Mathematics

23 pages, 3819 KiB

Open AccessEditor’s ChoiceArticle

Granule-Based-Classifier (GbC): A Lattice Computing Scheme Applied on Tree Data Structures

by Vassilis G. Kaburlasos, Chris Lytridis, Eleni Vrochidou, Christos Bazinas, George A. Papakostas, Anna Lekova, Omar Bouattane, Mohamed Youssfi and Takashi Hashimoto

Mathematics 2021, 9(22), 2889; https://doi.org/10.3390/math9222889 - 13 Nov 2021

Cited by 8 | Viewed by 2542

Abstract

Social robots keep proliferating. A critical challenge remains their sensible interaction with humans, especially in real world applications. Hence, computing with real world semantics is instrumental. Recently, the Lattice Computing (LC) paradigm has been proposed with a capacity to compute with semantics represented [...] Read more.

Social robots keep proliferating. A critical challenge remains their sensible interaction with humans, especially in real world applications. Hence, computing with real world semantics is instrumental. Recently, the Lattice Computing (LC) paradigm has been proposed with a capacity to compute with semantics represented by partial order in a mathematical lattice data domain. In the aforementioned context, this work proposes a parametric LC classifier, namely a Granule-based-Classifier (GbC), applicable in a mathematical lattice (T,⊑) of tree data structures, each of which represents a human face. A tree data structure here emerges from 68 facial landmarks (points) computed in a data preprocessing step by the OpenFace software. The proposed (tree) representation retains human anonymity during data processing. Extensive computational experiments regarding three different pattern recognition problems, namely (1) head orientation, (2) facial expressions, and (3) human face recognition, demonstrate GbC capacities, including good classification results, and a common human face representation in different pattern recognition problems, as well as data induced granular rules in (T,⊑) that allow for (a) explainable decision-making, (b) tunable generalization enabled also by formal logic/reasoning techniques, and (c) an inherent capacity for modular data fusion extensions. The potential of the proposed techniques is discussed. Full article

(This article belongs to the Special Issue Lattice Computing: A Mathematical Modelling Paradigm for Cyber–Physical System Applications)

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12 pages, 314 KiB

Open AccessEditor’s ChoiceArticle

Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method

by Mart Ratas, Jüri Majak and Andrus Salupere

Mathematics 2021, 9(21), 2809; https://doi.org/10.3390/math9212809 - 5 Nov 2021

Cited by 19 | Viewed by 3053

Abstract

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed [...] Read more.

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed. Full article

(This article belongs to the Special Issue Mathematical Problems in Materials Science)

87 pages, 665 KiB

Open AccessEditor’s ChoiceArticle

General Fractional Vector Calculus

by Vasily E. Tarasov

Mathematics 2021, 9(21), 2816; https://doi.org/10.3390/math9212816 - 5 Nov 2021

Cited by 35 | Viewed by 4564

Abstract

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus [...] Read more.

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of operators. In the generalization of FVC from power-law nonlocality to the general form of nonlocality in space, we use the general fractional calculus (GFC) in the Luchko approach, which was published in 2021. This paper proposed the following: (I) Self-consistent definitions of general fractional differential vector operators: the regional and line general fractional gradients, the regional and surface general fractional curl operators, the general fractional divergence are proposed. (II) Self-consistent definitions of general fractional integral vector operators: the general fractional circulation, general fractional flux and general fractional volume integral are proposed. (III) The general fractional gradient, Green’s, Stokes’ and Gauss’s theorems as fundamental theorems of general fractional vector calculus are proved for simple and complex regions. The fundamental theorems (Gradient, Green, Stokes, Gauss theorems) of the proposed general FVC are proved for a wider class of domains, surfaces and curves. All these three parts allow us to state that we proposed a calculus, which is a general fractional vector calculus (General FVC). The difficulties and problems of defining general fractional integral and differential vector operators are discussed to the nonlocal case, caused by the violation of standard product rule (Leibniz rule), chain rule (rule of differentiation of function composition) and semigroup property. General FVC for orthogonal curvilinear coordinates, which includes general fractional vector operators for the spherical and cylindrical coordinates, is also proposed. Full article

(This article belongs to the Special Issue Fractals, Fractional Calculus and Applied Statistics)

23 pages, 3100 KiB

Open AccessEditor’s ChoiceArticle

Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking

by Mircea-Bogdan Radac and Timotei Lala

Mathematics 2021, 9(21), 2752; https://doi.org/10.3390/math9212752 - 29 Oct 2021

Cited by 15 | Viewed by 2976

Abstract

A general control system tracking learning framework is proposed, by which an optimal learned tracking behavior called ‘primitive’ is extrapolated to new unseen trajectories without requiring relearning. This is considered intelligent behavior and strongly related to the neuro-motor cognitive control of biological (human-like) [...] Read more.

A general control system tracking learning framework is proposed, by which an optimal learned tracking behavior called ‘primitive’ is extrapolated to new unseen trajectories without requiring relearning. This is considered intelligent behavior and strongly related to the neuro-motor cognitive control of biological (human-like) systems that deliver suboptimal executions for tasks outside of their current knowledge base, by using previously memorized experience. However, biological systems do not solve explicit mathematical equations for solving learning and prediction tasks. This stimulates the proposed hierarchical cognitive-like learning framework, based on state-of-the-art model-free control: (1) at the low-level L1, an approximated iterative Value Iteration for linearizing the closed-loop system (CLS) behavior by a linear reference model output tracking is first employed; (2) an experiment-driven Iterative Learning Control (EDILC) applied to the CLS from the reference input to the controlled output learns simple tracking tasks called ‘primitives’ in the secondary L2 level, and (3) the tertiary level L3 extrapolates the primitives’ optimal tracking behavior to new tracking tasks without trial-based relearning. The learning framework relies only on input-output system data to build a virtual state space representation of the underlying controlled system that is assumed to be observable. It has been shown to be effective by experimental validation on a representative, coupled, nonlinear, multivariable real-world system. Able to cope with new unseen scenarios in an optimal fashion, the hierarchical learning framework is an advance toward cognitive control systems. Full article

(This article belongs to the Special Issue Mathematical Methods for Nonlinear Control)

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20 pages, 489 KiB

Open AccessEditor’s ChoiceArticle

Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?

by Erik M. Bollt and Shane D. Ross

Mathematics 2021, 9(21), 2731; https://doi.org/10.3390/math9212731 - 28 Oct 2021

Cited by 1 | Viewed by 3956

Abstract

This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to [...] Read more.

This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this construction easier, we find that such vector fields do exist, and we explore whether such vector fields have a special structure, thus making a link between the geometric theory and the transfer operator theory. Full article

(This article belongs to the Special Issue Dynamical Systems and Operator Theory)

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41 pages, 82819 KiB

Open AccessEditor’s ChoiceArticle

Evolutionary Game of Multi-Subjects in Live Streaming and Governance Strategies Based on Social Preference Theory during the COVID-19 Pandemic

by Tinggui Chen, Lijuan Peng, Jianjun Yang, Guodong Cong and Guoping Li

Mathematics 2021, 9(21), 2743; https://doi.org/10.3390/math9212743 - 28 Oct 2021

Cited by 53 | Viewed by 6871

Abstract

After the outbreak of the COVID-19, offline consumption has been significantly impacted. For the sake of safety, online consumption has become the most common manner, and this has generated e-commerce, which not only breaks the spatio-temporal or regional restrictions, but also conforms to [...] Read more.

