Editor's Choice Articles

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

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Article
A Comprehensive Analysis of Demand Response Pricing Strategies in a Smart Grid Environment Using Particle Swarm Optimization and the Strawberry Optimization Algorithm
Mathematics 2021, 9(18), 2338; https://doi.org/10.3390/math9182338 - 21 Sep 2021
Cited by 8 | Viewed by 1047
Abstract
In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to [...] Read more.
In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to the shortfall in power generation. The abovesaid deficit signifies the explicit need for a strategy that reduces the peak demand by rescheduling the load pattern, as well as reduces the stress on grids. Demand-side management (DSM) uses several algorithms for proper reallocation of loads, collectively known as demand response (DR). DR strategies effectively culminate in monetary benefits for customers and the utilities using dynamic pricing (DP) and incentive-based procedures. This study attempts to analyze the DP schemes of DR such as time-of-use (TOU) and real-time pricing (RTP) for different load scenarios in a smart grid (SG). Centralized and distributed algorithms are used to analyze the price-based DR problem using RTP. A techno-economic analysis was performed by using particle swarm optimization (PSO) and the strawberry (SBY) optimization algorithms used in handling the DP strategies with 109, 1992, and 7807 controllable industrial, commercial, and residential loads. A better optimization algorithm to go along with the pricing scheme to reduce the peak-to-average ratio (PAR) was identified. The results demonstrate that centralized RTP using the SBY optimization algorithm helped to achieve 14.80%, 21.7%, and 21.84% in cost reduction and outperformed the PSO. Full article
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Article
An Integrated Mathematical Attitude Utilizing Fully Fuzzy BWM and Fuzzy WASPAS for Risk Evaluation in a SOFC
Mathematics 2021, 9(18), 2328; https://doi.org/10.3390/math9182328 - 19 Sep 2021
Cited by 6 | Viewed by 846
Abstract
Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, [...] Read more.
Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, failure modes evaluations need an experts team to achieve uncertainties belongs to the risk assessment procedure. To improve the efficiency of the routine FMEA methodology and to represent a suitable hybrid fuzzy MCDM approach for FMEA, in this work, fully fuzzy best-worst method (FF-BWM) is employed to achieve the risk factors weights then fuzzy weighted aggregated sum product assessment (F-WASPAS) approach to detect the failure modes priorities is utilized. Ultimately, the sensitivity analyses demonstrate that the offered framework is verified and can make applicable data in risk management decision-making evaluation. Full article
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Article
An Innovative Hybrid Heap-Based and Jellyfish Search Algorithm for Combined Heat and Power Economic Dispatch in Electrical Grids
Mathematics 2021, 9(17), 2053; https://doi.org/10.3390/math9172053 - 26 Aug 2021
Cited by 10 | Viewed by 729
Abstract
This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two [...] Read more.
