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Mathematics, Volume 8, Issue 2 (February 2020) – 137 articles

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Cover Story (view full-size image) Stochastic models for oscillatory phenomena can be obtained from deterministic ones, e.g., the [...] Read more.
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Open AccessArticle
An Extended EDAS Method with a Single-Valued Complex Neutrosophic Set and Its Application in Green Supplier Selection
Mathematics 2020, 8(2), 282; https://doi.org/10.3390/math8020282 (registering DOI) - 19 Feb 2020
Abstract
The single-valued complex neutrosophic set is a useful tool for handling the data with uncertainty and periodicity. In this paper, a single-valued complex neutrosophic EDAS (evaluation based on distance from average slution) model has been established and applied in green supplier selection. Firstly, [...] Read more.
The single-valued complex neutrosophic set is a useful tool for handling the data with uncertainty and periodicity. In this paper, a single-valued complex neutrosophic EDAS (evaluation based on distance from average slution) model has been established and applied in green supplier selection. Firstly, the definition of single-valued complex neutrosophic set and corresponding operational laws are briefly introduced. Next, to fuse overall single-valued complex neutrosophic information, the SVCNEWA and SVCNEWG operators based on single-valued complex neutrosophic set, Einstein product and sum are proposed. Furthermore, the single-valued complex neutrosophic EDAS model has been established and all computing steps have been depicted in detail. Finally, a numerical example of green supplier selection and a comparison analysis have been given to illustrate the practicality and effectiveness of this new model. Full article
Open AccessArticle
Alternating Asymmetric Iterative Algorithm Based on Domain Decomposition for 3D Poisson Problem
Mathematics 2020, 8(2), 281; https://doi.org/10.3390/math8020281 (registering DOI) - 19 Feb 2020
Abstract
Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several [...] Read more.
Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several sub-domains, and eight asymmetric iterative schemes with the relaxation factor for 3D Poisson equation are constructed. When the numbers of iteration are odd or even, the computational process of the presented iterative algorithm are proposed respectively. In the calculation of the inner interfaces, the group explicit method is used, which makes the algorithm to be performed fast and in parallel, and avoids the difficulty of solving large-scale linear equations. Furthermore, the convergence of the algorithm is analyzed theoretically. Finally, by comparing with the numerical experimental results of Jacobi and Gauss Seidel iterative algorithms, it is shown that the alternating asymmetric iterative algorithm based on domain decomposition has shorter computation time, fewer iteration numbers and good parallelism. Full article
(This article belongs to the Special Issue Multivariate Approximation for solving ODE and PDE)
Open AccessArticle
A Spectral Conjugate Gradient Method with Descent Property
Mathematics 2020, 8(2), 280; https://doi.org/10.3390/math8020280 (registering DOI) - 19 Feb 2020
Abstract
Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a [...] Read more.
Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral parameter. Second, we propose a hybrid conjugate parameter. Such a way for yielding the two parameters can ensure that the search directions always possess descent property without depending on any line search rule. As a result, a new SCGM with the standard Wolfe line search is proposed. Under usual assumptions, the global convergence of the proposed SCGM is proved. Finally, by testing 108 test instances from 2 to 1,000,000 dimensions in the CUTE library and other classic test collections, a large number of numerical experiments, comparing with both SCGMs and CGMs, for the presented SCGM are executed. The detail results and their corresponding performance profiles are reported, which show that the proposed SCGM is effective and promising. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
Open AccessArticle
A Novel Tabu Search Algorithm for Multi-AGV Routing Problem
Mathematics 2020, 8(2), 279; https://doi.org/10.3390/math8020279 (registering DOI) - 19 Feb 2020
Abstract
In this paper, we propose a novel tabu search (NTS) algorithm that improves the efficiencies of picking goods of automated guided vehicles (AGVs) in an automatic warehouse by solving the conflicts that happen when multiple AGVs work at the same time. Relocation and [...] Read more.