After the outbreak of the COVID-19, offline consumption has been significantly impacted. For the sake of safety, online consumption has become the most common manner, and this has generated e-commerce, which not only breaks the spatio-temporal or regional restrictions, but also conforms to the normal economic development needs for epidemic prevention and control. However, this new business model causes problems such as the shortage of post-sales service, false publicity, and uneven quality of live streaming anchors, seriously affecting the interests of consumers. Therefore, it is urgent to strengthen the management of the chaos of live streaming. This study focuses on exploring the problems and the behavioral strategies of stakeholders in the governance process. The paper obtained online user comments by python, and used topic clustering and subject extraction methods to dig out the problems and related multiple subjects in live streaming at first. Secondly, the theory of social preference was introduced to construct an evolutionary game model among multiple subjects, and how to guide the behavioral decision-making of multiple subjects to standardize and rationalize was studied, so as to control the problem of live streaming. Finally, simulation experiments were conducted and the results demonstrated that: (1) Compared with strengthening the reciprocal preference of the government, live streaming platforms, and consumers, changing the individual’s altruistic preference is more effective in controlling the chaos of live streaming; (2) weakening the platform’s altruistic preference for anchors is conducive to creating a good live streaming environment; and (3) changing consumers’ altruistic preference or reciprocal preference is less effective in promoting the governance of the live streaming environment. Full article

(This article belongs to the Special Issue Evolutionary Games, Propagation Processes and Control in Complex Systems)

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17 pages, 10764 KiB

Open AccessEditor’s ChoiceArticle

Exploring an Efficient POI Recommendation Model Based on User Characteristics and Spatial-Temporal Factors

by Chonghuan Xu, Dongsheng Liu and Xinyao Mei

Mathematics 2021, 9(21), 2673; https://doi.org/10.3390/math9212673 - 21 Oct 2021

Cited by 37 | Viewed by 3675

Abstract

The advent of mobile scenario-based consumption popularizes and gradually maturates the application of point of interest (POI) recommendation services based on geographical location. However, the insufficient fusion of heterogeneous data in the current POI recommendation services leads to poor recommendation quality. In this [...] Read more.

The advent of mobile scenario-based consumption popularizes and gradually maturates the application of point of interest (POI) recommendation services based on geographical location. However, the insufficient fusion of heterogeneous data in the current POI recommendation services leads to poor recommendation quality. In this paper, we propose a novel hybrid POI recommendation model (NHRM) based on user characteristics and spatial-temporal factors to enhance the recommendation effect. The proposed model contains three sub-models. The first model considers user preferences, forgetting characteristics, user influence, and trajectories. The second model studies the impact of the correlation between the locations of POIs and calculates the check-in probability of POI with the two-dimensional kernel density estimation method. The third model analyzes the influence of category of POI. Consequently, the above results were combined and top-K POIs were recommended to target users. The experimental results on Yelp and Meituan data sets showed that the recommendation performance of our method is superior to some other methods, and the problems of cold-start and data sparsity are alleviated to a certain extent. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

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26 pages, 1950 KiB

Open AccessEditor’s ChoiceArticle

A Hybrid Spherical Fuzzy MCDM Approach to Prioritize Governmental Intervention Strategies against the COVID-19 Pandemic: A Case Study from Vietnam

by Phi-Hung Nguyen, Jung-Fa Tsai, Thanh-Tuan Dang, Ming-Hua Lin, Hong-Anh Pham and Kim-Anh Nguyen

Mathematics 2021, 9(20), 2626; https://doi.org/10.3390/math9202626 - 18 Oct 2021

Cited by 41 | Viewed by 5243

Abstract

The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, [...] Read more.

The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, few studies in the literature can assist governments in this topic. Selective governmental intervention during the COVID-19 outbreak is considered a Multi-Criteria Decision-Making (MCDM) problem under a vague and uncertain environment when governments and medical communities adjust their priorities in response to rising issues and the efficacy of interventions applied in various nations. In this study, a novel hybrid Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Fuzzy Weighted Aggregated Sum Product Assessment (WASPAS-F) model is proposed to help stakeholders such as governors and policymakers to prioritize governmental interventions for dealing with the COVID-19 outbreak. The SF-AHP is implemented to measure the significance of the criteria, while the WASPAS-F approach is deployed to rank intervention alternatives. An empirical case study is conducted in Vietnam. From the SF-AHP findings, the criteria of “effectiveness in preventing the spread of COVID-19”, “ease of implementation”, and “high acceptability to citizens” were recognized as the most important criteria. As for the ranking of strategies, “vaccinations”, “enhanced control of the country’s health resources”, “common health testing”, “formation of an emergency response team”, and “quarantining patients and those suspected of infection” are the top five strategies. Aside from that, the robustness of the approach was tested by performing a comparative analysis. The results illustrate that the applied methods reach the general best strategy rankings. The applied methodology and its analysis will provide insight to authorities for fighting against the severe pandemic in the long run. It may aid in solving many complicated challenges in government strategy selection and assessment. It is also a flexible design model for considering the evaluation criteria. Finally, this research provides valuable guidance for policymakers in other nations. Full article

(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)

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17 pages, 1597 KiB

Open AccessEditor’s ChoiceArticle

Active Suspension Control Using an MPC-LQR-LPV Controller with Attraction Sets and Quadratic Stability Conditions

by Daniel Rodriguez-Guevara, Antonio Favela-Contreras, Francisco Beltran-Carbajal, David Sotelo and Carlos Sotelo

Mathematics 2021, 9(20), 2533; https://doi.org/10.3390/math9202533 - 9 Oct 2021

Cited by 25 | Viewed by 4389

Abstract

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In [...] Read more.

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a model predictive control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, quadratic stability conditions are imposed in terms of Linear Matrix Inequalities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm. Full article

(This article belongs to the Special Issue Advances and Trends in Mathematical Modelling, Control and Identification of Vibrating Systems)

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14 pages, 4714 KiB

Open AccessEditor’s ChoiceArticle

Spatio-Temporal Spread Pattern of COVID-19 in Italy

by Nicoletta D’Angelo, Antonino Abbruzzo and Giada Adelfio

Mathematics 2021, 9(19), 2454; https://doi.org/10.3390/math9192454 - 2 Oct 2021

Cited by 9 | Viewed by 3809

Abstract

This paper investigates the spatio-temporal spread pattern of COVID-19 in Italy, during the first wave of infections, from February to October 2020. Disease mappings of the virus infections by using the Besag–York–Mollié model and some spatio-temporal extensions are provided. This modeling framework, which [...] Read more.

This paper investigates the spatio-temporal spread pattern of COVID-19 in Italy, during the first wave of infections, from February to October 2020. Disease mappings of the virus infections by using the Besag–York–Mollié model and some spatio-temporal extensions are provided. This modeling framework, which includes a temporal component, allows the studying of the time evolution of the spread pattern among the 107 Italian provinces. The focus is on the effect of citizens’ mobility patterns, represented here by the three distinct phases of the Italian virus first wave, identified by the Italian government, also characterized by the lockdown period. Results show the effectiveness of the lockdown action and an inhomogeneous spatial trend that characterizes the virus spread during the first wave. Furthermore, the results suggest that the temporal evolution of each province’s cases is independent of the temporal evolution of the other ones, meaning that the contagions and temporal trend may be caused by some province-specific aspects rather than by the subjects’ spatial movements. Full article

(This article belongs to the Section D1: Probability and Statistics)

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18 pages, 4512 KiB

Open AccessEditor’s ChoiceArticle

AB-Net: A Novel Deep Learning Assisted Framework for Renewable Energy Generation Forecasting

by Noman Khan, Fath U Min Ullah, Ijaz Ul Haq, Samee Ullah Khan, Mi Young Lee and Sung Wook Baik

Mathematics 2021, 9(19), 2456; https://doi.org/10.3390/math9192456 - 2 Oct 2021

Cited by 47 | Viewed by 5149

Abstract

Renewable energy (RE) power plants are deployed globally because the renewable energy sources (RESs) are sustainable, clean, and environmentally friendly. However, the demand for power increases on a daily basis due to population growth, technology, marketing, and the number of installed industries. This [...] Read more.

