Mathematics

15 pages, 61065 KiB

Open AccessArticle

Numerical Modeling of Face Shield Protection against a Sneeze

by Ainara Ugarte-Anero, Unai Fernandez-Gamiz, Iñigo Aramendia, Ekaitz Zulueta and Jose Manuel Lopez-Guede

Mathematics 2021, 9(13), 1582; https://doi.org/10.3390/math9131582 - 05 Jul 2021

Cited by 9 | Viewed by 3143

Abstract

The protection provided by wearing masks has been a guideline worldwide to prevent the risk of COVID-19 infection. The current work presents an investigation that analyzes the effectiveness of face shields as personal protective equipment. To that end, a multiphase computational fluid dynamic [...] Read more.

The protection provided by wearing masks has been a guideline worldwide to prevent the risk of COVID-19 infection. The current work presents an investigation that analyzes the effectiveness of face shields as personal protective equipment. To that end, a multiphase computational fluid dynamic study based on Eulerian–Lagrangian techniques was defined to simulate the spread of the droplets produced by a sneeze. Different scenarios were evaluated where the relative humidity, ambient temperature, evaporation, mass transfer, break up, and turbulent dispersion were taken into account. The saliva that the human body generates was modeled as a saline solution of 8.8 g per 100 mL. In addition, the influence of the wind speed was studied with a soft breeze of 7 km/h and a moderate wind of 14 km/h. The results indicate that the face shield does not provide accurate protection, because only the person who is sneezed on is protected. Moreover, with a wind of 14 km/h, none of the droplets exhaled into the environment hit the face shield, instead, they were deposited onto the neck and face of the wearer. In the presence of an airflow, the droplets exhaled into the environment exceeded the safe distance marked by the WHO. Relative humidity and ambient temperature play an important role in the lifetime of the droplets. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

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17 pages, 4110 KiB

Open AccessArticle

Hybrid Optimization Based Mathematical Procedure for Dimensional Synthesis of Slider-Crank Linkage

by Alfonso Hernández, Aitor Muñoyerro, Mónica Urízar and Enrique Amezua

Mathematics 2021, 9(13), 1581; https://doi.org/10.3390/math9131581 - 05 Jul 2021

Cited by 4 | Viewed by 2170

Abstract

In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, [...] Read more.

In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, a novel methodology to solve the resulting non-linear equations is developed. The solving procedure consists of decoupling two subsystems of equations which can be solved separately and following an iterative process. In relation to the global technique, a multi-start method based on a genetic algorithm is implemented. The fitness function incorporated in the genetic algorithm will take as arguments the set of dimensional parameters of the slider-crank mechanism. Several illustrative examples will prove the validity of the proposed optimization methodology, in some cases achieving an even better result compared to mechanisms with a higher number of dimensional parameters, such as the four-bar mechanism or the Watt’s mechanism. Full article

(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines)

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9 pages, 1840 KiB

Open AccessArticle

A Modified Recursive Regularization Factor Calculation for Sparse RLS Algorithm with l₁-Norm

by Junseok Lim, Keunhwa Lee and Seokjin Lee

Mathematics 2021, 9(13), 1580; https://doi.org/10.3390/math9131580 - 05 Jul 2021

Cited by 2 | Viewed by 1753

Abstract

In this paper, we propose a new calculation method for the regularization factor in sparse recursive least squares (SRLS) with

l_{1}

-norm penalty. The proposed regularization factor requires no prior knowledge of the actual system impulse response, and it also reduces computational [...] Read more.

In this paper, we propose a new calculation method for the regularization factor in sparse recursive least squares (SRLS) with

l_{1}

-norm penalty. The proposed regularization factor requires no prior knowledge of the actual system impulse response, and it also reduces computational complexity by about half. In the simulation, we use Mean Square Deviation (MSD) to evaluate the performance of SRLS, using the proposed regularization factor. The simulation results demonstrate that SRLS using the proposed regularization factor calculation shows a difference of less than 2 dB in MSD from SRLS, using the conventional regularization factor with a true system impulse response. Therefore, it is confirmed that the performance of the proposed method is very similar to that of the existing method, even with half the computational complexity. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)

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16 pages, 601 KiB

Open AccessArticle

Efficiency Analysis with Educational Data: How to Deal with Plausible Values from International Large-Scale Assessments

by Juan Aparicio, Jose M. Cordero and Lidia Ortiz

Mathematics 2021, 9(13), 1579; https://doi.org/10.3390/math9131579 - 05 Jul 2021

Cited by 12 | Viewed by 3393

Abstract

International large-scale assessments (ILSAs) provide several measures as a representation of educational outcomes, the so-called plausible values, which are frequently interpreted as a representation of the ability range of students. In this paper, we focus on how this information should be incorporated into [...] Read more.