In this paper, we propose a novel tabu search (NTS) algorithm that improves the efficiencies of picking goods of automated guided vehicles (AGVs) in an automatic warehouse by solving the conflicts that happen when multiple AGVs work at the same time. Relocation and exchanging operations are designed for the neighborhood searching process based on each pickup-point’s location in the warehouse, along with the initial solution generation and the termination condition in the proposed algorithm. The experimental results show that the tabu search algorithm can effectively optimize the order of pickup points, which could further reduce the total travel distance and improve the efficiencies of AGVs in automatic warehouses. Full article
(This article belongs to the Section Mathematics and Computer Science)
Open AccessFeature PaperArticle
On Reliability of a Double Redundant Renewable System with a Generally Distributed Life and Repair Times
Mathematics 2020, 8(2), 278; https://doi.org/10.3390/math8020278 (registering DOI) - 19 Feb 2020
Abstract
The paper provides reliability analysis of a cold double redundant renewable system assuming that both life-time and repair time distributions are arbitrary. The proposed approach is based on the theory of decomposable semi-regenerative processes. We derive the Laplace–Stieltjes transform of two main reliability [...] Read more.
The paper provides reliability analysis of a cold double redundant renewable system assuming that both life-time and repair time distributions are arbitrary. The proposed approach is based on the theory of decomposable semi-regenerative processes. We derive the Laplace–Stieltjes transform of two main reliability measures like the distribution of the time between failures and the time to the first failure. The transforms are used to calculate corresponding mean times. It is further derived in closed form the time-dependent and time stationary state probabilities in terms of the Laplace transforms. Numerical results illustrate the effect of the type of distributions as well as their parameters on the derived reliability and probabilistic measures. Full article
Open AccessArticle
Relevant Aspects for an EF3-Evaluation of E-Cognocracy
Mathematics 2020, 8(2), 277; https://doi.org/10.3390/math8020277 (registering DOI) - 19 Feb 2020
Abstract
The search for an appropriate response to the new challenges and needs posed by the Knowledge Society in the area of public decisions has led to the development of a number of participation models whose value must be assessed and analysed in an [...] Read more.
The search for an appropriate response to the new challenges and needs posed by the Knowledge Society in the area of public decisions has led to the development of a number of participation models whose value must be assessed and analysed in an integral manner. Using a theoretical model based on structural equations, the present work identifies the relevant factors for an EF3-approach to the democracy model named e-Cognocracy: it comprises a conjoint evaluation of its effectiveness (doing what is right), efficacy (achieving goals) and efficiency (doing things correctly). The model was applied to a real-life e-Cognocracy experience undertaken in the municipality of Cadrete, Zaragoza. The evaluation resulted in the extraction and identification of a series of relationships that allow the advancement of an EF3-participation acceptance model, in line with the TAM model of Davis and the work of Delone and MacLean, which can be used for the integral evaluation of any e-participation model. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
Open AccessArticle
A Bradley-Terry Model-Based Approach to Prioritize the Balance Scorecard Driving Factors: The Case Study of a Financial Software Factory
Mathematics 2020, 8(2), 276; https://doi.org/10.3390/math8020276 (registering DOI) - 19 Feb 2020
Abstract
The prioritization of factors has been widely studied applying different methods from the domain of the multiple-criteria decision-making, such as for example the Analytic Hierarchy Process method (AHP) based on decision-makers’ pairwise comparisons. Most of these methods are subjected to a complex analysis. [...] Read more.
The prioritization of factors has been widely studied applying different methods from the domain of the multiple-criteria decision-making, such as for example the Analytic Hierarchy Process method (AHP) based on decision-makers’ pairwise comparisons. Most of these methods are subjected to a complex analysis. The Bradley-Terry model is a probability model for paired evaluations. Although this model is usually known for its application to calculating probabilities, it can be also extended for ranking factors based on pairwise comparison. This application is much less used; however, this work shows that it can provide advantages, such as greater simplicity than traditional multiple-criteria decision methods in some contexts. This work presents a method for ranking the perspectives and indicators of a balance scorecard when the opinion of several decision-makers needs to be combined. The data come from an elicitation process, accounting for the number of times a factor is preferred to others by the decision-makers in a pairwise comparisons. No preference scale is used; the process just indicates the winner of the comparison. Then, the priority weights are derived from the Bradley-Terry model. The method is applied in a Financial Software Factory for demonstration and validation. The results are compared against the application of the AHP method for the same data, concluding that despite the simplifications made with the new approach, the results are very similar. The study contributes to the multiple-criteria decision-making domain by building an integrated framework, which can be used as a tool for scorecard prioritization. Full article
Open AccessArticle
A Constrained Production System Involving Production Flexibility and Carbon Emissions
Mathematics 2020, 8(2), 275; https://doi.org/10.3390/math8020275 (registering DOI) - 19 Feb 2020
Abstract
The proposed study presents an economic lot size and production rate model for a single vendor and a single buyer setup. This model involves greenhouse gas (GHG) emissions from industrial sources. The carbon emissions in this model are considered as two types: direct [...] Read more.