This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two recent algorithms: heap-based algorithm (HBA) and jellyfish search algorithm (JSA). The proposed hybrid HBJSA seeks to make use of the explorative features of HBA and the exploitative features of the JSA to overcome some of the problems found in their standard forms. The proposed hybrid HBJSA, HBA, and JSA are validated and statistically compared by attempting to solve a real-world optimization issue of the CHP economic dispatch. It aims to satisfy the power and heat demands and minimize the whole fuel cost (WFC) of the power and heat generation units. Additionally, a series of operational and electrical constraints such as non-convex feasible operating regions of CHP and valve-point effects of power-only plants, respectively, are considered in solving such a problem. The proposed hybrid HBJSA, HBA, and JSA are employed on two medium systems, which are 24-unit and 48-unit systems, and two large systems, which are 84- and 96-unit systems. The experimental results demonstrate that the proposed hybrid HBJSA outperforms the standard HBA and JSA and other reported techniques when handling the CHP economic dispatch. Otherwise, comparative analyses are carried out to demonstrate the suggested HBJSA’s strong stability and robustness in determining the lowest minimum, average, and maximum WFC values compared to the HBA and JSA. Full article
(This article belongs to the Topic Multi-Energy Systems)
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Article
Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell
Mathematics 2021, 9(17), 2025; https://doi.org/10.3390/math9172025 - 24 Aug 2021
Cited by 4 | Viewed by 1028
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+ 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
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Article
New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations
Mathematics 2021, 9(16), 2000; https://doi.org/10.3390/math9162000 - 21 Aug 2021
Cited by 5 | Viewed by 903
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 Lαm, 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 Lαm, given by Lαm:AnAn, Lαmf(z)=(1α)Rmf(z)+αSmf(z), where An={fH(U),f(z)=z+an+1zn+1+,zU} is the subclass of normalized holomorphic functions and the operators Rmf(z) and Smf(z) are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator Lαm, a certain fuzzy class of analytic functions denoted by SLFmδ,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
Article
Fast Terminal Sliding Control of Underactuated Robotic Systems Based on Disturbance Observer with Experimental Validation
Mathematics 2021, 9(16), 1935; https://doi.org/10.3390/math9161935 - 13 Aug 2021
Cited by 15 | Viewed by 1091
Abstract
In this study, a novel fast terminal sliding mode control technique based on the disturbance observer is recommended for the stabilization of underactuated robotic systems. The finite time disturbance observer is employed to estimate the exterior disturbances of the system and develop the [...] Read more.
In this study, a novel fast terminal sliding mode control technique based on the disturbance observer is recommended for the stabilization of underactuated robotic systems. The finite time disturbance observer is employed to estimate the exterior disturbances of the system and develop the finite time control law. The proposed controller can regulate the state trajectories of the underactuated systems to the origin within a finite time in the existence of external disturbances. The stability analysis of the proposed control scheme is verified via the Lyapunov stabilization theory. The designed control law is enough to drive a switching surface achieving the fast terminal sliding mode against severe model nonlinearities with large parametric uncertainties and external disturbances. Illustrative simulation results and experimental validations on a cart-inverted pendulum system are provided to display the success and efficacy of the offered method. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making
Mathematics 2021, 9(16), 1922; https://doi.org/10.3390/math9161922 - 12 Aug 2021
Cited by 12 | Viewed by 513
Abstract
In a conventional interpretation of decision-making based on ambiguity, a decision-maker must prefer the best possible opportunity including various feasible possibilities. However, the dilemma of picking the best possible alternative has continued to be a substantial task to resolve. In this manuscript, we [...] Read more.
In a conventional interpretation of decision-making based on ambiguity, a decision-maker must prefer the best possible opportunity including various feasible possibilities. However, the dilemma of picking the best possible alternative has continued to be a substantial task to resolve. In this manuscript, we improve the existing complex intuitionistic fuzzy soft set (CIFSS), which includes the grade of truth and falsity with the rule that the sum of the real and imaginary parts of both grades is confined to [0, 1]. CIFS is a valuable procedure to determine the authenticity and consistency of the elaborated approaches. The fundamental laws and their related examples are also determined. Moreover, by using these laws, we investigated the complex intuitionistic fuzzy soft prioritized weighted averaging operator (CIFSPWAO), the complex intuitionistic fuzzy soft prioritized ordered weighted averaging operator (CIFSPOWAO), the complex intuitionistic fuzzy soft prioritized weighted geometric operator (CIFSPWGO), complex intuitionistic fuzzy soft prioritized ordered weighted geometric operator (CIFSPOWGO), and their related properties are also developed. Based on the developed operators, the multiattribute decision-making (MADM) tool is developed by using the explored operators based on CIFSS. Some numerical examples are also illustrated by using the investigated operators to determine the feasibility and consistency of the developed approaches. Finally, the comparative analysis and their geometrical manifestations are also determined to enhance the excellence of the performed explorations. Full article
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Article
A Two Phase Integrated Fuzzy Decision-Making Framework for Green Supplier Selection in the Coffee Bean Supply Chain
Mathematics 2021, 9(16), 1923; https://doi.org/10.3390/math9161923 - 12 Aug 2021
Cited by 9 | Viewed by 951
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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Article
Fractional Growth Model Applied to COVID-19 Data
Mathematics 2021, 9(16), 1915; https://doi.org/10.3390/math9161915 - 11 Aug 2021
Cited by 3 | Viewed by 1140
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<β1, 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 R2>0.999. Full article
(This article belongs to the Special Issue Theory and Applications of Fractional Equations and Calculus)
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Article
A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices
Mathematics 2021, 9(16), 1895; https://doi.org/10.3390/math9161895 - 09 Aug 2021
Cited by 19 | Viewed by 931
Abstract
In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and [...] Read more.
