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Mathematics, Volume 8, Issue 7 (July 2020) – 102 articles

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Open AccessArticle
Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays
Mathematics 2020, 8(7), 1146; https://doi.org/10.3390/math8071146 (registering DOI) - 13 Jul 2020
Abstract
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state [...] Read more.
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria. Full article
Open AccessArticle
A Five-Component Generalized mKdV Equation and Its Exact Solutions
Mathematics 2020, 8(7), 1145; https://doi.org/10.3390/math8071145 (registering DOI) - 13 Jul 2020
Abstract
In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As [...] Read more.
In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As applications of the Darboux transformations, interesting exact solutions, including soliton-like solutions and a solution that consists of rational functions of e x and t, for the five-component equation are obtained. Full article
(This article belongs to the Section Difference and Differential Equations)
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Open AccessArticle
Reducing the Cost of Electricity by Optimizing Real-Time Consumer Planning Using a New Genetic Algorithm-Based Strategy
Mathematics 2020, 8(7), 1144; https://doi.org/10.3390/math8071144 (registering DOI) - 13 Jul 2020
Abstract
To ensure the use of energy produced from renewable energy sources, this paper presents a method for consumer planning in the consumer–producer–distributor structure. The proposed planning method is based on the genetic algorithm approach, which solves a cost minimization problem by considering several [...] Read more.
To ensure the use of energy produced from renewable energy sources, this paper presents a method for consumer planning in the consumer–producer–distributor structure. The proposed planning method is based on the genetic algorithm approach, which solves a cost minimization problem by considering several input parameters. These input parameters are: the consumption for each unit, the time interval in which the unit operates, the maximum value of the electricity produced from renewable sources, and the distribution of energy production per unit of time. A consumer can use the equipment without any planning, in which case he will consume energy supplied by a distributor or energy produced from renewable sources, if it is available at the time he operates the equipment. A consumer who plans his operating interval can use more energy from renewable sources, because the planning is done in the time interval in which the energy produced from renewable sources is available. The effect is that the total cost of energy to the consumer without any planning will be higher than the cost of energy to the consumer with planning, because the energy produced from renewable sources is cheaper than that provided from conventional sources. To be validated, the proposed approach was run on a simulator, and then tested in two real-world case studies targeting domestic and industrial consumers. In both situations, the solution proposed led to a reduction in the total cost of electricity of up to 25%. Full article
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Open AccessArticle
Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values
Mathematics 2020, 8(7), 1143; https://doi.org/10.3390/math8071143 (registering DOI) - 13 Jul 2020
Abstract
In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic [...] Read more.
In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
Open AccessArticle
Does the Autonomation Policy Really Help in a Smart Production System for Controlling Defective Production?
Mathematics 2020, 8(7), 1142; https://doi.org/10.3390/math8071142 (registering DOI) - 13 Jul 2020
Abstract
This study explains about a serial smart production system where a single-type of product is produced. This system uses an unequally sized batch policy in subsequent stages. The setup cost is not always deterministic, it can be controllable and reduced by increasing the [...] Read more.
This study explains about a serial smart production system where a single-type of product is produced. This system uses an unequally sized batch policy in subsequent stages. The setup cost is not always deterministic, it can be controllable and reduced by increasing the capital investment cost, and that the production rates in the system may vary within given limits across batches of shipments. Furthermore, as imperfect items are produced in long-run system, to clean the imperfectness autonomation policy is adopted for inspection, which make the process smarter. The shipment lot sizes of the deliveries are unequal and variable. In long-run production system, defective items are produced in “out-of-control” state. In this model, the defect rate is random with a uniform distribution which is clean from the system by autonomation. In addition, in the remanufacturing process, it is assuming that all defective products are repaired, and no defective products are scrapped. The main theme of developing this model is to determine the number of shipments and the optimal production lot size to adjust the production rates and decrease the total system cost under a reduced setup cost by considering the discrete investment and make a serial smart production system. A solution procedure along with an advanced algorithm was proposed for solving the model. Numerical examples with some graphical representations are provided to validate the model. Full article
Open AccessArticle
Tube-Based Taut String Algorithms for Total Variation Regularization
Mathematics 2020, 8(7), 1141; https://doi.org/10.3390/math8071141 (registering DOI) - 13 Jul 2020
Abstract
Removing noise from signals using total variation regularization is a challenging signal processing problem arising in many practical applications. The taut string method is one of the most efficient approaches for solving the 1D TV regularization problem. In this paper we propose a [...] Read more.
