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Mathematics, Volume 9, Issue 8 (April-2 2021) – 124 articles

Cover Story (view full-size image): A change in temperature drastically modifies the lifetime of a product. AFT models relate the distribution of the time-to-failure for usual conditions with the distribution of the accelerated failure times. Different optimal designs can be combined to obtain the best temperatures in which to take observations such that the most accurate estimates of the lifetime distribution parameters can be derived. View this paper.
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Article
Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold
Mathematics 2021, 9(8), 915; https://doi.org/10.3390/math9080915 - 20 Apr 2021
Cited by 2 | Viewed by 742
Abstract
This paper introduces a new methodology to estimate time-varying alphas and betas in conditional factor models, which allows substantial flexibility in a time-varying framework. To circumvent problems associated with the previous approaches, we introduce a Bayesian time-varying parameter model where innovations of the [...] Read more.
This paper introduces a new methodology to estimate time-varying alphas and betas in conditional factor models, which allows substantial flexibility in a time-varying framework. To circumvent problems associated with the previous approaches, we introduce a Bayesian time-varying parameter model where innovations of the state equation have a spike-and-slab mixture distribution. The mixture distribution specifies two states with a specific probability. In the first state, the innovation variance is set close to zero with a certain probability and parameters stay relatively constant. In the second state, the innovation variance is large and the change in parameters is normally distributed with mean zero and a given variance. The latent state is specified with a threshold that governs the state change. We allow a separate threshold for each parameter; thus, the parameters may shift in an unsynchronized manner such that the model moves from one state to another when the change in the parameter exceeds the threshold and vice versa. This approach offers great flexibility and nests a plethora of other time-varying model specifications, allowing us to assess whether the betas of conditional factor models evolve gradually over time or display infrequent, but large, shifts. We apply the proposed methodology to industry portfolios within a five-factor model setting and show that the threshold Capital Asset Pricing Model (CAPM) provides robust beta estimates coupled with smaller pricing errors compared to the alternative approaches. The results have significant implications for the implementation of smart beta strategies that rely heavily on the accuracy and stability of factor betas and yields. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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Review
Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives
Mathematics 2021, 9(8), 914; https://doi.org/10.3390/math9080914 - 20 Apr 2021
Cited by 3 | Viewed by 921
Abstract
Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting [...] Read more.
Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting from the well-known Matignon’s results on stability of single-order systems, for which a different proof is provided together with a clarification of a limit case, the investigation is moved towards multi-order systems as well. Due to the key role of the Mittag–Leffler function played in representing the solution of linear systems of FDEs, a detailed analysis of the asymptotic behavior of this function and of its derivatives is also proposed. Some numerical experiments are presented to illustrate the main results. Full article
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Article
Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units
Mathematics 2021, 9(8), 913; https://doi.org/10.3390/math9080913 - 20 Apr 2021
Cited by 3 | Viewed by 644
Abstract
A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels [...] Read more.
A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model. Full article
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Article
The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
Mathematics 2021, 9(8), 912; https://doi.org/10.3390/math9080912 - 20 Apr 2021
Viewed by 500
Abstract
In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert [...] Read more.
In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model. Full article
Article
μ-Synthesis for Fractional-Order Robust Controllers
Mathematics 2021, 9(8), 911; https://doi.org/10.3390/math9080911 - 20 Apr 2021
Cited by 6 | Viewed by 799
Abstract
The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with DK iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets [...] Read more.
The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with DK iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets the stability and performance criteria for a family of plants. Because this control problem is NP-hard, it is usually solved using an approximation, the most common being the DK iteration algorithm, but, this approximation leads to high-order controllers, which are not practically feasible. If a desired structure is imposed to the controller, the corresponding K step is a non-convex problem. The novelty of the paper consists in an artificial bee colony swarm optimization approach to compute the nearly optimal controller parameters. Further, a mixed-sensitivity μ-synthesis control problem is solved with the proposed approach for a two-axis Computer Numerical Control (CNC) machine benchmark problem. The resulting controller using the described algorithm manages to ensure, with mathematical guarantee, both robust stability and robust performance, while the high-order controller obtained with the classical μ-synthesis approach in MATLAB does not offer this. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
Mathematics 2021, 9(8), 910; https://doi.org/10.3390/math9080910 - 20 Apr 2021
Cited by 1 | Viewed by 499
Abstract
An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average [...] Read more.
