Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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30 pages, 7042 KiB  
Article
Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services
by Srinivas R. Chakravarthy
Mathematics 2022, 10(19), 3575; https://doi.org/10.3390/math10193575 - 30 Sep 2022
Cited by 5 | Viewed by 1515
Abstract
Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. [...] Read more.
Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b. The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a GI/M/1-type queue or as a QBD-model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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17 pages, 2923 KiB  
Article
Tensor of Order Two and Geometric Properties of 2D Metric Space
by Tomáš Stejskal, Jozef Svetlík and Marcela Lascsáková
Mathematics 2022, 10(19), 3524; https://doi.org/10.3390/math10193524 - 27 Sep 2022
Cited by 1 | Viewed by 1479
Abstract
A 2D metric space has a limited number of properties through which it can be described. This metric space may comprise objects such as a scalar, a vector, and a rank-2 tensor. The paper provides a comprehensive description of relations between objects in [...] Read more.
A 2D metric space has a limited number of properties through which it can be described. This metric space may comprise objects such as a scalar, a vector, and a rank-2 tensor. The paper provides a comprehensive description of relations between objects in 2D space using the matrix product of vectors, geometric product, and dot product of complex numbers. These relations are also an integral part of the Lagrange’s identity. The entire structure of derived theoretical relationships describing properties of 2D space draws on the Lagrange’s identity. The description of how geometric algebra and tensor calculus are interconnected is given here in a comprehensive and essentially clear manner, which is the main contribution of this paper. A new term in this regard is the total geometric and matrix product, which—in a simple manner—predetermines and defines the existence of differential relations such as the gradient, the divergence, and the curl of a vector field. In addition, geometric interpretation of tensors is pointed out, expressed through angular parameters known from the literature as a tensor glyph. This angular interpretation of the tensor has an unequivocal analytical form, and the paper shows how it is linked to the classical tensor denoted by indices. Full article
(This article belongs to the Section Engineering Mathematics)
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26 pages, 2529 KiB  
Article
Sampling Rate Optimization and Execution Time Analysis for Two-Degrees-of-Freedom Control Systems
by Mircea Şuşcă, Vlad Mihaly, Dora Morar and Petru Dobra
Mathematics 2022, 10(19), 3449; https://doi.org/10.3390/math10193449 - 22 Sep 2022
Cited by 2 | Viewed by 1484
Abstract
The current journal paper proposes an end-to-end analysis for the numerical implementation of a two-degrees-of-freedom (2DOF) control structure, starting from the sampling rate selection mechanism via a quasi-optimal manner, along with the estimation of the worst-case execution time (WCET) for the specified controller. [...] Read more.
The current journal paper proposes an end-to-end analysis for the numerical implementation of a two-degrees-of-freedom (2DOF) control structure, starting from the sampling rate selection mechanism via a quasi-optimal manner, along with the estimation of the worst-case execution time (WCET) for the specified controller. For the sampling rate selection, the classical Shannon–Nyquist sampling theorem is replaced by an optimization problem that encompasses the trade-off between the fidelity of the controllers’ representation, along with the fidelity of the resulting closed-loop systems, and the implementation difficulty of the controllers. Additionally, the WCET analysis can be seen as a verification step before automatic code generation, a computational model being provided. The proposed computational model encompasses infinite-impulse response (IIR) and finite-impulse response (FIR) filter models for the controller implementation, along with additional relevant phenomena being discussed, such as saturation, signal scaling and anti-windup techniques. All proposed results will be illustrated on a DC motor benchmark control problem. Full article
(This article belongs to the Section Engineering Mathematics)
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20 pages, 2324 KiB  
Article
A Population Pyramid Dynamics Model and Its Analytical Solution. Application Case for Spain
by Joan C. Micó
Mathematics 2022, 10(19), 3443; https://doi.org/10.3390/math10193443 - 22 Sep 2022
Cited by 2 | Viewed by 2061
Abstract
This paper presents the population pyramid dynamics model (PPDM) to study the evolution of the population pyramid of a determined country or society, deducing as a crucial objective its exact analytical solution. The PPDM is a first-order linear partial differential equation whose unknown [...] Read more.
This paper presents the population pyramid dynamics model (PPDM) to study the evolution of the population pyramid of a determined country or society, deducing as a crucial objective its exact analytical solution. The PPDM is a first-order linear partial differential equation whose unknown variable is the population density (population per age unit) depending on time and age, jointly an initial condition in the initial time and a boundary condition given by the births in the zero age. In addition, the dynamical patterns of the crude birth, death, immigration and emigration rates depending on time, jointly with the mathematical pattern of the initial population pyramid depending on ages, take part of the PPDM. These patterns can be obtained from the historical data. An application case of the PPDM analytical solution is presented: Spain, in the 2007–2021 period for its validation, and in the 2021–2026 period for its future forecasting. This application case also permits to obtain the forecasting limits of the PPDM by comparing the historical data with those provided by the PPDM. Other variables that can be obtained from the historical population pyramids data, such as the dependency ratio and the life expectancy at birth, are considered. Full article
(This article belongs to the Special Issue Mathematical Methods and Models in Nature and Society)
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27 pages, 836 KiB  
Article
The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process
by Serhii Lupenko
Mathematics 2022, 10(18), 3406; https://doi.org/10.3390/math10183406 - 19 Sep 2022
Cited by 5 | Viewed by 2529
Abstract
This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and [...] Read more.
This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation. Full article
(This article belongs to the Special Issue Dynamical Systems and System Analysis)
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13 pages, 780 KiB  
Article
Analytical Investigations into Anomalous Diffusion Driven by Stress Redistribution Events: Consequences of Lévy Flights
by Josiah D. Cleland and Martin A. K. Williams
Mathematics 2022, 10(18), 3235; https://doi.org/10.3390/math10183235 - 6 Sep 2022
Cited by 2 | Viewed by 1295
Abstract
This research is concerned with developing a generalised diffusion equation capable of describing diffusion processes driven by underlying stress-redistributing type events. The work utilises the development of an appropriate continuous time random walk framework as a foundation to consider a new generalised diffusion [...] Read more.
This research is concerned with developing a generalised diffusion equation capable of describing diffusion processes driven by underlying stress-redistributing type events. The work utilises the development of an appropriate continuous time random walk framework as a foundation to consider a new generalised diffusion equation. While previous work has explored the resulting generalised diffusion equation for jump-timings motivated by stick-slip physics, here non-Gaussian probability distributions of the jump displacements are also considered, specifically Lévy flights. This work illuminates several features of the analytic solution to such a generalised diffusion equation using several known properties of the Fox H function. Specifically demonstrated are the temporal behaviour of the resulting position probability density function, and its normalisation. The reduction of the proposed form to expected known solutions upon the insertion of simplifying parameter values, as well as a demonstration of asymptotic behaviours, is undertaken to add confidence to the validity of this equation. This work describes the analytical solution of such a generalised diffusion equation for the first time, and additionally demonstrates the capacity of the Fox H function and its properties in solving and studying generalised Fokker–Planck equations. Full article
(This article belongs to the Topic Fractional Calculus: Theory and Applications)
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25 pages, 13123 KiB  
Article
A Study of Learning Issues in Feedforward Neural Networks
by Adrian Teso-Fz-Betoño, Ekaitz Zulueta, Mireya Cabezas-Olivenza, Daniel Teso-Fz-Betoño and Unai Fernandez-Gamiz
Mathematics 2022, 10(17), 3206; https://doi.org/10.3390/math10173206 - 5 Sep 2022
Cited by 2 | Viewed by 1912
Abstract
When training a feedforward stochastic gradient descendent trained neural network, there is a possibility of not learning a batch of patterns correctly that causes the network to fail in the predictions in the areas adjacent to those patterns. This problem has usually been [...] Read more.
