.

In this paper, we use the ARA transform to solve families of fractional differential equations. New formulas about the ARA transform are presented and implemented in solving some applications. New results related to the ARA integral transform of the Riemann-Liouville fractional integral and the Caputo fractional derivative are obtained and the last one is implemented to create series solutions for the target equations. The procedure proposed in this article is mainly based on some theorems of particular solutions and the expansion coefficients of binomial series. In order to achieve the accuracy and simplicity of the new method, some numerical examples are considered and solved. We obtain the solutions of some families of fractional differential equations in a series form and we show how these solutions lead to some important results that include generalizations of some classical methods. Full article

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15 pages, 306 KiB

Open AccessEditor’s ChoiceArticle

Assessing the Role of Digital Finance on Shadow Economy and Financial Instability: An Empirical Analysis of Selected South Asian Countries

by Aamir Aijaz Syed, Farhan Ahmed, Muhammad Abdul Kamal and Juan E. Trinidad Segovia

Mathematics 2021, 9(23), 3018; https://doi.org/10.3390/math9233018 - 25 Nov 2021

Cited by 23 | Viewed by 4652

Abstract

The advancement in fintech technological development in emerging countries has accelerated the role of digital finance in economic development. Digital finance assists in financial inclusion; however, it may also increase the chances of financial instability due to systematic risks. Emerging countries are also [...] Read more.

The advancement in fintech technological development in emerging countries has accelerated the role of digital finance in economic development. Digital finance assists in financial inclusion; however, it may also increase the chances of financial instability due to systematic risks. Emerging countries are also in the clutches of shadow economic growth, which reduces taxable income revenue and creates pressure on financial inclusion prospects. The current study attempts to measure the impact of digital finance on the shadow economic growth and financial stability among the selected South Asian emerging countries. We have used the CUP-FM and CUP-BC estimation methods to measure the above relationship on two model frameworks from 2004 to 2018, with the former measuring the influence of digital finance on the shadow economy and the latter examining the relationship between digital finance and financial stability. In addition, the second-generation unit root test, and the Westerlund cointegration analysis are also employed to confirm the stationarity and cointegration among the variables. The result of the Westerlund’s cointegration confirms a long cointegration between the explanatory and outcome variables. Furthermore, the long-run estimation results conclude that an increase in digital finance helps in reducing the growth of the shadow economy among the selected sample countries. However, it also increases the likelihood of systematic risks and increases financial instability. The study also reveals that the control variables like unemployment and industrial productivity also have a significant influence on financial stability and the shadow economy. The findings will assist readers in comprehending how digital finance influences the shadow economy and promotes financial inclusion and stability in emerging nations. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

9 pages, 374 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

by Nikolay A. Kudryashov

Mathematics 2021, 9(23), 3024; https://doi.org/10.3390/math9233024 - 25 Nov 2021

Cited by 49 | Viewed by 2451

Abstract

Application of transformations for dependent and independent variables is used for finding solitary wave solutions of the generalized Schrödinger equations. This new form of equation can be considered as the model for the description of propagation pulse in a nonlinear optics. The method [...] Read more.

Application of transformations for dependent and independent variables is used for finding solitary wave solutions of the generalized Schrödinger equations. This new form of equation can be considered as the model for the description of propagation pulse in a nonlinear optics. The method for finding solutions of equation is given in the general case. Solitary waves of equation are obtained as implicit function taking into account the transformation of variables. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications)

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21 pages, 340 KiB

Open AccessEditor’s ChoiceArticle

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

by Mi Zhou, Naeem Saleem, Xiaolan Liu, Andreea Fulga and Antonio Francisco Roldán López de Hierro

Mathematics 2021, 9(23), 3001; https://doi.org/10.3390/math9233001 - 23 Nov 2021

Cited by 19 | Viewed by 1736

Abstract

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form

ψ (d (T x, T y)) \leq φ (d (x, y))

, Proinov [...] Read more.

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form

ψ (d (T x, T y)) \leq φ (d (x, y))

, Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions. Full article

(This article belongs to the Special Issue General Metric Spaces: Usage and Applications in Statistics and Fixed Point Theory)

9 pages, 255 KiB

Open AccessEditor’s ChoiceArticle

Semi-Hyers–Ulam–Rassias Stability of the Convection Partial Differential Equation via Laplace Transform

by Daniela Marian

Mathematics 2021, 9(22), 2980; https://doi.org/10.3390/math9222980 - 22 Nov 2021

Cited by 12 | Viewed by 1843

Abstract

In this paper, we study the semi-Hyers–Ulam–Rassias stability and the generalized semi-Hyers–Ulam–Rassias stability of some partial differential equations using Laplace transform. One of them is the convection partial differential equation. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)

13 pages, 302 KiB

Open AccessEditor’s ChoiceArticle

Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems

by Helena Myšková and Ján Plavka

Mathematics 2021, 9(22), 2951; https://doi.org/10.3390/math9222951 - 18 Nov 2021

Cited by 1 | Viewed by 1405

Abstract

Max-plus algebra is the similarity of the classical linear algebra with two binary operations, maximum and addition. The notation Ax = Bx, where A, B are given (interval) matrices, represents (interval) two-sided (max, plus)-linear system. For the solvability of Ax = Bx, there [...] Read more.

Max-plus algebra is the similarity of the classical linear algebra with two binary operations, maximum and addition. The notation Ax = Bx, where A, B are given (interval) matrices, represents (interval) two-sided (max, plus)-linear system. For the solvability of Ax = Bx, there are some pseudopolynomial algorithms, but a polynomial algorithm is still waiting for an appearance. The paper deals with the analysis of solvability of two-sided (max, plus)-linear equations with inexact (interval) data. The purpose of the paper is to get efficient necessary and sufficient conditions for solvability of the interval systems using the property of the solution set of the non-interval system Ax = Bx. The main contribution of the paper is a transformation of weak versions of solvability to either subeigenvector problems or to non-interval two-sided (max, plus)-linear systems and obtaining the equivalent polynomially checked conditions for the strong versions of solvability. Full article

(This article belongs to the Special Issue Combinatorics and Computation in Commutative Algebra)

18 pages, 2213 KiB

Open AccessEditor’s ChoiceArticle

A Bayesian-Deep Learning Model for Estimating COVID-19 Evolution in Spain

by Stefano Cabras

Mathematics 2021, 9(22), 2921; https://doi.org/10.3390/math9222921 - 16 Nov 2021

Cited by 13 | Viewed by 2386

Abstract

This work proposes a semi-parametric approach to estimate the evolution of COVID-19 (SARS-CoV-2) in Spain. Considering the sequences of 14-day cumulative incidence of all Spanish regions, it combines modern Deep Learning (DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma model for [...] Read more.

This work proposes a semi-parametric approach to estimate the evolution of COVID-19 (SARS-CoV-2) in Spain. Considering the sequences of 14-day cumulative incidence of all Spanish regions, it combines modern Deep Learning (DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma model for counts. The DL model provides a suitable description of the observed time series of counts, but it cannot give a reliable uncertainty quantification. The role of expert elicitation of the expected number of counts and its reliability is DL predictions’ role in the proposed modelling approach. Finally, the posterior predictive distribution of counts is obtained in a standard Bayesian analysis using the well known Poisson-Gamma model. The model allows to predict the future evolution of the sequences on all regions or estimates the consequences of eventual scenarios. Full article

(This article belongs to the Special Issue Advances in Computational Statistics and Applications)

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23 pages, 3819 KiB

Open AccessEditor’s ChoiceArticle

Granule-Based-Classifier (GbC): A Lattice Computing Scheme Applied on Tree Data Structures

by Vassilis G. Kaburlasos, Chris Lytridis, Eleni Vrochidou, Christos Bazinas, George A. Papakostas, Anna Lekova, Omar Bouattane, Mohamed Youssfi and Takashi Hashimoto

Mathematics 2021, 9(22), 2889; https://doi.org/10.3390/math9222889 - 13 Nov 2021

Cited by 8 | Viewed by 1859

Abstract

Social robots keep proliferating. A critical challenge remains their sensible interaction with humans, especially in real world applications. Hence, computing with real world semantics is instrumental. Recently, the Lattice Computing (LC) paradigm has been proposed with a capacity to compute with semantics represented [...] Read more.