In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study. Full article
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Article
Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach
Mathematics 2021, 9(16), 1841; https://doi.org/10.3390/math9161841 - 04 Aug 2021
Cited by 9 | Viewed by 683
Abstract
Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation [...] Read more.
Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation points, the governing equation transforms into a non-linear algebraic matrix equation. In the second approach, the technique of quasi-linearization is first employed to linearize the model problem and, then, the first collocation method is applied to the sequence of linearized equations iteratively. In the latter approach, we require to solve a linear algebraic matrix equation in each iteration. Moreover, the error analysis of the Bessel series solution is established. In the end, numerical simulations and computational results are provided to illustrate the utility and applicability of the presented collocation approaches. Numerical comparisons with some existing available methods are performed to validate our results. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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Article
Fixed-Time Third-Order Super-Twisting-like Sliding Mode Motion Control for Piezoelectric Nanopositioning Stage
Mathematics 2021, 9(15), 1770; https://doi.org/10.3390/math9151770 - 27 Jul 2021
Cited by 5 | Viewed by 865
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 Engineering Mathematics)
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Article
Connectedness and Local Connectedness on Infra Soft Topological Spaces
Mathematics 2021, 9(15), 1759; https://doi.org/10.3390/math9151759 - 26 Jul 2021
Cited by 10 | Viewed by 642
Abstract
This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We [...] Read more.
This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components. Full article
(This article belongs to the Special Issue Fuzzy Topology)
Article
Revisiting the Valuable Roles of Global Financial Assets for International Stock Markets: Quantile Coherence and Causality-in-Quantiles Approaches
Mathematics 2021, 9(15), 1750; https://doi.org/10.3390/math9151750 - 24 Jul 2021
Cited by 18 | Viewed by 785
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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Article
Discrete Time Hybrid Semi-Markov Models in Manpower Planning
Mathematics 2021, 9(14), 1681; https://doi.org/10.3390/math9141681 - 16 Jul 2021
Cited by 2 | Viewed by 931
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
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Article
Partial Diffusion Markov Model of Heterogeneous TCP Link: Optimization with Incomplete Information
Mathematics 2021, 9(14), 1632; https://doi.org/10.3390/math9141632 - 10 Jul 2021
Cited by 3 | Viewed by 1001
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
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Article
A Study on the Impact of Linguistic Persuasive Styles on the Sales Volume of Live Streaming Products in Social E-Commerce Environment
Mathematics 2021, 9(13), 1576; https://doi.org/10.3390/math9131576 - 04 Jul 2021
Cited by 3 | Viewed by 3511
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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Article
A Review of Matrix SIR Arino Epidemic Models
Mathematics 2021, 9(13), 1513; https://doi.org/10.3390/math9131513 - 28 Jun 2021
Cited by 5 | Viewed by 948
Abstract
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call [...] Read more.