When training a feedforward stochastic gradient descendent trained neural network, there is a possibility of not learning a batch of patterns correctly that causes the network to fail in the predictions in the areas adjacent to those patterns. This problem has usually been resolved by directly adding more complexity to the network, normally by increasing the number of learning layers, which means it will be heavier to run on the workstation. In this paper, the properties and the effect of the patterns on the network are analysed and two main reasons why the patterns are not learned correctly are distinguished: the disappearance of the Jacobian gradient on the processing layers of the network and the opposite direction of the gradient of those patterns. A simplified experiment has been carried out on a simple neural network and the errors appearing during and after training have been monitored. Taking into account the data obtained, the initial hypothesis of causes seems to be correct. Finally, some corrections to the network are proposed with the aim of solving those training issues and to be able to offer a sufficiently correct prediction, in order to increase the complexity of the network as little as possible. Full article
(This article belongs to the Section Network Science)
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14 pages, 6708 KiB  
Article
Utilisation of Initialised Observation Scheme for Multi-Joint Robotic Arm in Lyapunov-Based Adaptive Control Strategy
by Mohammad Soleimani Amiri and Rizauddin Ramli
Mathematics 2022, 10(17), 3126; https://doi.org/10.3390/math10173126 - 31 Aug 2022
Cited by 3 | Viewed by 1992
Abstract
In this paper, we present a modelling, dynamic analysis, and controller tuning comparison for a five-degree-of-freedom (DoF) multi-joint robotic arm based on the Lyapunov-based Adaptive Controller (LAC). In most pick-and-place applications of robotic arms, it is essential to control the end-effector trajectory to [...] Read more.
In this paper, we present a modelling, dynamic analysis, and controller tuning comparison for a five-degree-of-freedom (DoF) multi-joint robotic arm based on the Lyapunov-based Adaptive Controller (LAC). In most pick-and-place applications of robotic arms, it is essential to control the end-effector trajectory to reach a precise target position. The kinematic solution of the 5-DoF robotic arm has been determined by the Lagrangian technique, and the mathematical model of each joint has been obtained in the range of motion condition. The Proportional-Integral-Derivative (PID) control parameters of the LAC have been determined by the Lyapunov stability approach and are initialised by four observation methods based on the obtained transfer function. The effectiveness of the initialised controller’s parameters is compared by a unit step response as the desired input of the controller system. As a result, the average error (AE) for Ziegler–Nichols is 6.6%, 83%, and 53% lower than for Pettit & Carr, Chau, and Bucz. The performance of LAC for the robotic arm model is validated in a virtual 3D model under a robot operating system environment. The results of root mean square error by LAC are 0.021 (rad) and 0.025 (rad) for joint 1 and joint 2, respectively, which indicate the efficiency of the proposed LAC strategy in reaching the predetermined trajectory and the potential of minimizing the controller tuning complexity. Full article
(This article belongs to the Topic Intelligent Systems and Robotics)
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28 pages, 703 KiB  
Article
A Multi-Scale Model for Cholera Outbreaks
by Beryl Musundi, Johannes Müller and Zhilan Feng
Mathematics 2022, 10(17), 3114; https://doi.org/10.3390/math10173114 - 30 Aug 2022
Cited by 2 | Viewed by 1829
Abstract
Cholera, caused by the pathogenic Vibrio cholerae bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model [...] Read more.
Cholera, caused by the pathogenic Vibrio cholerae bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model that explicitly connects the within-host and between-host dynamics of the disease. To model the within-host dynamics, we assigned each susceptible individual with a pathogen load that increases through the uptake of contaminated food and water (booster event). We introduced minimal and maximal times when the booster events happen and defined a time since the last booster event. We then scaled the within-host dynamics to the population where we structured the susceptible population using the two variables (pathogen load and time since the last booster event). We analyzed the pathogen load’s invariant distribution and utilized the results and time scale assumptions to reduce the dimension of the multi-scale model. The resulting model is an SIR model whose incidence function has terms derived from the multi-scale model. We finally conducted numerical simulations to investigate the long-term behavior of the SIR model. The simulations revealed parameter regions where either no cholera cases happen, where cholera is present at a low prevalence, and where a full-blown cholera epidemic takes off. Full article
(This article belongs to the Special Issue Mathematical Methods and Models in Epidemiology)
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15 pages, 349 KiB  
Article
Fuzzy Partial Metric Spaces and Fixed Point Theorems
by Halis Aygün, Elif Güner, Juan-José Miñana and Oscar Valero
Mathematics 2022, 10(17), 3092; https://doi.org/10.3390/math10173092 - 28 Aug 2022
Cited by 3 | Viewed by 1666
Abstract
Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were [...] Read more.
Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown. Full article
(This article belongs to the Special Issue Topological Study on Fuzzy Metric Spaces and Their Generalizations)
33 pages, 1935 KiB  
Article
A Topological Machine Learning Pipeline for Classification
by Francesco Conti, Davide Moroni and Maria Antonietta Pascali
Mathematics 2022, 10(17), 3086; https://doi.org/10.3390/math10173086 - 27 Aug 2022
Cited by 9 | Viewed by 2751
Abstract
In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation methods and parameters. The development of such a [...] Read more.
In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation methods and parameters. The development of such a topological pipeline for Machine Learning involves two crucial steps that strongly affect its performance: firstly, digital data must be represented as an algebraic object with a proper associated filtration in order to compute its topological summary, the Persistence Diagram. Secondly, the persistence diagram must be transformed with suitable representation methods in order to be introduced in a Machine Learning algorithm. We assess the performance of our pipeline, and in parallel, we compare the different representation methods on popular benchmark datasets. This work is a first step toward both an easy and ready-to-use pipeline for data classification using persistent homology and Machine Learning, and to understand the theoretical reasons why, given a dataset and a task to be performed, a pair (filtration, topological representation) is better than another. Full article
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29 pages, 395 KiB  
Article
Generalized Approach to Differentiability
by Nikola Koceić-Bilan and Snježana Braić
Mathematics 2022, 10(17), 3085; https://doi.org/10.3390/math10173085 - 27 Aug 2022
Cited by 2 | Viewed by 964
Abstract
In the traditional approach to differentiability, found in almost all university textbooks, this notion is considered only for interior points of the domain of function or for functions with an open domain. This approach leads to the fact that differentiability has usually been [...] Read more.