Removing noise from signals using total variation regularization is a challenging signal processing problem arising in many practical applications. The taut string method is one of the most efficient approaches for solving the 1D TV regularization problem. In this paper we propose a geometric description of the linearized taut string method. This geometric description leads to the notion of the “tube”. We propose three tube-based taut string algorithms for total variation regularization. Different weight functionals can be used in the 1D TV regularization that lead to different types of tubes. We consider uniform, vertically nonuniform, vertically and horizontally nonuniform tubes. The proposed geometric approach is used to speed-up TV regularization processing by dividing the tubes into subtubes and using parallel processing. We introduce the concept of a relatively convex tube and describe the relationship between the geometric characteristics of tubes and exact solutions to the TV regularization. The properties of exact solutions can also be used to design efficient algorithms for solving the TV regularization problem. The performance of the proposed algorithms is discussed and illustrated by computer simulation. Full article
(This article belongs to the Special Issue Direct and Inverse Problems for Fractional Differential Equations)
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Open AccessArticle
A DEA Resampling Past-Present-Future Comparative Analysis of the Food and Beverage Industry: The Case Study on Thailand vs. Vietnam
Mathematics 2020, 8(7), 1140; https://doi.org/10.3390/math8071140 (registering DOI) - 13 Jul 2020
Abstract
The food and beverage industry plays a significant role in the economic development of developing and emerging countries in Asia through an immense contribution to the national income, employment, value-added inducement, and foreign exchange earnings. Among the developing countries in Asia, Thailand and [...] Read more.
The food and beverage industry plays a significant role in the economic development of developing and emerging countries in Asia through an immense contribution to the national income, employment, value-added inducement, and foreign exchange earnings. Among the developing countries in Asia, Thailand and Vietnam have recently experienced a significant growth in the industry due to their many advantages. However, the nascent stage of this industry was found to be lacking sustainable competitiveness in both countries. Therefore, this study aims to evaluate and forecast the performance efficiency of the food and beverage industry in Thailand and Vietnam to understand how efficient the food and beverage industry to these countries is and formulate suggestions to improve their productivity in accordance with the research findings. To achieve the research objectives, the resampling method in the data envelopment analysis is applied to measure and forecast the efficiency of 20 Vietnamese companies and 20 Thailand firms over the period of 2016 to 2023. The Malmquist productivity index is deployed to calculate the efficiency change over observed periods. The results reveal that Vietnam is found to have a higher efficiency than Thailand due to the outstanding performance of one company but have performed quite poorly due to low scores in technical and productivity change. The findings of this research can give useful information and practical suggestions to improve performance for inefficient companies as well as enhance competitiveness of the efficient companies trying to operate and reach global markets. Full article
(This article belongs to the Special Issue Mathematical Analysis in Economics and Management)
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Open AccessArticle
On the Polynomial Solutions and Limit Cycles of Some Generalized Polynomial Ordinary Differential Equations
Mathematics 2020, 8(7), 1139; https://doi.org/10.3390/math8071139 (registering DOI) - 12 Jul 2020
Viewed by 158
Abstract
We study equations of the form y d y / d x = P ( x , y ) where P ( x , y ) R [ x , y ] with degree n in the y-variable. We prove that [...] Read more.