Social robots keep proliferating. A critical challenge remains their sensible interaction with humans, especially in real world applications. Hence, computing with real world semantics is instrumental. Recently, the Lattice Computing (LC) paradigm has been proposed with a capacity to compute with semantics represented by partial order in a mathematical lattice data domain. In the aforementioned context, this work proposes a parametric LC classifier, namely a Granule-based-Classifier (GbC), applicable in a mathematical lattice (T,⊑) of tree data structures, each of which represents a human face. A tree data structure here emerges from 68 facial landmarks (points) computed in a data preprocessing step by the OpenFace software. The proposed (tree) representation retains human anonymity during data processing. Extensive computational experiments regarding three different pattern recognition problems, namely (1) head orientation, (2) facial expressions, and (3) human face recognition, demonstrate GbC capacities, including good classification results, and a common human face representation in different pattern recognition problems, as well as data induced granular rules in (T,⊑) that allow for (a) explainable decision-making, (b) tunable generalization enabled also by formal logic/reasoning techniques, and (c) an inherent capacity for modular data fusion extensions. The potential of the proposed techniques is discussed. Full article

(This article belongs to the Special Issue Lattice Computing: A Mathematical Modelling Paradigm for Cyber–Physical System Applications)

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19 pages, 4830 KiB

Open AccessEditor’s ChoiceArticle

Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms

by Mahmoud Elsisi, Minh-Quang Tran, Hany M. Hasanien, Rania A. Turky, Fahad Albalawi and Sherif S. M. Ghoneim

Mathematics 2021, 9(22), 2885; https://doi.org/10.3390/math9222885 - 12 Nov 2021

Cited by 59 | Viewed by 3698

Abstract

This paper introduces a robust model predictive controller (MPC) to operate an automatic voltage regulator (AVR). The design strategy tends to handle the uncertainty issue of the AVR parameters. Frequency domain conditions are derived from the Hermite–Biehler theorem to maintain the stability of [...] Read more.

This paper introduces a robust model predictive controller (MPC) to operate an automatic voltage regulator (AVR). The design strategy tends to handle the uncertainty issue of the AVR parameters. Frequency domain conditions are derived from the Hermite–Biehler theorem to maintain the stability of the perturbed system. The tuning of the MPC parameters is performed based on a new evolutionary algorithm named arithmetic optimization algorithm (AOA), while the expert designers use trial and error methods to achieve this target. The stability constraints are handled during the tuning process. An effective time-domain objective is formulated to guarantee good performance for the AVR by minimizing the voltage maximum overshoot and the response settling time simultaneously. The results of the suggested AOA-based robust MPC are compared with various techniques in the literature. The system response demonstrates the effectiveness and robustness of the proposed strategy with low control effort against the voltage variations and the parameters’ uncertainty compared with other techniques. Full article

(This article belongs to the Special Issue Systems Modeling, Analysis and Optimization)

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12 pages, 314 KiB

Open AccessEditor’s ChoiceArticle

Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method

by Mart Ratas, Jüri Majak and Andrus Salupere

Mathematics 2021, 9(21), 2809; https://doi.org/10.3390/math9212809 - 05 Nov 2021

Cited by 14 | Viewed by 2170

Abstract

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed [...] Read more.

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed. Full article

(This article belongs to the Special Issue Mathematical Problems in Materials Science)

87 pages, 665 KiB

Open AccessEditor’s ChoiceArticle

General Fractional Vector Calculus

by Vasily E. Tarasov

Mathematics 2021, 9(21), 2816; https://doi.org/10.3390/math9212816 - 05 Nov 2021

Cited by 25 | Viewed by 3537

Abstract

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus [...] Read more.

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of operators. In the generalization of FVC from power-law nonlocality to the general form of nonlocality in space, we use the general fractional calculus (GFC) in the Luchko approach, which was published in 2021. This paper proposed the following: (I) Self-consistent definitions of general fractional differential vector operators: the regional and line general fractional gradients, the regional and surface general fractional curl operators, the general fractional divergence are proposed. (II) Self-consistent definitions of general fractional integral vector operators: the general fractional circulation, general fractional flux and general fractional volume integral are proposed. (III) The general fractional gradient, Green’s, Stokes’ and Gauss’s theorems as fundamental theorems of general fractional vector calculus are proved for simple and complex regions. The fundamental theorems (Gradient, Green, Stokes, Gauss theorems) of the proposed general FVC are proved for a wider class of domains, surfaces and curves. All these three parts allow us to state that we proposed a calculus, which is a general fractional vector calculus (General FVC). The difficulties and problems of defining general fractional integral and differential vector operators are discussed to the nonlocal case, caused by the violation of standard product rule (Leibniz rule), chain rule (rule of differentiation of function composition) and semigroup property. General FVC for orthogonal curvilinear coordinates, which includes general fractional vector operators for the spherical and cylindrical coordinates, is also proposed. Full article

(This article belongs to the Special Issue Fractals, Fractional Calculus and Applied Statistics)

23 pages, 3100 KiB

Open AccessEditor’s ChoiceArticle

Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking

by Mircea-Bogdan Radac and Timotei Lala

Mathematics 2021, 9(21), 2752; https://doi.org/10.3390/math9212752 - 29 Oct 2021

Cited by 13 | Viewed by 2088

Abstract

A general control system tracking learning framework is proposed, by which an optimal learned tracking behavior called ‘primitive’ is extrapolated to new unseen trajectories without requiring relearning. This is considered intelligent behavior and strongly related to the neuro-motor cognitive control of biological (human-like) [...] Read more.

A general control system tracking learning framework is proposed, by which an optimal learned tracking behavior called ‘primitive’ is extrapolated to new unseen trajectories without requiring relearning. This is considered intelligent behavior and strongly related to the neuro-motor cognitive control of biological (human-like) systems that deliver suboptimal executions for tasks outside of their current knowledge base, by using previously memorized experience. However, biological systems do not solve explicit mathematical equations for solving learning and prediction tasks. This stimulates the proposed hierarchical cognitive-like learning framework, based on state-of-the-art model-free control: (1) at the low-level L1, an approximated iterative Value Iteration for linearizing the closed-loop system (CLS) behavior by a linear reference model output tracking is first employed; (2) an experiment-driven Iterative Learning Control (EDILC) applied to the CLS from the reference input to the controlled output learns simple tracking tasks called ‘primitives’ in the secondary L2 level, and (3) the tertiary level L3 extrapolates the primitives’ optimal tracking behavior to new tracking tasks without trial-based relearning. The learning framework relies only on input-output system data to build a virtual state space representation of the underlying controlled system that is assumed to be observable. It has been shown to be effective by experimental validation on a representative, coupled, nonlinear, multivariable real-world system. Able to cope with new unseen scenarios in an optimal fashion, the hierarchical learning framework is an advance toward cognitive control systems. Full article

(This article belongs to the Special Issue Mathematical Methods for Nonlinear Control)

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20 pages, 489 KiB

Open AccessEditor’s ChoiceArticle

Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?

by Erik M. Bollt and Shane D. Ross

Mathematics 2021, 9(21), 2731; https://doi.org/10.3390/math9212731 - 28 Oct 2021

Viewed by 3082

Abstract

This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to [...] Read more.