In the traditional approach to differentiability, found in almost all university textbooks, this notion is considered only for interior points of the domain of function or for functions with an open domain. This approach leads to the fact that differentiability has usually been considered only for functions with an open domain in Rn, which severely limits the possibility of applying the potential techniques and tools of differential calculus to a broader class of functions. Although there is a great need for generalization of the notion of differentiability of a function in various problems of mathematical analysis and other mathematical branches, the notion of differentiability of a function at the non-interior points of its domain has almost not been considered or successfully defined. In this paper, we have generalized the differentiability of scalar and vector functions of several variables by defining it at non-interior points of the domain of the function, which include not only boundary points but also all points at which the notion of linearization is meaningful (points admitting nbd rays). This generalization allows applications in all areas where standard differentiability can be applied. With this generalized approach to differentiability, some unexpected phenomena may occur, such as a function discontinuity at a point where a function is differentiable, the non-uniqueness of differentials… However, if one reduces this theory only to points with some special properties (points admitting a linearization space with dimension equal to the dimension of the ambient Euclidean space of the domain and admitting a raylike neighborhood, which includes the interior points of a domain), then all properties and theorems belonging to the known theory of differentiability remain valid in this extended theory. For generalized differentiability, the corresponding calculus (differentiation techniques) is also provided by matrices—representatives of differentials at points. In this calculus the role of partial derivatives (which in general cannot exist for differentiable functions at some points) is taken by directional derivatives. Full article
18 pages, 1892 KiB  
Article
A Robust Variable Selection Method for Sparse Online Regression via the Elastic Net Penalty
by Wentao Wang, Jiaxuan Liang, Rong Liu, Yunquan Song and Min Zhang
Mathematics 2022, 10(16), 2985; https://doi.org/10.3390/math10162985 - 18 Aug 2022
Cited by 6 | Viewed by 1811
Abstract
Variable selection has been a hot topic, with various popular methods including lasso, SCAD, and elastic net. These penalized regression algorithms remain sensitive to noisy data. Furthermore, “concept drift” fundamentally distinguishes streaming data learning from batch learning. This article presents a method for [...] Read more.
Variable selection has been a hot topic, with various popular methods including lasso, SCAD, and elastic net. These penalized regression algorithms remain sensitive to noisy data. Furthermore, “concept drift” fundamentally distinguishes streaming data learning from batch learning. This article presents a method for noise-resistant regularization and variable selection in noisy data streams with multicollinearity, dubbed canal-adaptive elastic net, which is similar to elastic net and encourages grouping effects. In comparison to lasso, the canal adaptive elastic net is especially advantageous when the number of predictions (p) is significantly larger than the number of observations (n), and the data are multi-collinear. Numerous simulation experiments have confirmed that canal-adaptive elastic net has higher prediction accuracy than lasso, ridge regression, and elastic net in data with multicollinearity and noise. Full article
(This article belongs to the Special Issue Mathematical and Computational Statistics and Their Applications)
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9 pages, 261 KiB  
Article
Blow-Up Time of Solutions for a Parabolic Equation with Exponential Nonlinearity
by Yanjin Wang and Jianzhen Qian
Mathematics 2022, 10(16), 2887; https://doi.org/10.3390/math10162887 - 12 Aug 2022
Viewed by 1338
Abstract
This paper studies a parabolic equation with exponential nonlinearity, which has several applications, for example the self-trapped beams in plasma. Based on a modified concavity method we prove the blow-up of the solution for initial data with high initial energy. We also proposed [...] Read more.
This paper studies a parabolic equation with exponential nonlinearity, which has several applications, for example the self-trapped beams in plasma. Based on a modified concavity method we prove the blow-up of the solution for initial data with high initial energy. We also proposed the solution’s lower and upper bound of the blow-up time for the equation. Our results complement the existing results. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
19 pages, 7799 KiB  
Article
Finite Gradient Models with Enriched RBF-Based Interpolation
by Pedro Areias, Rui Melicio, Fernando Carapau and José Carrilho Lopes
Mathematics 2022, 10(16), 2876; https://doi.org/10.3390/math10162876 - 11 Aug 2022
Cited by 4 | Viewed by 1251
Abstract
A finite strain gradient model for the 3D analysis of materials containing spherical voids is presented. A two-scale approach is proposed: a least-squares methodology for RVE analysis with quadratic displacements and a full high-order continuum with both fourth-order and sixth-order elasticity tensors. A [...] Read more.
A finite strain gradient model for the 3D analysis of materials containing spherical voids is presented. A two-scale approach is proposed: a least-squares methodology for RVE analysis with quadratic displacements and a full high-order continuum with both fourth-order and sixth-order elasticity tensors. A meshless method is adopted using radial basis function interpolation with polynomial enrichment. Both the first and second derivatives of the resulting shape functions are described in detail. Complete expressions for the deformation gradient F and its gradient F are derived and a consistent linearization is performed to ensure the Newton solution. A total of seven constitutive properties is required. The classical Lamé parameters corresponding to the pristine material are considered constant. From RVE homogenization, seven properties are obtained, two homogenized Lamé parameters plus five gradient-related properties. Two validation 3D numerical examples are presented. The first example exhibits the size effect (i.e., the stiffening of smaller specimens) and the second example shows the absence of stress singularity and hence the convergence of the discretization method. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
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26 pages, 21806 KiB  
Article
Chaotification of One-Dimensional Maps Based on Remainder Operator Addition
by Lazaros Moysis, Ioannis Kafetzis, Murilo S. Baptista and Christos Volos
Mathematics 2022, 10(15), 2801; https://doi.org/10.3390/math10152801 - 7 Aug 2022
Cited by 7 | Viewed by 1603
Abstract
In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher [...] Read more.
In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher Lyapunov exponent compared to its seed map, and all periodic orbits of any period will be unstable, leading to robust chaos. The technique is tested on several maps from the literature, yielding increased chaotic behavior in all cases, as indicated by comparison of the bifurcation and Lyapunov exponent diagrams of the original and resulting maps. Moreover, the effect of the proposed technique in the problem of pseudo-random bit generation is studied. Using a standard bit generation technique, it is shown that the proposed maps demonstrate increased statistical randomness compared to their seed ones, when used as a source for the bit generator. This study illustrates that the proposed method is an efficient chaotification technique for maps that can be used in chaos-based encryption and other relevant applications. Full article
(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography)
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12 pages, 1378 KiB  
Article
PEGANs: Phased Evolutionary Generative Adversarial Networks with Self-Attention Module
by Yu Xue, Weinan Tong, Ferrante Neri and Yixia Zhang
Mathematics 2022, 10(15), 2792; https://doi.org/10.3390/math10152792 - 5 Aug 2022
Cited by 7 | Viewed by 1858
Abstract
Generative adversarial networks have made remarkable achievements in generative tasks. However, instability and mode collapse are still frequent problems. We improve the framework of evolutionary generative adversarial networks (E-GANs), calling it phased evolutionary generative adversarial networks (PEGANs), and adopt a self-attention module to [...] Read more.
Generative adversarial networks have made remarkable achievements in generative tasks. However, instability and mode collapse are still frequent problems. We improve the framework of evolutionary generative adversarial networks (E-GANs), calling it phased evolutionary generative adversarial networks (PEGANs), and adopt a self-attention module to improve upon the disadvantages of convolutional operations. During the training process, the discriminator will play against multiple generators simultaneously, where each generator adopts a different objective function as a mutation operation. Every time after the specified number of training iterations, the generator individuals will be evaluated and the best performing generator offspring will be retained for the next round of evolution. Based on this, the generator can continuously adjust the training strategy during training, and the self-attention module also enables the model to obtain the modeling ability of long-range dependencies. Experiments on two datasets showed that PEGANs improve the training stability and are competitive in generating high-quality samples. Full article
(This article belongs to the Special Issue Evolutionary Computation for Deep Learning and Machine Learning)
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12 pages, 294 KiB  
Article
A Continuous-Time Semi-Markov System Governed by Stepwise Transitions
by Vlad Stefan Barbu, Guglielmo D’Amico and Andreas Makrides
Mathematics 2022, 10(15), 2745; https://doi.org/10.3390/math10152745 - 3 Aug 2022
Cited by 1 | Viewed by 1389
Abstract
In this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. [...] Read more.