International large-scale assessments (ILSAs) provide several measures as a representation of educational outcomes, the so-called plausible values, which are frequently interpreted as a representation of the ability range of students. In this paper, we focus on how this information should be incorporated into the estimation of efficiency measures of student or school performance using data envelopment analysis (DEA). Thus far, previous studies that have adopted this approach using data from ILSAs have used only one of the available plausible values or an average of all of them. We propose an approach based on the fuzzy DEA, which allows us to consider the whole distribution of results as a proxy of student abilities. To assess the extent to which our proposal offers similar results to those obtained in previous studies, we provide an empirical example using PISA data from 2015. Our results suggest that the performance measures estimated using the fuzzy DEA approach are strongly correlated with measures calculated using just one plausible value or an average measure. Therefore, we conclude that the studies that decide upon using one of these options do not seem to be making a significant error in their estimates. Full article

(This article belongs to the Special Issue Economics of Education: Quantitative Methods for Educational Policies)

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23 pages, 1510 KiB

Open AccessArticle

Automatic Group Organization for Collaborative Learning Applying Genetic Algorithm Techniques and the Big Five Model

by Oscar Revelo Sánchez, César A. Collazos and Miguel A. Redondo

Mathematics 2021, 9(13), 1578; https://doi.org/10.3390/math9131578 - 05 Jul 2021

Cited by 4 | Viewed by 2202

Abstract

In this paper, an approach based on genetic algorithms is proposed to form groups in collaborative learning scenarios, considering the students’ personality traits as a criterion for grouping. This formation is carried out in two stages: In the first, the information of the [...] Read more.

In this paper, an approach based on genetic algorithms is proposed to form groups in collaborative learning scenarios, considering the students’ personality traits as a criterion for grouping. This formation is carried out in two stages: In the first, the information of the students is collected from a psychometric instrument based on the Big Five personality model; whereas, in the second, this information feeds a genetic algorithm that is in charge of performing the grouping iteratively, seeking for an optimal formation. The results presented here correspond to the functional and empirical validation of the approach. It is found that the described methodology is useful to obtain groups with the desired characteristics. The specific objective is to provide a strategy that makes it possible to subsequently assess in the context what type of approach (homogeneous, heterogeneous, or mixed) is the most appropriate to organize the groups. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence and Statistical Techniques with Applications to Health and Education)

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12 pages, 3892 KiB

Open AccessArticle

An Embedding Strategy Using Q-Ary Convolutional Codes for Large and Small Payloads

by Jyun-Jie Wang, Chi-Yuan Lin, Sheng-Chih Yang, Hsi-Yuan Chang and Yin-Chen Lin

Mathematics 2021, 9(13), 1577; https://doi.org/10.3390/math9131577 - 04 Jul 2021

Viewed by 1938

Abstract

Matrix embedding (ME) code is a commonly used steganography technique, which uses linear block codes to improve embedding efficiency. However, its main disadvantage is the inability to perform maximum likelihood decoding due to the high complexity of decoding large ME codes. As such, [...] Read more.

Matrix embedding (ME) code is a commonly used steganography technique, which uses linear block codes to improve embedding efficiency. However, its main disadvantage is the inability to perform maximum likelihood decoding due to the high complexity of decoding large ME codes. As such, it is difficult to improve the embedding efficiency. The proposed q-ary embedding code can provide excellent embedding efficiency and is suitable for various embedding rates (large and small payloads). This article discusses that by using perforation technology, a convolutional code with a high embedding rate can be easily converted into a convolutional code with a low embedding rate. By keeping the embedding rate of the (2, 1) convolutional code unchanged, convolutional codes with different embedding rates can be designed through puncturing. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium on Computer, Consumer and Control (IS3C2020))

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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 - 04 Jul 2021

Cited by 46 | Viewed by 12519

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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19 pages, 835 KiB

Open AccessArticle

Application of Induced Preorderings in Score Function-Based Method for Solving Decision-Making with Interval-Valued Fuzzy Soft Information

by Mabruka Ali, Adem Kiliçman and Azadeh Zahedi Khameneh

Mathematics 2021, 9(13), 1575; https://doi.org/10.3390/math9131575 - 04 Jul 2021

Cited by 2 | Viewed by 1682

Abstract

Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the [...] Read more.

Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the literature. However, these algorithms are not able to overcome the issue of comparable alternatives and, in fact, might be ignored due to the lack of a comprehensive priority approach. In order to provide a partial solution to this problem, we present a group decision-making solution which is based on a preference relationship of interval-valued fuzzy soft information. Further, corresponding to each parameter, two crisp topological spaces, namely, lower topology and upper topology, are introduced based on the interval-valued fuzzy soft topology. Then, using the preorder relation on a topological space, a score function-based ranking system is also defined to design an adjustable multi-steps algorithm. Finally, some illustrative examples are given to compare the effectiveness of the present approach with some existing methods. 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))

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14 pages, 928 KiB

Open AccessArticle

A Cascade Deep Forest Model for Breast Cancer Subtype Classification Using Multi-Omics Data

by Ala’a El-Nabawy, Nahla A. Belal and Nashwa El-Bendary

Mathematics 2021, 9(13), 1574; https://doi.org/10.3390/math9131574 - 04 Jul 2021

Cited by 9 | Viewed by 2996

Abstract

Automated diagnosis systems aim to reduce the cost of diagnosis while maintaining the same efficiency. Many methods have been used for breast cancer subtype classification. Some use single data source, while others integrate many data sources, the case that results in reduced computational [...] Read more.

