Mathematics

10 pages, 936 KiB

Open AccessArticle

A Forgotten Differential Equation Studied by Jacopo Riccati Revisited in Terms of Lie Symmetries

by Daniele Ritelli

Mathematics 2021, 9(11), 1312; https://doi.org/10.3390/math9111312 - 07 Jun 2021

Cited by 2 | Viewed by 1863

In this paper we present a two parameter family of differential equations treated by Jacopo Riccati, which does not appear in any modern repertoires and we extend the original solution method to a four parameter family of equations, translating the Riccati approach in [...] Read more.

In this paper we present a two parameter family of differential equations treated by Jacopo Riccati, which does not appear in any modern repertoires and we extend the original solution method to a four parameter family of equations, translating the Riccati approach in terms of Lie symmetries. To get the complete solution, hypergeometric functions come into play, which, of course, were unknown in Riccati’s time. Re-discovering the method introduced by Riccati, called by himself dimidiata separazione (splitted separation), we arrive at the closed form integration of a differential equation, more general to the one treated in Riccati’s contribution, and which also does not appear in the known repertoires. Full article

(This article belongs to the Special Issue Mathematical Modeling with Differential Equations in Physics, Chemistry, Biology, and Economics)

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10 pages, 2700 KiB

Open AccessArticle

Fractal Dimension as Quantifier of EEG Activity in Driving Simulation

by Mª Victoria Sebastián, Mª Antonia Navascués, Antonio Otal, Carlos Ruiz, Mª Ángeles Idiazábal, Leandro L. Di Stasi and Carolina Díaz-Piedra

Mathematics 2021, 9(11), 1311; https://doi.org/10.3390/math9111311 - 07 Jun 2021

Cited by 5 | Viewed by 2120

Abstract

Dynamical systems and fractal theory methodologies have been proved useful for the modeling and analysis of experimental datasets and, in particular, for electroencephalographic signals. The computation of the fractal dimension of approximation curves in the plane enables the assignment of numerical values to [...] Read more.

Dynamical systems and fractal theory methodologies have been proved useful for the modeling and analysis of experimental datasets and, in particular, for electroencephalographic signals. The computation of the fractal dimension of approximation curves in the plane enables the assignment of numerical values to bioelectric recordings in order to discriminate between different states of the observed system. The procedure does not require the stationarity of the signals nor extremely long segments of data. In previous works, we checked that this parameter is a good index for brain activity. In this paper, we consider this measurement in order to quantify the geometric complexity of the brain waves in states of rest and during vehicle driving simulation in different scenarios. This work presents evidence that the fractal dimension allows the detection of the brain bioelectric changes produced in the areas that carry out the different driving simulation tasks, increasing with their complexity. Full article

(This article belongs to the Section Engineering Mathematics)

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20 pages, 1895 KiB

Open AccessArticle

Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions

by Johny Pambabay-Calero, Sergio Bauz-Olvera, Ana Nieto-Librero, Ana Sánchez-García and Puri Galindo-Villardón

Mathematics 2021, 9(11), 1310; https://doi.org/10.3390/math9111310 - 07 Jun 2021

Cited by 3 | Viewed by 2973

Abstract

Models implemented in statistical software for the precision analysis of diagnostic tests include random-effects modeling (bivariate model) and hierarchical regression (hierarchical summary receiver operating characteristic). However, these models do not provide an overall mean, but calculate the mean of a central study when [...] Read more.