We study equations of the form y d y / d x = P ( x , y ) where P ( x , y ) R [ x , y ] with degree n in the y-variable. We prove that this ordinary differential equation has at most n polynomial solutions (not necessarily constant but coprime among each other) and this bound is sharp. We also consider polynomial limit cycles and their multiplicity. Full article
(This article belongs to the Section Difference and Differential Equations)
Open AccessArticle
λ-Symmetry and μ-Symmetry Reductions and Invariant Solutions of Four Nonlinear Differential Equations
Mathematics 2020, 8(7), 1138; https://doi.org/10.3390/math8071138 (registering DOI) - 12 Jul 2020
Viewed by 149
Abstract
On one hand, we construct λ -symmetries and their corresponding integrating factors and invariant solutions for two kinds of ordinary differential equations. On the other hand, we present μ -symmetries for a (2+1)-dimensional diffusion equation and derive group-reductions of a first-order partial differential [...] Read more.
On one hand, we construct λ -symmetries and their corresponding integrating factors and invariant solutions for two kinds of ordinary differential equations. On the other hand, we present μ -symmetries for a (2+1)-dimensional diffusion equation and derive group-reductions of a first-order partial differential equation. A few specific group invariant solutions of those two partial differential equations are constructed. Full article
Open AccessArticle
On the Zero-Hopf Bifurcation of the Lotka–Volterra Systems in R3
Mathematics 2020, 8(7), 1137; https://doi.org/10.3390/math8071137 (registering DOI) - 12 Jul 2020
Viewed by 148
Abstract
Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least [...] Read more.
Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. We remark that these systems with such six periodic orbits are non-competitive Lotka–Volterra systems. The proof is done using the algorithm that we provide for computing the periodic solutions that bifurcate from a zero-Hopf equilibrium based in the averaging theory of third order. This algorithm can be applied to any differential system having a zero-Hopf equilibrium. Full article
(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)
Open AccessFeature PaperArticle
The Effect of Setting a Warning Vaccination Level on a Stochastic SIVS Model with Imperfect Vaccine
Mathematics 2020, 8(7), 1136; https://doi.org/10.3390/math8071136 (registering DOI) - 11 Jul 2020
Viewed by 201
Abstract
This paper deals with a stochastic Susceptible-Infective-Vaccinated-Susceptible (SIVS) model with infection reintroduction. Health policies depend on vaccine coverage, v 0 , that guarantees herd immunity levels in the population. Vaccine failures occur when an organism develops a disease despite of being [...] Read more.
This paper deals with a stochastic Susceptible-Infective-Vaccinated-Susceptible (SIVS) model with infection reintroduction. Health policies depend on vaccine coverage, v 0 , that guarantees herd immunity levels in the population. Vaccine failures occur when an organism develops a disease despite of being vaccinated against it. After vaccination, a proportion of healthy individuals unsuccessfully tries to increase antibody levels and, consequently these individuals are not immune to the vaccine preventable disease. When an infectious process is in progress, the initial vaccine coverage drops down and herd immunity will be lost. Our objective was to introduce a warning vaccination level and define random measures quantifying the time until the number of vaccinated descends to a warning vaccination level (i.e., the so-called sleeping period), and the epidemic size. A sensitivity analysis was performed to assess the influence of the model parameters on the variation and robustness of the sleeping period and the number of infections observed within it. Full article
(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research)
Open AccessFeature PaperArticle
On a Simplified Method of Defining Characteristic Function in Stochastic Games
Mathematics 2020, 8(7), 1135; https://doi.org/10.3390/math8071135 (registering DOI) - 11 Jul 2020
Viewed by 133
Abstract
In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of [...] Read more.
In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of the characteristic function is based on a calculation of the maximin values of zero-sum games between a coalition and its anti-coalition for each state of the game. The proposed characteristic function has some advantages in comparison with previously defined characteristic functions for stochastic games. In particular, the advantages include computation simplicity and strong subgame consistency of the core calculated with the values of the new characteristic function. Full article
(This article belongs to the Special Issue Game Theory)
Open AccessArticle
A Numerical Method for A System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control
Mathematics 2020, 8(7), 1134; https://doi.org/10.3390/math8071134 (registering DOI) - 11 Jul 2020
Viewed by 126
Abstract
Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method [...] Read more.
Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and the fractional calculus definition of Grünwald–Letnikov. The algebraic equation is considered as the sliding mode surface. The validity of the present method is verified by comparing with an example with exact solutions. The accuracy and efficiency of the present method are studied. It is found that the present method has very high accuracy and low time consumption. The effect of violation corrections on the accuracy is investigated for different time steps. Full article
Open AccessArticle
Analysis of Perturbed Volterra Integral Equations on Time Scales
Mathematics 2020, 8(7), 1133; https://doi.org/10.3390/math8071133 - 10 Jul 2020
Viewed by 149
Abstract
This paper describes the effect of perturbation of the kernel on the solutions of linear Volterra integral equations on time scales and proposes a new perspective for the stability analysis of numerical methods. Full article
(This article belongs to the Special Issue Numerical Methods for Solving Differential Problems)
Open AccessArticle
The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game
Mathematics 2020, 8(7), 1132; https://doi.org/10.3390/math8071132 - 10 Jul 2020
Viewed by 149
Abstract
We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give [...] Read more.
We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give any advantages but affects the stability of the game’s equilibrium points. Theoretically, we prove that the equilibrium points can be destabilized through Neimark-Sacker followed by flip bifurcation. Numerically, we prove that the map describing the game is noninvertible and gives rise to several stable attractors (multistability). Furthermore, the dynamics of the map give different shapes of quite complicated attraction basins of periodic cycles. Full article
(This article belongs to the Special Issue Mathematical Analysis in Economics and Management)
Open AccessArticle
On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty
Mathematics 2020, 8(7), 1131; https://doi.org/10.3390/math8071131 - 10 Jul 2020
Viewed by 158
Abstract
In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both [...] Read more.
In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs. Full article
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
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Open AccessArticle
Packing Oblique 3D Objects
Mathematics 2020, 8(7), 1130; https://doi.org/10.3390/math8071130 - 10 Jul 2020
Viewed by 143
Abstract
Packing irregular 3D objects in a cuboid of minimum volume is considered. Each object is composed of a number of convex shapes, such as oblique and right circular cylinders, cones and truncated cones. New analytical tools are introduced to state placement constraints for [...] Read more.
Packing irregular 3D objects in a cuboid of minimum volume is considered. Each object is composed of a number of convex shapes, such as oblique and right circular cylinders, cones and truncated cones. New analytical tools are introduced to state placement constraints for oblique shapes. Using the phi-function technique, optimized packing is reduced to a nonlinear programming problem. Novel solution approach is provided and illustrated by numerical examples. Full article
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
Open AccessArticle
Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values
Mathematics 2020, 8(7), 1129; https://doi.org/10.3390/math8071129 - 10 Jul 2020
Viewed by 150
Abstract
A class of solutions are introduced by lexicographically minimizing the complaint of coalitions for cooperative games with transferable utility. Among them, the nucleolus is an important representative. From the perspective of measuring the satisfaction of coalitions with respect to a payoff vector, we [...] Read more.
A class of solutions are introduced by lexicographically minimizing the complaint of coalitions for cooperative games with transferable utility. Among them, the nucleolus is an important representative. From the perspective of measuring the satisfaction of coalitions with respect to a payoff vector, we define a family of optimal satisfaction values in this paper. The proportional division value and the proportional allocation of non-separable contribution value are then obtained by lexicographically maximizing two types of satisfaction criteria, respectively, which are defined by the lower bound and the upper bound of the core from the viewpoint of optimism and pessimism respectively. Correspondingly, we characterize these two proportional values by introducing the equal minimal satisfaction property and the associated consistency property. Furthermore, we analyze the duality of these axioms and propose more approaches to characterize these two values on basis of the dual axioms. Full article
(This article belongs to the Special Issue Game Theory)
Open AccessArticle
The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating
Mathematics 2020, 8(7), 1128; https://doi.org/10.3390/math8071128 (registering DOI) - 10 Jul 2020
Viewed by 130
Abstract
In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under [...] Read more.