Automated diagnosis systems aim to reduce the cost of diagnosis while maintaining the same efficiency. Many methods have been used for breast cancer subtype classification. Some use single data source, while others integrate many data sources, the case that results in reduced computational performance as opposed to accuracy. Breast cancer data, especially biological data, is known for its imbalance, with lack of extensive amounts of histopathological images as biological data. Recent studies have shown that cascade Deep Forest ensemble model achieves a competitive classification accuracy compared with other alternatives, such as the general ensemble learning methods and the conventional deep neural networks (DNNs), especially for imbalanced training sets, through learning hyper-representations through using cascade ensemble decision trees. In this work, a cascade Deep Forest is employed to classify breast cancer subtypes, IntClust and Pam50, using multi-omics datasets and different configurations. The results obtained recorded an accuracy of 83.45% for 5 subtypes and 77.55% for 10 subtypes. The significance of this work is that it is shown that using gene expression data alone with the cascade Deep Forest classifier achieves comparable accuracy to other techniques with higher computational performance, where the time recorded is about 5 s for 10 subtypes, and 7 s for 5 subtypes. Full article

(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications)

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28 pages, 449 KiB

Open AccessArticle

New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas

by Waleed Mohamed Abd-Elhameed and Badah Mohamed Badah

Mathematics 2021, 9(13), 1573; https://doi.org/10.3390/math9131573 - 04 Jul 2021

Cited by 7 | Viewed by 1643

Abstract

This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new formula in which the moments of the [...] Read more.

This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new formula in which the moments of the shifted Jacobi polynomials are expressed in terms of other shifted Jacobi polynomials. The derived moments formula involves a hypergeometric function of the type

4 F_{3} (1)

, which cannot be summed in general, but for special choices of the involved parameters, it can be summed. The reduced moments formulas lead to establishing new linearization formulas of certain parameters of Jacobi polynomials. Another approach for obtaining other linearization formulas of some Jacobi polynomials depends on making use of the connection formulas between two different Jacobi polynomials. In the two suggested approaches, we utilize some standard reduction formulas for certain hypergeometric functions of the unit argument such as Watson’s and Chu-Vandermonde identities. Furthermore, some symbolic algebraic computations such as the algorithms of Zeilberger, Petkovsek and van Hoeij may be utilized for the same purpose. As an application of some of the derived linearization formulas, we propose a numerical algorithm to solve the non-linear Riccati differential equation based on the application of the spectral tau method. Full article

(This article belongs to the Special Issue Polynomial Sequences and Their Applications)

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44 pages, 1750 KiB

Open AccessArticle

A Multi-Depot Vehicle Routing Problem with Stochastic Road Capacity and Reduced Two-Stage Stochastic Integer Linear Programming Models for Rollout Algorithm

by Wadi Khalid Anuar, Lai Soon Lee, Hsin-Vonn Seow and Stefan Pickl

Mathematics 2021, 9(13), 1572; https://doi.org/10.3390/math9131572 - 04 Jul 2021

Cited by 6 | Viewed by 3895

Abstract

A matheuristic approach based on a reduced two-stage Stochastic Integer Linear Programming (SILP) model is presented. The proposed approach is suitable for obtaining a policy constructed dynamically on the go during the rollout algorithm. The rollout algorithm is part of the Approximate Dynamic [...] Read more.

A matheuristic approach based on a reduced two-stage Stochastic Integer Linear Programming (SILP) model is presented. The proposed approach is suitable for obtaining a policy constructed dynamically on the go during the rollout algorithm. The rollout algorithm is part of the Approximate Dynamic Programming (ADP) lookahead solution approach for a Markov Decision Processes (MDP) framed Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity (MDDVRPSRC). First, a Deterministic Multi-Depot VRP with Road Capacity (D-MDVRPRC) is presented. Then an extension, MDVRPSRC-2S, is presented as an offline two-stage SILP model of the MDDVRPSRC. These models are validated using small simulated instances with CPLEX. Next, two reduced versions of the MDVRPSRC-2S model (MDVRPSRC-2S1 and MDVRPSRC-2S2) are derived. They have a specific task in routing: replenishment and delivering supplies. These reduced models are to be utilised interchangeably depending on the capacity of the vehicle, and repeatedly during the execution of rollout in reinforcement learning. As a result, it is shown that a base policy consisting of an exact optimal decision at each decision epoch can be obtained constructively through these reduced two-stage stochastic integer linear programming models. The results obtained from the resulting rollout policy with CPLEX execution during rollout are also presented to validate the reduced model and the matheuristic algorithm. This approach is proposed as a simple implementation when performing rollout for the lookahead approach in ADP. Full article

(This article belongs to the Special Issue Mathematical Models and Exact and Heuristic Algorithms for Solving Complex Optimization Problems)

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8 pages, 258 KiB

Open AccessFeature PaperArticle

On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

by Irina Shevtsova and Mikhail Tselishchev

Mathematics 2021, 9(13), 1571; https://doi.org/10.3390/math9131571 - 04 Jul 2021

Cited by 4 | Viewed by 1625

Abstract

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds [...] Read more.