This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this construction easier, we find that such vector fields do exist, and we explore whether such vector fields have a special structure, thus making a link between the geometric theory and the transfer operator theory. Full article

(This article belongs to the Special Issue Dynamical Systems and Operator Theory)

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41 pages, 82819 KiB

Open AccessEditor’s ChoiceArticle

Evolutionary Game of Multi-Subjects in Live Streaming and Governance Strategies Based on Social Preference Theory during the COVID-19 Pandemic

by Tinggui Chen, Lijuan Peng, Jianjun Yang, Guodong Cong and Guoping Li

Mathematics 2021, 9(21), 2743; https://doi.org/10.3390/math9212743 - 28 Oct 2021

Cited by 40 | Viewed by 5206

Abstract

After the outbreak of the COVID-19, offline consumption has been significantly impacted. For the sake of safety, online consumption has become the most common manner, and this has generated e-commerce, which not only breaks the spatio-temporal or regional restrictions, but also conforms to [...] Read more.

After the outbreak of the COVID-19, offline consumption has been significantly impacted. For the sake of safety, online consumption has become the most common manner, and this has generated e-commerce, which not only breaks the spatio-temporal or regional restrictions, but also conforms to the normal economic development needs for epidemic prevention and control. However, this new business model causes problems such as the shortage of post-sales service, false publicity, and uneven quality of live streaming anchors, seriously affecting the interests of consumers. Therefore, it is urgent to strengthen the management of the chaos of live streaming. This study focuses on exploring the problems and the behavioral strategies of stakeholders in the governance process. The paper obtained online user comments by python, and used topic clustering and subject extraction methods to dig out the problems and related multiple subjects in live streaming at first. Secondly, the theory of social preference was introduced to construct an evolutionary game model among multiple subjects, and how to guide the behavioral decision-making of multiple subjects to standardize and rationalize was studied, so as to control the problem of live streaming. Finally, simulation experiments were conducted and the results demonstrated that: (1) Compared with strengthening the reciprocal preference of the government, live streaming platforms, and consumers, changing the individual’s altruistic preference is more effective in controlling the chaos of live streaming; (2) weakening the platform’s altruistic preference for anchors is conducive to creating a good live streaming environment; and (3) changing consumers’ altruistic preference or reciprocal preference is less effective in promoting the governance of the live streaming environment. Full article

(This article belongs to the Special Issue Evolutionary Games, Propagation Processes and Control in Complex Systems)

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10 pages, 1140 KiB

Open AccessEditor’s ChoiceArticle

The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation by Using (

\frac{G^{'}}{G}

)-Expansion Method

by Wael W. Mohammed, Meshari Alesemi, Sahar Albosaily, Naveed Iqbal and M. El-Morshedy

Mathematics 2021, 9(21), 2712; https://doi.org/10.3390/math9212712 - 26 Oct 2021

Cited by 31 | Viewed by 1874

Abstract

In this paper, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation forced by multiplicative noise. To obtain the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation, we apply the

\frac{G^{'}}{G}

-expansion method. Furthermore, we generalize some previous results that did not use [...] Read more.

In this paper, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation forced by multiplicative noise. To obtain the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation, we apply the

\frac{G^{'}}{G}

-expansion method. Furthermore, we generalize some previous results that did not use this equation with multiplicative noise and fractional space. Additionally, we show the influence of the stochastic term on the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications)

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16 pages, 3698 KiB

Open AccessEditor’s ChoiceArticle

A Significant Solar Energy Note on Powell-Eyring Nanofluid with Thermal Jump Conditions: Implementing Cattaneo-Christov Heat Flux Model

by Nidal H. Abu-Hamdeh, Radi A. Alsulami, Muhyaddin J. H. Rawa, Mashhour A. Alazwari, Marjan Goodarzi and Mohammad Reza Safaei

Mathematics 2021, 9(21), 2669; https://doi.org/10.3390/math9212669 - 21 Oct 2021

Cited by 52 | Viewed by 1981

Abstract

PTSCs (parabolic trough solar collectors) are widely employed in solar-thermal applications to attain high temperatures. The purpose of this study is to determine how much entropy is created when Powell-Eyring nanofluid (P-ENF) flows across porous media on a horizontal plane under thermal jump [...] Read more.

PTSCs (parabolic trough solar collectors) are widely employed in solar-thermal applications to attain high temperatures. The purpose of this study is to determine how much entropy is created when Powell-Eyring nanofluid (P-ENF) flows across porous media on a horizontal plane under thermal jump circumstances. The flow in PTSC was generated by nonlinear surface stretching, thermal radiation, and Cattaneo-Christov heat flux, which was utilized to compute heat flux in the thermal boundary layer. Using a similarity transformation approach, partial differential equations were converted into ordinary differential equations with boundary constraints. Then, the boundary restrictions and partial differential equations were merged to form a single set of nonlinear ordinary differential equations. To obtain approximate solutions to ordinary differential equations, the Keller-Box approach is utilized. Nanofluids derived from silver- and copper-based engine oil (EO) has been employed as working fluids. The researchers observed that changing the permeability parameter reduced the Nusselt number while increasing the skin frictional coefficient. Total entropy variation was also calculated using the Brinkman number for flow rates with Reynolds number and viscosity changes. The key result is that thermal efficiency is inversely proportional to particular entropy production. For example, using Cu-EO nanofluid instead of Ag-EO nanofluid increased the heat transport rate efficiency to 15–36%. Full article

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17 pages, 10764 KiB

Open AccessEditor’s ChoiceArticle

Exploring an Efficient POI Recommendation Model Based on User Characteristics and Spatial-Temporal Factors

by Chonghuan Xu, Dongsheng Liu and Xinyao Mei

Mathematics 2021, 9(21), 2673; https://doi.org/10.3390/math9212673 - 21 Oct 2021

Cited by 31 | Viewed by 2488

Abstract

The advent of mobile scenario-based consumption popularizes and gradually maturates the application of point of interest (POI) recommendation services based on geographical location. However, the insufficient fusion of heterogeneous data in the current POI recommendation services leads to poor recommendation quality. In this [...] Read more.

The advent of mobile scenario-based consumption popularizes and gradually maturates the application of point of interest (POI) recommendation services based on geographical location. However, the insufficient fusion of heterogeneous data in the current POI recommendation services leads to poor recommendation quality. In this paper, we propose a novel hybrid POI recommendation model (NHRM) based on user characteristics and spatial-temporal factors to enhance the recommendation effect. The proposed model contains three sub-models. The first model considers user preferences, forgetting characteristics, user influence, and trajectories. The second model studies the impact of the correlation between the locations of POIs and calculates the check-in probability of POI with the two-dimensional kernel density estimation method. The third model analyzes the influence of category of POI. Consequently, the above results were combined and top-K POIs were recommended to target users. The experimental results on Yelp and Meituan data sets showed that the recommendation performance of our method is superior to some other methods, and the problems of cold-start and data sparsity are alleviated to a certain extent. Full article

(This article belongs to the Section Mathematics and Computer Science)

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32 pages, 3548 KiB

Open AccessEditor’s ChoiceReview

Nature-Inspired Metaheuristic Techniques for Combinatorial Optimization Problems: Overview and Recent Advances

by Md Ashikur Rahman, Rajalingam Sokkalingam, Mahmod Othman, Kallol Biswas, Lazim Abdullah and Evizal Abdul Kadir

Mathematics 2021, 9(20), 2633; https://doi.org/10.3390/math9202633 - 19 Oct 2021

Cited by 23 | Viewed by 4907

Abstract

Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have [...] Read more.

Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have been evolved and modified with respect to the problem nature since it was recommended for the first time. As there is a growing interest in incorporating necessary methods to develop metaheuristics, there is a need to rediscover the recent advancement of metaheuristics in combinatorial optimization. From the authors’ point of view, there is still a lack of comprehensive surveys on current research directions. Therefore, a substantial part of this paper is devoted to analyzing and discussing the modern age metaheuristic algorithms that gained popular use in mostly cited combinatorial optimization problems such as vehicle routing problems, traveling salesman problems, and supply chain network design problems. A survey of seven different metaheuristic algorithms (which are proposed after 2000) for combinatorial optimization problems is carried out in this study, apart from conventional metaheuristics like simulated annealing, particle swarm optimization, and tabu search. These metaheuristics have been filtered through some key factors like easy parameter handling, the scope of hybridization as well as performance efficiency. In this study, a concise description of the framework of the selected algorithm is included. Finally, a technical analysis of the recent trends of implementation is discussed, along with the impacts of algorithm modification on performance, constraint handling strategy, the handling of multi-objective situations using hybridization, and future research opportunities. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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26 pages, 1950 KiB

Open AccessEditor’s ChoiceArticle

A Hybrid Spherical Fuzzy MCDM Approach to Prioritize Governmental Intervention Strategies against the COVID-19 Pandemic: A Case Study from Vietnam

by Phi-Hung Nguyen, Jung-Fa Tsai, Thanh-Tuan Dang, Ming-Hua Lin, Hong-Anh Pham and Kim-Anh Nguyen

Mathematics 2021, 9(20), 2626; https://doi.org/10.3390/math9202626 - 18 Oct 2021

Cited by 37 | Viewed by 3526

Abstract

The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, [...] Read more.

The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, few studies in the literature can assist governments in this topic. Selective governmental intervention during the COVID-19 outbreak is considered a Multi-Criteria Decision-Making (MCDM) problem under a vague and uncertain environment when governments and medical communities adjust their priorities in response to rising issues and the efficacy of interventions applied in various nations. In this study, a novel hybrid Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Fuzzy Weighted Aggregated Sum Product Assessment (WASPAS-F) model is proposed to help stakeholders such as governors and policymakers to prioritize governmental interventions for dealing with the COVID-19 outbreak. The SF-AHP is implemented to measure the significance of the criteria, while the WASPAS-F approach is deployed to rank intervention alternatives. An empirical case study is conducted in Vietnam. From the SF-AHP findings, the criteria of “effectiveness in preventing the spread of COVID-19”, “ease of implementation”, and “high acceptability to citizens” were recognized as the most important criteria. As for the ranking of strategies, “vaccinations”, “enhanced control of the country’s health resources”, “common health testing”, “formation of an emergency response team”, and “quarantining patients and those suspected of infection” are the top five strategies. Aside from that, the robustness of the approach was tested by performing a comparative analysis. The results illustrate that the applied methods reach the general best strategy rankings. The applied methodology and its analysis will provide insight to authorities for fighting against the severe pandemic in the long run. It may aid in solving many complicated challenges in government strategy selection and assessment. It is also a flexible design model for considering the evaluation criteria. Finally, this research provides valuable guidance for policymakers in other nations. Full article

(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)

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22 pages, 4496 KiB

Open AccessEditor’s ChoiceArticle

Entropy Optimization of First-Grade Viscoelastic Nanofluid Flow over a Stretching Sheet by Using Classical Keller-Box Scheme

by Mashhour A. Alazwari, Nidal H. Abu-Hamdeh and Marjan Goodarzi

Mathematics 2021, 9(20), 2563; https://doi.org/10.3390/math9202563 - 13 Oct 2021

Cited by 57 | Viewed by 2266

Abstract

Nanofluids have better surface stability, thermal absorption, and distribution capacities are produced as heat transfer fluids. In current nanofluid-transport studies, together with the heat transfer mechanisms, entropy reduction in thermo- and non-Newtonian nanofluid models with changing thermophysical characteristics is heavily addressed. The entropy [...] Read more.

Nanofluids have better surface stability, thermal absorption, and distribution capacities are produced as heat transfer fluids. In current nanofluid-transport studies, together with the heat transfer mechanisms, entropy reduction in thermo- and non-Newtonian nanofluid models with changing thermophysical characteristics is heavily addressed. The entropy production is examined as thermodynamically stable first-grade viscoelastic nanofluid (FGVNF) flow over a flat penetrable, porous barrier. The uniform porous horizontal stretching of the surface in a Darcy type of pore media results in a fluid motion disturbance. In addition, this study also includes the effects of thermal radiation, viscous dissipation, and slip conditions at the border. Under boundary layer flow and Rosseland approximations, the governing mathematical equations defining the physical features of the FGVNF flow and heat transfer models are summarized. The governing nonlinear partial differential equation is transformed by similarity variables to achieve solutions in nonlinear ordinary differential equations. Approximative solutions for reduced ordinary differential equations are obtained by the Keller Box Scheme. Two distinct types of nanofluids, Copper-Engine Oil (Cu-EO) and Zirconium Dioxide-Engine Oil (ZrO₂-EO), are considered in this research. The graphs are produced to examine the effects of the different physical factors for the speed, temperature, and entropy distributions. The significant findings of this study are that the critical characteristics of (boundary layer) BL collectively promote temperature variation, including slip speed, diverse thermal conductivity, and non-Newtonian first-grade viscoelastic nanofluid, the concentration of nanoparticles as well as thermal radiation, and a high porous media. The other noteworthy observation of this study demonstrates that the (Cu-EO) FGVNF is a better conductor than (ZrO₂-EO) FGVNF transmission. The entropy of the system grows the Deborah number and volume fraction parameter. Full article

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17 pages, 1597 KiB

Open AccessEditor’s ChoiceArticle

Active Suspension Control Using an MPC-LQR-LPV Controller with Attraction Sets and Quadratic Stability Conditions

by Daniel Rodriguez-Guevara, Antonio Favela-Contreras, Francisco Beltran-Carbajal, David Sotelo and Carlos Sotelo

Mathematics 2021, 9(20), 2533; https://doi.org/10.3390/math9202533 - 09 Oct 2021

Cited by 18 | Viewed by 3063

Abstract

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In [...] Read more.

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a model predictive control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, quadratic stability conditions are imposed in terms of Linear Matrix Inequalities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm. Full article

(This article belongs to the Special Issue Advances and Trends in Mathematical Modelling, Control and Identification of Vibrating Systems)

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14 pages, 4714 KiB

Open AccessEditor’s ChoiceArticle

Spatio-Temporal Spread Pattern of COVID-19 in Italy

by Nicoletta D’Angelo, Antonino Abbruzzo and Giada Adelfio

Mathematics 2021, 9(19), 2454; https://doi.org/10.3390/math9192454 - 02 Oct 2021

Cited by 7 | Viewed by 2248

Abstract

This paper investigates the spatio-temporal spread pattern of COVID-19 in Italy, during the first wave of infections, from February to October 2020. Disease mappings of the virus infections by using the Besag–York–Mollié model and some spatio-temporal extensions are provided. This modeling framework, which [...] Read more.