Models implemented in statistical software for the precision analysis of diagnostic tests include random-effects modeling (bivariate model) and hierarchical regression (hierarchical summary receiver operating characteristic). However, these models do not provide an overall mean, but calculate the mean of a central study when the random effect is equal to zero; hence, it is difficult to calculate the covariance between sensitivity and specificity when the number of studies in the meta-analysis is small. Furthermore, the estimation of the correlation between specificity and sensitivity is affected by the number of studies included in the meta-analysis, or the variability among the analyzed studies. To model the relationship of diagnostic test results, a binary covariance matrix is assumed. Here we used copulas as an alternative to capture the dependence between sensitivity and specificity. The posterior values were estimated using methods that consider sampling algorithms from a probability distribution (Markov chain Monte Carlo), and estimates were compared with the results of the bivariate model, which assumes statistical independence in the test results. To illustrate the applicability of the models and their respective comparisons, data from 14 published studies reporting estimates of the accuracy of the Alcohol Use Disorder Identification Test were used. Using simulations, we investigated the performance of four copula models that incorporate scenarios designed to replicate realistic situations for meta-analyses of diagnostic accuracy of the tests. The models’ performances were evaluated based on p-values using the Cramér–von Mises goodness-of-fit test. Our results indicated that copula models are valid when the assumptions of the bivariate model are not fulfilled. Full article

(This article belongs to the Special Issue Multivariate Statistics: Theory and Its Applications)

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14 pages, 317 KiB

Open AccessArticle

Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

by Pilar Ruiz Gordoa and Andrew Pickering

Mathematics 2021, 9(11), 1309; https://doi.org/10.3390/math9111309 - 07 Jun 2021

Cited by 2 | Viewed by 1470

Abstract

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the [...] Read more.

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model. Full article

(This article belongs to the Special Issue Advances in Mathematical Analysis with Applications)

20 pages, 1223 KiB

Open AccessArticle

How Sustainability Is Defined: An Analysis of 100 Theoretical Approximations

by Arturo Luque González, Jesús Ángel Coronado Martín, Ana Cecilia Vaca-Tapia and Francklin Rivas

Mathematics 2021, 9(11), 1308; https://doi.org/10.3390/math9111308 - 07 Jun 2021

Cited by 6 | Viewed by 2804

Abstract

Sustainability processes are imperfect, hence there is a need to analyze their construction, evolution and deployment. To this end, a sample of one hundred sustainability constructs was taken, together with their conceptual approaches, in order to gauge their impact and to ascertain the [...] Read more.

Sustainability processes are imperfect, hence there is a need to analyze their construction, evolution and deployment. To this end, a sample of one hundred sustainability constructs was taken, together with their conceptual approaches, in order to gauge their impact and to ascertain the dimensions to which they belong. A frequency count and categorization were carried out using Google, which saturated in seven dimensions: economic, social, environmental, legal, political, ethical and cultural. A higher-order association of these hierarchies was then proposed, establishing a triad model that indicated only the most representative combinations of dimensions resulting from the extraction of the most significant definitions. From these definitions and in accordance with their frequency of use in Google, it is inferred that the current concept of sustainability is based on the economic-social-ethical category. This highlights the distance between what, a priori, seems to implicitly allow any definition of sustainability and the existing reality. Full article

(This article belongs to the Special Issue Recent Advances in Business and Industry: Mathematical Analysis, Sustainability Assessment Instruments and Methods)

18 pages, 5215 KiB

Open AccessArticle

Ordering of Omics Features Using Beta Distributions on Montecarlo p-Values

by Angela L. Riffo-Campos, Guillermo Ayala and Juan Domingo

Mathematics 2021, 9(11), 1307; https://doi.org/10.3390/math9111307 - 07 Jun 2021

Viewed by 1662

Abstract

The current trend in genetic research is the study of omics data as a whole, either combining studies or omics techniques. This raises the need for new robust statistical methods that can integrate and order the relevant biological information. A good way to [...] Read more.

