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Mathematics, Volume 8, Issue 2 (February 2020) – 156 articles

Cover Story (view full-size image): Stochastic models for oscillatory phenomena can be obtained from deterministic ones, e.g., the oscillabolastic model. Following modified ODEs, diffusion processes for oscillabolastic growth are considered. Parameter estimation requires numerical methods, and strategies for initial solutions are proposed, taking advantage of some properties. View this paper.
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Open AccessArticle
Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding
Mathematics 2020, 8(2), 301; https://doi.org/10.3390/math8020301 - 24 Feb 2020
Cited by 1 | Viewed by 603
Abstract
The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. [...] Read more.
The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. In this paper, we adopt a kind of explicit interaction index, the nonadditivity index, to construct two types of quasi-random generation methods of capacity under a given decision interaction preference. Compared to the existing random generation algorithms, the methods have relatively satisfactory performance on the statistics characteristic of generated capacities but need rather less calculation effort on the generation process. We also show the effectiveness of proposed quasi-random generation methods by an illustrative decision example. Full article
(This article belongs to the Section Mathematics and Computer Science)
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Open AccessArticle
Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding
Mathematics 2020, 8(2), 300; https://doi.org/10.3390/math8020300 - 24 Feb 2020
Cited by 4 | Viewed by 631
Abstract
The identification of partially observed continuous nonlinear systems from noisy and incomplete data series is an actual problem in many branches of science, for example, biology, chemistry, physics, and others. Two stages are needed to reconstruct a partially observed dynamical system. First, one [...] Read more.
The identification of partially observed continuous nonlinear systems from noisy and incomplete data series is an actual problem in many branches of science, for example, biology, chemistry, physics, and others. Two stages are needed to reconstruct a partially observed dynamical system. First, one should reconstruct the entire phase space to restore unobserved state variables. For this purpose, the integration or differentiation of the observed data series can be performed. Then, a fast-algebraic method can be used to obtain a nonlinear system in the form of a polynomial dynamical system. In this paper, we extend the algebraic method proposed by Kera and Hasegawa to Laurent polynomials which contain negative powers of variables, unlike ordinary polynomials. We provide a theoretical basis and experimental evidence that the integration of a data series can give more accurate results than the widely used differentiation. With this technique, we reconstruct Lorenz attractor from a one-dimensional data series and B. Muthuswamy’s circuit equations from a three-dimensional data series. Full article
(This article belongs to the Section Dynamical Systems)
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Open AccessArticle
Information Length as a Useful Index to Understand Variability in the Global Circulation
Mathematics 2020, 8(2), 299; https://doi.org/10.3390/math8020299 - 24 Feb 2020
Cited by 2 | Viewed by 626
Abstract
With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. [...] Read more.
With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability Density Functions (PDFs) miss crucial information about the dynamics associated with variability. It is thus critical to go beyond a traditional approach and deal with time-dependent PDFs. Here, we consider atmospheric data from the Whole Atmosphere Community Climate Model (WACCM) and calculate time-dependent PDFs and the information length from these PDFs, which is the total number of statistically different states that a system evolves through in time. Specifically, we consider the three cases of sampling data to investigate the distribution of information (information budget) along the altitude and longitude to gain a new perspective of understanding variabilities, correlation among different variables and regions. Time-dependent PDFs are shown to be non-Gaussian in general; the information length tends to increase with the altitude albeit in a complex form; this tendency is more robust for flows/shears than temperature. Much similarity among flows and shears in the information length is also found in comparison with the temperature. This means a strong correlation among flows/shears because of their coupling through gravity waves in this particular WACCM model. We also find the increase of the information length with the latitude and interesting hemispheric asymmetry for flows/shears/temperature, with the tendency of anti-correlation (correlation) between flows/shears and temperature at high (low) latitude. These results suggest the importance of high latitude/altitude in the information budget in the Earth’s atmosphere, the spatial gradient of the information length being a useful proxy for information flow. Full article
(This article belongs to the Special Issue Turbulence Modeling)
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Open AccessArticle
A Deep Learning Algorithm for the Max-Cut Problem Based on Pointer Network Structure with Supervised Learning and Reinforcement Learning Strategies
Mathematics 2020, 8(2), 298; https://doi.org/10.3390/math8020298 - 22 Feb 2020
Cited by 2 | Viewed by 1309
Abstract
The Max-cut problem is a well-known combinatorial optimization problem, which has many real-world applications. However, the problem has been proven to be non-deterministic polynomial-hard (NP-hard), which means that exact solution algorithms are not suitable for large-scale situations, as it is too time-consuming to [...] Read more.