An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters. Full article
(This article belongs to the Special Issue Nonlinear Boundary Value Problems and Their Applications)
Article
Advanced Metaheuristic Method for Decision-Making in a Dynamic Job Shop Scheduling Environment
Mathematics 2021, 9(8), 909; https://doi.org/10.3390/math9080909 - 19 Apr 2021
Cited by 2 | Viewed by 744
Abstract
As a well-known NP-hard problem, the dynamic job shop scheduling problem has significant practical value, so this paper proposes an Improved Heuristic Kalman Algorithm to solve this problem. In Improved Heuristic Kalman Algorithm, the cellular neighbor network is introduced, together with the boundary [...] Read more.
As a well-known NP-hard problem, the dynamic job shop scheduling problem has significant practical value, so this paper proposes an Improved Heuristic Kalman Algorithm to solve this problem. In Improved Heuristic Kalman Algorithm, the cellular neighbor network is introduced, together with the boundary handling function, and the best position of each individual is recorded for constructing the cellular neighbor network. The encoding method is introduced based on the relative position index so that the Improved Heuristic Kalman Algorithm can be applied to solve the dynamic job shop scheduling problem. Solving the benchmark example of dynamic job shop scheduling problem and comparing it with the original Heuristic Kalman Algorithm and Genetic Algorithm-Mixed, the results show that Improved Heuristic Kalman Algorithm is effective for solving the dynamic job shop scheduling problem. The convergence rate of the Improved Heuristic Kalman Algorithm is reduced significantly, which is beneficial to avoid the algorithm from falling into the local optimum. For all 15 benchmark instances, Improved Heuristic Kalman Algorithm and Heuristic Kalman Algorithm have obtained the best solution obtained by Genetic Algorithm-Mixed. Moreover, for 9 out of 15 benchmark instances, they achieved significantly better solutions than Genetic Algorithm-Mixed. They have better robustness and reasonable running time (less than 30 s even for large size problems), which means that they are very suitable for solving the dynamic job shop scheduling problem. According to the dynamic job shop scheduling problem applicability, the integration-communication protocol was presented, which enables the transfer and use of the Improved Heuristic Kalman Algorithm optimization results in the conventional Simio simulation environment. The results of the integration-communication protocol proved the numerical and graphical matching of the optimization results and, thus, the correctness of the data transfer, ensuring high-level usability of the decision-making method in a real-world environment. Full article
(This article belongs to the Special Issue Advances of Metaheuristic Computation)
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Article
A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations
Mathematics 2021, 9(8), 908; https://doi.org/10.3390/math9080908 - 19 Apr 2021
Cited by 5 | Viewed by 710
Abstract
In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach [...] Read more.
In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples. Full article
(This article belongs to the Section Fuzzy Set Theory)
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Article
Multidisciplinary Lightweight Optimization for Front Impact Structure of Body Frame Based on Active and Passive Safety
Mathematics 2021, 9(8), 907; https://doi.org/10.3390/math9080907 - 19 Apr 2021
Viewed by 682
Abstract
The Analytic Target Cascading (ATC) is an effective method for solving hierarchical Multidisciplinary Design Optimization (MDO) problems. At the same time, this method suffers from poor convergence and low accuracy, which is caused by the inconsistency of system constraints. In this paper, a [...] Read more.
The Analytic Target Cascading (ATC) is an effective method for solving hierarchical Multidisciplinary Design Optimization (MDO) problems. At the same time, this method suffers from poor convergence and low accuracy, which is caused by the inconsistency of system constraints. In this paper, a novel ATC method based on dynamic relaxation factor is proposed. The dynamic relaxation factor of consistency constraint is added in the system level and is adjusted by the deviation of the linking variables between the levels to ensure the feasible region of the design space. The effectiveness and accuracy of this method are verified by a mathematical example. This method is used to solve the lightweight problem of the trussed front part of the vehicle body frame based on active and passive safety to achieve the collaborative optimization of lightweight trussed frame, crash safety, and aerodynamic characteristics. The important value of the novel ATC method based on dynamic relaxation factor in engineering applications is proven. Full article
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)
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Article
Coping with Challenges in Teaching Foreign Languages to Children with Mild Intellectual Disabilities: Stakeholders’ Perspectives
Mathematics 2021, 9(8), 906; https://doi.org/10.3390/math9080906 - 19 Apr 2021
Viewed by 709
Abstract
In this qualitative study, we aim to gain insight into the stakeholders’ perspectives around the inclusion of a mild intellectual disability (MID) student of perinatal origin in the foreign language (FL) classroom, and their perspectives on the student’s working conditions, and the support [...] Read more.