In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they are well proven. It is hoped that the obtained results will be valuable in micro/nano electro-mechanical systems, especially in the manufacture and design of actuators and electro-elastic sensors. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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Open AccessArticle
Construction of Solitary Two-Wave Solutions for a New Two-Mode Version of the Zakharov-Kuznetsov Equation
Mathematics 2020, 8(7), 1127; https://doi.org/10.3390/math8071127 - 10 Jul 2020
Viewed by 157
Abstract
A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using Korsunsky’s method. This dynamical model describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction that depends on an embedded phase-velocity parameter. Three different methods are [...] Read more.
A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using Korsunsky’s method. This dynamical model describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction that depends on an embedded phase-velocity parameter. Three different methods are used to obtain exact bell-shaped soliton solutions and singular soliton solutions to the proposed model. Two-dimensional and three-dimensional plots are also provided to illustrate the interaction dynamics of the obtained two-wave exact solutions upon increasing the phase-velocity parameter. Full article
(This article belongs to the Section Computational Mathematics)
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Open AccessArticle
Trading Strategy for Market Situation Estimation Based on Hidden Markov Model
Mathematics 2020, 8(7), 1126; https://doi.org/10.3390/math8071126 - 09 Jul 2020
Viewed by 182
Abstract
Determining states of the market and scientific laws of transfer between these states is an important subject in the field of financial mathematics. According to the results of market situation estimation, formulating corresponding trading strategies can gain profits in the market through machine [...] Read more.
Determining states of the market and scientific laws of transfer between these states is an important subject in the field of financial mathematics. According to the results of market situation estimation, formulating corresponding trading strategies can gain profits in the market through machine trading. The market situation is mainly divided into three types: bull market, mixed market and bear market, and it can be further subdivided into multiple types. Using the hidden Markov model (HMM) to estimate the market situation is not restricted by linear conditions compared to the traditional use of linear models. In this paper, we first use HMM to model the market situation, perform feature analysis on the hidden state of the model input, and then estimate the three market situations, and propose the Markov situation estimation trading strategy. On this basis, we have made a more fine-grained division of the market situation and increased the number of hidden sequences in the model. Experiments verify that this method can improve the profitability of the strategy. Full article
(This article belongs to the Section Financial Mathematics)
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Open AccessArticle
Cubic q-Rung Orthopair Fuzzy Heronian Mean Operators and Their Applications to Multi-Attribute Group Decision Making
Mathematics 2020, 8(7), 1125; https://doi.org/10.3390/math8071125 - 09 Jul 2020
Viewed by 139
Abstract
The cubic q-rung orthopair fuzzy set (Cq-ROFS) contains much more information to determine the interval valued q-rung orthopair fuzzy sets (IVq-ROFSs) and q-rung orthopair fuzzy sets (q-ROFSs) simultaneously for coping with the vagueness in information. It provides more space for decision makers (DMs) [...] Read more.