The current trend in genetic research is the study of omics data as a whole, either combining studies or omics techniques. This raises the need for new robust statistical methods that can integrate and order the relevant biological information. A good way to approach the problem is to order the features studied according to the different kinds of data so a key point is to associate good values to the features that permit us a good sorting of them. These values are usually the p-values corresponding to a hypothesis which has been tested for each feature studied. The Montecarlo method is certainly one of the most robust methods for hypothesis testing. However, a large number of simulations is needed to obtain a reliable p-value, so the method becomes computationally infeasible in many situations. We propose a new way to order genes according to their differential features by using a score defined from a beta distribution fitted to the generated p-values. Our approach has been tested using simulated data and colorectal cancer datasets from Infinium methylationEPIC array, Affymetrix gene expression array and Illumina RNA-seq platforms. The results show that this approach allows a proper ordering of genes using a number of simulations much lower than with the Montecarlo method. Furthermore, the score can be interpreted as an estimated p-value and compared with Montecarlo and other approaches like the p-value of the moderated t-tests. We have also identified a new expression pattern of eighteen genes common to all colorectal cancer microarrays, i.e., 21 datasets. Thus, the proposed method is effective for obtaining biological results using different datasets. Our score shows a slightly smaller type I error for small sizes than the Montecarlo p-value. The type II error of Montecarlo p-value is lower than the one obtained with the proposed score and with a moderated p-value, but these differences are highly reduced for larger sample sizes and higher false discovery rates. Similar performances from type I and II errors and the score enable a clear ordering of the features being evaluated. Full article

(This article belongs to the Special Issue Models and Methods in Bioinformatics: Theory and Applications)

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15 pages, 1790 KiB

Open AccessArticle

A Comparative Study among New Hybrid Root Finding Algorithms and Traditional Methods

by Elsayed Badr, Sultan Almotairi and Abdallah El Ghamry

Mathematics 2021, 9(11), 1306; https://doi.org/10.3390/math9111306 - 07 Jun 2021

Cited by 12 | Viewed by 4270

Abstract

In this paper, we propose a novel blended algorithm that has the advantages of the trisection method and the false position method. Numerical results indicate that the proposed algorithm outperforms the secant, the trisection, the Newton–Raphson, the bisection and the regula falsi methods, [...] Read more.

In this paper, we propose a novel blended algorithm that has the advantages of the trisection method and the false position method. Numerical results indicate that the proposed algorithm outperforms the secant, the trisection, the Newton–Raphson, the bisection and the regula falsi methods, as well as the hybrid of the last two methods proposed by Sabharwal, with regard to the number of iterations and the average running time. Full article

(This article belongs to the Special Issue Dynamical Systems in Engineering)

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22 pages, 15662 KiB

Open AccessArticle

Wildfires Vegetation Recovery through Satellite Remote Sensing and Functional Data Analysis

by Feliu Serra-Burriel, Pedro Delicado and Fernando M. Cucchietti

Mathematics 2021, 9(11), 1305; https://doi.org/10.3390/math9111305 - 07 Jun 2021

Cited by 3 | Viewed by 3079

Abstract

In recent years, wildfires have caused havoc across the world, which are especially aggravated in certain regions due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on vegetation over the following [...] Read more.

In recent years, wildfires have caused havoc across the world, which are especially aggravated in certain regions due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on vegetation over the following years. We aim to explain the dynamics of wildfires’ effects on a vegetation index (previously estimated by causal inference through synthetic controls) from pre-wildfire available information (mainly proceeding from satellites). For this purpose, we use regression models from Functional Data Analysis, where wildfire effects are considered functional responses, depending on elapsed time after each wildfire, while pre-wildfire information acts as scalar covariates. Our main findings show that vegetation recovery after wildfires is a slow process, affected by many pre-wildfire conditions, among which the richness and diversity of vegetation is one of the best predictors for the recovery. Full article

(This article belongs to the Special Issue Methodological and Applied Contributions on Stochastic Modelling and Forecasting)

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30 pages, 1247 KiB

Open AccessEditor’s ChoiceArticle

An Integrated Decision-Making Approach for Green Supplier Selection in an Agri-Food Supply Chain: Threshold of Robustness Worthiness

by Erfan Babaee Tirkolaee, Zahra Dashtian, Gerhard-Wilhelm Weber, Hana Tomaskova, Mehdi Soltani and Nasim Sadat Mousavi