In this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. This is an extension of a previous work on discrete-time step semi-Markov processes. After defining the models and the main characteristics of interest, we derive the recursive evolution equations for two-step semi-Markov processes. Full article
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
41 pages, 23839 KiB  
Review
Survey on Synthetic Data Generation, Evaluation Methods and GANs
by Alvaro Figueira and Bruno Vaz
Mathematics 2022, 10(15), 2733; https://doi.org/10.3390/math10152733 - 2 Aug 2022
Cited by 52 | Viewed by 17973
Abstract
Synthetic data consists of artificially generated data. When data are scarce, or of poor quality, synthetic data can be used, for example, to improve the performance of machine learning models. Generative adversarial networks (GANs) are a state-of-the-art deep generative models that can generate [...] Read more.
Synthetic data consists of artificially generated data. When data are scarce, or of poor quality, synthetic data can be used, for example, to improve the performance of machine learning models. Generative adversarial networks (GANs) are a state-of-the-art deep generative models that can generate novel synthetic samples that follow the underlying data distribution of the original dataset. Reviews on synthetic data generation and on GANs have already been written. However, none in the relevant literature, to the best of our knowledge, has explicitly combined these two topics. This survey aims to fill this gap and provide useful material to new researchers in this field. That is, we aim to provide a survey that combines synthetic data generation and GANs, and that can act as a good and strong starting point for new researchers in the field, so that they have a general overview of the key contributions and useful references. We have conducted a review of the state-of-the-art by querying four major databases: Web of Sciences (WoS), Scopus, IEEE Xplore, and ACM Digital Library. This allowed us to gain insights into the most relevant authors, the most relevant scientific journals in the area, the most cited papers, the most significant research areas, the most important institutions, and the most relevant GAN architectures. GANs were thoroughly reviewed, as well as their most common training problems, their most important breakthroughs, and a focus on GAN architectures for tabular data. Further, the main algorithms for generating synthetic data, their applications and our thoughts on these methods are also expressed. Finally, we reviewed the main techniques for evaluating the quality of synthetic data (especially tabular data) and provided a schematic overview of the information presented in this paper. Full article
(This article belongs to the Special Issue New Insights in Machine Learning and Deep Neural Networks)
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18 pages, 1454 KiB  
Article
Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?
by J. Alberto Conejero, Jonathan Franceschi and Enric Picó-Marco
Mathematics 2022, 10(15), 2719; https://doi.org/10.3390/math10152719 - 1 Aug 2022
Cited by 8 | Viewed by 2018
Abstract
The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is [...] Read more.
The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models. Full article
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18 pages, 339 KiB  
Article
Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions
by Cornelia-Livia Bejan and Galia Nakova
Mathematics 2022, 10(15), 2625; https://doi.org/10.3390/math10152625 - 27 Jul 2022
Cited by 1 | Viewed by 1185
Abstract
The Riemann extension, introduced by E. K. Patterson and A. G. Walker, is a semi-Riemannian metric with a neutral signature on the cotangent bundle TM of a smooth manifold M, induced by a symmetric linear connection ∇ on M. In [...] Read more.
The Riemann extension, introduced by E. K. Patterson and A. G. Walker, is a semi-Riemannian metric with a neutral signature on the cotangent bundle TM of a smooth manifold M, induced by a symmetric linear connection ∇ on M. In this paper we deal with a natural Riemann extension g¯, which is a generalization (due to M. Sekizawa and O. Kowalski) of the Riemann extension. We construct an almost complex structure J¯ on the cotangent bundle TM of an almost complex manifold (M,J,) with a symmetric linear connection ∇ such that (TM,J¯,g¯) is an almost complex manifold, where the natural Riemann extension g¯ is a Norden metric. We obtain necessary and sufficient conditions for (TM,J¯,g¯) to belong to the main classes of the Ganchev–Borisov classification of the almost complex manifolds with Norden metric. We also examine the cases when the base manifold is an almost complex manifold with Norden metric or it is a complex manifold (M,J,) endowed with an almost complex connection (J=0). We investigate the harmonicity with respect to g¯ of the almost complex structure J¯, according to the type of the base manifold. Moreover, we define an almost hypercomplex structure (J¯1,J¯2,J¯3) on the cotangent bundle TM4n of an almost hypercomplex manifold (M4n,J1,J2,J3,) with a symmetric linear connection ∇. The natural Riemann extension g¯ is a Hermitian metric with respect to J¯1 and a Norden metric with respect to J¯2 and J¯3. Full article
(This article belongs to the Special Issue Differential Geometry: Theory and Applications Part II)
14 pages, 356 KiB  
Article
Iteration of Operators with Contractive Mutual Relations of Kannan Type
by Ram N. Mohapatra, María A. Navascués, María V. Sebastián and Saurabh Verma
Mathematics 2022, 10(15), 2632; https://doi.org/10.3390/math10152632 - 27 Jul 2022
Cited by 6 | Viewed by 1308
Abstract
Inspired by the ideas of R. Kannan, we define the new concepts of mutual Kannan contractivity and mutual contractivity between two self-maps on a metric space that generalize the concepts of the Kannan map and contraction. We give some examples and deduce the [...] Read more.
Inspired by the ideas of R. Kannan, we define the new concepts of mutual Kannan contractivity and mutual contractivity between two self-maps on a metric space that generalize the concepts of the Kannan map and contraction. We give some examples and deduce the properties of the operators satisfying this type of condition; in particular, we study the case where the space is normed, and the maps are linear. Then we generalize some theorems proposed by this author on the existence of a fixed point of one operator or a common fixed point for two operators. Our results first prove the existence of a common fixed point of a set of self-maps of any cardinal number (countable or uncountable) satisfying the conditions of Kannan type in metric spaces. The same is proved for a set of maps satisfying the mutual relations of classical contractivity. We prove in both cases the convergence of iterative schemes involving operators with mutual relations of contractivity, proposing sufficient conditions for the iteration of the operators on any element of the space to converge to the common fixed point when a different operator is taken in each step. The results obtained are applied to operators acting on real functions, coming from the fractal convolution with the null function. Full article
(This article belongs to the Special Issue Fractal and Computational Geometry)
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23 pages, 1216 KiB  
Article
Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation
by Laura Vicente-Gonzalez  and Jose Luis Vicente-Villardon
Mathematics 2022, 10(15), 2580; https://doi.org/10.3390/math10152580 - 25 Jul 2022
Cited by 4 | Viewed by 2666
Abstract
In this paper, we propose a generalization of Partial Least Squares Regression (PLS-R) for a matrix of several binary responses and a a set of numerical predictors. We call the method Partial Least Squares Binary Logistic Regression (PLS-BLR). That is equivalent to a [...] Read more.
In this paper, we propose a generalization of Partial Least Squares Regression (PLS-R) for a matrix of several binary responses and a a set of numerical predictors. We call the method Partial Least Squares Binary Logistic Regression (PLS-BLR). That is equivalent to a PLS-2 model for binary responses. Biplot and even triplot graphical representations for visualizing PLS-BLR models are described, and an application to real data is presented. Software packages for the calculation of the main results are also provided. We conclude that the proposed method and its visualization using triplots are powerful tools for the interpretation of the relations among predictors and responses. Full article
(This article belongs to the Special Issue Multivariate Statistics: Theory and Its Applications)
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16 pages, 427 KiB  
Article
Testing for the Presence of the Leverage Effect without Estimation
by Zhi Liu
Mathematics 2022, 10(14), 2511; https://doi.org/10.3390/math10142511 - 19 Jul 2022
Viewed by 1326
Abstract
Problem: The leverage effect plays an important role in finance. However, the statistical test for the presence of the leverage effect is still lacking study. Approach: In this paper, by using high frequency data, we propose a novel procedure to test if [...] Read more.