The cubic q-rung orthopair fuzzy set (Cq-ROFS) contains much more information to determine the interval valued q-rung orthopair fuzzy sets (IVq-ROFSs) and q-rung orthopair fuzzy sets (q-ROFSs) simultaneously for coping with the vagueness in information. It provides more space for decision makers (DMs) to describe their opinion in the environment of fuzzy set (FS) theory. In this paper, firstly, we introduce the conception of Cq-ROFS and their characteristics. Further, the Heronian mean (HM) operator based on Cq-ROFS, called the weighted HM operator, are explored. To overcome the deficiency of HM operator and keeping in mind the partitioned structure in real decision situations, we offer Cubic q-rung orthopair fuzzy partitioned HM operator and its weighted shape. An algorithm of the proposed operators based on multi-attribute group decision making (MAGDM) problems for the selection of best alternative among the given ones is established. Lastly, we provide an example to depict the authenticity and advantages of the exposed methods by contrasting with other existing drawbacks. Full article
(This article belongs to the Section Fuzzy Set Theory)
Open AccessArticle
Analysis of the Thermoelastic Damping Effect in Electrostatically Actuated MEMS Resonators
Mathematics 2020, 8(7), 1124; https://doi.org/10.3390/math8071124 - 09 Jul 2020
Viewed by 136
Abstract
An important aspect that must be considered when designing micro-electro-mechanical systems (MEMS) for all domains, including robotics, is the thermoelastic damping which occurs when the MEMS material is subjected to cyclic stress. This paper is focused on a model for the thermoelastic damping [...] Read more.
An important aspect that must be considered when designing micro-electro-mechanical systems (MEMS) for all domains, including robotics, is the thermoelastic damping which occurs when the MEMS material is subjected to cyclic stress. This paper is focused on a model for the thermoelastic damping developed based on the generalized thermoelastic theory with the non-Fourier thermal conduction equation. The model was implemented in MATLAB and several simulations were performed. The theoretical results show a decrease in the deflection amplitude with the increase in time. The deflection amplitude decrease was validated by the experimental investigations, consisting of measuring the loss in amplitude and velocity of oscillations as a function of time. Moreover, this paper also presents the influence of the geometric dimensions on the mentioned decrease, as well as on the initial and final values of the amplitude for several polysilicon resonators investigated in this paper. Full article
(This article belongs to the Special Issue New Formulations in the Applied Mechanics to Robotics)
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Open AccessArticle
Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration
Mathematics 2020, 8(7), 1123; https://doi.org/10.3390/math8071123 - 09 Jul 2020
Viewed by 159
Abstract
We considered the time-inhomogeneous linear birth–death processes with immigration. For these processes closed form expressions for the transition probabilities were obtained in terms of the complete Bell polynomials. The conditional mean and the conditional variance were explicitly evaluated. Several time-inhomogeneous processes were studied [...] Read more.
We considered the time-inhomogeneous linear birth–death processes with immigration. For these processes closed form expressions for the transition probabilities were obtained in terms of the complete Bell polynomials. The conditional mean and the conditional variance were explicitly evaluated. Several time-inhomogeneous processes were studied in detail in view of their potential applications in population growth models and in queuing systems. A time-inhomogeneous linear birth–death processes with finite state-space was also taken into account. Special attention was devoted to the cases of periodic immigration intensity functions that play an important role in the description of the evolution of dynamic systems influenced by seasonal immigration or other regular environmental cycles. Various numerical computations were performed for periodic immigration intensity functions. Full article
(This article belongs to the Special Issue Stochastic Modeling in Biology)
Open AccessArticle
dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS
Mathematics 2020, 8(7), 1122; https://doi.org/10.3390/math8071122 - 09 Jul 2020
Viewed by 141
Abstract
We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of [...] Read more.
We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of the discrete measure keeping the reached G-efficiency, via an accelerated version of the Lawson-Hanson algorithm for Non-Negative Least Squares (NNLS) problems. This package can solve on a personal computer large-scale problems where c a r d ( X ) × dim ( P 2 m d ) is up to 10 8 10 9 , being dim ( P 2 m d ) = 2 m + d d = 2 m + d 2 m . Several numerical tests are presented on complex shapes in d = 3 and on hypercubes in d > 3 . Full article
(This article belongs to the Special Issue Numerical Methods)
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Open AccessArticle
Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model
Mathematics 2020, 8(7), 1121; https://doi.org/10.3390/math8071121 - 09 Jul 2020
Viewed by 144
Abstract
On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional [...] Read more.