Mathematics 2021, 9(11), 1304; https://doi.org/10.3390/math9111304 - 07 Jun 2021

Cited by 50 | Viewed by 4355

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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17 pages, 307 KiB

Open AccessArticle

On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

by Pshtiwan Othman Mohammed, Thabet Abdeljawad and Faraidun Kadir Hamasalh

Mathematics 2021, 9(11), 1303; https://doi.org/10.3390/math9111303 - 07 Jun 2021

Cited by 26 | Viewed by 1943

Abstract

Monotonicity analysis of delta fractional sums and differences of order

υ \in (0, 1]

on the time scale

h Z

are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There [...] Read more.

Monotonicity analysis of delta fractional sums and differences of order

υ \in (0, 1]

on the time scale

h Z

are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that

y (z)

is

υ

-increasing on

M_{a + υ h, h}

, where the delta Riemann–Liouville fractional h-difference of order

υ

of a function

y (z)

starting at

a + υ h

is greater or equal to zero, and then, we can show that

y (z)

is

υ

-increasing on

M_{a + υ h, h}

, where the delta Caputo fractional h-difference of order

υ

of a function

y (z)

starting at

a + υ h

is greater or equal to

- \frac{1}{Γ (1 - υ)} {(z - (a + υ h))}_{h}^{(- υ)} y (a + υ h)

for each

z \in M_{a + h, h}

. Conversely, if

y (a + υ h)

is greater or equal to zero and

y (z)

is increasing on

M_{a + υ h, h}

, we show that the delta Riemann–Liouville fractional h-difference of order

υ

of a function

y (z)

starting at

a + υ h

is greater or equal to zero, and consequently, we can show that the delta Caputo fractional h-difference of order

υ

of a function

y (z)

starting at

a + υ h

is greater or equal to

- \frac{1}{Γ (1 - υ)} {(z - (a + υ h))}_{h}^{(- υ)} y (a + υ h)

on

M_{a, h}

. Furthermore, we consider some related results for strictly increasing, decreasing, and strictly decreasing cases. Finally, the fractional forward difference initial value problems and their solutions are investigated to test the mean value theorem on the time scale

h Z

utilizing the monotonicity results. Full article

15 pages, 4001 KiB

Open AccessEditor’s ChoiceArticle

On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy

by Khaled S. Mekheimer, Bangalore M. Shankar, Shaimaa F. Ramadan, Hosahalli E. Mallik and Mohamed S. Mohamed

Mathematics 2021, 9(11), 1302; https://doi.org/10.3390/math9111302 - 06 Jun 2021

Cited by 16 | Viewed by 2258

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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12 pages, 510 KiB

Open AccessArticle

Optimal Investment in Preservation Technology for Variable Demand under Trade-Credit and Shortages

by Mrudul Y. Jani, Manish R. Betheja, Urmila Chaudhari and Biswajit Sarkar

Mathematics 2021, 9(11), 1301; https://doi.org/10.3390/math9111301 - 06 Jun 2021

Cited by 20 | Viewed by 2136

Abstract

In particular business transactions, the supplier usually provides an admissible delay in settlement to its vendor to encourage further sales. Additionally, the demand for the commodity is inversely proportional to the function of the sales price, which is non-linear and, in some situations, [...] Read more.

In particular business transactions, the supplier usually provides an admissible delay in settlement to its vendor to encourage further sales. Additionally, the demand for the commodity is inversely proportional to the function of the sales price, which is non-linear and, in some situations, a holding cost rises over time. Moreover, many goods often deteriorate consistently and shall not be sold after their expiration dates. This study analyses a model for perishable products with a maximum life span with price-dependent demand and trade credit by assimilating these variations and under the supposition of time-varying holding cost. Furthermore, to diminish the rate of deterioration, investment for preservation technology is often taken into account beforehand. Based on real-life circumstances, shortages are admitted and backlogged partially, with an exponential rise in wait time before the new good emerges. The key ambition is to calculate the optimum investment under preservation, sales price, and cycle time using the classical optimization algorithm to maximize the vendor’s net profit. Additionally, to clarify the outcomes, the numerical illustrations are addressed, and the sensitivity analysis of significant parameters is eventually implemented. Full article