Problem: The leverage effect plays an important role in finance. However, the statistical test for the presence of the leverage effect is still lacking study. Approach: In this paper, by using high frequency data, we propose a novel procedure to test if the driving Brownian motion of an Ito^ semi-martingale is correlated to its volatility (referred to as the leverage effect in financial econometrics) over a long time period. The asymptotic setting is based on observations within a long time interval with the mesh of the observation grid shrinking to zero. We construct a test statistic via forming a sequence of Studentized statistics whose distributions are asymptotically normal over blocks of a fixed time span, and then collect the sequence based on the whole data set of a long time span. Result: The asymptotic behaviour of the Studentized statistics was obtained from the cubic variation of the underlying semi-martingale and the asymptotic distribution of the proposed test statistic under the null hypothesis that the leverage effect is absent was established, and we also show that the test has an asymptotic power of one against the alternative hypothesis that the leverage effect is present. Implications: We conducted extensive simulation studies to assess the finite sample performance of the test statistics, and the results show a satisfactory performance for the test. Finally, we implemented the proposed test procedure to a dataset of the SP500 index. We see that the null hypothesis of the absence of the leverage effect is rejected for most of the time period. Therefore, this provides a strong evidence that the leverage effect is a necessary ingredient in modelling high-frequency data. Full article
(This article belongs to the Section Financial Mathematics)
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8 pages, 259 KiB  
Article
On the Extremality of Harmonic Beltrami Coefficients
by Samuel L. Krushkal
Mathematics 2022, 10(14), 2460; https://doi.org/10.3390/math10142460 - 14 Jul 2022
Cited by 2 | Viewed by 858
Abstract
We prove a general theorem, which provides a broad collection of univalent functions with equal Grunsky and Teichmüller norms and thereby the Fredholm eigenvalues and the reflection coefficients of associated quasicircles. It concerns an important problem to establish the exact or approximate values [...] Read more.
We prove a general theorem, which provides a broad collection of univalent functions with equal Grunsky and Teichmüller norms and thereby the Fredholm eigenvalues and the reflection coefficients of associated quasicircles. It concerns an important problem to establish the exact or approximate values of basic quasiinvariant functionals of Jordan curves, which is crucial in applications and in the numerical aspect of quasiconformal analysis. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)
20 pages, 577 KiB  
Article
A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem
by Juan F. Gomez, Javier Panadero, Rafael D. Tordecilla, Juliana Castaneda and Angel A. Juan
Mathematics 2022, 10(14), 2405; https://doi.org/10.3390/math10142405 - 9 Jul 2022
Cited by 5 | Viewed by 1606
Abstract
The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, [...] Read more.
The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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18 pages, 1357 KiB  
Article
Application of Fuzzy-Based Support Vector Regression to Forecast of International Airport Freight Volumes
by Cheng-Hong Yang, Jen-Chung Shao, Yen-Hsien Liu, Pey-Huah Jou and Yu-Da Lin
Mathematics 2022, 10(14), 2399; https://doi.org/10.3390/math10142399 - 8 Jul 2022
Cited by 6 | Viewed by 1710
Abstract
As freight volumes increase, airports are likely to require additional infrastructure development, increased air services, and expanded facilities. Prediction of freight volumes could ensure effective investment. Among the computational intelligence models, support vector regression (SVR) has become the dominant modeling paradigm. In this [...] Read more.
As freight volumes increase, airports are likely to require additional infrastructure development, increased air services, and expanded facilities. Prediction of freight volumes could ensure effective investment. Among the computational intelligence models, support vector regression (SVR) has become the dominant modeling paradigm. In this study, a fuzzy-based SVR (FSVR) model was used to solve the freight volume prediction problem in international airports. The FSVR model can use a fuzzy time series of historical traffic changes for predictions. A fuzzy classification algorithm was used for elements of similar levels in the time series to appropriately divide traffic changes into fuzzy sets, generate membership function values, and establish a fuzzy relationship to produce a fuzzy interpolation with a minimal error. A comparison of the FSVR model with other models revealed that the FSVR model had the lowest mean absolute percentage error (all < 2.5%), mean absolute error, and root mean square error for all types of traffic at all the analyzed airports. Fuzzy sets can handle uncertainty and imprecision in time series. Therefore, the prediction accuracy of the entire time series model is improved by taking advantage of SVR and fuzzy sets. By using the highly accurate FSVR model to predict the future growth of air freight volume, airport management could analyze their existing facilities and service capacity to identify operational bottlenecks and plan future development. The FSVR model is the most accurate forecasting model for air traffic forecasting. Full article
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15 pages, 3706 KiB  
Article
Nonlinear Transient Dynamics of Graphene Nanoplatelets Reinforced Pipes Conveying Fluid under Blast Loads and Thermal Environment
by Siyu Liu, Aiwen Wang, Wei Li, Hongyan Chen, Yufen Xie and Dongmei Wang
Mathematics 2022, 10(13), 2349; https://doi.org/10.3390/math10132349 - 5 Jul 2022
Cited by 4 | Viewed by 1575
Abstract
This work aims at investigating the nonlinear transient response of fluid-conveying pipes made of graphene nanoplatelet (GPL)-reinforced composite (GPLRC) under blast loads and in a thermal environment. A modified Halpin–Tsai model is used to approximate the effective Young’s modulus of the GPLRC pipes [...] Read more.
This work aims at investigating the nonlinear transient response of fluid-conveying pipes made of graphene nanoplatelet (GPL)-reinforced composite (GPLRC) under blast loads and in a thermal environment. A modified Halpin–Tsai model is used to approximate the effective Young’s modulus of the GPLRC pipes conveying fluid; the mass density and Poisson’s ratio are determined by using the Voigt model. A slender Euler–Bernoulli beam is considered for modeling the pipes conveying fluid. The vibration control equation of the GPLRC pipes conveying fluid under blast loads is obtained by using Hamilton’s principle. A set of second-order ordinary differential equations are obtained by using the second-order Galerkin discrete method and are solved by using the adaptive Runge–Kutta method. Numerical experiments show that GPL distribution and temperature; GPL weight fraction; pipe length-to-thickness ratio; flow velocity; and blast load parameters have important effects on the nonlinear transient response of the GPLRC pipes conveying fluid. The numerical results also show that due to the fluid–structure interaction, the vibration amplitudes of the GPLRC pipes conveying fluid decay after the impact of blast loads. Full article
(This article belongs to the Special Issue Modeling and Analysis in Dynamical Systems and Bistability)
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11 pages, 295 KiB  
Article
Exponential Convergence to Equilibrium for Solutions of the Homogeneous Boltzmann Equation for Maxwellian Molecules
by Emanuele Dolera
Mathematics 2022, 10(13), 2347; https://doi.org/10.3390/math10132347 - 4 Jul 2022
Viewed by 1174
Abstract
This paper is concerned with the spatially homogeneous Boltzmann equation, with the assumption of Maxwellian interaction. We consider initial data that belong to a small neighborhood of the equilibrium, which is a Maxwellian distribution. We prove that the solution remains in another small [...] Read more.