On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy β -covering (FOF β -covering) and fractional orthotriple fuzzy β -neighborhood (FOF β -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
Open AccessFeature PaperArticle
Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis
Mathematics 2020, 8(7), 1120; https://doi.org/10.3390/math8071120 - 09 Jul 2020
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Abstract
Epilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it [...] Read more.
Epilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it have some adverse effects, which influence the quality of life outcomes of the patients. In this paper, we study the effectiveness of anti-epileptic drugs taking into account the inherent uncertainty. We establish a model, which allows to represent the natural history of epilepsy, using Markov chains. After randomizing the mathematical model, we compute the first probability density function of the solution stochastic process applying the random variable transformation technique. We also take advantage of this method to determine the distribution of some key quantities in medical decision, such as the time until a certain proportion of the population remains in each state and the incremental cost-effectiveness ratio. The study is completed computing all these quantities using data available in the literature. In addition, regarding the incremental cost-effectiveness ratio, different third generation anti-epileptic treatments are compared with the Brivaracetam, a new third generation anti-epileptic drug. Full article
(This article belongs to the Special Issue Advances on Uncertainty Quantification: Theory and Modelling)
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Open AccessArticle
Entropy-Randomized Forecasting of Stochastic Dynamic Regression Models
Mathematics 2020, 8(7), 1119; https://doi.org/10.3390/math8071119 - 08 Jul 2020
Viewed by 152
Abstract
We propose a new forecasting procedure that includes randomized hierarchical dynamic regression models with random parameters, measurement noises and random input. We developed the technology of entropy-randomized machine learning, which includes the estimation of characteristics of a dynamic regression model and its testing [...] Read more.
We propose a new forecasting procedure that includes randomized hierarchical dynamic regression models with random parameters, measurement noises and random input. We developed the technology of entropy-randomized machine learning, which includes the estimation of characteristics of a dynamic regression model and its testing by generating ensembles of predicted trajectories through the sampling of the entropy-optimal probability density functions of the model parameters and measurement noises. The density functions are determined at the learning stage by solving the constrained maximization problem of an information entropy functional subject to the empirical balances with real data. The proposed procedure is applied to the randomized forecasting of the daily electrical load in a regional power system. We construct a two-layer dynamic model of the daily electrical load. One of the layers describes the dependence of electrical load on ambient temperature while the other simulates the stochastic quasi-fluctuating temperature dynamics. Full article
(This article belongs to the Special Issue Machine Learning and Data Mining in Pattern Recognition)
Open AccessArticle
Starlikness Associated with Cosine Hyperbolic Function
Mathematics 2020, 8(7), 1118; https://doi.org/10.3390/math8071118 - 08 Jul 2020
Viewed by 89
Abstract
The main contribution of this article is to define a family of starlike functions associated with a cosine hyperbolic function. We investigate convolution conditions, integral preserving properties, and coefficient sufficiency criteria for this family. We also study the differential subordinations problems which relate [...] Read more.
The main contribution of this article is to define a family of starlike functions associated with a cosine hyperbolic function. We investigate convolution conditions, integral preserving properties, and coefficient sufficiency criteria for this family. We also study the differential subordinations problems which relate the Janowski and cosine hyperbolic functions. Furthermore, we use these results to obtain sufficient conditions for starlike functions connected with cosine hyperbolic function. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
Open AccessReview
History, Developments and Open Problems on Approximation Properties
Mathematics 2020, 8(7), 1117; https://doi.org/10.3390/math8071117 - 07 Jul 2020
Viewed by 229
Abstract
In this paper, we give a comprehensive review of the classical approximation property. Then, we present some important results on modern variants, such as the weak bounded approximation property, the strong approximation property and p-approximation property. Most recent progress on E-approximation [...] Read more.
In this paper, we give a comprehensive review of the classical approximation property. Then, we present some important results on modern variants, such as the weak bounded approximation property, the strong approximation property and p-approximation property. Most recent progress on E-approximation property and open problems are discussed at the end. Full article
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics)
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