The proposed study presents an economic lot size and production rate model for a single vendor and a single buyer setup. This model involves greenhouse gas (GHG) emissions from industrial sources. The carbon emissions in this model are considered as two types: direct emissions and indirect emissions. The production rate affects carbon emissions generation in production, i.e., generally, higher production rates result in more emissions, which is governable in many real-life cases. The production rate also impacts the process reliability and quality. Faster production deteriorates the production system quickly, leading to machine failure and defective items. Such reliability and quality problems increase energy consumptions and supply chain (SC) costs. This paper formulates a vendor-buyer SC model that tackles these issues. It considers two decision-making policies: integrated or centralized as well as decentralized, where the aim is to obtain the optimal values of the decision variables that give the minimum total SC cost. It includes the costs of setup, holding inventory, carbon emissions, order processing, production, reworking, and inspection processes. The decision variables are the production rate, lead time, order quantity, the number of shipments, and the investments for setup cost reduction. In the later sections, this paper compares the numerical outcomes of the two centralized and decentralized policies. It also provides sensitivity analysis and useful insights on the economic and environmental execution of the SC. Full article
(This article belongs to the Section Mathematics and Computer Science)
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Open AccessArticle
Impact on Stability by the Use of Memory in Traub-Type Schemes
Mathematics 2020, 8(2), 274; https://doi.org/10.3390/math8020274 - 18 Feb 2020
Viewed by 131
Abstract
In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub’s method, they have been designed using linear approximations or the Newton’s interpolation polynomials. In both cases, the [...] Read more.
In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub’s method, they have been designed using linear approximations or the Newton’s interpolation polynomials. In both cases, the parameters use information from the current and the previous iterations, so they define a method with memory. Moreover, they achieve higher order of convergence than Traub’s scheme without any additional functional evaluations. The real dynamical analysis verifies that the proposed methods with memory not only converge faster, but they are also more stable than the original scheme. The methods selected by means of this analysis can be applied for solving nonlinear problems with a wider set of initial estimations than their original partners. This fact also involves a lower number of iterations in the process. Full article
Open AccessFeature PaperArticle
Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results
Mathematics 2020, 8(2), 273; https://doi.org/10.3390/math8020273 - 18 Feb 2020
Viewed by 134
Abstract
With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see “Am. Math. Month. 1967, 74, 436–437”) that a [...] Read more.
With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see “Am. Math. Month. 1967, 74, 436–437”) that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see “Fixed Point Theory 2005, 6, 71–78”) also allows us to characterize the fuzzy metric completeness. Full article
Open AccessArticle
A Multisecret-Sharing Scheme Based on LCD Codes
Mathematics 2020, 8(2), 272; https://doi.org/10.3390/math8020272 - 18 Feb 2020
Viewed by 80
Abstract
Secret sharing is one of the most important cryptographic protocols. Secret sharing schemes (SSS) have been created to that end. This protocol requires a dealer and several participants. The dealer divides the secret into several pieces ( the shares), and one share is [...] Read more.
Secret sharing is one of the most important cryptographic protocols. Secret sharing schemes (SSS) have been created to that end. This protocol requires a dealer and several participants. The dealer divides the secret into several pieces ( the shares), and one share is given to each participant. The secret can be recovered once a subset of the participants (a coalition) shares their information. In this paper, we present a new multisecret-sharing scheme inspired by Blakley’s method based on hyperplanes intersection but adapted to a coding theoretic situation. Unique recovery requires the use of linear complementary (LCD) codes, that is, codes in which intersection with their duals is trivial. For a given code length and dimension, our system allows dealing with larger secrets and more users than other code-based schemes. Full article
(This article belongs to the Special Issue Algebra and Its Applications)
Open AccessArticle
A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems
Mathematics 2020, 8(2), 271; https://doi.org/10.3390/math8020271 - 18 Feb 2020
Viewed by 81
Abstract
Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as [...] Read more.
Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu’s, Fisher’s, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes. Full article
Open AccessArticle
A Novel Meshfree Approach with a Radial Polynomial for Solving Nonhomogeneous Partial Differential Equations
Mathematics 2020, 8(2), 270; https://doi.org/10.3390/math8020270 - 18 Feb 2020
Viewed by 76
Abstract
In this article, a novel radial–based meshfree approach for solving nonhomogeneous partial differential equations is proposed. Stemming from the radial basis function collocation method, the novel meshfree approach is formulated by incorporating the radial polynomial as the basis function. The solution of the [...] Read more.
In this article, a novel radial–based meshfree approach for solving nonhomogeneous partial differential equations is proposed. Stemming from the radial basis function collocation method, the novel meshfree approach is formulated by incorporating the radial polynomial as the basis function. The solution of the nonhomogeneous partial differential equation is therefore approximated by the discretization of the governing equation using the radial polynomial basis function. To avoid the singularity, the minimum order of the radial polynomial basis function must be greater than two for the second order partial differential equations. Since the radial polynomial basis function is a non–singular series function, accurate numerical solutions may be obtained by increasing the terms of the radial polynomial. In addition, the shape parameter in the radial basis function collocation method is no longer required in the proposed method. Several numerical implementations, including homogeneous and nonhomogeneous Laplace and modified Helmholtz equations, are conducted. The results illustrate that the proposed approach may obtain highly accurate solutions with the use of higher order radial polynomial terms. Finally, compared with the radial basis function collocation method, the proposed approach may produce more accurate solutions than the other. Full article
(This article belongs to the Special Issue Numerical Modeling and Analysis)
Open AccessArticle
Cumulative Sum Chart Modeled under the Presence of Outliers
Mathematics 2020, 8(2), 269; https://doi.org/10.3390/math8020269 - 18 Feb 2020
Viewed by 82
Abstract
Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width [...] Read more.
Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey’s outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals’ movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II. Full article
(This article belongs to the Special Issue Statistics and Modeling in Reliability Engineering)
Open AccessArticle
Initialization Methods for Multiple Seasonal Holt–Winters Forecasting Models
Mathematics 2020, 8(2), 268; https://doi.org/10.3390/math8020268 - 18 Feb 2020
Viewed by 76
Abstract
The Holt–Winters models are one of the most popular forecasting algorithms. As well-known, these models are recursive and thus, an initialization value is needed to feed the model, being that a proper initialization of the Holt–Winters models is crucial for obtaining a good [...] Read more.
The Holt–Winters models are one of the most popular forecasting algorithms. As well-known, these models are recursive and thus, an initialization value is needed to feed the model, being that a proper initialization of the Holt–Winters models is crucial for obtaining a good accuracy of the predictions. Moreover, the introduction of multiple seasonal Holt–Winters models requires a new development of methods for seed initialization and obtaining initial values. This work proposes new initialization methods based on the adaptation of the traditional methods developed for a single seasonality in order to include multiple seasonalities. Thus, new methods to initialize the level, trend, and seasonality in multiple seasonal Holt–Winters models are presented. These new methods are tested with an application for electricity demand in Spain and analyzed for their impact on the accuracy of forecasts. As a consequence of the analysis carried out, which initialization method to use for the level, trend, and seasonality in multiple seasonal Holt–Winters models with an additive and multiplicative trend is provided. Full article
(This article belongs to the Section Financial Mathematics)
Open AccessFeature PaperArticle
A New Look at the Single Ladder Problem (SLP) via Integer Parametric Solutions to the Corresponding Quartic Equation
Mathematics 2020, 8(2), 267; https://doi.org/10.3390/math8020267 - 18 Feb 2020
Viewed by 118
Abstract
The aim is to put new light on the single ladder problem (SLP). Some new methods for finding complete integer solutions to the corresponding quartic equation z 4 2 L z 3 + ( L 2 a 2 b 2 [...] Read more.