Renewable energy (RE) power plants are deployed globally because the renewable energy sources (RESs) are sustainable, clean, and environmentally friendly. However, the demand for power increases on a daily basis due to population growth, technology, marketing, and the number of installed industries. This challenge has raised a critical issue of how to intelligently match the power generation with the consumption for efficient energy management. To handle this issue, we propose a novel architecture called ‘AB-Net’: a one-step forecast of RE generation for short-term horizons by incorporating an autoencoder (AE) with bidirectional long short-term memory (BiLSTM). Firstly, the data acquisition step is applied, where the data are acquired from various RESs such as wind and solar. The second step performs deep preprocessing of the acquired data via several de-noising and cleansing filters to clean the data and normalize them prior to actual processing. Thirdly, an AE is employed to extract the discriminative features from the cleaned data sequence through its encoder part. BiLSTM is used to learn these features to provide a final forecast of power generation. The proposed AB-Net was evaluated using two publicly available benchmark datasets where the proposed method obtains state-of-the-art results in terms of the error metrics. Full article

(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)

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19 pages, 4114 KiB

Open AccessEditor’s ChoiceArticle

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

by Igor Sazonov, Dmitry Grebennikov, Andreas Meyerhans and Gennady Bocharov

Mathematics 2021, 9(17), 2025; https://doi.org/10.3390/math9172025 - 24 Aug 2021

Cited by 13 | Viewed by 3888

Abstract

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4

^{+}

T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in [...] Read more.

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4

^{+}

T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4

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T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

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12 pages, 285 KiB

Open AccessEditor’s ChoiceArticle

New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations

by Alina Alb Lupaş and Georgia Irina Oros

Mathematics 2021, 9(16), 2000; https://doi.org/10.3390/math9162000 - 21 Aug 2021

Cited by 24 | Viewed by 2569

Abstract

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator

L_{α}^{m}

, given by [...] Read more.

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator

L_{α}^{m}

, given by

L_{α}^{m} : A_{n} \to A_{n}

,

L_{α}^{m} f (z) = (1 - α) R^{m} f (z) + α S^{m} f (z),

where

A_{n} = {f \in H (U), f (z) = z + a_{n + 1} z^{n + 1} + \dots, z \in U}

is the subclass of normalized holomorphic functions and the operators

R^{m} f (z)

and

S^{m} f (z)

are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator

L_{α}^{m}

, a certain fuzzy class of analytic functions denoted by

S L_{F}^{m} (δ, α)

is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries. Full article

(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))

22 pages, 2552 KiB

Open AccessEditor’s ChoiceArticle

A Two Phase Integrated Fuzzy Decision-Making Framework for Green Supplier Selection in the Coffee Bean Supply Chain

by Ngoc Bao Tu Nguyen, Gu-Hong Lin and Thanh-Tuan Dang

Mathematics 2021, 9(16), 1923; https://doi.org/10.3390/math9161923 - 12 Aug 2021

Cited by 32 | Viewed by 4595

Abstract

In Vietnam, as more and more organizations are moving toward globalization, green supplier selection (GSS) has emerged as a strategic approach in supply chain management that requires supplier practices in lessening the environmental risks to society. Based on both conventional and environmental criteria, [...] Read more.

In Vietnam, as more and more organizations are moving toward globalization, green supplier selection (GSS) has emerged as a strategic approach in supply chain management that requires supplier practices in lessening the environmental risks to society. Based on both conventional and environmental criteria, this paper aims to evaluate a set of suppliers by establishing a multi-criteria decision-making (MCDM)-based framework using an integrated fuzzy analytical hierarchy process (FAHP) with the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Initially, five GSS criteria of the environmental aspect (wastewater treatment, solid waste generation, energy consumption, air pollution, corporate social responsibility) and conventional criteria (quality, cost, delivery, and technology) are identified from the literature and consulting field experts to employ the MCDM approach. The trustworthiness of the proposed integrated framework is presented by discussing a case study in the coffee bean supply chain in Vietnam. The FAHP is used to generate criteria weights in which fuzzy set theory is applied to translate the linguistic evaluation statements of experts, and VIKOR is used to rank the alternatives against the selected criteria. From FAHP findings, the most important criteria are quantity discount, solid waste generation, order fulfillment rate, logistics cost, and purchasing cost. A consistency test is performed to ensure the uniformity of the expert’s input. The best suppliers are determined through the final ranking of the VIKOR model for the case study. The work presented provides insight to decision-makers of supplier selection that helps determine significant GSS criteria and aids in the minimization of environmental risks to society arising from the supply chain on corporate sustainability standards. Full article

(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)

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13 pages, 1608 KiB

Open AccessEditor’s ChoiceArticle

Fractional Growth Model Applied to COVID-19 Data

by Fernando Alcántara-López, Carlos Fuentes, Carlos Chávez, Fernando Brambila-Paz and Antonio Quevedo

Mathematics 2021, 9(16), 1915; https://doi.org/10.3390/math9161915 - 11 Aug 2021

Cited by 4 | Viewed by 3094

Abstract

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed [...] Read more.

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order

0 < β \leq 1

, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination

R^{2} > 0.999

. Full article

(This article belongs to the Special Issue Theory and Applications of Fractional Equations and Calculus)

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12 pages, 1030 KiB

Open AccessEditor’s ChoiceArticle

Fixed-Time Third-Order Super-Twisting-like Sliding Mode Motion Control for Piezoelectric Nanopositioning Stage

by Guangwei Wang, Bo Wang and Chengxi Zhang

Mathematics 2021, 9(15), 1770; https://doi.org/10.3390/math9151770 - 27 Jul 2021

Cited by 16 | Viewed by 2957

Abstract

This paper presents a novel third-order super-twisting-like integral sliding mode controller (3-ISMC) for trajectory tracking of nanopositioning applications. Different from traditional sliding mode control methods presenting with chattering problems, the proposed approach provides continuous control inputs, which brings much convenience for practical applications. [...] Read more.

This paper presents a novel third-order super-twisting-like integral sliding mode controller (3-ISMC) for trajectory tracking of nanopositioning applications. Different from traditional sliding mode control methods presenting with chattering problems, the proposed approach provides continuous control inputs, which brings much convenience for practical applications. Moreover, the fixed-time convergence of the proposed 3-ISMC is guaranteed independently of initial conditions. The estimation of the fixed convergence time and stability are derived based on the Lyapunov method. Simulation results demonstrate that the proposed controller exhibits chattering free and quick transient response performance for a piezoelectric nanopositioning system under model uncertainties and external disturbances. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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18 pages, 2400 KiB

Open AccessEditor’s ChoiceArticle

Revisiting the Valuable Roles of Global Financial Assets for International Stock Markets: Quantile Coherence and Causality-in-Quantiles Approaches

by Zhenghui Li, Zhiming Ao and Bin Mo

Mathematics 2021, 9(15), 1750; https://doi.org/10.3390/math9151750 - 24 Jul 2021

Cited by 40 | Viewed by 4094

Abstract

We employ the quantile-coherency approach and causality-in-quantile method to revisit the roles of Bitcoin, U.S. dollar, crude oil and gold for USA, Chinese, UK, and Japanese stock markets. The main results show that the impact of global financial assets varies across different investment [...] Read more.