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies. Full article
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Communication
Figures of Graph Partitioning by Counting, Sequence and Layer Matrices
Mathematics 2021, 9(12), 1419; https://doi.org/10.3390/math9121419 - 18 Jun 2021
Cited by 6 | Viewed by 886
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 C28 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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Article
Analysis of User Needs on Downloading Behavior of English Vocabulary APPs Based on Data Mining for Online Comments
Mathematics 2021, 9(12), 1341; https://doi.org/10.3390/math9121341 - 09 Jun 2021
Cited by 23 | Viewed by 1561
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 Fuzzy Set Theory)
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Article
An Integrated Decision-Making Approach for Green Supplier Selection in an Agri-Food Supply Chain: Threshold of Robustness Worthiness
Mathematics 2021, 9(11), 1304; https://doi.org/10.3390/math9111304 - 07 Jun 2021
Cited by 17 | Viewed by 1479
Abstract
Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price and higher quality. On the other hand, consideration of environmental criteria in the conventional supplier selection methodologies is required for companies trying [...] Read more.
Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price and higher quality. On the other hand, consideration of environmental criteria in the conventional supplier selection methodologies is required for companies trying to promote green supply chain management (GSCM). In this regard, a multi-criteria decision-making (MCDM) technique based on analytic hierarchy process (AHP) and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) is used to evaluate and rate the suppliers. Then, considering the resource constraint, weight of criteria and a rank of suppliers are taken into account in a multi-objective mixed-integer linear programming (MOMILP) to determine the optimum order quantity of each supplier under uncertain conditions. To deal with the uncertain multi-objectiveness of the proposed model, a robust goal programming (RGP) approach based on Shannon entropy is applied. The offered methodology is applied to a real case study from a green service food manufacturing company in Iran in order to verify its applicability with a sensitivity analysis performed on different uncertainty levels. Furthermore, the threshold of robustness worthiness (TRW) is studied by applying different budgets of uncertainty for the green service food manufacturing company. Finally, a discussion and conclusion on the applicability of the methodology is provided, and an outlook to future research projects is given. Full article
(This article belongs to the Special Issue Decision Making and Its Applications)
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Article
On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy
Mathematics 2021, 9(11), 1302; https://doi.org/10.3390/math9111302 - 06 Jun 2021
Cited by 7 | Viewed by 1031
Abstract
We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due [...] Read more.
We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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Article
Stability Analysis of Systems with Fuzzy PI Controllers Applied to Electric Drives
Mathematics 2021, 9(11), 1246; https://doi.org/10.3390/math9111246 - 29 May 2021
Cited by 3 | Viewed by 839
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 Logic Control Systems)
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Article
Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach
Mathematics 2021, 9(11), 1247; https://doi.org/10.3390/math9111247 - 29 May 2021
Cited by 12 | Viewed by 2167
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
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Article
Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovskiĭ Approach
Mathematics 2021, 9(11), 1196; https://doi.org/10.3390/math9111196 - 25 May 2021
Cited by 9 | Viewed by 729
Abstract
In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and [...] Read more.
In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and boundedness of solutions of a perturbed system. We construct two appropriate Lyapunov–Krasovskiĭ functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov–Krasovskiĭ method. For illustration, two examples are provided in particular cases. An advantage of the new LKFs used here is that they allow to eliminate using Gronwall’s inequality. When we compare our results with recent results in the literature, the established conditions are more general, less restrictive and optimal for applications. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
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Article
Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms
Mathematics 2021, 9(11), 1194; https://doi.org/10.3390/math9111194 - 25 May 2021
Cited by 6 | Viewed by 914
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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Article
A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
Mathematics 2021, 9(11), 1161; https://doi.org/10.3390/math9111161 - 21 May 2021
Cited by 6 | Viewed by 600
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)
Article
On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique
Mathematics 2021, 9(10), 1134; https://doi.org/10.3390/math9101134 - 17 May 2021
Cited by 10 | Viewed by 757
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 Mathematical Physics)
Article
New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation
Mathematics 2021, 9(10), 1111; https://doi.org/10.3390/math9101111 - 14 May 2021
Cited by 11 | Viewed by 830
Abstract
In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form [...] Read more.