The aim is to put new light on the single ladder problem (SLP). Some new methods for finding complete integer solutions to the corresponding quartic equation z 4 2 L z 3 + ( L 2 a 2 b 2 ) z 2 + 2 L a 2 z L 2 a 2 = 0 are developed. For the case L L min , these methods imply a complete parametric representation for integer solutions of SLP in the first quadrant. Some corresponding (less complete) results for the case L > L min are also pointed out. Full article
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Open AccessArticle
Self-Similar Inverse Semigroups from Wieler Solenoids
Mathematics 2020, 8(2), 266; https://doi.org/10.3390/math8020266 - 17 Feb 2020
Viewed by 136
Abstract
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs [...] Read more.
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs and the tight groupoids of these inverse semigroups are equivalent to the unstable groupoids of Wieler solenoids. We also show that the C -algebras of the groupoids of germs have a unique tracial state. Full article
(This article belongs to the Special Issue Operator Algebras)
Open AccessArticle
Modified Accelerated Bundle-Level Methods and Their Application in Two-Stage Stochastic Programming
Mathematics 2020, 8(2), 265; https://doi.org/10.3390/math8020265 - 17 Feb 2020
Viewed by 98
Abstract
The accelerated prox-level (APL) and uniform smoothing level (USL) methods recently proposed by Lan (Math Program, 149: 1–45, 2015) can achieve uniformly optimal complexity when solving black-box convex programming (CP) and structure non-smooth CP problems. In this paper, we propose two modified accelerated [...] Read more.
The accelerated prox-level (APL) and uniform smoothing level (USL) methods recently proposed by Lan (Math Program, 149: 1–45, 2015) can achieve uniformly optimal complexity when solving black-box convex programming (CP) and structure non-smooth CP problems. In this paper, we propose two modified accelerated bundle-level type methods, namely, the modified APL (MAPL) and modified USL (MUSL) methods. Compared with the original APL and USL methods, the MAPL and MUSL methods reduce the number of subproblems by one in each iteration, thereby improving the efficiency of the algorithms. Conclusions of optimal iteration complexity of the proposed algorithms are established. Furthermore, the modified methods are applied to the two-stage stochastic programming, and numerical experiments are implemented to illustrate the advantages of our methods in terms of efficiency and accuracy. Full article
(This article belongs to the Special Issue Computational Methods in Applied Analysis and Mathematical Modeling)
Open AccessArticle
Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples
Mathematics 2020, 8(2), 264; https://doi.org/10.3390/math8020264 - 17 Feb 2020
Viewed by 130
Abstract
Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate [...] Read more.
Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions. Full article
(This article belongs to the Section Computational Mathematics)
Open AccessArticle
Fuzzy Reduced Hypergroups
Mathematics 2020, 8(2), 263; https://doi.org/10.3390/math8020263 - 17 Feb 2020
Viewed by 93
Abstract
The fuzzyfication of hypercompositional structures has developed in several directions. In this note we follow one direction and extend the classical concept of reducibility in hypergroups to the fuzzy case. In particular we define and study the fuzzy reduced hypergroups. New fundamental relations [...] Read more.
The fuzzyfication of hypercompositional structures has developed in several directions. In this note we follow one direction and extend the classical concept of reducibility in hypergroups to the fuzzy case. In particular we define and study the fuzzy reduced hypergroups. New fundamental relations are defined on a crisp hypergroup endowed with a fuzzy set, that lead to the concept of fuzzy reduced hypergroup. This is a hypergroup in which the equivalence class of any element, with respect to a determined fuzzy set, is a singleton. The most well known fuzzy set considered on a hypergroup is the grade fuzzy set, used for the study of the fuzzy grade of a hypergroup. Based on this, in the second part of the paper, we study the fuzzy reducibility of some particular classes of crisp hypergroups with respect to the grade fuzzy set. Full article
(This article belongs to the Special Issue Hypercompositional Algebra and Applications)
Open AccessArticle
Mobile User Location Inference Attacks Fusing with Multiple Background Knowledge in Location-Based Social Networks
Mathematics 2020, 8(2), 262; https://doi.org/10.3390/math8020262 - 17 Feb 2020
Viewed by 127
Abstract
Location-based social networks have been widely used. However, due to the lack of effective and safe data management, a large number of privacy disclosures commonly occur. Thus, academia and industry have needed to focus more on location privacy protection. This paper proposes a [...] Read more.