This paper is concerned with the spatially homogeneous Boltzmann equation, with the assumption of Maxwellian interaction. We consider initial data that belong to a small neighborhood of the equilibrium, which is a Maxwellian distribution. We prove that the solution remains in another small neighborhood with the same center and converges to this equilibrium exponentially fast, with an explicit quantification. Full article
(This article belongs to the Section Mathematical Physics)
13 pages, 1094 KiB  
Article
A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas
by M. Mossa Al-Sawalha, Ravi P. Agarwal, Rasool Shah, Osama Y. Ababneh and Wajaree Weera
Mathematics 2022, 10(13), 2293; https://doi.org/10.3390/math10132293 - 30 Jun 2022
Cited by 14 | Viewed by 1618
Abstract
In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop [...] Read more.
In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
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27 pages, 577 KiB  
Article
A Variable Neighborhood Search Approach for the Dynamic Single Row Facility Layout Problem
by Gintaras Palubeckis, Armantas Ostreika and Jūratė Platužienė
Mathematics 2022, 10(13), 2174; https://doi.org/10.3390/math10132174 - 22 Jun 2022
Cited by 2 | Viewed by 1465
Abstract
The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost [...] Read more.
The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost is the sum of the products of the flow costs and center-to-center distances between facilities. In this paper, we focus on metaheuristic algorithms for this problem. The main contributions of the paper are three-fold. First, a variable neighborhood search (VNS) algorithm for the DSRFLP is proposed. The main version of VNS uses an innovative strategy to start the search from a solution obtained by constructing an instance of the single row facility layout problem (SRFLP) from a given instance of the DSRFLP and applying a heuristic algorithm for the former problem. Second, a fast local search (LS) procedure is developed. The innovations of this procedure are two-fold: (i) the fast insertion and swap neighborhood exploration techniques are adapted for the case of the dynamic version of the SRFLP; and (ii) to reduce the computational time, the swap operation is restricted on pairs of facilities of equal lengths. Provided the number of planning periods is a constant, the neighborhood exploration procedures for n facilities have only O(n2) time complexity. The superiority of these procedures over traditional LS techniques is also shown by performing numerical tests. Third, computational experiments on DSRFLP instances with up to 200 facilities and three or five planning periods are carried out to validate the effectiveness of the VNS approach. The proposed VNS heuristic is compared with the simulated annealing (SA) method which is the state of the art algorithm for the DSRFLP. Experiments show that VNS outperforms SA by a significant margin. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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24 pages, 357 KiB  
Article
Matrix Power Function Based Block Cipher Operating in CBC Mode
by Lina Dindiene, Aleksejus Mihalkovich, Kestutis Luksys and Eligijus Sakalauskas
Mathematics 2022, 10(12), 2123; https://doi.org/10.3390/math10122123 - 18 Jun 2022
Cited by 2 | Viewed by 1869
Abstract
In our previous study, we proposed a perfectly secure Shannon cipher based on the so-called matrix power function. There we also introduced a concept of single round symmetric encryption, i.e., we used the matrix power function together with some rather simple operations to [...] Read more.
In our previous study, we proposed a perfectly secure Shannon cipher based on the so-called matrix power function. There we also introduced a concept of single round symmetric encryption, i.e., we used the matrix power function together with some rather simple operations to define a three-step encryption algorithm that needs no additional rounds. Interestingly enough, the newly proposed Shannon cipher possesses the option of parallelization—an important property of efficiently performing calculations using several processors. Relying on our previous proposal, in this study we introduce a concept of a one round block cipher, which can be used to encrypt an arbitrary large message by dividing it into several blocks. In other words, we construct a block cipher operating in cipher block chaining mode on the basis of the previously defined Shannon cipher. Moreover, due to the perfect secrecy property of the original algorithm, we show that our proposal is able to withstand the chosen plaintext attack. Full article
(This article belongs to the Special Issue Advances in Algebraic Coding Theory and Cryptography)
28 pages, 3310 KiB  
Article
Multiple Scenarios of Quality of Life Index Using Fuzzy Linguistic Quantifiers: The Case of 85 Countries in Numbeo
by Ziwei Shu, Ramón Alberto Carrasco, Javier Portela García-Miguel and Manuel Sánchez-Montañés
Mathematics 2022, 10(12), 2091; https://doi.org/10.3390/math10122091 - 16 Jun 2022
Cited by 9 | Viewed by 2862
Abstract
In economic development, in addition to comparing the gross domestic product (GDP) between nations, it is critical to assess the quality of life to gain a holistic perspective of their different aspects. However, the quality of life index (QOLI) is a subjective term [...] Read more.
In economic development, in addition to comparing the gross domestic product (GDP) between nations, it is critical to assess the quality of life to gain a holistic perspective of their different aspects. However, the quality of life index (QOLI) is a subjective term that can be difficult to quantify. Although this composite index is typically calculated using universal weights proposed by experts to aggregate indicators, such as safety indexes, healthcare indexes, pollution indexes, and housing indicators, it is complicated to balance multiple dimensions whose weights are adjusted to account for different countries’ circumstances. Therefore, this paper aims to construct various scenarios of the QOLI, using linguistic quantifiers of the ordered weighted averaging (OWA) operator, and the 2-tuple linguistic model. Numbeo, one of the largest quality of life information databases, was used in this paper to estimate the QOLI in 85 countries. Uncertainty and sensitivity analyses were employed to assess the robustness of the QOLI. The results of the proposed model are compared with those obtained using the Numbeo formulation. The results show that the proposed model increases the linguistic interpretability of the QOLI, and obtains different QOLIs, based on diverse country contexts. Full article
(This article belongs to the Topic Multi-Criteria Decision Making)
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16 pages, 586 KiB  
Article
Benchmarking Cost-Effective Opinion Injection Strategies in Complex Networks
by Alexandru Topîrceanu
Mathematics 2022, 10(12), 2067; https://doi.org/10.3390/math10122067 - 15 Jun 2022
Cited by 2 | Viewed by 1660
Abstract
Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly [...] Read more.
Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly imply an optimal selection of spreaders used to diffuse and indoctrinate neighboring peers, often overlooking realistic limitations of time, space, and budget. Thus, finding trade-offs between a minimal number of influential nodes and maximizing opinion coverage is a relevant scientific problem. Therefore, we study the relationship between specific parameters that influence the effectiveness of opinion diffusion, such as the underlying topology, the number of active spreaders, the periodicity of spreader activity, and the injection strategy. We introduce an original benchmarking methodology by integrating time and cost into an augmented linear threshold model and measure indoctrination expense as a trade-off between the cost of maintaining spreaders’ active and real-time opinion coverage. Simulations show that indoctrination expense increases polynomially with the number of spreaders and linearly with the activity periodicity. In addition, keeping spreaders continuously active instead of periodically activating them can increase expenses by 69–84% in our simulation scenarios. Lastly, we outline a set of general rules for cost-effective opinion injection strategies. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications)
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15 pages, 325 KiB  
Article
Free Resolutions and Generalized Hamming Weights of Binary Linear Codes
by Ignacio García-Marco, Irene Márquez-Corbella, Edgar Martínez-Moro and Yuriko Pitones
Mathematics 2022, 10(12), 2079; https://doi.org/10.3390/math10122079 - 15 Jun 2022
Cited by 1 | Viewed by 2113
Abstract
In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure that is smaller than the set of codewords of minimal support [...] Read more.