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15 pages, 498 KiB

Open AccessArticle

Greenness as a Differentiating Strategy

by Nahid Masoudi

Mathematics 2021, 9(11), 1300; https://doi.org/10.3390/math9111300 - 06 Jun 2021

Viewed by 1642

Abstract

In a vertical differentiation model, we study a market where consumers, depending on their level of environmental consciousness, value the greenness of the product they consume and are distributed according to a Kumaraswamy distribution. Three scenarios are studied: only one firm takes some [...] Read more.

In a vertical differentiation model, we study a market where consumers, depending on their level of environmental consciousness, value the greenness of the product they consume and are distributed according to a Kumaraswamy distribution. Three scenarios are studied: only one firm takes some green measures and firms compete upon prices; only one firm takes some green measures, and this firm acts as the leader of the price competition; and finally, both firms choose their level of greenness and compete upon their location and price. The results suggest that as consumers become more environmentally conscious, the marginal consumer and the greener firm’s location move to the right. In contrast, the less green firm’s response is non-monotonic. In fact, when the two firms choose their location along with their prices, the latter firm chooses to produce a less green product in response to more environmentally conscious consumers. In the extreme case where all consumers are fully environmentally conscious, the latter firm produces a brown product and sells it at a price equal to its marginal cost. In this case, the greener firm’s price and location choices make the consumers indifferent between the two products. These results could explain why despite all the improvements in the consumers’ environmental consciousness, brown (in its general term) products are still widely produced and consumed, even by environmentally conscious consumers. Full article

(This article belongs to the Special Issue Application of Optimal Control and Game Theory to the Problem of Resource Management)

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16 pages, 1100 KiB

Open AccessArticle

Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

by Shengli Lv

Mathematics 2021, 9(11), 1299; https://doi.org/10.3390/math9111299 - 06 Jun 2021

Viewed by 1717

Abstract

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and [...] Read more.

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices. Full article

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15 pages, 2110 KiB

Open AccessArticle

Sparse HJ Biplot: A New Methodology via Elastic Net

by Mitzi Cubilla-Montilla, Ana Belén Nieto-Librero, M. Purificación Galindo-Villardón and Carlos A. Torres-Cubilla

Mathematics 2021, 9(11), 1298; https://doi.org/10.3390/math9111298 - 05 Jun 2021

Cited by 11 | Viewed by 3253

Abstract

The HJ biplot is a multivariate analysis technique that allows us to represent both individuals and variables in a space of reduced dimensions. To adapt this approach to massive datasets, it is necessary to implement new techniques that are capable of reducing the [...] Read more.

The HJ biplot is a multivariate analysis technique that allows us to represent both individuals and variables in a space of reduced dimensions. To adapt this approach to massive datasets, it is necessary to implement new techniques that are capable of reducing the dimensionality of the data and improving interpretation. Because of this, we propose a modern approach to obtaining the HJ biplot called the elastic net HJ biplot, which applies the elastic net penalty to improve the interpretation of the results. It is a novel algorithm in the sense that it is the first attempt within the biplot family in which regularisation methods are used to obtain modified loadings to optimise the results. As a complement to the proposed method, and to give practical support to it, a package has been developed in the R language called SparseBiplots. This package fills a gap that exists in the context of the HJ biplot through penalized techniques since in addition to the elastic net, it also includes the ridge and lasso to obtain the HJ biplot. To complete the study, a practical comparison is made with the standard HJ biplot and the disjoint biplot, and some results common to these methods are analysed. Full article