Location-based social networks have been widely used. However, due to the lack of effective and safe data management, a large number of privacy disclosures commonly occur. Thus, academia and industry have needed to focus more on location privacy protection. This paper proposes a novel location attack method using multiple background options to infer the hidden locations of mobile users. In order to estimate the possibility of a hidden position being visited by a user, two hidden location attack models are proposed, i.e., a Bayesian hidden location inference model and the multi-factor fusion based hidden location inference model. Multiple background factors, including the check-in sequences, temporal information, user social networks, personalized service preferences, point of interest (POI) popularities, etc., are considered in the two models. Moreover, a hidden location inference algorithm is provided as well. Finally, a series of experiments are conducted on two real check-in data examples to evaluate the accuracy of the model and verify the validity of the proposed algorithm. The experimental results show that multiple background knowledge fusion provides benefits for improving location inference precision. Full article
(This article belongs to the Section Mathematics and Computer Science)
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Open AccessArticle
An Alternative Approach to Measure Co-Movement between Two Time Series
Mathematics 2020, 8(2), 261; https://doi.org/10.3390/math8020261 - 17 Feb 2020
Viewed by 96
Abstract
The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were [...] Read more.
The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were proposed by researchers. ARCH, GARCH or EGARCH models, among others, are very popular to model volatility autocorrelation. In this paper, a new simple method called HP is introduced to measure the co-movement between two time series. This method, based on the Hurst exponent of the product series, is designed to detect correlation, even if the relationship is weak, but it also works fine with cointegration as well as non linear correlations or more complex relationships given by a copula. This method and different variations thereaof are tested in statistical arbitrage. Results show that HP is able to detect the relationship between assets better than the traditional correlation method. Full article
(This article belongs to the Section Financial Mathematics)
Open AccessArticle
Clones of Terms of a Fixed Variable
Mathematics 2020, 8(2), 260; https://doi.org/10.3390/math8020260 - 17 Feb 2020
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Abstract
Let τ be a type of algebras. This paper introduces special terms of type τ called terms of a fixed variable. It turns out that the set of all terms of a fixed variable of type τ forms the many-sorted clone satisfying the [...] Read more.
Let τ be a type of algebras. This paper introduces special terms of type τ called terms of a fixed variable. It turns out that the set of all terms of a fixed variable of type τ forms the many-sorted clone satisfying the superassociative law as identity, under the many-sorted superposition operations. Moreover, based on terms of a fixed variable of type τ , hypersubstitutions of a fixed variable and the related closed identities of a fixed variable and closed variety of a fixed variable are introduced and studied. Full article
(This article belongs to the Section Mathematics and Computer Science)
Open AccessFeature PaperArticle
Responsive Economic Model Predictive Control for Next-Generation Manufacturing
Mathematics 2020, 8(2), 259; https://doi.org/10.3390/math8020259 - 16 Feb 2020
Viewed by 199
Abstract
There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance [...] Read more.
There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types would advance the move toward artificial intelligence properties for this controller beyond those which it has today and would provide new thoughts on interpretability and verification for the controller. This work provides theoretical studies which relate nonlinear systems considerations for EMPC to these higher-level concepts using two ideas for EMPC formulations motivated by specific situations related to self-modification of a control design after human perceptions of the process response are received and to controller handling of anomalies. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
Open AccessArticle
Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection
Mathematics 2020, 8(2), 258; https://doi.org/10.3390/math8020258 - 16 Feb 2020
Viewed by 169
Abstract
We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted [...] Read more.
We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example. Full article
(This article belongs to the Section Mathematics and Computer Science)
Open AccessArticle
A Parameter Identification Method for Stewart Manipulator Based on Wavelet Transform
Mathematics 2020, 8(2), 257; https://doi.org/10.3390/math8020257 - 15 Feb 2020
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Abstract
Aiming at inertial and viscous parameter identification for the Stewart manipulator regardless of the influence of Coulomb friction, a simple and effective dynamical parameter identification method based on wavelet transform and joint velocity analysis is proposed in this paper. Compared with previously known [...] Read more.