This paper investigates the spatio-temporal spread pattern of COVID-19 in Italy, during the first wave of infections, from February to October 2020. Disease mappings of the virus infections by using the Besag–York–Mollié model and some spatio-temporal extensions are provided. This modeling framework, which includes a temporal component, allows the studying of the time evolution of the spread pattern among the 107 Italian provinces. The focus is on the effect of citizens’ mobility patterns, represented here by the three distinct phases of the Italian virus first wave, identified by the Italian government, also characterized by the lockdown period. Results show the effectiveness of the lockdown action and an inhomogeneous spatial trend that characterizes the virus spread during the first wave. Furthermore, the results suggest that the temporal evolution of each province’s cases is independent of the temporal evolution of the other ones, meaning that the contagions and temporal trend may be caused by some province-specific aspects rather than by the subjects’ spatial movements. Full article

(This article belongs to the Section Probability and Statistics)

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18 pages, 4512 KiB

Open AccessEditor’s ChoiceArticle

AB-Net: A Novel Deep Learning Assisted Framework for Renewable Energy Generation Forecasting

by Noman Khan, Fath U Min Ullah, Ijaz Ul Haq, Samee Ullah Khan, Mi Young Lee and Sung Wook Baik

Mathematics 2021, 9(19), 2456; https://doi.org/10.3390/math9192456 - 02 Oct 2021

Cited by 35 | Viewed by 4084

Abstract

Renewable energy (RE) power plants are deployed globally because the renewable energy sources (RESs) are sustainable, clean, and environmentally friendly. However, the demand for power increases on a daily basis due to population growth, technology, marketing, and the number of installed industries. This [...] Read more.

Renewable energy (RE) power plants are deployed globally because the renewable energy sources (RESs) are sustainable, clean, and environmentally friendly. However, the demand for power increases on a daily basis due to population growth, technology, marketing, and the number of installed industries. This challenge has raised a critical issue of how to intelligently match the power generation with the consumption for efficient energy management. To handle this issue, we propose a novel architecture called ‘AB-Net’: a one-step forecast of RE generation for short-term horizons by incorporating an autoencoder (AE) with bidirectional long short-term memory (BiLSTM). Firstly, the data acquisition step is applied, where the data are acquired from various RESs such as wind and solar. The second step performs deep preprocessing of the acquired data via several de-noising and cleansing filters to clean the data and normalize them prior to actual processing. Thirdly, an AE is employed to extract the discriminative features from the cleaned data sequence through its encoder part. BiLSTM is used to learn these features to provide a final forecast of power generation. The proposed AB-Net was evaluated using two publicly available benchmark datasets where the proposed method obtains state-of-the-art results in terms of the error metrics. Full article

(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)

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24 pages, 87297 KiB

Open AccessEditor’s ChoiceArticle

A Comprehensive Analysis of Demand Response Pricing Strategies in a Smart Grid Environment Using Particle Swarm Optimization and the Strawberry Optimization Algorithm

by Emad M. Ahmed, Rajarajeswari Rathinam, Suchitra Dayalan, George S. Fernandez, Ziad M. Ali, Shady H. E. Abdel Aleem and Ahmed I. Omar

Mathematics 2021, 9(18), 2338; https://doi.org/10.3390/math9182338 - 21 Sep 2021

Cited by 29 | Viewed by 3128

Abstract

In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to [...] Read more.

In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to the shortfall in power generation. The abovesaid deficit signifies the explicit need for a strategy that reduces the peak demand by rescheduling the load pattern, as well as reduces the stress on grids. Demand-side management (DSM) uses several algorithms for proper reallocation of loads, collectively known as demand response (DR). DR strategies effectively culminate in monetary benefits for customers and the utilities using dynamic pricing (DP) and incentive-based procedures. This study attempts to analyze the DP schemes of DR such as time-of-use (TOU) and real-time pricing (RTP) for different load scenarios in a smart grid (SG). Centralized and distributed algorithms are used to analyze the price-based DR problem using RTP. A techno-economic analysis was performed by using particle swarm optimization (PSO) and the strawberry (SBY) optimization algorithms used in handling the DP strategies with 109, 1992, and 7807 controllable industrial, commercial, and residential loads. A better optimization algorithm to go along with the pricing scheme to reduce the peak-to-average ratio (PAR) was identified. The results demonstrate that centralized RTP using the SBY optimization algorithm helped to achieve 14.80%, 21.7%, and 21.84% in cost reduction and outperformed the PSO. Full article

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18 pages, 807 KiB

Open AccessEditor’s ChoiceArticle

An Integrated Mathematical Attitude Utilizing Fully Fuzzy BWM and Fuzzy WASPAS for Risk Evaluation in a SOFC

by Zeyu Lin, Hamdi Ayed, Belgacem Bouallegue, Hana Tomaskova, Saeid Jafarzadeh Ghoushchi and Gholamreza Haseli

Mathematics 2021, 9(18), 2328; https://doi.org/10.3390/math9182328 - 19 Sep 2021

Cited by 18 | Viewed by 2158

Abstract

Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, [...] Read more.

Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, failure modes evaluations need an experts team to achieve uncertainties belongs to the risk assessment procedure. To improve the efficiency of the routine FMEA methodology and to represent a suitable hybrid fuzzy MCDM approach for FMEA, in this work, fully fuzzy best-worst method (FF-BWM) is employed to achieve the risk factors weights then fuzzy weighted aggregated sum product assessment (F-WASPAS) approach to detect the failure modes priorities is utilized. Ultimately, the sensitivity analyses demonstrate that the offered framework is verified and can make applicable data in risk management decision-making evaluation. Full article

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25 pages, 2162 KiB

Open AccessEditor’s ChoiceArticle

An Innovative Hybrid Heap-Based and Jellyfish Search Algorithm for Combined Heat and Power Economic Dispatch in Electrical Grids

by Ahmed Ginidi, Abdallah Elsayed, Abdullah Shaheen, Ehab Elattar and Ragab El-Sehiemy

Mathematics 2021, 9(17), 2053; https://doi.org/10.3390/math9172053 - 26 Aug 2021

Cited by 39 | Viewed by 2354

Abstract

This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two [...] Read more.

This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two recent algorithms: heap-based algorithm (HBA) and jellyfish search algorithm (JSA). The proposed hybrid HBJSA seeks to make use of the explorative features of HBA and the exploitative features of the JSA to overcome some of the problems found in their standard forms. The proposed hybrid HBJSA, HBA, and JSA are validated and statistically compared by attempting to solve a real-world optimization issue of the CHP economic dispatch. It aims to satisfy the power and heat demands and minimize the whole fuel cost (WFC) of the power and heat generation units. Additionally, a series of operational and electrical constraints such as non-convex feasible operating regions of CHP and valve-point effects of power-only plants, respectively, are considered in solving such a problem. The proposed hybrid HBJSA, HBA, and JSA are employed on two medium systems, which are 24-unit and 48-unit systems, and two large systems, which are 84- and 96-unit systems. The experimental results demonstrate that the proposed hybrid HBJSA outperforms the standard HBA and JSA and other reported techniques when handling the CHP economic dispatch. Otherwise, comparative analyses are carried out to demonstrate the suggested HBJSA’s strong stability and robustness in determining the lowest minimum, average, and maximum WFC values compared to the HBA and JSA. Full article

(This article belongs to the Topic Multi-Energy Systems)

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19 pages, 4114 KiB

Open AccessEditor’s ChoiceArticle

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

by Igor Sazonov, Dmitry Grebennikov, Andreas Meyerhans and Gennady Bocharov

Mathematics 2021, 9(17), 2025; https://doi.org/10.3390/math9172025 - 24 Aug 2021

Cited by 12 | Viewed by 2868

Abstract

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4

^{+}

T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in [...] Read more.

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4

^{+}

T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4

^{+}

T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

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12 pages, 285 KiB

Open AccessEditor’s ChoiceArticle

New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations

by Alina Alb Lupaş and Georgia Irina Oros

Mathematics 2021, 9(16), 2000; https://doi.org/10.3390/math9162000 - 21 Aug 2021

Cited by 23 | Viewed by 1988

Abstract

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator

L_{α}^{m}

, given by [...] Read more.