We employ the quantile-coherency approach and causality-in-quantile method to revisit the roles of Bitcoin, U.S. dollar, crude oil and gold for USA, Chinese, UK, and Japanese stock markets. The main results show that the impact of global financial assets varies across different investment horizons and quantiles. We find that in most cases, the correlation between global financial assets and stock indexes is not significant or is weakly positive. From the perspective of investment horizons (frequency domain), the correlation in the short term is mostly manifested in Bitcoin, while in the medium and long term it is shifted to dollar assets. At the same time, the relationships are significantly higher in the medium and long term than in the short term. From the point of view of quantiles, it shows a weak positive correlation at the lower quantile. However, the correlation between the two is not significant at the median quantile. At the high quantiles, there is a weak negative linkage. According to the causality-in-quantiles approach results, in most cases global financial assets have different degrees of predictive capacity for the selected stock markets. Especially around the median quantile, the predictive ability was strongest. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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13 pages, 308 KiB

Open AccessEditor’s ChoiceArticle

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

by Brecht Verbeken and Marie-Anne Guerry

Mathematics 2021, 9(14), 1681; https://doi.org/10.3390/math9141681 - 16 Jul 2021

Cited by 10 | Viewed by 3280

Abstract

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of [...] Read more.

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria. Full article

(This article belongs to the Special Issue Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields)

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31 pages, 6058 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Partial Diffusion Markov Model of Heterogeneous TCP Link: Optimization with Incomplete Information

by Andrey Borisov, Alexey Bosov, Gregory Miller and Igor Sokolov

Mathematics 2021, 9(14), 1632; https://doi.org/10.3390/math9141632 - 10 Jul 2021

Cited by 5 | Viewed by 2834

Abstract

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via [...] Read more.

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via an unobservable controllable MJP (Markov jump process) with finite-state space. Observations are formed by low-frequency counting processes of packet losses and timeouts and a high-frequency compound Poisson process of packet acknowledgments. The information transmission through the TCP-equipped channel is considered a stochastic control problem with incomplete information. The main idea to solve it is to impose the separation principle on the problem. The paper proposes a mathematical framework and algorithmic support to implement the solution. It includes a solution to the stochastic control problem with complete information, a diffusion approximation of the high-frequency observations, a solution to the MJP state filtering problem given the observations with multiplicative noises, and a numerical scheme of the filtering algorithm. The paper also contains the results of a comparative study of the proposed state-based congestion control algorithm with the contemporary TCP versions: Illinois, CUBIC, Compound, and BBR (Bottleneck Bandwidth and RTT). Full article

(This article belongs to the Special Issue Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields)

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21 pages, 21971 KiB

Open AccessEditor’s ChoiceArticle

A Study on the Impact of Linguistic Persuasive Styles on the Sales Volume of Live Streaming Products in Social E-Commerce Environment

by Hanyang Luo, Sijia Cheng, Wanhua Zhou, Sumin Yu and Xudong Lin

Mathematics 2021, 9(13), 1576; https://doi.org/10.3390/math9131576 - 4 Jul 2021

Cited by 69 | Viewed by 18017

Abstract

Live-stream shopping is developing rapidly, but the sales levels of live streaming products vary by different hosts. How to increase the sales volume of live streaming products has become a problem. Consumers’ purchase behavior in live streaming is determined by some subjective factors, [...] Read more.

Live-stream shopping is developing rapidly, but the sales levels of live streaming products vary by different hosts. How to increase the sales volume of live streaming products has become a problem. Consumers’ purchase behavior in live streaming is determined by some subjective factors, and the persuasiveness of linguistic style affects this subjective judgment to a certain extent. Therefore, the persuasiveness of the hosts’ linguistic style will lead to changes in consumers’ purchase intentions, which will affect the sales volume of products sold in the live streaming. Based on Hovland’s persuasion model, Aristotle’s rhetoric skills, text analysis, Latent Dirichlet Allocation (LDA) topic extraction model and grounded theory, this study divides the host’s linguistic persuasive style in the social e-commerce environment into five types: appealing to personality, appealing to logic, appealing to emotion, appealing to reward, and appealing to exaggeration. Combined with the sales volume of the product, we establish a regression model, and obtain the influence results of the host’s various linguistic persuasive styles on the sales of live streaming products. The results show that: the linguistic persuasive style of appealing to personality has the greatest positive impact on the sales volume of live broadcast products, but the linguistic style of appealing to logic has a negative impact. Interestingly, the same linguistic style has different effects for different types of products: the linguistic style of appealing to exaggeration has a negative effect on the sales volume of apparel products, but it has a positive influence on the sales volume of digital electrical products. Therefore, different linguistic styles should be used for different product types. Full article

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26 pages, 385 KiB

Open AccessEditor’s ChoiceReview

General Fractional Dynamics

by Vasily E. Tarasov

Mathematics 2021, 9(13), 1464; https://doi.org/10.3390/math9131464 - 22 Jun 2021

Cited by 52 | Viewed by 4816

Abstract

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with [...] Read more.

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general form of nonlocality, which can be described by general-form operator kernels and not by its particular implementations and representations. In this paper, the concept of “general nonlocal mappings” is proposed; these are the exact solutions of equations with GFI and GFD at discrete points. In these mappings, the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs. These types of kernels are used in general fractional integrals and derivatives for the initial equations. Using general fractional calculus, we considered fractional systems with general nonlocality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order were also used to derive general nonlocal mappings. The exact solutions for these general fractional differential and integral equations with kicks were obtained. These exact solutions with discrete timepoints were used to derive general nonlocal mappings without approximations. Some examples of nonlocality in time are described. Full article

25 pages, 764 KiB

Open AccessEditor’s ChoiceCommunication

Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

by Mihaela Aurelia Tomescu, Lorentz Jäntschi and Doina Iulia Rotaru

Mathematics 2021, 9(12), 1419; https://doi.org/10.3390/math9121419 - 18 Jun 2021

Cited by 22 | Viewed by 4069

Abstract

A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented [...] Read more.

A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented with colors. Following this fundamental idea, it was proposed to color the graphs according to the partitions of the graph vertices. Two alternative cases were identified: when the order of the sets in the partition is relevant (the sets are distinguished by their positions) and when the order of the sets in the partition is not relevant (the sets are not distinguished by their positions). The two isomers of

C_{28}

fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures. Full article

(This article belongs to the Collection Topology and Foundations)

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26 pages, 3649 KiB

Open AccessEditor’s ChoiceArticle

Analysis of User Needs on Downloading Behavior of English Vocabulary APPs Based on Data Mining for Online Comments

by Tinggui Chen, Lijuan Peng, Jianjun Yang and Guodong Cong

Mathematics 2021, 9(12), 1341; https://doi.org/10.3390/math9121341 - 9 Jun 2021

Cited by 45 | Viewed by 5549

Abstract

With highly developed social media, English learning Applications have become a new type of mobile learning resources, and online comments posted by users after using them have not only become an important source of intellectual competition for enterprises, but can also help understand [...] Read more.