Aiming at inertial and viscous parameter identification for the Stewart manipulator regardless of the influence of Coulomb friction, a simple and effective dynamical parameter identification method based on wavelet transform and joint velocity analysis is proposed in this paper. Compared with previously known identification methods, the advantages of the new approach are that (1) the excitation trajectory is easy to design, and (2) it can not only identify the inertial matrix, but also the viscous matrix accurately regardless of the influence of Coulomb friction. Comparison is made among the identification method proposed in this paper, another identification method proposed previously, and the true value calculated with a formula. The errors from results of different identification methods demonstrate that the method proposed in this paper shows great adaptability and accuracy. Full article
(This article belongs to the Special Issue Applied Mathematical Methods in Mechanical Engineering)
Open AccessArticle
Modeling Y-Linked Pedigrees through Branching Processes
Mathematics 2020, 8(2), 256; https://doi.org/10.3390/math8020256 - 15 Feb 2020
Viewed by 118
Abstract
A multidimensional two-sex branching process is introduced to model the evolution of a pedigree originating from the mutation of an allele of a Y-linked gene in a monogamous population. The study of the extinction of the mutant allele and the analysis of the [...] Read more.
A multidimensional two-sex branching process is introduced to model the evolution of a pedigree originating from the mutation of an allele of a Y-linked gene in a monogamous population. The study of the extinction of the mutant allele and the analysis of the dominant allele in the pedigree is addressed on the basis of the classical theory of multi-type branching processes. The asymptotic behavior of the number of couples of different types in the pedigree is also derived. Finally, using the estimates of the mean growth rates of the allele and its mutation provided by a Gibbs sampler, a real Y-linked pedigree associated with hearing loss is analyzed, concluding that this mutation will persist in the population although without dominating the pedigree. Full article
(This article belongs to the Special Issue Stochastic Modeling in Biology)
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Open AccessArticle
Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions
Mathematics 2020, 8(2), 255; https://doi.org/10.3390/math8020255 - 14 Feb 2020
Viewed by 146
Abstract
This paper deals with the study of the existence and non-existence of solutions of a three-parameter family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the α -Riemann-Liouville fractional derivative, with α ( 1 , 2 ] . [...] Read more.
This paper deals with the study of the existence and non-existence of solutions of a three-parameter family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the α -Riemann-Liouville fractional derivative, with α ( 1 , 2 ] . To deduce the existence and non-existence results, we first study the linear equation, by deducing the main properties of the related Green functions. We obtain the optimal set of parameters where the Green function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results. Full article
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)
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Open AccessArticle
Divisibility Patterns within Pascal Divisibility Networks
Mathematics 2020, 8(2), 254; https://doi.org/10.3390/math8020254 - 14 Feb 2020
Viewed by 200
Abstract
The Pascal triangle is so simple and rich that it has always attracted the interest of professional and amateur mathematicians. Their coefficients satisfy a myriad of properties. Inspired by the work of Shekatkar et al., we study the divisibility patterns within the elements [...] Read more.
The Pascal triangle is so simple and rich that it has always attracted the interest of professional and amateur mathematicians. Their coefficients satisfy a myriad of properties. Inspired by the work of Shekatkar et al., we study the divisibility patterns within the elements of the Pascal triangle, through its decomposition into Pascal’s matrices, from the perspective of network science. Applying Kolmogorov–Smirnov test, we determine that the degree distribution of the resulting network follows a power-law distribution. We also study degrees, global and local clustering coefficients, stretching graph, averaged path length and the mixing assortative. Full article
(This article belongs to the Section Network Science)
Open AccessFeature PaperReview
Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains
Mathematics 2020, 8(2), 253; https://doi.org/10.3390/math8020253 - 14 Feb 2020
Viewed by 152
Abstract
This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the [...] Read more.
This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the construction of perturbation estimates for the main five classes of such chains associated with queuing models. Several specific models are considered for which the limit characteristics and perturbation bounds for admissible “perturbed” processes are calculated. Full article
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
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