The Max-cut problem is a well-known combinatorial optimization problem, which has many real-world applications. However, the problem has been proven to be non-deterministic polynomial-hard (NP-hard), which means that exact solution algorithms are not suitable for large-scale situations, as it is too time-consuming to obtain a solution. Therefore, designing heuristic algorithms is a promising but challenging direction to effectively solve large-scale Max-cut problems. For this reason, we propose a unique method which combines a pointer network and two deep learning strategies (supervised learning and reinforcement learning) in this paper, in order to address this challenge. A pointer network is a sequence-to-sequence deep neural network, which can extract data features in a purely data-driven way to discover the hidden laws behind data. Combining the characteristics of the Max-cut problem, we designed the input and output mechanisms of the pointer network model, and we used supervised learning and reinforcement learning to train the model to evaluate the model performance. Through experiments, we illustrated that our model can be well applied to solve large-scale Max-cut problems. Our experimental results also revealed that the new method will further encourage broader exploration of deep neural network for large-scale combinatorial optimization problems. Full article
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
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Open AccessArticle
Some Fixed Point Theorems of Ćirić Type in Fuzzy Metric Spaces
Mathematics 2020, 8(2), 297; https://doi.org/10.3390/math8020297 - 21 Feb 2020
Cited by 6 | Viewed by 836
Abstract
The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general [...] Read more.
The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms. Full article
(This article belongs to the Section Fuzzy Set Theory)
Open AccessArticle
Evaluation of the One-Dimensional Lp Sobolev Type Inequality
Mathematics 2020, 8(2), 296; https://doi.org/10.3390/math8020296 - 21 Feb 2020
Viewed by 598
Abstract
This study applies the extended L 2 Sobolev type inequality to the L p Sobolev type inequality using Hölder’s inequality. The sharp constant and best function of the L p Sobolev type inequality are found using a Green function for the nth order ordinary differential equation. The sharp constant is shown to be equal to the L p norm of the Green function and to the pth root of the value of the origin of the best function. Full article
(This article belongs to the Section Difference and Differential Equations)
Open AccessArticle
The Relations between Residuated Frames and Residuated Connections
Mathematics 2020, 8(2), 295; https://doi.org/10.3390/math8020295 - 21 Feb 2020
Cited by 1 | Viewed by 507
Abstract
We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. [...] Read more.
We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. As a result, we show that the Alexandrov topology induced by fuzzy posets is a fuzzy complete lattice with residuated connections. From this result, we obtain fuzzy rough sets on the Alexandrov topology. Moreover, as a generalization of the Dedekind–MacNeille completion, we introduce R-R (resp. D R - D R ) embedding maps and R-R (resp. D R - D R ) frame embedding maps. Full article
(This article belongs to the Section Fuzzy Set Theory)
Open AccessArticle
A Note on Minimal Hypersurfaces of an Odd Dimensional Sphere
Mathematics 2020, 8(2), 294; https://doi.org/10.3390/math8020294 - 21 Feb 2020
Viewed by 588
Abstract
We obtain the Wang-type integral inequalities for compact minimal hypersurfaces in the unit sphere S 2 n + 1 with Sasakian structure and use these inequalities to find two characterizations of minimal Clifford hypersurfaces in the unit sphere S 2 n + 1 . Full article
(This article belongs to the Special Issue Inequalities in Geometry and Applications)
Open AccessArticle
The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
Mathematics 2020, 8(2), 293; https://doi.org/10.3390/math8020293 - 21 Feb 2020
Viewed by 622
Abstract
We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4 + effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) play a role in limiting auto-immune diseases due to their immune-suppressive ability. Here, we present explicit exact formulas that give the relationship between the concentration of T cells, the concentration of Tregs, and the antigenic stimulation of T cells, when the system is at equilibria, stable or unstable. We found a parameter region of bistability, limited by two thresholds of antigenic stimulation of T cells (hysteresis). Moreover, there are values of the slope parameter of the tuning for which an isola-center bifurcation appears, and, for some other values, there is a transcritical bifurcation. We also present time evolutions of the ODE system. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)
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Open AccessArticle
Common Fixed Point and Endpoint Theorems for a Countable Family of Multi-Valued Mappings
Mathematics 2020, 8(2), 292; https://doi.org/10.3390/math8020292 - 21 Feb 2020
Cited by 1 | Viewed by 657
Abstract
We prove some common fixed point and endpoint theorems for a countable infinite family of multi-valued mappings, as well as Allahyari et al. (2015) did for self-mappings. An example and an application to a system of integral equations are given to show the [...] Read more.