In this qualitative study, we aim to gain insight into the stakeholders’ perspectives around the inclusion of a mild intellectual disability (MID) student of perinatal origin in the foreign language (FL) classroom, and their perspectives on the student’s working conditions, and the support needed to effectively develop this student’s basic FL skills. The research hypothesis holds that the stakeholders face numerous technical, contextual, and formative challenges which hinder the MID student’s learning conditions in the FL classroom. The study was carried out in a state secondary school of the metropolitan area of Granada (Spain). Different stakeholders participated in this study. As an instrument of research, we designed an in-depth interview with open questions. The data were perused, sifted, and interpreted by means of a content analysis methodology. The main results confirm the research hypothesis since stakeholders’ perspectives are positive towards the theoretical bases of inclusive education. Conversely, we observe that these perspectives are negative when it comes to the real and effective practice of inclusive education in the FL classroom, which would allow them to tailor their teaching methodology to the real needs of the MID student and the rest of students with special educational needs (SEN). Full article
Article
A Reliability Growth Process Model with Time-Varying Covariates and Its Application
Mathematics 2021, 9(8), 905; https://doi.org/10.3390/math9080905 - 19 Apr 2021
Viewed by 658
Abstract
The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of [...] Read more.
The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
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Article
An Approximation of Solutions for the Problem with Quasistatic Contact in the Case of Dry Friction
Mathematics 2021, 9(8), 904; https://doi.org/10.3390/math9080904 - 19 Apr 2021
Viewed by 457
Abstract
In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get [...] Read more.
In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get the necessary optimality conditions, we use some regularization techniques, and this leads us to a problem of control for an inequality of the variational type. The optimal control problem consists, in our case, of minimizing a sequence of optimal control problems, where the control variable is given by a Neumann-type boundary condition. The state system is represented by a limit of a sequence, whose terms are obtained from the discretization, in time with finite difference and space with the finite element method of a regularized quasistatic contact problem with Coulomb friction. The purpose of this optimal control problem is that the traction force (the control variable) acting on one side of the boundary (the Neumann boundary condition) of the elastic body produces a displacement field (the state system solution) close enough to the imposed displacement field, and the traction force from the boundary remains small enough. Full article
(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)
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Article
Nonlinear Control of Hydrostatic Thrust Bearing Using Multivariable Optimization
Mathematics 2021, 9(8), 903; https://doi.org/10.3390/math9080903 - 19 Apr 2021
Cited by 1 | Viewed by 654
Abstract
This research work is focused on the nonlinear modeling and control of a hydrostatic thrust bearing. In the proposed work, a mathematical model is formulated for a hydrostatic thrust bearing system that includes the effects of uncertainties, unmodelled dynamics, and nonlinearities. Depending on [...] Read more.
This research work is focused on the nonlinear modeling and control of a hydrostatic thrust bearing. In the proposed work, a mathematical model is formulated for a hydrostatic thrust bearing system that includes the effects of uncertainties, unmodelled dynamics, and nonlinearities. Depending on the type of inputs, the mathematical model is divided into three subsystems. Each subsystem has the same output, i.e., fluid film thickness with different types of input, i.e., viscosity, supply pressure, and recess pressure. An extended state observer is proposed to estimate the unavailable states. A backstepping control technique is presented to achieve the desired tracking performance and stabilize the closed-loop dynamics. The proposed control technique is based on the Lyapunov stability theorem. Moreover, particle swarm optimization is used to search for the best tuning parameters for the backstepping controller and extended state observer. The effectiveness of the proposed method is verified using numerical simulations. Full article
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Article
The Impact of Candidates’ Profile and Campaign Decisions in Electoral Results: A Data Analytics Approach
Mathematics 2021, 9(8), 902; https://doi.org/10.3390/math9080902 - 19 Apr 2021
Viewed by 654
Abstract
In recent years, a wide range of techniques has been developed to predict electoral results and to measure the influence of different factors in these results. In this paper, we analyze the influence of the political profile of candidates (characterized by personal and [...] Read more.