With highly developed social media, English learning Applications have become a new type of mobile learning resources, and online comments posted by users after using them have not only become an important source of intellectual competition for enterprises, but can also help understand customers’ requirements, thereby improving product functionalities and service quality, and solve the pain points of product iteration and innovation. Based on this, this paper crawled the online user comments of three typical APPs (BaiCiZhan, MoMoBeiDanCi and BuBeiDanCi), through emotion analysis and hotspot mining technology, to obtain user requirements and then the K-means clustering method was used to analyze user requirements. Finally, quantile regression is used to find out which user needs have an impact on the downloads of English vocabulary APPs. The results show that: (1) Positive comments have a more significant impact on users’ downloads behavior than negative online comments. (2) English vocabulary APPs with higher downloads, both the 5-star user ratings and the increase of emotional requirement have a negative effect on the increase in APP downloads, while the enterprise’s service requirement improvement has a positive effect on the increase of APP downloads. (3) Regarding English vocabulary APPs with average or high downloads, improving the adaptability and Appearance requirements have significant negative impact on downloads. (4) The functional requirements to improve products will have a significant positive impact on the increase in downloads of English vocabulary APPs. Full article

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

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32 pages, 8244 KiB

Open AccessEditor’s ChoiceArticle

Stability Analysis of Systems with Fuzzy PI Controllers Applied to Electric Drives

by Constantin Voloşencu

Mathematics 2021, 9(11), 1246; https://doi.org/10.3390/math9111246 - 29 May 2021

Cited by 7 | Viewed by 2592

Abstract

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of [...] Read more.

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers. Full article

(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)

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33 pages, 37135 KiB

Open AccessEditor’s ChoiceArticle

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

by Tobias Gerach, Steffen Schuler, Jonathan Fröhlich, Laura Lindner, Ekaterina Kovacheva, Robin Moss, Eike Moritz Wülfers, Gunnar Seemann, Christian Wieners and Axel Loewe

Mathematics 2021, 9(11), 1247; https://doi.org/10.3390/math9111247 - 29 May 2021

Cited by 76 | Viewed by 11688

Abstract

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a [...] Read more.

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling. Full article

(This article belongs to the Special Issue Development and Applications of Multi-Scale Mathematical Models in Cardiology)

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22 pages, 3520 KiB

Open AccessEditor’s ChoiceArticle

Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms

by Jose-Cruz Nuñez-Perez, Vincent-Ademola Adeyemi, Yuma Sandoval-Ibarra, Francisco-Javier Perez-Pinal and Esteban Tlelo-Cuautle

Mathematics 2021, 9(11), 1194; https://doi.org/10.3390/math9111194 - 25 May 2021

Cited by 18 | Viewed by 3744

Abstract

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), [...] Read more.

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation. Full article

(This article belongs to the Special Issue Optimization Theory and Applications)

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14 pages, 517 KiB

Open AccessEditor’s ChoiceReview

A Survey on Software Defect Prediction Using Deep Learning

by Elena N. Akimova, Alexander Yu. Bersenev, Artem A. Deikov, Konstantin S. Kobylkin, Anton V. Konygin, Ilya P. Mezentsev and Vladimir E. Misilov

Mathematics 2021, 9(11), 1180; https://doi.org/10.3390/math9111180 - 24 May 2021

Cited by 64 | Viewed by 11153

Abstract

Defect prediction is one of the key challenges in software development and programming language research for improving software quality and reliability. The problem in this area is to properly identify the defective source code with high accuracy. Developing a fault prediction model is [...] Read more.

Defect prediction is one of the key challenges in software development and programming language research for improving software quality and reliability. The problem in this area is to properly identify the defective source code with high accuracy. Developing a fault prediction model is a challenging problem, and many approaches have been proposed throughout history. The recent breakthrough in machine learning technologies, especially the development of deep learning techniques, has led to many problems being solved by these methods. Our survey focuses on the deep learning techniques for defect prediction. We analyse the recent works on the topic, study the methods for automatic learning of the semantic and structural features from the code, discuss the open problems and present the recent trends in the field. Full article

(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)

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15 pages, 283 KiB

Open AccessEditor’s ChoiceArticle

A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

by Hari Mohan Srivastava and Sama Arjika

Mathematics 2021, 9(11), 1161; https://doi.org/10.3390/math9111161 - 21 May 2021

Cited by 21 | Viewed by 2240

Abstract

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of [...] Read more.

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called

(p, q)

-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant. Full article

(This article belongs to the Special Issue Orthogonal Polynomials and Special Functions)

16 pages, 269 KiB

Open AccessEditor’s ChoiceArticle

On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique

by Ahmed Refice, Mohammed Said Souid and Ivanka Stamova

Mathematics 2021, 9(10), 1134; https://doi.org/10.3390/math9101134 - 17 May 2021

Cited by 30 | Viewed by 2991

Abstract

In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with [...] Read more.

In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of the observed results. Full article

(This article belongs to the Section E4: Mathematical Physics)

11 pages, 711 KiB

Open AccessEditor’s ChoiceArticle

Developing a Novel Fuzzy Evaluation Model by One-Sided Specification Capability Indices

by Wei Lo, Chun-Ming Yang, Kuei-Kuei Lai, Shao-Yu Li and Chi-Han Chen

Mathematics 2021, 9(10), 1076; https://doi.org/10.3390/math9101076 - 11 May 2021

Cited by 15 | Viewed by 2048

Abstract

When all of the one-sided specification indices of each quality characteristic reach the requirements of the process quality level, they can ensure that the process capability of the product meets the requirements of the process quality level. This study constructs a fuzzy membership [...] Read more.

When all of the one-sided specification indices of each quality characteristic reach the requirements of the process quality level, they can ensure that the process capability of the product meets the requirements of the process quality level. This study constructs a fuzzy membership function based on the upper confidence limit of the index, derives the fuzzy critical value, and then labels the fuzzy critical value on the axis of the visualized radar chart as well as connects adjacent critical points to shape a regular polygonal critical region. Next, this study calculates the observed value of the index to estimate and mark it on the axis for forming a visualized fuzzy radar evaluation chart. Obviously, this fuzzy evaluation model not only reduces the testing cost but also makes the quality level quickly meet the requirements of the specifications. Further, the radar chart can reduce the risk of misjudgment attributable to sampling errors and help improve the accuracy of evaluation by a confidence-upper-limit-based fuzzy evaluation model. Therefore, this easy-to-use visualized fuzzy radar evaluation chart is used as an evaluation interface, which has good and convenient management performance to identify and improve critical-to-quality quickly. Improving the quality of the process before the product is completed will also have the advantage of reducing social losses and environmental damage costs. Full article

(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)

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32 pages, 2447 KiB

Open AccessEditor’s ChoiceArticle

Carbon Futures Trading and Short-Term Price Prediction: An Analysis Using the Fractal Market Hypothesis and Evolutionary Computing

by Marc Lamphiere, Jonathan Blackledge and Derek Kearney

Mathematics 2021, 9(9), 1005; https://doi.org/10.3390/math9091005 - 29 Apr 2021

Cited by 14 | Viewed by 3671

Abstract

This paper presents trend prediction results based on backtesting of the European Union Emissions Trading Scheme futures market. This is based on the Intercontinental Exchange from 2005 to 2019. An alternative trend prediction strategy is taken that is predicated on an application of [...] Read more.