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution. Full article

(This article belongs to the Special Issue Analytical Methods and Convergence in Probability with Applications)

20 pages, 2052 KiB

Open AccessArticle

A Robust Approach for Identifying the Major Components of the Bribery Tolerance Index

by Daniel Homocianu, Aurelian-Petruș Plopeanu and Rodica Ianole-Calin

Mathematics 2021, 9(13), 1570; https://doi.org/10.3390/math9131570 - 03 Jul 2021

Cited by 4 | Viewed by 2149

Abstract

The paper aims to emphasize the advantages of several advanced statistical and data mining techniques when applied to the dense literature on corruption measurements and determinants. For this purpose, we used all seven waves of the World Values Survey and we employed the [...] Read more.

The paper aims to emphasize the advantages of several advanced statistical and data mining techniques when applied to the dense literature on corruption measurements and determinants. For this purpose, we used all seven waves of the World Values Survey and we employed the Naive Bayes technique in SQL Server Analysis Services 2016, the LASSO package together with logit and melogit regressions with raw coefficients in Stata 16. We further conducted different types of tests and cross-validations on the wave, country, gender, and age categories. For eliminating multicollinearity, we used predictor correlation matrices. Moreover, we assessed the maximum computed variance inflation factor (VIF) against a maximum acceptable threshold, depending on the model’s R squared in Ordinary Least Square (OLS) regressions. Our main contribution consists of a methodology for exploring and validating the most important predictors of the risk associated with bribery tolerance. We found the significant role of three influences corresponding to questions about attitudes towards the property, authority, and public services, and other people in terms of anti-cheating, anti-evasion, and anti-violence. We used scobit, probit, and logit regressions with average marginal effects to build and test the index based on these attitudes. We successfully tested the index using also risk prediction nomograms and accuracy measurements (AUCROC > 0.9). Full article

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16 pages, 4534 KiB

Open AccessArticle

A Tool for the Analysis and Characterization of School Mathematical Models

by Jesús Montejo-Gámez, Elvira Fernández-Ahumada and Natividad Adamuz-Povedano

Mathematics 2021, 9(13), 1569; https://doi.org/10.3390/math9131569 - 03 Jul 2021

Cited by 3 | Viewed by 2205

Abstract

This paper shows a tool for the analysis of written productions that allows for the characterization of the mathematical models that students develop when solving modeling tasks. For this purpose, different conceptualizations of mathematical models in education are discussed, paying special attention to [...] Read more.

This paper shows a tool for the analysis of written productions that allows for the characterization of the mathematical models that students develop when solving modeling tasks. For this purpose, different conceptualizations of mathematical models in education are discussed, paying special attention to the evidence that characterizes a school model. The discussion leads to the consideration of three components, which constitute the main categories of the proposed tool: the real system to be modeled, its mathematization and the representations used to express both. These categories and the corresponding analysis procedure are explained and illustrated through two working examples, which expose the value of the tool in establishing the foci of analysis when investigating school models, and thus, suggest modeling skills. The connection of this tool with other approaches to educational research on mathematical modeling is also discussed. Full article

(This article belongs to the Section Engineering Mathematics)

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11 pages, 298 KiB

Open AccessFeature PaperArticle

On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families

by Shaul K. Bar-Lev

Mathematics 2021, 9(13), 1568; https://doi.org/10.3390/math9131568 - 03 Jul 2021

Viewed by 1350

Abstract

Let

F = \{F_{θ} : θ \in Θ \subset R\}

be a family of probability distributions indexed by a parameter

θ

and let

X_{1}, \dots, X_{n}

be i.i.d. r.v.’s with

L (X_{1}) =

[...] Read more.

Let

F = \{F_{θ} : θ \in Θ \subset R\}

be a family of probability distributions indexed by a parameter

θ

and let

X_{1}, \dots, X_{n}

be i.i.d. r.v.’s with

L (X_{1}) =

F_{θ} \in F

. Then,

F

is said to be reproducible if for all

θ \in Θ

and

n \in N

, there exists a sequence

{(α_{n})}_{n \geq 1}

and a mapping

g_{n} : Θ \to Θ,

θ ⟼ g_{n} (θ)

such that

L (α_{n} \sum_{i = 1}^{n} X_{i}) = F_{g_{n} (θ)} \in F .

In this paper, we prove that a natural exponential family

F

is reproducible iff it possesses a variance function which is a power function of its mean. Such a result generalizes that of Bar-Lev and Enis (1986, The Annals of Statistics) who proved a similar but partial statement under the assumption that

F

is steep as and under rather restricted constraints on the forms of

α_{n}

and

g_{n} (θ)

. We show that such restrictions are not required. In addition, we examine various aspects of reproducibility, both theoretically and practically, and discuss the relationship between reproducibility, convolution and infinite divisibility. We suggest new avenues for characterizing other classes of families of distributions with respect to their reproducibility and convolution properties . Full article

(This article belongs to the Special Issue Advances in Applications of Probability Theory and Stochastic Processes)

15 pages, 10412 KiB

Open AccessArticle

Graph Theory for Primary School Students with High Skills in Mathematics

by Rocío Blanco and Melody García-Moya

Mathematics 2021, 9(13), 1567; https://doi.org/10.3390/math9131567 - 03 Jul 2021

Cited by 2 | Viewed by 2917

Abstract

Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The [...] Read more.

Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies. Full article

(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)

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18 pages, 343 KiB

Open AccessFeature PaperArticle

Local Dynamics of Logistic Equation with Delay and Diffusion

by Sergey Kashchenko

Mathematics 2021, 9(13), 1566; https://doi.org/10.3390/math9131566 - 03 Jul 2021

Cited by 3 | Viewed by 2166

Abstract

The behavior of all the solutions of the logistic equation with delay and diffusion in a sufficiently small positive neighborhood of the equilibrium state is studied. It is assumed that the Andronov–Hopf bifurcation conditions are met for the coefficients of the problem. Small [...] Read more.

The behavior of all the solutions of the logistic equation with delay and diffusion in a sufficiently small positive neighborhood of the equilibrium state is studied. It is assumed that the Andronov–Hopf bifurcation conditions are met for the coefficients of the problem. Small perturbations of all coefficients are considered, including the delay coefficient and the coefficients of the boundary conditions. The conditions are studied when these perturbations depend on the spatial variable and when they are time-periodic functions. Equations on the central manifold are constructed as the main results. Their nonlocal dynamics determines the behavior of all the solutions of the original boundary value problem in a sufficiently small neighborhood of the equilibrium state. The ability to control the dynamics of the original problem using the phase change in the perturbing force is set. The numerical and analytical results regarding the dynamics of the system with parametric perturbation are obtained. The asymptotic formulas for the solutions of the original boundary value problem are given. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)

11 pages, 1294 KiB

Open AccessArticle

SIAM—Colombia MMC: A Challenge-Based Math Modeling Learning Strategy

by Rafael Alberto Méndez-Romero, Diana H. Bueno-Carreño, Carlos Díez-Fonnegra and Johan Manuel Redondo

Mathematics 2021, 9(13), 1565; https://doi.org/10.3390/math9131565 - 03 Jul 2021

Viewed by 3063

Abstract

The math modeling challenge CoSIAM is a competition based on interdisciplinary collaborative work challenges. This research seeks to demonstrate the value of this type of challenge-based competition as a learning strategy outside the classroom. Based on data, we conducted a qualitative study on [...] Read more.

The math modeling challenge CoSIAM is a competition based on interdisciplinary collaborative work challenges. This research seeks to demonstrate the value of this type of challenge-based competition as a learning strategy outside the classroom. Based on data, we conducted a qualitative study on the perception of the participants in the last three versions of the mathematical modeling challenge, in terms of the learning achieved, the benefits of their participation, the knowledge and skills they brought into play, and the change in their conception of modeling. The participants were undergraduate and graduate students in mathematics and other areas, from several Colombian and Mexican universities. The research yielded results in three directions. The first is related to the advantages and limitations of teamwork, the second explores the learning that arises from this experience, and the third is oriented to the disciplinary knowledge mobilized for the solution of this type of problematic situation. The study allowed concluding, among other issues, that learning based on interdisciplinary problem solving, formulated from a global perspective, enhances the acquisition of valuable skills for the participants. Full article

(This article belongs to the Special Issue Mathematics as a Language and Other Languages for Learning Supported with ICT)

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22 pages, 555 KiB

Open AccessArticle

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

by Gilberto Gonzalez-Parra and Abraham J. Arenas

Mathematics 2021, 9(13), 1564; https://doi.org/10.3390/math9131564 - 03 Jul 2021

Cited by 6 | Viewed by 2519

Abstract

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect [...] Read more.

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number

R_{0}

using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population. Full article

(This article belongs to the Section Mathematical Biology)

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11 pages, 309 KiB

Open AccessArticle

The Cohomological Genus and Symplectic Genus for 4-Manifolds of Rational or Ruled Types

by Bo Dai and Chung-I Ho

Mathematics 2021, 9(13), 1563; https://doi.org/10.3390/math9131563 - 03 Jul 2021

Cited by 1 | Viewed by 1573

Abstract

An important problem in low dimensional topology is to understand the properties of embedded or immersed surfaces in 4-dimensional manifolds. In this article, we estimate the lower genus bound of closed, connected, smoothly embedded, oriented surfaces in a smooth, closed, connected, oriented 4-manifold [...] Read more.

An important problem in low dimensional topology is to understand the properties of embedded or immersed surfaces in 4-dimensional manifolds. In this article, we estimate the lower genus bound of closed, connected, smoothly embedded, oriented surfaces in a smooth, closed, connected, oriented 4-manifold with the cohomology algebra of a rational or ruled surface. Our genus bound depends only on the cohomology algebra rather than on the geometric structure of the 4-manifold. It provides evidence for the genus minimizing property of rational and ruled surfaces. Full article

(This article belongs to the Section Dynamical Systems)

20 pages, 664 KiB

Open AccessArticle

A New Forward–Backward Algorithm with Line Searchand Inertial Techniques for Convex Minimization Problems with Applications

by Dawan Chumpungam, Panitarn Sarnmeta and Suthep Suantai

Mathematics 2021, 9(13), 1562; https://doi.org/10.3390/math9131562 - 02 Jul 2021

Cited by 2 | Viewed by 1702

Abstract

For the past few decades, various algorithms have been proposed to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. The convergence of these algorithms was guaranteed under the L-Lipschitz condition on the gradient of [...] Read more.