In recent years, a wide range of techniques has been developed to predict electoral results and to measure the influence of different factors in these results. In this paper, we analyze the influence of the political profile of candidates (characterized by personal and political features) and their campaign effort (characterized by electoral expenditure and by territorial deployment strategies retrieved from social networks activity) on the electoral results. This analysis is carried out by using three of the most frequent data analyitcs algorithms in the literature. For our analysis, we consider the 2017 Parliamentary elections in Chile, which are the first elections after a major reform of the electoral system, that encompassed a transition from a binomial to a proportional system, a modification of the districts’ structure, an increase in the number of seats, and the requirement of gender parity in the lists of the different coalitions. The obtained results reveal that, regardless of the political coalition, the electoral experience of candidates, in particular in the same seat they are running for (even when the corresponding district is modified), is by large the most influential factor to explain the electoral results. However, the attained results show that the influence of other features, such as campaign expenditures, depends on the political coalition. Additionally, by means of a simulation procedure, we show how different levels of territorial deployment efforts might impact on the results of candidates. This procedure could be used by parties and coalitions when planning their campaign strategies. Full article
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Article
The Fuzzy Methodology’s Digitalization of the Biological Assets Evaluation in Agricultural Enterprises in Accordance with the IFRS
Mathematics 2021, 9(8), 901; https://doi.org/10.3390/math9080901 - 19 Apr 2021
Cited by 1 | Viewed by 834
Abstract
The study of the assessment and reflection of biological assets in the economic processes of agricultural enterprises can be represented as a chain of phenomena in which scientists and practitioners try to study and understand the nature and essence of biological assets in [...] Read more.
The study of the assessment and reflection of biological assets in the economic processes of agricultural enterprises can be represented as a chain of phenomena in which scientists and practitioners try to study and understand the nature and essence of biological assets in various aspects. This article discusses the principles of accounting for biological assets in the agricultural enterprises’ economic life of the Republic of Tajikistan and identifies the reasons and mechanisms for their reflection based on the principles of the International Financial Reporting System (IFRS) in refraction to the specifics and national features of accounting. The author gives his own interpretation of these approaches and constructs the architecture of the information module for accounting for biological assets and the results of biotransformation, based on the web services architecture (WSA) within the framework of the development trend of these and new accounting models in connection with the transition of the world economy to a digital format. The article provides specific authors’ approaches to implementing this architecture in PHP (Hypertext Preprocessor) and also implements one of the approaches to assessing the value of biological assets, based on the theory of fuzzy sets, taking into account the risk of investment inefficiency. Full article
(This article belongs to the Special Issue Mathematical and Instrumental Methods in the Digital Economy)
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Article
Interdependence between Green Financial Instruments and Major Conventional Assets: A Wavelet-Based Network Analysis
Mathematics 2021, 9(8), 900; https://doi.org/10.3390/math9080900 - 19 Apr 2021
Cited by 5 | Viewed by 1174
Abstract
This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based [...] Read more.
This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based network approach that allows for assessing the degree of interconnection between green financial products and traditional asset classes across different investment horizons is applied. The empirical results show that green bonds are tightly linked to Treasury and investment-grade corporate bonds, while green stocks are strongly tied to general stocks, regardless of the specific time period and investment horizon considered. However, despite their common climate-friendly nature, there is no a remarkable association between green bonds and green stocks. This means that these green investments constitute basically two independent asset classes, with a distinct risk-return profile and aimed at a different type of investor. Furthermore, green financial products have a weak connection with high-yield corporate bonds and crude oil. These findings can have important implications for investors and policy makers in terms of investment decision, hedging strategies, and sustainability and energy policies. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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Article
Factorization à la Dirac Applied to Some Equations of Classical Physics
Mathematics 2021, 9(8), 899; https://doi.org/10.3390/math9080899 - 18 Apr 2021
Viewed by 660
Abstract
In this paper, we present an application of Dirac’s factorization method to three types of the partial differential equations, i.e., the wave equation, the scattering equation, and the telegrapher’s equation. This method gives results that contribute to a better understanding of physical phenomena [...] Read more.