In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure that is smaller than the set of codewords of minimal support that provides us with some information about the GHWs. We prove that the first and second generalized Hamming weights of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated with a binomial ideal related with the code. Moreover, the remaining weights are bounded above by the degrees of the syzygies in the resolution. Full article
(This article belongs to the Special Issue Combinatorics and Computation in Commutative Algebra)
17 pages, 752 KiB  
Article
Kernel Matrix-Based Heuristic Multiple Kernel Learning
by Stanton R. Price, Derek T. Anderson, Timothy C. Havens and Steven R. Price
Mathematics 2022, 10(12), 2026; https://doi.org/10.3390/math10122026 - 11 Jun 2022
Cited by 4 | Viewed by 1758
Abstract
Kernel theory is a demonstrated tool that has made its way into nearly all areas of machine learning. However, a serious limitation of kernel methods is knowing which kernel is needed in practice. Multiple kernel learning (MKL) is an attempt to learn a [...] Read more.
Kernel theory is a demonstrated tool that has made its way into nearly all areas of machine learning. However, a serious limitation of kernel methods is knowing which kernel is needed in practice. Multiple kernel learning (MKL) is an attempt to learn a new tailored kernel through the aggregation of a set of valid known kernels. There are generally three approaches to MKL: fixed rules, heuristics, and optimization. Optimization is the most popular; however, a shortcoming of most optimization approaches is that they are tightly coupled with the underlying objective function and overfitting occurs. Herein, we take a different approach to MKL. Specifically, we explore different divergence measures on the values in the kernel matrices and in the reproducing kernel Hilbert space (RKHS). Experiments on benchmark datasets and a computer vision feature learning task in explosive hazard detection demonstrate the effectiveness and generalizability of our proposed methods. Full article
(This article belongs to the Special Issue Mathematical Methods for Pattern Recognition)
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15 pages, 29218 KiB  
Article
Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems
by Muhammad Marwan, Vagner Dos Santos, Muhammad Zainul Abidin and Anda Xiong
Mathematics 2022, 10(11), 1914; https://doi.org/10.3390/math10111914 - 2 Jun 2022
Cited by 9 | Viewed by 2229
Abstract
This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different [...] Read more.
This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different basins, several approaches such as bifurcation diagrams, Lyapunov exponents, and the Poincaré section are applied. The second half of the study synchronizes two mechanical chaotic systems using a novel controller, with gyrostat and quadrotor unmanned aerial vehicle (QUAV) chaotic systems acting as master and slave systems, respectively. The error dynamical system and the parameter updated law are built using Lyapunov’s theory, and it is discovered that under certain parametric conditions, the trajectories of the QUAV chaotic system overlap and begin to match the features of the gyrostat chaotic system. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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74 pages, 751 KiB  
Review
Centrally Essential Rings and Semirings
by Askar Tuganbaev
Mathematics 2022, 10(11), 1867; https://doi.org/10.3390/math10111867 - 30 May 2022
Viewed by 1357
Abstract
This paper is a survey of results on centrally essential rings and semirings. A ring (respectively, semiring) is said to be centrally essential if it is either commutative or satisfies the property that for any non-central element a, there exist non-zero central [...] Read more.
This paper is a survey of results on centrally essential rings and semirings. A ring (respectively, semiring) is said to be centrally essential if it is either commutative or satisfies the property that for any non-central element a, there exist non-zero central elements x and y with ax = y. The class of centrally essential rings is very large; many corresponding examples are given in the work. Full article
15 pages, 1612 KiB  
Article
A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process
by Hyunju Lee, Ji Hwan Cha and Maxim Finkelstein
Mathematics 2022, 10(11), 1833; https://doi.org/10.3390/math10111833 - 26 May 2022
Cited by 2 | Viewed by 1419
Abstract
Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover [...] Read more.
Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover this important in-practice setting. Therefore, our paper is the first to deal with these issues by modeling dependence in the bivariate set up when a system consists of two dependent parts. We employ the bivariate generalized Polya process to model the corresponding failure and repair process. Relevant stochastic properties of this process have been obtained in order to propose and further discuss the new optimal bivariate preventive maintenance policy with two decision parameters: age and operational history. Moreover, introducing these two parameters in the considered context is also a new feature of the study. Under the proposed policy, the long-run average cost rate is derived and the optimal replacement policies are investigated. Detailed numerical examples illustrate our findings and show the potential efficiency of the obtained results in practice. Full article
(This article belongs to the Special Issue Probability Theory and Stochastic Modeling with Applications)
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14 pages, 3760 KiB  
Article
An Efficient Computational Technique for the Electromagnetic Scattering by Prolate Spheroids
by Ludovica Tognolatti, Cristina Ponti, Massimo Santarsiero and Giuseppe Schettini
Mathematics 2022, 10(10), 1761; https://doi.org/10.3390/math10101761 - 21 May 2022
Cited by 3 | Viewed by 1972
Abstract
In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one [...] Read more.
In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one of its axes, which is also known as a spheroid. We have developed a fast and ad hoc code to solve the electromagnetic scattering problem, using spheroidal vector wave functions, which are special functions used to describe physical problems in which a prolate or oblate spheroidal reference system is considered. Numerical results are presented, both for TE and TM polarization of the incident wave, and are validated by a comparison with results obtained by a commercial electromagnetic simulator. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)
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14 pages, 1158 KiB  
Article
State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays
by Yaning Yu and Ziye Zhang
Mathematics 2022, 10(10), 1725; https://doi.org/10.3390/math10101725 - 18 May 2022
Cited by 8 | Viewed by 1819
Abstract
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix [...] Read more.
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method. Full article
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25 pages, 414 KiB  
Article
Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations
by Shaomin Li, Haoyu Wei and Xiaoyu Lei
Mathematics 2022, 10(10), 1700; https://doi.org/10.3390/math10101700 - 16 May 2022
Cited by 2 | Viewed by 1840
Abstract
Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed the dispersion parameter as a constant, which may not be satisfied in practice. This paper studies the variable selection and dispersion [...] Read more.
Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed the dispersion parameter as a constant, which may not be satisfied in practice. This paper studies the variable selection and dispersion estimation for the heterogeneous NBR models, which model the dispersion parameter as a function. Specifically, we proposed a double regression and applied a double 1-penalty to both regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for the lasso estimators of two partial regression coefficients for the first time, using concentration inequalities of empirical processes. Furthermore, derived from the oracle inequalities, the consistency and convergence rate for the estimators are the theoretical guarantees for further statistical inference. Finally, both simulations and a real data analysis demonstrate that the new methods are effective. Full article
(This article belongs to the Special Issue New Advances in High-Dimensional and Non-asymptotic Statistics)
22 pages, 1091 KiB  
Article
Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures
by Klaus Gürlebeck, Dmitrii Legatiuk and Kemmar Webber
Mathematics 2022, 10(10), 1670; https://doi.org/10.3390/math10101670 - 13 May 2022
Viewed by 1539
Abstract
The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and [...] Read more.
The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing II)
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16 pages, 359 KiB  
Article
Fisher, Bayes, and Predictive Inference
by Sandy Zabell
Mathematics 2022, 10(10), 1634; https://doi.org/10.3390/math10101634 - 11 May 2022
Cited by 2 | Viewed by 1823
Abstract
We review historically the position of Sir R.A. Fisher towards Bayesian inference and, particularly, the classical Bayes–Laplace paradigm. We focus on his Fiducial Argument. Full article
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10 pages, 431 KiB  
Article
Andness Directedness for t-Norms and t-Conorms
by Vicenç Torra
Mathematics 2022, 10(9), 1598; https://doi.org/10.3390/math10091598 - 8 May 2022
Cited by 2 | Viewed by 1740
Abstract
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation [...] Read more.