We prove some common fixed point and endpoint theorems for a countable infinite family of multi-valued mappings, as well as Allahyari et al. (2015) did for self-mappings. An example and an application to a system of integral equations are given to show the usability of the results. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
Open AccessArticle
A-Statistical Convergence Properties of Kantorovich Type λ-Bernstein Operators Via (p, q)-Calculus
Mathematics 2020, 8(2), 291; https://doi.org/10.3390/math8020291 - 21 Feb 2020
Cited by 1 | Viewed by 607
Abstract
In the present paper, Kantorovich type λ -Bernstein operators via (p, q)-calculus are constructed, and the first and second moments and central moments of these operators are estimated in order to achieve our main results. An A-statistical convergence theorem and the rate of A-statistical convergence theorems are obtained according to some analysis methods and the definitions of A-statistical convergence, the rate of A-statistical convergence and modulus of smoothness. Full article
Open AccessArticle
xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes
Mathematics 2020, 8(2), 290; https://doi.org/10.3390/math8020290 - 20 Feb 2020
Cited by 1 | Viewed by 633
Abstract
This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written [...] Read more.
This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward. Full article
(This article belongs to the Special Issue Mathematical and Computational Cosmology)
Open AccessArticle
Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation
Mathematics 2020, 8(2), 289; https://doi.org/10.3390/math8020289 - 20 Feb 2020
Viewed by 569
Abstract
This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newtonian fluid, which is held by a spring. [...] Read more.
This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newtonian fluid, which is held by a spring. From this model, we can derive an FDE for the particular case of lacking the spring. Here, we find conditions for the source term ensuring that the solutions to the equation of the motion are bounded, which has a clear physical meaning. Full article
(This article belongs to the Special Issue Stability Analysis of Fractional Systems)
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Open AccessArticle
A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing
Mathematics 2020, 8(2), 288; https://doi.org/10.3390/math8020288 - 20 Feb 2020
Cited by 2 | Viewed by 591
Abstract
In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments [...] Read more.
In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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Open AccessArticle
On the Connection between Spherical Laplace Transform and Non-Euclidean Fourier Analysis
Mathematics 2020, 8(2), 287; https://doi.org/10.3390/math8020287 - 20 Feb 2020
Cited by 1 | Viewed by 678
Abstract
We prove that, if the coefficients of a Fourier–Legendre expansion satisfy a suitable Hausdorff-type condition, then the series converges to a function which admits a holomorphic extension to a cut-plane. Next, we introduce a Laplace-type transform (the so-called Spherical Laplace Transform) of [...] Read more.
We prove that, if the coefficients of a Fourier–Legendre expansion satisfy a suitable Hausdorff-type condition, then the series converges to a function which admits a holomorphic extension to a cut-plane. Next, we introduce a Laplace-type transform (the so-called Spherical Laplace Transform) of the jump function across the cut. The main result of this paper is to establish the connection between the Spherical Laplace Transform and the Non-Euclidean Fourier Transform in the sense of Helgason. In this way, we find a connection between the unitary representation of SO ( 3 ) and the principal series of the unitary representation of SU ( 1 , 1 ) . Full article
(This article belongs to the Special Issue Mathematical Physics II)
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Open AccessArticle
A New K-Nearest Neighbors Classifier for Big Data Based on Efficient Data Pruning
Mathematics 2020, 8(2), 286; https://doi.org/10.3390/math8020286 - 20 Feb 2020
Cited by 10 | Viewed by 1806
Abstract
The K-nearest neighbors (KNN) machine learning algorithm is a well-known non-parametric classification method. However, like other traditional data mining methods, applying it on big data comes with computational challenges. Indeed, KNN determines the class of a new sample based on the class of [...] Read more.