In this paper, we present an application of Dirac’s factorization method to three types of the partial differential equations, i.e., the wave equation, the scattering equation, and the telegrapher’s equation. This method gives results that contribute to a better understanding of physical phenomena by generalizing the Euler and constituent equations. Its application to the wave equation shows that it is indeed a factorization method, since it gives d’Alembert’s solutions in a more general framework. In the case of the diffusion equation, a fractional differential equation has been established that has already been highlighted by other authors in particular cases, but by indirect methods. Dirac’s method brings several new results in the case of the telegraphers’ equation corresponding to the propagation of an acoustic wave in a dissipative fluid. On the one hand, its formalism facilitates the temporal interpretation of phenomena, in particular the density and compressibility of the fluid become temporal operators, which can be “seen” as susceptibilities of the fluid. On the other hand, a consequence of this temporal modeling is the highlighting in Euler’s equation of a term similar to the one that was introduced by Boussinesq and Basset in the equation of the motion of a solid sphere in a unsteady fluid. Full article
(This article belongs to the Special Issue Fractional Calculus in Anomalous Transport Theory)
Article
Numerical Solution of Bending of the Beam with Given Friction
Mathematics 2021, 9(8), 898; https://doi.org/10.3390/math9080898 - 18 Apr 2021
Viewed by 605
Abstract
We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the [...] Read more.
We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the contact mechanics in the sustainable building construction design. The analysis and the practical solution plays a crucial role in the process and cannot be ignored. In this paper, we consider the classical Euler–Bernoulli beam model, which we formulate, analyze, and numerically solve. The objective function of the corresponding optimization problem for finding the coefficients in the finite element basis combines a quadratic function and an additional non-differentiable part with absolute values representing the influence of considered friction. We present two basic algorithms for the solution: the regularized primal solution, where the non-differentiable part is approximated, and the dual formulation. We discuss the disadvantages of the methods on the solution of the academic benchmarks. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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Article
Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure
Mathematics 2021, 9(8), 897; https://doi.org/10.3390/math9080897 - 17 Apr 2021
Cited by 2 | Viewed by 507
Abstract
The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated porous media involves phase coupling, the resulting system is highly nonlinear in [...] Read more.
The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated porous media involves phase coupling, the resulting system is highly nonlinear in nature. To this end, the local approximation is adopted in conjunction with Newton–Raphson method. Nevertheless, to unveil the performance of the method in the nonlinear analysis, only single thermal natural convection is of major concern herein. A unit square is designated as the model problem to investigate the parameters in the system related to the convergence; several benchmark problems are used to verify the accuracy of the approximation, in which the stability of the method is demonstrated by considering various initial conditions, disturbance of discretization, inclination, aspect ratio, and reproducing kernel support size. It is shown that a larger support size can be flexible in approximating highly irregular discretized problems. The derivation of explicit operators with two-phase variables in solving the nonlinear system using the direct collocation is carried out in detail. Full article
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Article
Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy
Mathematics 2021, 9(8), 896; https://doi.org/10.3390/math9080896 - 17 Apr 2021
Cited by 10 | Viewed by 710
Abstract
Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and [...] Read more.
Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy. Full article
(This article belongs to the Special Issue Numerical Analysis of Artificial Neural Networks)
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Review
Graph Metrics for Network Robustness—A Survey
Mathematics 2021, 9(8), 895; https://doi.org/10.3390/math9080895 - 17 Apr 2021
Cited by 6 | Viewed by 1447
Abstract
Research on the robustness of networks, and in particular the Internet, has gained critical importance in recent decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business processes and e-commerce. In particular, modeling [...] Read more.
Research on the robustness of networks, and in particular the Internet, has gained critical importance in recent decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business processes and e-commerce. In particular, modeling the structure of the Internet has inspired several novel graph metrics for assessing important topological robustness features of large complex networks. This survey provides a comparative overview of these metrics, presents their strengths and limitations for analyzing the robustness of the Internet topology, and outlines a conceptual tool set in order to facilitate their future adoption by Internet research and practice but also other areas of network science. Full article
(This article belongs to the Special Issue Distributed Computer and Communication Networks)
Article
Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components
Mathematics 2021, 9(8), 894; https://doi.org/10.3390/math9080894 - 17 Apr 2021
Cited by 4 | Viewed by 406
Abstract
The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated [...] Read more.