In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))))+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ξ0dξa(ξ)= and ξ0dξa(ξ)<. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results. Full article
Article
Developing a Novel Fuzzy Evaluation Model by One-Sided Specification Capability Indices
Mathematics 2021, 9(10), 1076; https://doi.org/10.3390/math9101076 - 11 May 2021
Cited by 5 | Viewed by 635
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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Article
Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms
Mathematics 2021, 9(9), 1021; https://doi.org/10.3390/math9091021 - 30 Apr 2021
Cited by 7 | Viewed by 770
Abstract
The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the [...] Read more.
The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions. Full article
(This article belongs to the Special Issue Mathematical Analysis with Applications)
Article
Carbon Futures Trading and Short-Term Price Prediction: An Analysis Using the Fractal Market Hypothesis and Evolutionary Computing
Mathematics 2021, 9(9), 1005; https://doi.org/10.3390/math9091005 - 29 Apr 2021
Cited by 6 | Viewed by 975
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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Article
Interdependence between Green Financial Instruments and Major Conventional Assets: A Wavelet-Based Network Analysis
Mathematics 2021, 9(8), 900; https://doi.org/10.3390/math9080900 - 19 Apr 2021
Cited by 6 | Viewed by 1229
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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Article
A Compromised Decision-Making Approach to Third-Party Logistics Selection in Sustainable Supply Chain Using Fuzzy AHP and Fuzzy VIKOR Methods
Mathematics 2021, 9(8), 886; https://doi.org/10.3390/math9080886 - 16 Apr 2021
Cited by 30 | Viewed by 2876
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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Article
Deep Learning for Wave Energy Converter Modeling Using Long Short-Term Memory
Mathematics 2021, 9(8), 871; https://doi.org/10.3390/math9080871 - 15 Apr 2021
Cited by 22 | Viewed by 1315
Abstract
Accurate forecasts of ocean waves energy can not only reduce costs for investment, but it is also essential for the management and operation of electrical power. This paper presents an innovative approach based on long short-term memory (LSTM) to predict the power generation [...] Read more.
Accurate forecasts of ocean waves energy can not only reduce costs for investment, but it is also essential for the management and operation of electrical power. This paper presents an innovative approach based on long short-term memory (LSTM) to predict the power generation of an economical wave energy converter named “Searaser”. The data for analysis is provided by collecting the experimental data from another study and the exerted data from a numerical simulation of Searaser. The simulation is performed with Flow-3D software, which has high capability in analyzing fluid–solid interactions. The lack of relation between wind speed and output power in previous studies needs to be investigated in this field. Therefore, in this study, wind speed and output power are related with an LSTM method. Moreover, it can be inferred that the LSTM network is able to predict power in terms of height more accurately and faster than the numerical solution in a field of predicting. The network output figures show a great agreement, and the root mean square is 0.49 in the mean value related to the accuracy of the LSTM method. Furthermore, the mathematical relation between the generated power and wave height was introduced by curve fitting of the power function to the result of the LSTM method. Full article
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Article
An Exhaustive Power Comparison of Normality Tests
Mathematics 2021, 9(7), 788; https://doi.org/10.3390/math9070788 - 06 Apr 2021
Cited by 9 | Viewed by 1278
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 n118. Full article
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
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Article
A Continuous Review Production-Inventory System with a Variable Preparation Time in a Fuzzy Random Environment
Mathematics 2021, 9(7), 747; https://doi.org/10.3390/math9070747 - 31 Mar 2021
Cited by 24 | Viewed by 903
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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Article
Unified CACSD Toolbox for Hybrid Simulation and Robust Controller Synthesis with Applications in DC-to-DC Power Converter Control
Mathematics 2021, 9(7), 731; https://doi.org/10.3390/math9070731 - 28 Mar 2021
Cited by 8 | Viewed by 1348
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 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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Article
Nonlinearities and Chaos: A New Analysis of CEE Stock Markets
Mathematics 2021, 9(7), 707; https://doi.org/10.3390/math9070707 - 25 Mar 2021
Cited by 6 | Viewed by 947
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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Article
On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (p,q)-Calculus
Mathematics 2021, 9(7), 698; https://doi.org/10.3390/math9070698 - 24 Mar 2021
Cited by 9 | Viewed by 825
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
Article
Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect
Mathematics 2021, 9(6), 643; https://doi.org/10.3390/math9060643 - 18 Mar 2021
Cited by 13 | Viewed by 933
Abstract
The mathematical modeling of dusty Cu-Al2O3/water nanofluid flow driven by a permeable deformable sheet was explored numerically. Rather than no–slip conditions at the boundary, velocity slip and thermal slip were considered. To achieve the system of nonlinear ordinary differential [...] Read more.