This paper presents trend prediction results based on backtesting of the European Union Emissions Trading Scheme futures market. This is based on the Intercontinental Exchange from 2005 to 2019. An alternative trend prediction strategy is taken that is predicated on an application of the Fractal Market Hypothesis (FMH) in order to develop an indicator that is predictive of short term future behaviour. To achieve this, we consider that a change in the polarity of the Lyapunov-to-Volatility Ratio precedes an associated change in the trend of the European Union Allowances (EUAs) price signal. The application of the FMH in this case is demonstrated to provide a useful tool in order to assess the likelihood of the market becoming bear or bull dominant, thereby helping to inform carbon trading investment decisions. Under specific conditions, Evolutionary Computing methods are utilised in order to optimise specific trading execution points within a trend and improve the potential profitability of trading returns. Although the approach may well be of value for general energy commodity futures trading (and indeed the wider financial and commodity derivative markets), this paper presents the application of an investment indicator for EUA carbon futures risk modelling and investment trend analysis only. Full article

(This article belongs to the Special Issue Fractal Market Hypothesis, Trend Analysis and Future Price Prediction)

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20 pages, 1966 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Interdependence between Green Financial Instruments and Major Conventional Assets: A Wavelet-Based Network Analysis

by Román Ferrer, Rafael Benítez and Vicente J. Bolós

Mathematics 2021, 9(8), 900; https://doi.org/10.3390/math9080900 - 19 Apr 2021

Cited by 38 | Viewed by 6487

Abstract

This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based [...] Read more.

This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based network approach that allows for assessing the degree of interconnection between green financial products and traditional asset classes across different investment horizons is applied. The empirical results show that green bonds are tightly linked to Treasury and investment-grade corporate bonds, while green stocks are strongly tied to general stocks, regardless of the specific time period and investment horizon considered. However, despite their common climate-friendly nature, there is no a remarkable association between green bonds and green stocks. This means that these green investments constitute basically two independent asset classes, with a distinct risk-return profile and aimed at a different type of investor. Furthermore, green financial products have a weak connection with high-yield corporate bonds and crude oil. These findings can have important implications for investors and policy makers in terms of investment decision, hedging strategies, and sustainability and energy policies. Full article

(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)

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27 pages, 2828 KiB

Open AccessEditor’s ChoiceArticle

A Compromised Decision-Making Approach to Third-Party Logistics Selection in Sustainable Supply Chain Using Fuzzy AHP and Fuzzy VIKOR Methods

by Chia-Nan Wang, Ngoc-Ai-Thy Nguyen, Thanh-Tuan Dang and Chen-Ming Lu

Mathematics 2021, 9(8), 886; https://doi.org/10.3390/math9080886 - 16 Apr 2021

Cited by 118 | Viewed by 10096

Abstract

With the effects of the COVID-19 pandemic, the e-commerce trend is driving faster, significantly impacting supply chains around the world. Thus, the importance of logistics and supply chain functions has been amplified in almost every business that ships physical goods. In Vietnam, the [...] Read more.

With the effects of the COVID-19 pandemic, the e-commerce trend is driving faster, significantly impacting supply chains around the world. Thus, the importance of logistics and supply chain functions has been amplified in almost every business that ships physical goods. In Vietnam, the logistics service sector has seen rapid expansion. Since more and more businesses are seeking third-party logistics (3PL) providers to outsource the logistics functions, this article aims to offer decision-makers an integrated and consistent model for evaluating and selecting the most efficient 3PLs. To this end, the authors exploit a hybrid multi-criteria method which is fuzzy analytic hierarchy process (FAHP) and fuzzy vlsekriterijumska optimizacija i kompromisno resenje (FVIKOR) while examining the most influential and conflicting criteria regarding economic, service level, environmental, social, and risk aspects. Fuzzy information in the natural decision-making process is considered, linguistic variables are used to mitigate the uncertain levels in the criteria weights. First, FAHP (the weighting method) is adopted to evaluate and calculate each criterion’s relative significant fuzzy weight. FVIKOR (the compromised ranking method) is then used to rank the alternatives. The combination of FAHP and FVIKOR methods provides more accurate ranking results. As a result, reliability and delivery time, voice of customer, logistics cost, network management, and quality of service are the most impactful factors to the logistics outsourcing problem. Eventually, the optimized 3PLs were determined that fully meet the criteria of sustainable development. The developed integrated model offers the complete and robust 3PLs evaluation and selection process and can also be a powerful decision support tool for other industries. Full article

(This article belongs to the Special Issue Advances in Multiple Criteria Decision Analysis)

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20 pages, 2097 KiB

Open AccessEditor’s ChoiceArticle

An Exhaustive Power Comparison of Normality Tests

by Jurgita Arnastauskaitė, Tomas Ruzgas and Mindaugas Bražėnas

Mathematics 2021, 9(7), 788; https://doi.org/10.3390/math9070788 - 6 Apr 2021

Cited by 31 | Viewed by 7748

Abstract

A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the [...] Read more.

A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size

n \geq 118

. Full article

(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)

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27 pages, 884 KiB

Open AccessEditor’s ChoiceArticle

A Continuous Review Production-Inventory System with a Variable Preparation Time in a Fuzzy Random Environment

by Amalendu Singha Mahapatra, Hardik N Soni, Maheswar Singha Mahapatra, Biswajit Sarkar and Sanat Majumder

Mathematics 2021, 9(7), 747; https://doi.org/10.3390/math9070747 - 31 Mar 2021

Cited by 38 | Viewed by 3818

Abstract

With the increase in the varieties products and the increasing uncertainty about product demand, the production preparation time is a significant factor in addressing these issues. The trade-off between the reduction of the production preparation time and the associated cost remains a critical [...] Read more.

With the increase in the varieties products and the increasing uncertainty about product demand, the production preparation time is a significant factor in addressing these issues. The trade-off between the reduction of the production preparation time and the associated cost remains a critical decision. With this backdrop, this study presents a continuous review production-inventory model with a variable production preparation time and a time-dependent setup cost. The demand during the preparation time is captured through a min-max distribution-free approach. In a stochastic framework, the order quantity, reorder point, and setup time are optimized by minimizing the expected cost considering the time-value effect. Further, a fuzzy model is formulated to tackle the imprecise nature of the production setup time and demand. Two algorithms are developed using an analytical approach to obtain the optimal solution. A numerical illustration is given to present the key insights of the model for effective inventory management. It is observed that order quantity and total cost are more sensitive at the lower side of the optimal setup time rather than at the higher side. The discount rate is also found to be a sensitive factor while minimizing the total expected cost. Full article

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31 pages, 1777 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Unified CACSD Toolbox for Hybrid Simulation and Robust Controller Synthesis with Applications in DC-to-DC Power Converter Control

by Mircea Şuşcă, Vlad Mihaly, Mihai Stănese, Dora Morar and Petru Dobra

Mathematics 2021, 9(7), 731; https://doi.org/10.3390/math9070731 - 28 Mar 2021

Cited by 15 | Viewed by 3803

Abstract

The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using

μ

synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and [...] Read more.