The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems. Full article
Article
On a Dual Pair of Multiobjective Interval-Valued Variational Control Problems
Mathematics 2021, 9(8), 893; https://doi.org/10.3390/math9080893 - 17 Apr 2021
Cited by 3 | Viewed by 442
Abstract
In this paper, by using the new concept of (ϱ,ψ,ω)-quasiinvexity associated with interval-valued path-independent curvilinear integral functionals, we establish some duality results for a new class of multiobjective variational control problems with interval-valued components. More concretely, [...] Read more.
In this paper, by using the new concept of (ϱ,ψ,ω)-quasiinvexity associated with interval-valued path-independent curvilinear integral functionals, we establish some duality results for a new class of multiobjective variational control problems with interval-valued components. More concretely, we formulate and prove weak, strong, and converse duality theorems under (ϱ,ψ,ω)-quasiinvexity hypotheses for the considered class of optimization problems. Full article
Article
Business Performance and Sustainability in Cultural and Rural Tourism Destinations
Mathematics 2021, 9(8), 892; https://doi.org/10.3390/math9080892 - 16 Apr 2021
Cited by 4 | Viewed by 1078
Abstract
This study analyzes business performance through efficiency score estimation in two sustainable tourism models: cultural tourism and rural tourism. The study uses microeconomic data (microdata) of Spanish firms with different characteristics in terms of size, region, location and financial variables. Using multistage modeling [...] Read more.
This study analyzes business performance through efficiency score estimation in two sustainable tourism models: cultural tourism and rural tourism. The study uses microeconomic data (microdata) of Spanish firms with different characteristics in terms of size, region, location and financial variables. Using multistage modeling (Data envelopment analysis, DEA, non-parametric frontier and non-parametric tests), the main results show that the average efficiency is higher for rural tourism destinations than for cultural tourism destinations. Similar to other tourism industries, efficiency results by geographical and regional destination confirm that location is a driver of the efficiency levels in rural and cultural tourism destinations. Furthermore, the results do not support the scale economies hypothesis: the average efficiency is higher for very small firms compared to other firm sizes, although the average efficiency for large firms is higher than that for medium-size firms. Regarding dynamic efficiency, the results reveal slight variations among the years examined, but the differences are not statistically significant. Finally, the study sheds light on the link between the efficiency of rural tourism and sustainable practices as the investment in environmental protection developed by regions during the period. Full article
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Article
Visualizing Profiles of Large Datasets of Weighted and Mixed Data
Mathematics 2021, 9(8), 891; https://doi.org/10.3390/math9080891 - 16 Apr 2021
Cited by 4 | Viewed by 938
Abstract
This work provides a procedure with which to construct and visualize profiles, i.e., groups of individuals with similar characteristics, for weighted and mixed data by combining two classical multivariate techniques, multidimensional scaling (MDS) and the k-prototypes clustering algorithm. The well-known drawback of [...] Read more.
This work provides a procedure with which to construct and visualize profiles, i.e., groups of individuals with similar characteristics, for weighted and mixed data by combining two classical multivariate techniques, multidimensional scaling (MDS) and the k-prototypes clustering algorithm. The well-known drawback of classical MDS in large datasets is circumvented by selecting a small random sample of the dataset, whose individuals are clustered by means of an adapted version of the k-prototypes algorithm and mapped via classical MDS. Gower’s interpolation formula is used to project remaining individuals onto the previous configuration. In all the process, Gower’s distance is used to measure the proximity between individuals. The methodology is illustrated on a real dataset, obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE), which was carried out in 19 countries and represents over 124 million aged individuals in Europe. The performance of the method was evaluated through a simulation study, whose results point out that the new proposal solves the high computational cost of the classical MDS with low error. Full article
(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications)
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Article
A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting
Mathematics 2021, 9(8), 890; https://doi.org/10.3390/math9080890 - 16 Apr 2021
Cited by 1 | Viewed by 654
Abstract
In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild [...] Read more.
In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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Article
Environmental Efficiency Evaluation in the Top Asian Economies: An Application of DEA
Mathematics 2021, 9(8), 889; https://doi.org/10.3390/math9080889 - 16 Apr 2021
Cited by 8 | Viewed by 924
Abstract
Sustainable development has become a global catchphrase in the recent development age. This leads to the growth of various methodologies in evaluating environmental efficiency, such as the Data Envelopment Analysis (DEA) method. The purpose of this study is to propose an extended DEA [...] Read more.