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation functions, andness-directedness is one of them. A crucial aspect in any decision is the degree of compromise between criteria. Given an aggregation function, andness establishes to what degree the function behaves in a conjunctive manner. That is, to what degree some criteria are mandatory. Nevertheless, from an engineering perspective, what we know is that some criteria are strongly required and we cannot ignore a bad evaluation even when other criteria are correctly evaluated. That is, given our requirements of andness, what are the aggregation functions we need to select. Andness is not only for mean-like functions, but it also applies to t-norms and t-conorms. In this paper, we study this problem and show how to select t-norms and t-conorms based on the andness level. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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24 pages, 3902 KiB  
Article
A Safe and Efficient Lane Change Decision-Making Strategy of Autonomous Driving Based on Deep Reinforcement Learning
by Kexuan Lv, Xiaofei Pei, Ci Chen and Jie Xu
Mathematics 2022, 10(9), 1551; https://doi.org/10.3390/math10091551 - 5 May 2022
Cited by 15 | Viewed by 3598
Abstract
As an indispensable branch of machine learning (ML), reinforcement learning (RL) plays a prominent role in the decision-making process of autonomous driving (AD), which enables autonomous vehicles (AVs) to learn an optimal driving strategy through continuous interaction with the environment. This paper proposes [...] Read more.
As an indispensable branch of machine learning (ML), reinforcement learning (RL) plays a prominent role in the decision-making process of autonomous driving (AD), which enables autonomous vehicles (AVs) to learn an optimal driving strategy through continuous interaction with the environment. This paper proposes a deep reinforcement learning (DRL)-based motion planning strategy for AD tasks in the highway scenarios where an AV merges into two-lane road traffic flow and realizes the lane changing (LC) maneuvers. We integrate the DRL model into the AD system relying on the end-to-end learning method. An improved DRL algorithm based on deep deterministic policy gradient (DDPG) is developed with well-defined reward functions. In particular, safety rules (SR), safety prediction (SP) module and trauma memory (TM) as well as the dynamic potential-based reward shaping (DPBRS) function are adopted to further enhance safety and accelerate learning of the LC behavior. For validation, the proposed DSSTD algorithm is trained and tested on the dual-computer co-simulation platform. The comparative experimental results show that our proposal outperforms other benchmark algorithms in both driving safety and efficiency. Full article
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16 pages, 697 KiB  
Article
Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks
by Lu Pang, Cheng Hu, Juan Yu and Haijun Jiang
Mathematics 2022, 10(9), 1533; https://doi.org/10.3390/math10091533 - 3 May 2022
Cited by 7 | Viewed by 1631
Abstract
This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of [...] Read more.
This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of fuzzy-based impulsive complex networks and the estimation of the synchronized time is given. Ultimately, the presented control scheme and synchronization criteria are verified by numerical simulation. Full article
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16 pages, 310 KiB  
Article
Stability of Solutions to Systems of Nonlinear Differential Equations with Discontinuous Right-Hand Sides: Applications to Hopfield Artificial Neural Networks
by Ilya Boykov, Vladimir Roudnev and Alla Boykova
Mathematics 2022, 10(9), 1524; https://doi.org/10.3390/math10091524 - 2 May 2022
Cited by 6 | Viewed by 2157
Abstract
In this paper, we study the stability of solutions to systems of differential equations with discontinuous right-hand sides. We have investigated nonlinear and linear equations. Stability sufficient conditions for linear equations are expressed as a logarithmic norm for coefficients of systems of equations. [...] Read more.
In this paper, we study the stability of solutions to systems of differential equations with discontinuous right-hand sides. We have investigated nonlinear and linear equations. Stability sufficient conditions for linear equations are expressed as a logarithmic norm for coefficients of systems of equations. Stability sufficient conditions for nonlinear equations are expressed as the logarithmic norm of the Jacobian of the right-hand side of the system of equations. Sufficient conditions for the stability of solutions of systems of differential equations expressed in terms of logarithmic norms of the right-hand sides of equations (for systems of linear equations) and the Jacobian of right-hand sides (for nonlinear equations) have the following advantages: (1) in investigating stability in different metrics from the same standpoints, we have obtained a set of sufficient conditions; (2) sufficient conditions are easily expressed; (3) robustness areas of systems are easily determined with respect to the variation of their parameters; (4) in case of impulse action, information on moments of impact distribution is not required; (5) a method to obtain sufficient conditions of stability is extended to other definitions of stability (in particular, to p-moment stability). The obtained sufficient conditions are used to study Hopfield neural networks with discontinuous synapses and discontinuous activation functions. Full article
43 pages, 606 KiB  
Article
General Non-Local Continuum Mechanics: Derivation of Balance Equations
by Vasily E. Tarasov
Mathematics 2022, 10(9), 1427; https://doi.org/10.3390/math10091427 - 23 Apr 2022
Cited by 15 | Viewed by 1621
Abstract
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are used as mathematical tools for constructing [...] Read more.
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are used as mathematical tools for constructing mechanics of media with general form of nonlocality in space and time. Balance equations for mass, momentum, and energy, which describe conservation laws for nonlocal continuum, are derived by using the fundamental theorems of the GFC. The general balance equation in the integral form are derived by using the second fundamental theorems of the GFC. The first fundamental theorems of GFC and the proposed fractional analogue of the Titchmarsh theorem are used to derive the differential form of general balance equations from the integral form of balance equations. Using the general fractional vector calculus, the equations of conservation of mass, momentum, and energy are also suggested for a wide class of regions and surfaces. Full article
(This article belongs to the Section Mathematical Physics)
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10 pages, 1798 KiB  
Article
Confidence-Interval-Based Fuzzy Testing for the Lifetime Performance Index of Electronic Product
by Chun-Min Yu, Kuen-Suan Chen and Ting-Hsin Hsu
Mathematics 2022, 10(9), 1405; https://doi.org/10.3390/math10091405 - 22 Apr 2022
Cited by 5 | Viewed by 1282
Abstract
When the lifetime of an electronic component does not reach the required level, it can be enhanced by means of the paralleling current sharing backup system or the redundant backup system. The lifetime of the redundant backup system is the sum of lifetimes [...] Read more.
When the lifetime of an electronic component does not reach the required level, it can be enhanced by means of the paralleling current sharing backup system or the redundant backup system. The lifetime of the redundant backup system is the sum of lifetimes of all electronic components, which is the maximum of all the electronic components’ lifetimes, compared with the lifetime of the parallel current sharing backup system. For the purpose of enhancing products’ reliability, electronic goods are usually designed with spare electronic components. If it is assumed that there are m1 redundant backup components for each electronic product, then the lifetime of the electronic product will be distributed as a Gamma distribution with two parameters—m and λ, where λ is the mean for each lifetime of each electronic component. According to numerous studies, the sample size is not large, as it takes a long time to test the lifetime of an electronic product, and enterprises consider cost and timeliness. This paper concerns the performance index of the lifetime of the electronic product. Therefore, based on the confidence interval, this paper aims to develop a fuzzy testing model. As this model can integrate past data and expert experience, the testing accuracy can be retained despite small-sized samples. In fact, through adopting the testing model proposed by this paper, companies can make precise and intelligent decisions instantly with the use of small-sized samples to grasp the opportunities for improvement. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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