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19 pages, 5751 KiB

Open AccessArticle

Improving Reliability and Energy Efficiency of Three Parallel Pumps by Selecting Trade-Off Operating Points

by Safarbek Oshurbekov, Vadim Kazakbaev, Vladimir Prakht and Vladimir Dmitrievskii

Mathematics 2021, 9(11), 1297; https://doi.org/10.3390/math9111297 - 05 Jun 2021

Cited by 7 | Viewed by 2729

Abstract

Reliability, along with energy efficiency, is an important characteristic of pump units in various applications. In practical pump applications, it is important to strike a balance between reliability and energy efficiency. These indicators strongly depend on the applied control method of the pump [...] Read more.

Reliability, along with energy efficiency, is an important characteristic of pump units in various applications. In practical pump applications, it is important to strike a balance between reliability and energy efficiency. These indicators strongly depend on the applied control method of the pump unit. This study analyzes a trade-off method for regulating a system with three parallel pumps equipped with only one frequency converter (multi-pump single-drive system). A typical operating cycle of a pumping system with variable flow rate requirements is considered. The proposed trade-off method is compared with the traditional regulation, when a change in the operating point of the pump is achieved only by changing the rotation speed, and with the method for maximum reliability. It is shown that the proposed trade-off method makes it possible to ensure sufficient reliability of the multi-pump system operation without a significant increase in energy consumption. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

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21 pages, 845 KiB

Open AccessArticle

The Assessment of Car Making Plants with an Integrated Stochastic Frontier Analysis Model

by Seog-Chan Oh and Jaemin Shin

Mathematics 2021, 9(11), 1296; https://doi.org/10.3390/math9111296 - 05 Jun 2021

Cited by 4 | Viewed by 2543

Abstract

As global competition has intensified in the automotive industry, there is a strong need for management teams to develop methods that allow accurate and objective assessments of plant productivity and to identify productivity improvement opportunities for the best manufacturing practices. Stochastic frontier analysis [...] Read more.

As global competition has intensified in the automotive industry, there is a strong need for management teams to develop methods that allow accurate and objective assessments of plant productivity and to identify productivity improvement opportunities for the best manufacturing practices. Stochastic frontier analysis (SFA) models have been used as a statistical benchmarking tool to provide a bird’s-eye view of an industrial sector. SFA models can also be adapted for plant productivity assessment. However, owing to the problem of multicollinearity, the general form of SFA is difficult to apply to the assessment of complex manufacturing systems in the automotive industry, which is characterized by many control and external factors that are intercorrelated to each other. This study proposes a method for applying SFA to vehicle manufacturing plants with a focus on gaining high accuracy in model parameter estimation, by decomposing a plant into components (i.e., shops), building an SFA model for each shop, and reintegrating the general plant system through the appropriate combination of shop-level inefficiency distributions. In particular, this study focuses on documenting the derivation of a new probability density function that integrates three different inefficiency distributions. For illustration of the proposed approach, hypothetical vehicle assembly plants are assessed as examples, where the total labor hours are split into Bodyshop, Paintshop, and General Assembly, exclusively and collectively. Finally, this study offers a solution process to clarify the reasons for underperforming plants in terms of labor productivity and identify the course of actions to cure the issues with some managerial insights emphasizing the balanced approach, incorporating people, process and technology. Full article

(This article belongs to the Special Issue Distribution Theory and Stochastic Frontier Analysis)

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18 pages, 872 KiB

Open AccessArticle

Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

by Francisco G. Montoya, Raúl Baños, Alfredo Alcayde, Francisco Manuel Arrabal-Campos and Javier Roldán-Pérez

Mathematics 2021, 9(11), 1295; https://doi.org/10.3390/math9111295 - 04 Jun 2021

Cited by 12 | Viewed by 3059

Abstract

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra [...] Read more.