The K-nearest neighbors (KNN) machine learning algorithm is a well-known non-parametric classification method. However, like other traditional data mining methods, applying it on big data comes with computational challenges. Indeed, KNN determines the class of a new sample based on the class of its nearest neighbors; however, identifying the neighbors in a large amount of data imposes a large computational cost so that it is no longer applicable by a single computing machine. One of the proposed techniques to make classification methods applicable on large datasets is pruning. LC-KNN is an improved KNN method which first clusters the data into some smaller partitions using the K-means clustering method; and then applies the KNN for each new sample on the partition which its center is the nearest one. However, because the clusters have different shapes and densities, selection of the appropriate cluster is a challenge. In this paper, an approach has been proposed to improve the pruning phase of the LC-KNN method by taking into account these factors. The proposed approach helps to choose a more appropriate cluster of data for looking for the neighbors, thus, increasing the classification accuracy. The performance of the proposed approach is evaluated on different real datasets. The experimental results show the effectiveness of the proposed approach and its higher classification accuracy and lower time cost in comparison to other recent relevant methods. Full article
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Open AccessArticle
Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees
Mathematics 2020, 8(2), 285; https://doi.org/10.3390/math8020285 - 20 Feb 2020
Cited by 1 | Viewed by 745
Abstract
This paper deals with the maximum weighted independent set (MWIS) problem. We consider several robust variants of the MWIS problem on trees and prove that most of them are NP-hard. We propose a heuristic for solving the considered robust MWIS variants, which is [...] Read more.
This paper deals with the maximum weighted independent set (MWIS) problem. We consider several robust variants of the MWIS problem on trees and prove that most of them are NP-hard. We propose a heuristic for solving the considered robust MWIS variants, which is customized for trees. We demonstrate by experiments that our algorithm produces high-quality solutions and runs much faster than a general-purpose optimization software. Full article
(This article belongs to the Section Mathematics and Computer Science)
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Open AccessArticle
New Construction of Strongly Relatively Nonexpansive Sequences by Firmly Nonexpansive-Like Mappings
Mathematics 2020, 8(2), 284; https://doi.org/10.3390/math8020284 - 20 Feb 2020
Viewed by 545
Abstract
In recent works, many authors generated strongly relatively nonexpansive sequences of mappings by the sequences of firmly nonexpansive-like mappings. In this paper, we introduce a new method for construction of strongly relatively nonexpansive sequences from firmly nonexpansive-like mappings. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
Open AccessArticle
Linear Optimization of Polynomial Rational Functions: Applications for Positivity Analysis
Mathematics 2020, 8(2), 283; https://doi.org/10.3390/math8020283 - 20 Feb 2020
Cited by 1 | Viewed by 641
Abstract
In this paper, we provide tight linear lower bounding functions for multivariate polynomials given over boxes. These functions are obtained by the expansion of polynomials into Bernstein basis and using the linear least squares function. Convergence properties for the absolute difference between the [...] Read more.
In this paper, we provide tight linear lower bounding functions for multivariate polynomials given over boxes. These functions are obtained by the expansion of polynomials into Bernstein basis and using the linear least squares function. Convergence properties for the absolute difference between the given polynomials and their lower bounds are shown with respect to raising the degree and the width of boxes and subdivision. Subsequently, we provide a new method for constructing an affine lower bounding function for a multivariate continuous rational function based on the Bernstein control points, the convex hull of a non-positive polynomial s, and degree elevation. Numerical comparisons with the well-known Bernstein constant lower bounding function are given. Finally, with these affine functions, the positivity of polynomials and rational functions can be certified by computing the Bernstein coefficients of their linear lower bounds. Full article
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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 - 19 Feb 2020
Cited by 1 | Viewed by 598
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 - 19 Feb 2020
Viewed by 539
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)
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Open AccessArticle
A Spectral Conjugate Gradient Method with Descent Property
Mathematics 2020, 8(2), 280; https://doi.org/10.3390/math8020280 - 19 Feb 2020
Cited by 3 | Viewed by 725
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)
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Open AccessArticle
A Novel Tabu Search Algorithm for Multi-AGV Routing Problem
Mathematics 2020, 8(2), 279; https://doi.org/10.3390/math8020279 - 19 Feb 2020
Cited by 3 | Viewed by 865
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)
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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 - 19 Feb 2020
Viewed by 636
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
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Open AccessArticle
Relevant Aspects for an EF3-Evaluation of E-Cognocracy
Mathematics 2020, 8(2), 277; https://doi.org/10.3390/math8020277 - 19 Feb 2020
Viewed by 666
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)
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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 - 19 Feb 2020
Viewed by 934
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
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Open AccessArticle
A Constrained Production System Involving Production Flexibility and Carbon Emissions
Mathematics 2020, 8(2), 275; https://doi.org/10.3390/math8020275 - 19 Feb 2020
Cited by 7 | Viewed by 783
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 680
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
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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
Cited by 4 | Viewed by 723
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
Cited by 6 | Viewed by 743
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)
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