The mathematical modeling of dusty Cu-Al2O3/water nanofluid flow driven by a permeable deformable sheet was explored numerically. Rather than no–slip conditions at the boundary, velocity slip and thermal slip were considered. To achieve the system of nonlinear ordinary differential equations (ODEs), we employed some appropriate transformations and solved them numerically using MATLAB software (built–in solver called bvp4c). The influences of relevant parameters on fluid flow and heat transfer characteristics are discussed and presented in graphs. The findings showed that double solutions appeared in the case of stretching and shrinking sheets which contributed to the analysis of stability. The stability analysis, therefore, confirmed that merely the first solution was a stable solution. The addition of nanometer-sized particles (Cu) was found to significantly strengthen the heat transfer rate of the dusty nanofluid. Meanwhile, an upsurge in the velocity and thermal slip was shown to decrease the local Nusselt number. The result also revealed that an increment of fluid particle interaction decreased the boundary layer thickness. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter
Mathematics 2021, 9(6), 636; https://doi.org/10.3390/math9060636 - 17 Mar 2021
Cited by 37 | Viewed by 4370
Abstract
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), [...] Read more.
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods against the COVID-19 Pandemics)
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Article
General Fractional Integrals and Derivatives with the Sonine Kernels
Mathematics 2021, 9(6), 594; https://doi.org/10.3390/math9060594 - 10 Mar 2021
Cited by 26 | Viewed by 2394
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
Article
Stochastic Chebyshev Goal Programming Mixed Integer Linear Model for Sustainable Global Production Planning
Mathematics 2021, 9(5), 483; https://doi.org/10.3390/math9050483 - 26 Feb 2021
Cited by 7 | Viewed by 892
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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Article
On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n
Mathematics 2021, 9(5), 482; https://doi.org/10.3390/math9050482 - 26 Feb 2021
Cited by 9 | Viewed by 897
Abstract
Given a commutative ring R with identity 10, 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 10, 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(Zn) for n=pN1qN2, where p<q are primes and N1,N2 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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Article
Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces
Mathematics 2021, 9(4), 437; https://doi.org/10.3390/math9040437 - 22 Feb 2021
Cited by 9 | Viewed by 785
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)
Article
Comprehensive Assessment of Distance Learning Modules by Fuzzy AHP-TOPSIS Method
Mathematics 2021, 9(4), 409; https://doi.org/10.3390/math9040409 - 19 Feb 2021
Cited by 9 | Viewed by 1863
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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Article
Application of Hexagonal Fuzzy MCDM Methodology for Site Selection of Electric Vehicle Charging Station
Mathematics 2021, 9(4), 393; https://doi.org/10.3390/math9040393 - 16 Feb 2021
Cited by 8 | Viewed by 1580
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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Article
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
Mathematics 2021, 9(4), 342; https://doi.org/10.3390/math9040342 - 09 Feb 2021
Cited by 9 | Viewed by 1231
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 Computational and Applied Mathematics)
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Article
A Clustering Perspective of the Collatz Conjecture
Mathematics 2021, 9(4), 314; https://doi.org/10.3390/math9040314 - 05 Feb 2021
Cited by 5 | Viewed by 2231
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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