For the past few decades, various algorithms have been proposed to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. The convergence of these algorithms was guaranteed under the L-Lipschitz condition on the gradient of the objective function. In recent years, an inertial technique has been widely used to accelerate the convergence behavior of an algorithm. In this work, we introduce a new forward–backward splitting algorithm using a new line search and inertial technique to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. A weak convergence of our proposed method is established without assuming the L-Lipschitz continuity of the gradient of the objective function. Moreover, a complexity theorem is also given. As applications, we employed our algorithm to solve data classification and image restoration by conducting some experiments on these problems. The performance of our algorithm was evaluated using various evaluation tools. Furthermore, we compared its performance with other algorithms. Based on the experiments, we found that the proposed algorithm performed better than other algorithms mentioned in the literature. Full article

(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)

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22 pages, 5419 KiB

Open AccessArticle

Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models

by Ryan Thiessen and Thomas Hillen

Mathematics 2021, 9(13), 1561; https://doi.org/10.3390/math9131561 - 02 Jul 2021

Cited by 2 | Viewed by 1569

Abstract

For this paper, we are interested in network formation of endothelial cells. Randomly distributed endothelial cells converge together to create a vascular system. To develop a mathematical model, we make assumptions on individual cell movement, leading to a velocity jump model with chemotaxis. [...] Read more.

For this paper, we are interested in network formation of endothelial cells. Randomly distributed endothelial cells converge together to create a vascular system. To develop a mathematical model, we make assumptions on individual cell movement, leading to a velocity jump model with chemotaxis. We use scaling arguments to derive an anisotropic chemotaxis model on the population level. For this macroscopic model, we develop a new numerical solver and investigate network-type pattern formation. Our model is able to reproduce experiments on network formation by Serini et al. Moreover, to our surprise, we found new spatial criss-cross patterns due to competing cues, one direction given by tissue anisotropy versus a different direction due to chemotaxis. A full analysis of these new patterns is left for future work. Full article

(This article belongs to the Special Issue Mathematical Models for Cell Migration and Spread)

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26 pages, 4620 KiB

Open AccessArticle

Simulation and Analysis of Renewable and Nonrenewable Capacity Scenarios under Hybrid Modeling: A Case Study

by José D. Morcillo, Fabiola Angulo and Carlos J. Franco

Mathematics 2021, 9(13), 1560; https://doi.org/10.3390/math9131560 - 02 Jul 2021

Cited by 4 | Viewed by 1967

Abstract

This work analyzes the response of the electricity market to varied renewable and nonrenewable installed capacity scenarios while taking into account the variability of renewables due to seasonality and El Niño-Southern Oscillation (ENSO) episodes. A hybrid system dynamics/dynamic systems (SD/DS) model was developed [...] Read more.

This work analyzes the response of the electricity market to varied renewable and nonrenewable installed capacity scenarios while taking into account the variability of renewables due to seasonality and El Niño-Southern Oscillation (ENSO) episodes. A hybrid system dynamics/dynamic systems (SD/DS) model was developed by first deriving an SD hypothesis and stock-flow structure from the Colombian electricity supply and demand dynamics. The model’s dynamic behavior was then transformed into a Simulink model and analyzed using the DS tools of bifurcation and control theory to provide deeper insights into the system, both from a Colombian perspective and from the perspective of other market scenarios. Applying the developed hybrid model to the Colombian electricity market provided a detailed description of its dynamics under a broad range of permanent (fossil fuel) and variable (renewable) installed capacity scenarios, including a number of counterintuitive insights. Greater shares of permanent capacity were found to guarantee the security of supply and system robustness in the short-term (2021–2029), whereas greater shares of variable capacity make the system more vulnerable to increased prices and blackouts, especially in the long-term (2040–2050). These critical situations can be avoided only if additional capacity from either conventional or non-conventional generation is quickly installed. Overall, the methodology proposed for building the hybrid SD/DS model was found to provide deeper insights and a broader spectrum of analysis than traditional SD model analysis, and thus can be exploited by policy makers to suggest improvements in their respective market structures. Full article

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

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17 pages, 959 KiB

Open AccessArticle

Case-Based Reasoning for Hidden Property Analysis of Judgment Debtors

by Huirong Zhang, Zhenyu Zhang, Lixin Zhou and Shuangsheng Wu

Mathematics 2021, 9(13), 1559; https://doi.org/10.3390/math9131559 - 02 Jul 2021

Cited by 10 | Viewed by 1854

Abstract

Many judgment debtors try to evade, confront, and delay law enforcement using concealing and transferring their property to resist law enforcement in China. The act of hiding property seriously affects people’s legitimate rights and interests and China’s legal authority. Therefore, it is essential [...] Read more.