Sustainable development has become a global catchphrase in the recent development age. This leads to the growth of various methodologies in evaluating environmental efficiency, such as the Data Envelopment Analysis (DEA) method. The purpose of this study is to propose an extended DEA model, i.e., the undesirable output model, in measuring the relative eco-efficiency scores across nations. The study collected the data of inputs, namely bad outputs and good outputs of the top 20 Asian economies in the period of 2005–2019, and then estimated the environmental efficiency of each country and classified them. The results have shown that there are four nations having higher average environmental efficiency than others. Japan is a good example of sustainable development that simultaneously balances economic development and environmental protection. The study has also discussed possible solutions for improvement to the group of nations with low environmental efficiency. Contributing to applying a novelty extended DEA model, this work recommends a more precise model, taking the weight of outputs into account for further studies. Full article
(This article belongs to the Special Issue Application of Mathematics in Applied Economic)
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Article
Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model
Mathematics 2021, 9(8), 888; https://doi.org/10.3390/math9080888 - 16 Apr 2021
Viewed by 628
Abstract
This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on [...] Read more.
This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one. Full article
(This article belongs to the Special Issue Mathematics in Biomedicine)
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Article
Generalized and Extended Versions of Ankeny–Rivlin and Improved, Generalized, and Extended Versions of Rivlin Type Inequalities for the sth Derivative of a Polynomial
Mathematics 2021, 9(8), 887; https://doi.org/10.3390/math9080887 - 16 Apr 2021
Viewed by 425
Abstract
Let p(z) be a polynomial of degree n having no zeros in |z|<1. In this paper, we generalize and extend a well-known result proven by Ankeny and Rivlin for the sth derivative of [...] Read more.
Let p(z) be a polynomial of degree n having no zeros in |z|<1. In this paper, we generalize and extend a well-known result proven by Ankeny and Rivlin for the sth derivative of the polynomial. Furthermore, another well-known result proven by Rivlin is also improved, generalized and extended for the sth derivative of p(z). Our results also give a number of interesting consequences as special cases. Full article
Article
A Compromised Decision-Making Approach to Third-Party Logistics Selection in Sustainable Supply Chain Using Fuzzy AHP and Fuzzy VIKOR Methods
Mathematics 2021, 9(8), 886; https://doi.org/10.3390/math9080886 - 16 Apr 2021
Cited by 26 | Viewed by 2638
Abstract
With the effects of the COVID-19 pandemic, the e-commerce trend is driving faster, significantly impacting supply chains around the world. Thus, the importance of logistics and supply chain functions has been amplified in almost every business that ships physical goods. In Vietnam, the [...] Read more.
With the effects of the COVID-19 pandemic, the e-commerce trend is driving faster, significantly impacting supply chains around the world. Thus, the importance of logistics and supply chain functions has been amplified in almost every business that ships physical goods. In Vietnam, the logistics service sector has seen rapid expansion. Since more and more businesses are seeking third-party logistics (3PL) providers to outsource the logistics functions, this article aims to offer decision-makers an integrated and consistent model for evaluating and selecting the most efficient 3PLs. To this end, the authors exploit a hybrid multi-criteria method which is fuzzy analytic hierarchy process (FAHP) and fuzzy vlsekriterijumska optimizacija i kompromisno resenje (FVIKOR) while examining the most influential and conflicting criteria regarding economic, service level, environmental, social, and risk aspects. Fuzzy information in the natural decision-making process is considered, linguistic variables are used to mitigate the uncertain levels in the criteria weights. First, FAHP (the weighting method) is adopted to evaluate and calculate each criterion’s relative significant fuzzy weight. FVIKOR (the compromised ranking method) is then used to rank the alternatives. The combination of FAHP and FVIKOR methods provides more accurate ranking results. As a result, reliability and delivery time, voice of customer, logistics cost, network management, and quality of service are the most impactful factors to the logistics outsourcing problem. Eventually, the optimized 3PLs were determined that fully meet the criteria of sustainable development. The developed integrated model offers the complete and robust 3PLs evaluation and selection process and can also be a powerful decision support tool for other industries. Full article
(This article belongs to the Special Issue Advances in Multiple Criteria Decision Analysis)
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