The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using

μ

synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and hybrid systems, automatic computation of equilibrium points for nonlinear systems, and optimization of least conservative uncertainty bounds, with direct applicability for

μ

synthesis. A unified approach is presented for the step-down (buck), step-up (boost), and single-ended primary-inductor (SEPIC) converters to showcase the use and flexibility of the toolbox. Robust controllers were computed by minimization of the

H_{\infty}

norm of the augmented performance systems, encompassing a wide range of uncertainty types, and have been designed using the well-known mixed-sensitivity closed loop shaping

μ

synthesis method. Full article

(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)

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13 pages, 488 KiB

Open AccessEditor’s ChoiceArticle

Nonlinearities and Chaos: A New Analysis of CEE Stock Markets

by Claudiu Tiberiu Albulescu, Aviral Kumar Tiwari and Phouphet Kyophilavong

Mathematics 2021, 9(7), 707; https://doi.org/10.3390/math9070707 - 25 Mar 2021

Cited by 16 | Viewed by 3094

Abstract

After a long transition period, the Central and Eastern European (CEE) capital markets have consolidated their place in the financial systems. However, little is known about the price behavior and efficiency of these markets. In this context, using a battery of tests for [...] Read more.

After a long transition period, the Central and Eastern European (CEE) capital markets have consolidated their place in the financial systems. However, little is known about the price behavior and efficiency of these markets. In this context, using a battery of tests for nonlinear and chaotic behavior, we look for the presence of nonlinearities and chaos in five CEE stock markets. We document, in general, the presence of nonlinearities and chaos which questions the efficient market hypothesis. However, if all tests highlight a chaotic behavior for the analyzed index returns, there are noteworthy differences between the analyzed stock markets underlined by nonlinearity tests, which question, thus, their level of significance. Moreover, the results of nonlinearity tests partially contrast the previous findings reported in the literature on the same group of stock markets, showing, thus, a change in their recent behavior, compared with the 1990s. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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19 pages, 334 KiB

Open AccessEditor’s ChoiceArticle

On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (p,q)-Calculus

by Fongchan Wannalookkhee, Kamsing Nonlaopon, Jessada Tariboon and Sotiris K. Ntouyas

Mathematics 2021, 9(7), 698; https://doi.org/10.3390/math9070698 - 24 Mar 2021

Cited by 16 | Viewed by 2777

Abstract

In this paper, we define

(p, q)

-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using

(p, q)

-integrals. Many results obtained in this paper provide [...] Read more.

In this paper, we define

(p, q)

-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using

(p, q)

-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results. Full article

17 pages, 311 KiB

Open AccessEditor’s ChoiceArticle

General Fractional Integrals and Derivatives with the Sonine Kernels

by Yuri Luchko

Mathematics 2021, 9(6), 594; https://doi.org/10.3390/math9060594 - 10 Mar 2021

Cited by 108 | Viewed by 6193

Abstract

In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed. In [...] Read more.

In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed. In particular, we introduce a class of the Sonine kernels that possess an integrable singularity of power function type at the point zero. For the general fractional integrals and derivatives with the Sonine kernels from this class, two fundamental theorems of fractional calculus are proved. Then, we construct the n-fold general fractional integrals and derivatives and study their properties. Full article

(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False” II)

17 pages, 491 KiB

Open AccessEditor’s ChoiceArticle

On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n

by Bilal A. Rather, Shariefuddin Pirzada, Tariq A. Naikoo and Yilun Shang

Mathematics 2021, 9(5), 482; https://doi.org/10.3390/math9050482 - 26 Feb 2021

Cited by 50 | Viewed by 3374

Abstract

Given a commutative ring R with identity

1 \neq 0

, let the set

Z (R)

denote the set of zero-divisors and let

Z^{*} (R) = Z (R) ∖ {0}

be the set of [...] Read more.

Given a commutative ring R with identity

1 \neq 0

, let the set

Z (R)

denote the set of zero-divisors and let

Z^{*} (R) = Z (R) ∖ {0}

be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by

Γ (R)

, is a simple graph whose vertex set is

Z^{*} (R)

and each pair of vertices in

Z^{*} (R)

are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs

Γ (Z_{n})

for

n = p^{N_{1}} q^{N_{2}}

, where

p < q

are primes and

N_{1}, N_{2}

are positive integers. Full article

(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)

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22 pages, 3723 KiB

Open AccessEditor’s ChoiceArticle

Stochastic Chebyshev Goal Programming Mixed Integer Linear Model for Sustainable Global Production Planning

by Chia-Nan Wang, Nhat-Luong Nhieu and Trang Thi Thu Tran

Mathematics 2021, 9(5), 483; https://doi.org/10.3390/math9050483 - 26 Feb 2021

Cited by 25 | Viewed by 4179

Abstract

Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective [...] Read more.

Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective mixed-integer optimization model is developed to ensure production efficiency in uncertainty conditions and satisfy the requirements of sustainable development. The efficiency of the production system is ensured through objective functions that optimize backorder quantity, machine uptime and customer satisfaction. The other three objective functions of the proposed model are related to optimization of profits, emissions, and employment changing. The objective functions respectively represent the three elements of sustainable development: economy, environment, and sociality. The proposed model also assures the production manager’s discretion over whether or not to adopt production options such as backorder, overtime, and employment of temporary workers. At the same time, the resource limits of the above options can also be adjusted according to the situation of each production facility via the model’s parameters. The solutions that compromise the above objective functions are determined with the Chebyshev goal programming approach together with the weights of the goals. The model is applied to the multinational production system of a Southeast Asian supplier in the textile industry. The goal programming solution of the model shows an improvement in many aspects compared to this supplier’s manufacturing practices under the same production conditions. Last but not least, the study develops different scenarios based on different random distributions of uncertainty demand and different weights between the objective functions. The analysis and evaluation of these scenarios provide a reference basis for managers to adjust the production system in different situations. Analysis of uncertain demand with more complex random distributions as well as making predictions about the effectiveness of scenarios through the advantages of machine learning can be considered in future studies. Full article

(This article belongs to the Special Issue Statistical Methods in Economics)

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12 pages, 297 KiB

Open AccessEditor’s ChoiceArticle

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

by Volodymyr Berezovski, Yevhen Cherevko, Josef Mikeš and Lenka Rýparová

Mathematics 2021, 9(4), 437; https://doi.org/10.3390/math9040437 - 22 Feb 2021

Cited by 10 | Viewed by 2301

Abstract

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed [...] Read more.

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained results extend an amount of research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš. Full article

(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Their Applications)

25 pages, 2582 KiB

Open AccessEditor’s ChoiceArticle

Comprehensive Assessment of Distance Learning Modules by Fuzzy AHP-TOPSIS Method

by Svajone Bekesiene, Aidas Vasilis Vasiliauskas, Šárka Hošková-Mayerová and Virgilija Vasilienė-Vasiliauskienė

Mathematics 2021, 9(4), 409; https://doi.org/10.3390/math9040409 - 19 Feb 2021

Cited by 24 | Viewed by 5268

Abstract

This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities [...] Read more.

This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities to Ideal Solution) is one of the best solutions. Therefore, this paper presents the distance learning quality assessment surveys when the Fuzzy AHP (Analytic Hierarchy Process) and TOPSIS methods are used. Research results describe the application of the Fuzzy AHP—TOPSIS hybrid method. MCDM (Multi-Criteria Decision Making) programs with MATLAB (R2020b) mathematical package were written to calculate the evaluation results for three distance learning courses. In the practical implementation of the proposed distance learning module evaluation methodology, the experts’ evaluation method was applied. Thirty-four judges were chosen with specific knowledge and skills and with very different competencies to assess three alternatives by fourteen criteria. Following the experts’ evaluation, a statistical analysis method was used to process the data. After applying the complex evaluation, the comparative analysis method was used to summarize the obtained results. This work further provides useful guidelines for the development of an easily understandable hierarchy of criteria model that reflects the main goal of study quality assessment. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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27 pages, 6191 KiB

Open AccessEditor’s ChoiceArticle

Application of Hexagonal Fuzzy MCDM Methodology for Site Selection of Electric Vehicle Charging Station

by Arijit Ghosh, Neha Ghorui, Sankar Prasad Mondal, Suchitra Kumari, Biraj Kanti Mondal, Aditya Das and Mahananda Sen Gupta

Mathematics 2021, 9(4), 393; https://doi.org/10.3390/math9040393 - 16 Feb 2021

Cited by 52 | Viewed by 5613

Abstract

In this paper, the application of hexagonal fuzzy multiple-criteria decision-making (MCDM) methodology for the site selection of electric vehicle charging stations is considered. In this regard, four factors and thirteen sub-factors have been taken into consideration for E-vehicle charging site selection. In this [...] Read more.