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator

L_{α}^{m}

, given by

L_{α}^{m} : A_{n} \to A_{n}

,

L_{α}^{m} f (z) = (1 - α) R^{m} f (z) + α S^{m} f (z),

where

A_{n} = {f \in H (U), f (z) = z + a_{n + 1} z^{n + 1} + \dots, z \in U}

is the subclass of normalized holomorphic functions and the operators

R^{m} f (z)

and

S^{m} f (z)

are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator

L_{α}^{m}

, a certain fuzzy class of analytic functions denoted by

S L_{F}^{m} (δ, α)

is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries. Full article

(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))

17 pages, 3697 KiB

Open AccessEditor’s ChoiceArticle

Fast Terminal Sliding Control of Underactuated Robotic Systems Based on Disturbance Observer with Experimental Validation

by Thaned Rojsiraphisal, Saleh Mobayen, Jihad H. Asad, Mai The Vu, Arthur Chang and Jirapong Puangmalai

Mathematics 2021, 9(16), 1935; https://doi.org/10.3390/math9161935 - 13 Aug 2021

Cited by 42 | Viewed by 3706

Abstract

In this study, a novel fast terminal sliding mode control technique based on the disturbance observer is recommended for the stabilization of underactuated robotic systems. The finite time disturbance observer is employed to estimate the exterior disturbances of the system and develop the [...] Read more.

In this study, a novel fast terminal sliding mode control technique based on the disturbance observer is recommended for the stabilization of underactuated robotic systems. The finite time disturbance observer is employed to estimate the exterior disturbances of the system and develop the finite time control law. The proposed controller can regulate the state trajectories of the underactuated systems to the origin within a finite time in the existence of external disturbances. The stability analysis of the proposed control scheme is verified via the Lyapunov stabilization theory. The designed control law is enough to drive a switching surface achieving the fast terminal sliding mode against severe model nonlinearities with large parametric uncertainties and external disturbances. Illustrative simulation results and experimental validations on a cart-inverted pendulum system are provided to display the success and efficacy of the offered method. Full article

(This article belongs to the Section Engineering Mathematics)

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29 pages, 1282 KiB

Open AccessEditor’s ChoiceArticle

Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making

by Zeeshan Ali, Tahir Mahmood, Muhammad Aslam and Ronnason Chinram

Mathematics 2021, 9(16), 1922; https://doi.org/10.3390/math9161922 - 12 Aug 2021

Cited by 40 | Viewed by 1970

Abstract

In a conventional interpretation of decision-making based on ambiguity, a decision-maker must prefer the best possible opportunity including various feasible possibilities. However, the dilemma of picking the best possible alternative has continued to be a substantial task to resolve. In this manuscript, we [...] Read more.

In a conventional interpretation of decision-making based on ambiguity, a decision-maker must prefer the best possible opportunity including various feasible possibilities. However, the dilemma of picking the best possible alternative has continued to be a substantial task to resolve. In this manuscript, we improve the existing complex intuitionistic fuzzy soft set (CIFSS), which includes the grade of truth and falsity with the rule that the sum of the real and imaginary parts of both grades is confined to [0, 1]. CIFS is a valuable procedure to determine the authenticity and consistency of the elaborated approaches. The fundamental laws and their related examples are also determined. Moreover, by using these laws, we investigated the complex intuitionistic fuzzy soft prioritized weighted averaging operator (CIFSPWAO), the complex intuitionistic fuzzy soft prioritized ordered weighted averaging operator (CIFSPOWAO), the complex intuitionistic fuzzy soft prioritized weighted geometric operator (CIFSPWGO), complex intuitionistic fuzzy soft prioritized ordered weighted geometric operator (CIFSPOWGO), and their related properties are also developed. Based on the developed operators, the multiattribute decision-making (MADM) tool is developed by using the explored operators based on CIFSS. Some numerical examples are also illustrated by using the investigated operators to determine the feasibility and consistency of the developed approaches. Finally, the comparative analysis and their geometrical manifestations are also determined to enhance the excellence of the performed explorations. Full article

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22 pages, 2552 KiB

Open AccessEditor’s ChoiceArticle

A Two Phase Integrated Fuzzy Decision-Making Framework for Green Supplier Selection in the Coffee Bean Supply Chain

by Ngoc Bao Tu Nguyen, Gu-Hong Lin and Thanh-Tuan Dang

Mathematics 2021, 9(16), 1923; https://doi.org/10.3390/math9161923 - 12 Aug 2021

Cited by 22 | Viewed by 3203

Abstract

In Vietnam, as more and more organizations are moving toward globalization, green supplier selection (GSS) has emerged as a strategic approach in supply chain management that requires supplier practices in lessening the environmental risks to society. Based on both conventional and environmental criteria, [...] Read more.

In Vietnam, as more and more organizations are moving toward globalization, green supplier selection (GSS) has emerged as a strategic approach in supply chain management that requires supplier practices in lessening the environmental risks to society. Based on both conventional and environmental criteria, this paper aims to evaluate a set of suppliers by establishing a multi-criteria decision-making (MCDM)-based framework using an integrated fuzzy analytical hierarchy process (FAHP) with the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Initially, five GSS criteria of the environmental aspect (wastewater treatment, solid waste generation, energy consumption, air pollution, corporate social responsibility) and conventional criteria (quality, cost, delivery, and technology) are identified from the literature and consulting field experts to employ the MCDM approach. The trustworthiness of the proposed integrated framework is presented by discussing a case study in the coffee bean supply chain in Vietnam. The FAHP is used to generate criteria weights in which fuzzy set theory is applied to translate the linguistic evaluation statements of experts, and VIKOR is used to rank the alternatives against the selected criteria. From FAHP findings, the most important criteria are quantity discount, solid waste generation, order fulfillment rate, logistics cost, and purchasing cost. A consistency test is performed to ensure the uniformity of the expert’s input. The best suppliers are determined through the final ranking of the VIKOR model for the case study. The work presented provides insight to decision-makers of supplier selection that helps determine significant GSS criteria and aids in the minimization of environmental risks to society arising from the supply chain on corporate sustainability standards. Full article

(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)

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13 pages, 1608 KiB

Open AccessEditor’s ChoiceArticle

Fractional Growth Model Applied to COVID-19 Data

by Fernando Alcántara-López, Carlos Fuentes, Carlos Chávez, Fernando Brambila-Paz and Antonio Quevedo

Mathematics 2021, 9(16), 1915; https://doi.org/10.3390/math9161915 - 11 Aug 2021

Cited by 4 | Viewed by 2419

Abstract

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed [...] Read more.

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order

0 < β \leq 1

, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination

R^{2} > 0.999

. Full article

(This article belongs to the Special Issue Theory and Applications of Fractional Equations and Calculus)

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15 pages, 9978 KiB

Open AccessEditor’s ChoiceArticle

A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

by Hari M. Srivastava, Khursheed J. Ansari, Faruk Özger and Zeynep Ödemiş Özger

Mathematics 2021, 9(16), 1895; https://doi.org/10.3390/math9161895 - 09 Aug 2021

Cited by 34 | Viewed by 2698

Abstract

In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and [...] Read more.

In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study. Full article

(This article belongs to the Special Issue Higher Transcendental Functions and Their Multi-Disciplinary Applications)

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16 pages, 1237 KiB

Open AccessEditor’s ChoiceArticle

Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach

by Mohammad Izadi, Şuayip Yüzbaşi and Samad Noeiaghdam

Mathematics 2021, 9(16), 1841; https://doi.org/10.3390/math9161841 - 04 Aug 2021

Cited by 18 | Viewed by 1890

Abstract

Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation [...] Read more.

Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation points, the governing equation transforms into a non-linear algebraic matrix equation. In the second approach, the technique of quasi-linearization is first employed to linearize the model problem and, then, the first collocation method is applied to the sequence of linearized equations iteratively. In the latter approach, we require to solve a linear algebraic matrix equation in each iteration. Moreover, the error analysis of the Bessel series solution is established. In the end, numerical simulations and computational results are provided to illustrate the utility and applicability of the presented collocation approaches. Numerical comparisons with some existing available methods are performed to validate our results. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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12 pages, 1030 KiB

Open AccessEditor’s ChoiceArticle

Fixed-Time Third-Order Super-Twisting-like Sliding Mode Motion Control for Piezoelectric Nanopositioning Stage

by Guangwei Wang, Bo Wang and Chengxi Zhang

Mathematics 2021, 9(15), 1770; https://doi.org/10.3390/math9151770 - 27 Jul 2021

Cited by 7 | Viewed by 2283

Abstract

This paper presents a novel third-order super-twisting-like integral sliding mode controller (3-ISMC) for trajectory tracking of nanopositioning applications. Different from traditional sliding mode control methods presenting with chattering problems, the proposed approach provides continuous control inputs, which brings much convenience for practical applications. [...] Read more.

This paper presents a novel third-order super-twisting-like integral sliding mode controller (3-ISMC) for trajectory tracking of nanopositioning applications. Different from traditional sliding mode control methods presenting with chattering problems, the proposed approach provides continuous control inputs, which brings much convenience for practical applications. Moreover, the fixed-time convergence of the proposed 3-ISMC is guaranteed independently of initial conditions. The estimation of the fixed convergence time and stability are derived based on the Lyapunov method. Simulation results demonstrate that the proposed controller exhibits chattering free and quick transient response performance for a piezoelectric nanopositioning system under model uncertainties and external disturbances. Full article

(This article belongs to the Section Engineering Mathematics)

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13 pages, 803 KiB

Open AccessEditor’s ChoiceArticle

Connectedness and Local Connectedness on Infra Soft Topological Spaces

by Tareq M. Al-shami and El-Sayed A. Abo-Tabl

Mathematics 2021, 9(15), 1759; https://doi.org/10.3390/math9151759 - 26 Jul 2021

Cited by 19 | Viewed by 1899

Abstract

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We [...] Read more.

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components. Full article

(This article belongs to the Special Issue Fuzzy Topology)

18 pages, 2400 KiB

Open AccessEditor’s ChoiceArticle

Revisiting the Valuable Roles of Global Financial Assets for International Stock Markets: Quantile Coherence and Causality-in-Quantiles Approaches

by Zhenghui Li, Zhiming Ao and Bin Mo

Mathematics 2021, 9(15), 1750; https://doi.org/10.3390/math9151750 - 24 Jul 2021

Cited by 36 | Viewed by 2780

Abstract

We employ the quantile-coherency approach and causality-in-quantile method to revisit the roles of Bitcoin, U.S. dollar, crude oil and gold for USA, Chinese, UK, and Japanese stock markets. The main results show that the impact of global financial assets varies across different investment [...] Read more.

We employ the quantile-coherency approach and causality-in-quantile method to revisit the roles of Bitcoin, U.S. dollar, crude oil and gold for USA, Chinese, UK, and Japanese stock markets. The main results show that the impact of global financial assets varies across different investment horizons and quantiles. We find that in most cases, the correlation between global financial assets and stock indexes is not significant or is weakly positive. From the perspective of investment horizons (frequency domain), the correlation in the short term is mostly manifested in Bitcoin, while in the medium and long term it is shifted to dollar assets. At the same time, the relationships are significantly higher in the medium and long term than in the short term. From the point of view of quantiles, it shows a weak positive correlation at the lower quantile. However, the correlation between the two is not significant at the median quantile. At the high quantiles, there is a weak negative linkage. According to the causality-in-quantiles approach results, in most cases global financial assets have different degrees of predictive capacity for the selected stock markets. Especially around the median quantile, the predictive ability was strongest. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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13 pages, 308 KiB

Open AccessEditor’s ChoiceArticle

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

by Brecht Verbeken and Marie-Anne Guerry

Mathematics 2021, 9(14), 1681; https://doi.org/10.3390/math9141681 - 16 Jul 2021

Cited by 5 | Viewed by 2533

Abstract

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of [...] Read more.

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria. Full article

(This article belongs to the Special Issue Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields)

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31 pages, 6058 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Partial Diffusion Markov Model of Heterogeneous TCP Link: Optimization with Incomplete Information

by Andrey Borisov, Alexey Bosov, Gregory Miller and Igor Sokolov

Mathematics 2021, 9(14), 1632; https://doi.org/10.3390/math9141632 - 10 Jul 2021

Cited by 5 | Viewed by 2301

Abstract

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via [...] Read more.

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via an unobservable controllable MJP (Markov jump process) with finite-state space. Observations are formed by low-frequency counting processes of packet losses and timeouts and a high-frequency compound Poisson process of packet acknowledgments. The information transmission through the TCP-equipped channel is considered a stochastic control problem with incomplete information. The main idea to solve it is to impose the separation principle on the problem. The paper proposes a mathematical framework and algorithmic support to implement the solution. It includes a solution to the stochastic control problem with complete information, a diffusion approximation of the high-frequency observations, a solution to the MJP state filtering problem given the observations with multiplicative noises, and a numerical scheme of the filtering algorithm. The paper also contains the results of a comparative study of the proposed state-based congestion control algorithm with the contemporary TCP versions: Illinois, CUBIC, Compound, and BBR (Bottleneck Bandwidth and RTT). Full article

(This article belongs to the Special Issue Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields)

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21 pages, 21971 KiB

Open AccessEditor’s ChoiceArticle

A Study on the Impact of Linguistic Persuasive Styles on the Sales Volume of Live Streaming Products in Social E-Commerce Environment

by Hanyang Luo, Sijia Cheng, Wanhua Zhou, Sumin Yu and Xudong Lin

Mathematics 2021, 9(13), 1576; https://doi.org/10.3390/math9131576 - 04 Jul 2021

Cited by 46 | Viewed by 12666

Abstract

Live-stream shopping is developing rapidly, but the sales levels of live streaming products vary by different hosts. How to increase the sales volume of live streaming products has become a problem. Consumers’ purchase behavior in live streaming is determined by some subjective factors, [...] Read more.

Live-stream shopping is developing rapidly, but the sales levels of live streaming products vary by different hosts. How to increase the sales volume of live streaming products has become a problem. Consumers’ purchase behavior in live streaming is determined by some subjective factors, and the persuasiveness of linguistic style affects this subjective judgment to a certain extent. Therefore, the persuasiveness of the hosts’ linguistic style will lead to changes in consumers’ purchase intentions, which will affect the sales volume of products sold in the live streaming. Based on Hovland’s persuasion model, Aristotle’s rhetoric skills, text analysis, Latent Dirichlet Allocation (LDA) topic extraction model and grounded theory, this study divides the host’s linguistic persuasive style in the social e-commerce environment into five types: appealing to personality, appealing to logic, appealing to emotion, appealing to reward, and appealing to exaggeration. Combined with the sales volume of the product, we establish a regression model, and obtain the influence results of the host’s various linguistic persuasive styles on the sales of live streaming products. The results show that: the linguistic persuasive style of appealing to personality has the greatest positive impact on the sales volume of live broadcast products, but the linguistic style of appealing to logic has a negative impact. Interestingly, the same linguistic style has different effects for different types of products: the linguistic style of appealing to exaggeration has a negative effect on the sales volume of apparel products, but it has a positive influence on the sales volume of digital electrical products. Therefore, different linguistic styles should be used for different product types. Full article

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14 pages, 454 KiB

Open AccessEditor’s ChoiceArticle

A Review of Matrix SIR Arino Epidemic Models

by Florin Avram, Rim Adenane and David I. Ketcheson

Mathematics 2021, 9(13), 1513; https://doi.org/10.3390/math9131513 - 28 Jun 2021

Cited by 8 | Viewed by 3598

Abstract

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “

(x, y, z)

” groups, which we will call [...] Read more.