Many judgment debtors try to evade, confront, and delay law enforcement using concealing and transferring their property to resist law enforcement in China. The act of hiding property seriously affects people’s legitimate rights and interests and China’s legal authority. Therefore, it is essential to find an effective method of analyzing whether a judgment debtor hides property. Aiming at the hidden property analysis problem, we propose a case-based reasoning method for the judgment debtor’s hidden property analysis. In the hidden property analysis process, we present the attributes of the enforcement case by crisp symbols, crisp numbers, interval numbers, and fuzzy linguistic variables and develop a hybrid similarity measure between the historical enforcement case and the target enforcement case. The results show that the recommendations obtained with the information and knowledge of similar historical cases are consistent with judicial practice, which can reduce the work pressure of law enforcement officers and improve the efficiency of handling enforcement cases. Full article

(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)

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13 pages, 1434 KiB

Open AccessArticle

Modeling COVID-19 Cases Statistically and Evaluating Their Effect on the Economy of Countries

by Hanns de la Fuente-Mella, Rolando Rubilar, Karime Chahuán-Jiménez and Víctor Leiva

Mathematics 2021, 9(13), 1558; https://doi.org/10.3390/math9131558 - 02 Jul 2021

Cited by 31 | Viewed by 4227

Abstract

COVID-19 infections have plagued the world and led to deaths with a heavy pneumonia manifestation. The main objective of this investigation is to evaluate the performance of certain economies during the crisis derived from the COVID-19 pandemic. The gross domestic product (GDP) and [...] Read more.

COVID-19 infections have plagued the world and led to deaths with a heavy pneumonia manifestation. The main objective of this investigation is to evaluate the performance of certain economies during the crisis derived from the COVID-19 pandemic. The gross domestic product (GDP) and global health security index (GHSI) of the countries belonging–or not–to the Organization for Economic Cooperation and Development (OECD) are considered. In this paper, statistical models are formulated to study this performance. The models’ specifications include, as the response variable, the GDP variation/growth percentage in 2020, and as the covariates: the COVID-19 disease rate from its start in March 2020 until 31 December 2020; the GHSI of 2019; the countries’ risk by default spreads from July 2019 to May 2020; belongingness or not to the OECD; and the GDP per capita in 2020. We test the heteroscedasticity phenomenon present in the modeling. The variable “COVID-19 cases per million inhabitants” is statistically significant, showing its impact on each country’s economy through the GDP variation. Therefore, we report that COVID-19 cases affect domestic economies, but that OECD membership and other risk factors are also relevant. Full article

(This article belongs to the Special Issue Machine Learning and Statistical Modeling with Applications in Real-World Data and Artificial Intelligence)

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8 pages, 800 KiB

Open AccessArticle

A Compact Octa-Band Frequency Reconfigurable Antenna for Wireless Applications

by Adnan Ghaffar, Wahaj Abbas Awan, Niamat Hussain and Xue-Jun Li

Mathematics 2021, 9(13), 1557; https://doi.org/10.3390/math9131557 - 02 Jul 2021

Cited by 7 | Viewed by 2331

Abstract

This paper presents the design and realization of a compact frequency reconfigurable antenna for multiband wireless applications. The antenna can operate at overall eight different bands in four dual-band modes. A slot in the radiator and defected ground structure are utilized to achieve [...] Read more.

This paper presents the design and realization of a compact frequency reconfigurable antenna for multiband wireless applications. The antenna can operate at overall eight different bands in four dual-band modes. A slot in the radiator and defected ground structure are utilized to achieve a compact size, while PIN diodes are used for frequency reconfigurability in the proposed antenna. The antenna shows broad bandwidth in each operating frequency and has a compact size of 18 mm × 18 mm × 1.524 mm. Moreover, stable radiation patterns and a high value of efficiency make it a potential candidate for various wireless applications. Furthermore, to demonstrate the worth of this work, its performance is compared with state-of-the-art designs reported for similar applications. Full article

(This article belongs to the Special Issue Evolutionary Optimization Algorithms for Electromagnetic Devices)

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20 pages, 3332 KiB

Open AccessArticle

A Two-Dimensional Thermoelasticity Solution for Bimodular Material Beams under the Combination Action of Thermal and Mechanical Loads

by Si-Rui Wen, Xiao-Ting He, Hao Chang and Jun-Yi Sun

Mathematics 2021, 9(13), 1556; https://doi.org/10.3390/math9131556 - 02 Jul 2021

Cited by 5 | Viewed by 1765

Abstract

A typical characteristic of bimodular material beams is that when bending, the neutral layer of the beam does not coincide with its geometric middle surface since the mechanical properties of materials in tension and compression are different. In the classical theory of elasticity, [...] Read more.