In this paper, the application of hexagonal fuzzy multiple-criteria decision-making (MCDM) methodology for the site selection of electric vehicle charging stations is considered. In this regard, four factors and thirteen sub-factors have been taken into consideration for E-vehicle charging site selection. In this research, the geographic information system (GIS) has been incorporated with MCDM techniques. The fuzzy analytic hierarchy process (FAHP) is used to obtain a fuzzy weight of factors and sub-factors. MCDM tools fuzzy technique for order of preference by similarity to ideal solution (FTOPSIS) and fuzzy complex proportional assessment (FCOPRAS) have been used to rank the selected sites. A centroid-based method for defuzzification and distance measure between two hexagonal fuzzy numbers (HFN) has been developed for this paper. A practical example in Howrah, India, is considered to show the applicability and usefulness of the model. The results depict the suitability of the proposed research. Comparative and sensitivity analyses have been demonstrated to check the reliability, robustness and effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)

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12 pages, 566 KiB

Open AccessEditor’s ChoiceArticle

Inverse Problem of Recovering the Initial Condition for a Nonlinear Equation of the Reaction–Diffusion–Advection Type by Data Given on the Position of a Reaction Front with a Time Delay

by Dmitry Lukyanenko, Tatyana Yeleskina, Igor Prigorniy, Temur Isaev, Andrey Borzunov and Maxim Shishlenin

Mathematics 2021, 9(4), 342; https://doi.org/10.3390/math9040342 - 9 Feb 2021

Cited by 16 | Viewed by 3616

Abstract

In this paper, approaches to the numerical recovering of the initial condition in the inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are considered. The feature of the formulation of the inverse problem is the use of additional information about the value [...] Read more.

In this paper, approaches to the numerical recovering of the initial condition in the inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are considered. The feature of the formulation of the inverse problem is the use of additional information about the value of the solution of the equation at the known position of a reaction front, measured experimentally with a delay relative to the initial moment of time. In this case, for the numerical solution of the inverse problem, the gradient method of minimizing the cost functional is applied. In the case when only the position of the reaction front is known, the method of deep machine learning is applied. Numerical experiments demonstrated the possibility of solving such kinds of considered inverse problems. Full article

(This article belongs to the Section E: Applied Mathematics)

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14 pages, 3399 KiB

Open AccessEditor’s ChoiceArticle

A Clustering Perspective of the Collatz Conjecture

by José A. Tenreiro Machado, Alexandra Galhano and Daniel Cao Labora

Mathematics 2021, 9(4), 314; https://doi.org/10.3390/math9040314 - 5 Feb 2021

Cited by 10 | Viewed by 7989

Abstract

This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of [...] Read more.

This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of why is it hard from the mathematical point of view. The second part is dedicated to the visualization of behaviors of the Collatz iteration function and the analysis of the results. Full article

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16 pages, 757 KiB

Open AccessEditor’s ChoiceArticle

Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models

by Ángeles Cebrián-Hernández and Enrique Jiménez-Rodríguez

Mathematics 2021, 9(3), 267; https://doi.org/10.3390/math9030267 - 29 Jan 2021

Cited by 13 | Viewed by 4502

Abstract

Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and [...] Read more.

Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and its high return potential have generated the attention of portfolio managers. In this context, understanding how its volatility is explained is a critical element of investor decision-making. By modeling the volatility of classic assets, nonlinear models such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH) offer suitable results. Therefore, taking GARCH(1,1) as a reference point, the main aim of this study is to model and assess the relationship between the Bitcoin volatility and key financial environment variables through a Conditional Correlation (CC) Multivariate GARCH (MGARCH) approach. For this, several commodities, exchange rates, stock market indices, and company stocks linked to cryptocurrencies have been tested. The results obtained show certain heterogeneity in the fit of the different variables, highlighting the uncorrelation with respect to traditional safe haven assets such as gold and oil. Focusing on the CC-MGARCH model, a better behavior of the dynamic conditional correlation is found compared to the constant. Full article

(This article belongs to the Special Issue Application of Mathematical Analysis and Models to Financial Economics)

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16 pages, 5839 KiB

Open AccessEditor’s ChoiceArticle

Design of Constrained Robust Controller for Active Suspension of In-Wheel-Drive Electric Vehicles

by Xianjian Jin, Jiadong Wang, Shaoze Sun, Shaohua Li, Junpeng Yang and Zeyuan Yan

Mathematics 2021, 9(3), 249; https://doi.org/10.3390/math9030249 - 27 Jan 2021

Cited by 35 | Viewed by 4296

Abstract

This paper presents a constrained robust H_∞ controller design of active suspension system for in-wheel-independent-drive electric vehicles considering control constraint and parameter variation. In the active suspension system model, parameter uncertainties of sprung mass are analyzed via linear fraction transformation, and the [...] Read more.

This paper presents a constrained robust H_∞ controller design of active suspension system for in-wheel-independent-drive electric vehicles considering control constraint and parameter variation. In the active suspension system model, parameter uncertainties of sprung mass are analyzed via linear fraction transformation, and the perturbation bounds can be also limited, then the uncertain quarter-vehicle active suspension model where the in-wheel motor is suspended as a dynamic vibration absorber is built. The constrained robust H_∞ feedback controller of the closed-loop active suspension system is designed using the concept of reachable sets and ellipsoids, in which the dynamic tire displacements and the suspension working spaces are constrained, and a comprehensive solution is finally derived from H_∞ performance and robust stability. Simulations on frequency responses and road excitations are implemented to verify and evaluate the performance of the designed controller; results show that the active suspension with a developed H_∞ controller can effectively achieve better ride comfort and road-holding ability compared with passive suspension despite the existence of control constraints and parameter variations. Full article

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16 pages, 1270 KiB

Open AccessEditor’s ChoiceArticle

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

by Ángel Berihuete, Marta Sánchez-Sánchez and Alfonso Suárez-Llorens

Mathematics 2021, 9(3), 228; https://doi.org/10.3390/math9030228 - 25 Jan 2021

Cited by 15 | Viewed by 4267

Abstract

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an [...] Read more.

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain. Full article

(This article belongs to the Special Issue Stochastic Models with Applications)

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24 pages, 596 KiB

Open AccessEditor’s ChoiceArticle

Diffusion–Advection Equations on a Comb: Resetting and Random Search

by Trifce Sandev, Viktor Domazetoski, Alexander Iomin and Ljupco Kocarev

Mathematics 2021, 9(3), 221; https://doi.org/10.3390/math9030221 - 22 Jan 2021

Cited by 18 | Viewed by 3086

Abstract

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical [...] Read more.

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting. Full article

(This article belongs to the Special Issue Fractional Calculus in Anomalous Transport Theory)

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