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “

(x, y, z)

” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number

R

has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for

(x, y, z)

models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity

Y (t)

which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)

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26 pages, 385 KiB

Open AccessEditor’s ChoiceReview

General Fractional Dynamics

by Vasily E. Tarasov

Mathematics 2021, 9(13), 1464; https://doi.org/10.3390/math9131464 - 22 Jun 2021

Cited by 39 | Viewed by 3811

Abstract

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with [...] Read more.

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general form of nonlocality, which can be described by general-form operator kernels and not by its particular implementations and representations. In this paper, the concept of “general nonlocal mappings” is proposed; these are the exact solutions of equations with GFI and GFD at discrete points. In these mappings, the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs. These types of kernels are used in general fractional integrals and derivatives for the initial equations. Using general fractional calculus, we considered fractional systems with general nonlocality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order were also used to derive general nonlocal mappings. The exact solutions for these general fractional differential and integral equations with kicks were obtained. These exact solutions with discrete timepoints were used to derive general nonlocal mappings without approximations. Some examples of nonlocality in time are described. Full article

(This article belongs to the Special Issue Fractional Calculus in Natural and Social Sciences)

25 pages, 764 KiB

Open AccessEditor’s ChoiceCommunication

Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

by Mihaela Aurelia Tomescu, Lorentz Jäntschi and Doina Iulia Rotaru

Mathematics 2021, 9(12), 1419; https://doi.org/10.3390/math9121419 - 18 Jun 2021

Cited by 18 | Viewed by 2949

Abstract

A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented [...] Read more.

A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented with colors. Following this fundamental idea, it was proposed to color the graphs according to the partitions of the graph vertices. Two alternative cases were identified: when the order of the sets in the partition is relevant (the sets are distinguished by their positions) and when the order of the sets in the partition is not relevant (the sets are not distinguished by their positions). The two isomers of

C_{28}

fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures. Full article

(This article belongs to the Collection Topology and Foundations)

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26 pages, 3649 KiB

Open AccessEditor’s ChoiceArticle

Analysis of User Needs on Downloading Behavior of English Vocabulary APPs Based on Data Mining for Online Comments

by Tinggui Chen, Lijuan Peng, Jianjun Yang and Guodong Cong

Mathematics 2021, 9(12), 1341; https://doi.org/10.3390/math9121341 - 09 Jun 2021

Cited by 37 | Viewed by 4169

Abstract

With highly developed social media, English learning Applications have become a new type of mobile learning resources, and online comments posted by users after using them have not only become an important source of intellectual competition for enterprises, but can also help understand [...] Read more.

With highly developed social media, English learning Applications have become a new type of mobile learning resources, and online comments posted by users after using them have not only become an important source of intellectual competition for enterprises, but can also help understand customers’ requirements, thereby improving product functionalities and service quality, and solve the pain points of product iteration and innovation. Based on this, this paper crawled the online user comments of three typical APPs (BaiCiZhan, MoMoBeiDanCi and BuBeiDanCi), through emotion analysis and hotspot mining technology, to obtain user requirements and then the K-means clustering method was used to analyze user requirements. Finally, quantile regression is used to find out which user needs have an impact on the downloads of English vocabulary APPs. The results show that: (1) Positive comments have a more significant impact on users’ downloads behavior than negative online comments. (2) English vocabulary APPs with higher downloads, both the 5-star user ratings and the increase of emotional requirement have a negative effect on the increase in APP downloads, while the enterprise’s service requirement improvement has a positive effect on the increase of APP downloads. (3) Regarding English vocabulary APPs with average or high downloads, improving the adaptability and Appearance requirements have significant negative impact on downloads. (4) The functional requirements to improve products will have a significant positive impact on the increase in downloads of English vocabulary APPs. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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30 pages, 1247 KiB

Open AccessEditor’s ChoiceArticle

An Integrated Decision-Making Approach for Green Supplier Selection in an Agri-Food Supply Chain: Threshold of Robustness Worthiness

by Erfan Babaee Tirkolaee, Zahra Dashtian, Gerhard-Wilhelm Weber, Hana Tomaskova, Mehdi Soltani and Nasim Sadat Mousavi

Mathematics 2021, 9(11), 1304; https://doi.org/10.3390/math9111304 - 07 Jun 2021

Cited by 50 | Viewed by 4367

Abstract

Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price and higher quality. On the other hand, consideration of environmental criteria in the conventional supplier selection methodologies is required for companies trying [...] Read more.

Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price and higher quality. On the other hand, consideration of environmental criteria in the conventional supplier selection methodologies is required for companies trying to promote green supply chain management (GSCM). In this regard, a multi-criteria decision-making (MCDM) technique based on analytic hierarchy process (AHP) and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) is used to evaluate and rate the suppliers. Then, considering the resource constraint, weight of criteria and a rank of suppliers are taken into account in a multi-objective mixed-integer linear programming (MOMILP) to determine the optimum order quantity of each supplier under uncertain conditions. To deal with the uncertain multi-objectiveness of the proposed model, a robust goal programming (RGP) approach based on Shannon entropy is applied. The offered methodology is applied to a real case study from a green service food manufacturing company in Iran in order to verify its applicability with a sensitivity analysis performed on different uncertainty levels. Furthermore, the threshold of robustness worthiness (TRW) is studied by applying different budgets of uncertainty for the green service food manufacturing company. Finally, a discussion and conclusion on the applicability of the methodology is provided, and an outlook to future research projects is given. Full article

(This article belongs to the Special Issue Decision Making and Its Applications)

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15 pages, 4001 KiB

Open AccessEditor’s ChoiceArticle

On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy

by Khaled S. Mekheimer, Bangalore M. Shankar, Shaimaa F. Ramadan, Hosahalli E. Mallik and Mohamed S. Mohamed

Mathematics 2021, 9(11), 1302; https://doi.org/10.3390/math9111302 - 06 Jun 2021

Cited by 16 | Viewed by 2263

Abstract

We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due [...] Read more.

We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)

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32 pages, 8244 KiB

Open AccessEditor’s ChoiceArticle

Stability Analysis of Systems with Fuzzy PI Controllers Applied to Electric Drives

by Constantin Voloşencu

Mathematics 2021, 9(11), 1246; https://doi.org/10.3390/math9111246 - 29 May 2021

Cited by 5 | Viewed by 1970

Abstract

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of [...] Read more.

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers. Full article

(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)

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33 pages, 37135 KiB

Open AccessEditor’s ChoiceArticle

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

by Tobias Gerach, Steffen Schuler, Jonathan Fröhlich, Laura Lindner, Ekaterina Kovacheva, Robin Moss, Eike Moritz Wülfers, Gunnar Seemann, Christian Wieners and Axel Loewe

Mathematics 2021, 9(11), 1247; https://doi.org/10.3390/math9111247 - 29 May 2021

Cited by 50 | Viewed by 7266

Abstract

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a [...] Read more.

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling. Full article

(This article belongs to the Special Issue Development and Applications of Multi-Scale Mathematical Models in Cardiology)

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