A typical characteristic of bimodular material beams is that when bending, the neutral layer of the beam does not coincide with its geometric middle surface since the mechanical properties of materials in tension and compression are different. In the classical theory of elasticity, however, this characteristic has not been considered. In this study, a bimodular simply-supported beam under the combination action of thermal and mechanical loads is theoretically analyzed. First, a simplified mechanical model concerning the neutral layer is established. Based on this mechanical model, Duhamel’s theorem is used to transform the thermoelastical problem into a pure elasticity problem with imaginary body force and surface force. In solving the governing equation expressed in terms of displacement, a special solution of the displacement equation is found first, and then by utilizing the stress function method based on subarea in tension and compression, a supplement solution for the displacement governing equation without the thermal effect is derived. Lastly, the special solution and supplement solution are superimposed to satisfy boundary conditions, thus obtaining a two-dimensional thermoelasticity solution. In addition, the bimodular effect and temperature effect on the thermoelasticity solution are illustrated by computational examples. Full article

(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)

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15 pages, 619 KiB

Open AccessArticle

Selecting Bloggers for Hotels via an Innovative Mixed MCDM Model

by Jung-Fa Tsai, Chin-Po Wang, Kuei-Lun Chang and Yi-Chung Hu

Mathematics 2021, 9(13), 1555; https://doi.org/10.3390/math9131555 - 02 Jul 2021

Cited by 14 | Viewed by 2657

Abstract

The global coronavirus disease 2019 (COVID-19) outbreak had a great impact on the tourism industry. Numerous hotels have ceased operations. Because of the increasing influence of blogs, various industries have adopted blogs as a publicity and marketing strategy. Companies utilize consumers’ trust and [...] Read more.

The global coronavirus disease 2019 (COVID-19) outbreak had a great impact on the tourism industry. Numerous hotels have ceased operations. Because of the increasing influence of blogs, various industries have adopted blogs as a publicity and marketing strategy. Companies utilize consumers’ trust and loyalty toward bloggers to effectively contact them. Hence, bloggers play a crucial role in the hotel industry. No past study has researched blogger selection by hotel managers. In this study, an innovative mixed multiple-criteria decision-making (MCDM) model including importance-performance analysis (IPA), analytic hierarchy process (AHP), and technique for order preference by similarity to ideal solution (TOPSIS) is established to assist hotel managers in selecting bloggers. We firstly collect the selection criteria via interviews with hotel managers and a review of literature on blogger selection. Messages with stick are understood, remembered, and have an enduring influence on opinions and behavior. Hence, we also introduce the concept of stick to the selection criteria. Based on IPA and the literature review, a hierarchical structure for blogger selection is constructed. Then, AHP and TOPSIS are integrated to assist the case company managers to select suitable bloggers. Full article

(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)

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16 pages, 864 KiB

Open AccessArticle

A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

by Dragiša Stanujkić, Darjan Karabašević, Gabrijela Popović, Predrag S. Stanimirović, Muzafer Saračević, Florentin Smarandache, Vasilios N. Katsikis and Alptekin Ulutaş

Mathematics 2021, 9(13), 1554; https://doi.org/10.3390/math9131554 - 01 Jul 2021

Cited by 17 | Viewed by 2982

Abstract

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey [...] Read more.

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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21 pages, 2999 KiB

Open AccessArticle

Fuzzy Set Qualitative Comparative Analysis on the Adoption of Environmental Practices: Exploring Technological- and Human-Resource-Based Contributions

by Lucía Muñoz-Pascual, Carla Curado and Jesús Galende

Mathematics 2021, 9(13), 1553; https://doi.org/10.3390/math9131553 - 01 Jul 2021

Cited by 2 | Viewed by 2332

Abstract

Our main objective was to analyze which paths can lead to the adoption of environmental practices (PRAC) in firms, for which we developed three original alternative research models. Model 1 involves five sources for the adoption of environmental practices: human resource costs, organizational [...] Read more.

Our main objective was to analyze which paths can lead to the adoption of environmental practices (PRAC) in firms, for which we developed three original alternative research models. Model 1 involves five sources for the adoption of environmental practices: human resource costs, organizational learning capability, firm size, manager educational level and manager experience. Model 2 adopts five sources for PRAC: human resource costs, information technology support, firm size, manager educational level and manager experience. Finally, Model 3 adopts six sources for PRAC: human resource costs, organizational learning capability, information technology support, firm size, manager educational level and manager experience. Therefore, Model 1 uses the organizational learning capability for PRAC, Model 2 uses the information technology support for PRAC and Model 3 uses both organizational learning capability and information technology support for PRAC. We used a fuzzy set qualitative comparative analysis on 349 small- and medium-sized Portuguese firms in twelve industrial sectors. The results show that organizational learning capability (OLC) and information technology support (ITS) are important sources for the development of PRAC. In this line, the three research models show that there are different pathways that lead to PRAC. These research models also show pathways that lead to the absence of PRAC. Therefore, the qualitative findings show the relevancy of OLC and ITS to PRAC. In addition, our findings indicate that, by focusing on variables such as OLC, a firm can find more paths that lead to PRAC. Additionally, with the combination of OLC and ITS, it must be taken into account that only developing ITS without OLC is riskier when obtaining PRAC. Full article

(This article belongs to the Special Issue Fuzzy Sets in Business Management, Finance, and Economics)

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