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been introduced to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, electrical power theories for single-phase systems based on GA were revisited. Several drawbacks and inconsistencies of previous works were identified, and some amendments were introduced. An alternative expression is presented for the electric power in the geometric domain. Its norm is compatible with the traditional apparent power defined as the product of the RMS voltage and current. The use of this expression simplifies calculations such as those required for current decomposition. This proposal is valid even for distorted currents and voltages. Concepts are presented in a simple way so that a strong background on GA is not required. The paper included some examples and experimental results in which measurements from a utility supply were analysed. Full article

(This article belongs to the Special Issue New Trends in Algebraic Geometry and Its Applications)

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14 pages, 1877 KiB

Open AccessArticle

Masked Implementation of Format Preserving Encryption on Low-End AVR Microcontrollers and High-End ARM Processors

by Hyunjun Kim, Minjoo Sim, Kyoungbae Jang, Hyeokdong Kwon, Siwoo Uhm and Hwajeong Seo

Mathematics 2021, 9(11), 1294; https://doi.org/10.3390/math9111294 - 04 Jun 2021

Cited by 4 | Viewed by 1990

Abstract

Format-Preserving Encryption (FPE) for Internet of Things (IoT) enables the data encryption while preserving the format and length of original data. With these advantages, FPE can be utilized in many IoT applications. However, FPE requires complicated computations and these are high overheads on [...] Read more.

Format-Preserving Encryption (FPE) for Internet of Things (IoT) enables the data encryption while preserving the format and length of original data. With these advantages, FPE can be utilized in many IoT applications. However, FPE requires complicated computations and these are high overheads on IoT embedded devices. In this paper, we proposed an efficient implementation of Format-preserving Encryption Algorithm (FEA), which is the Korean standard of FPE, and the first-order masked implementation of FEA on both low-end (i.e., AVR microcontroller) and high-end (i.e., ARM processor) IoT devices. Firstly, we show the vulnerability of FEA when it comes to the Correlation Power Analysis (CPA) approach. Afterward, we propose an efficient implementation method and the masking technique for both low-end IoT device and high-end IoT device. The proposed method is secure against power analysis attacks but the performance degradation of masked measure is only 2.53∼3.77% than the naïve FEA implementation. Full article

(This article belongs to the Special Issue Mathematical Mitigation Techniques for Network and Cyber Security)

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19 pages, 748 KiB

Open AccessArticle

Identifying the Maximum Concentration of Results in Bilateral Sports Competitions

by Antonio Avila-Cano, Amparo Ruiz-Sepulveda and Francisco Triguero-Ruiz

Mathematics 2021, 9(11), 1293; https://doi.org/10.3390/math9111293 - 04 Jun 2021

Cited by 12 | Viewed by 2582

Abstract

There are situations in which a monopoly solution cannot be reached. In these cases, which situation represents the maximum concentration (minimum competitive balance)? It is a relevant question, given that in sports economics, measuring the competitive balance of a league is done through [...] Read more.

There are situations in which a monopoly solution cannot be reached. In these cases, which situation represents the maximum concentration (minimum competitive balance)? It is a relevant question, given that in sports economics, measuring the competitive balance of a league is done through normalized indices. These indices require that the maximum level of concentration be known. Until now, the distribution of results that generates the maximum level of concentration has been identified in the literature as Complete cascade distribution. However, if the scoring system used does not fulfil the stability condition, which implies that the total number of points of a championship is constant, it can be demonstrated that the Complete cascade distribution does not generate the maximum level of concentration. This is the case, for example, with major European football leagues. In this article, we constructed a perfectly unbalanced distribution, which we called a Truncated cascade distribution. This distribution generates the maximum concentration level. Therefore, if we do not use Truncated cascade distribution, there is an overestimation of the concentration measured with normalized indices. Then, the calculated competitive balance will be wrong, that is, underestimated. We provided a spreadsheet for identifying this distribution. Full article

(This article belongs to the Special Issue Application of Mathematics in Applied Economic)

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16 pages, 1525 KiB

Open AccessArticle

An Improved Approach of Incomplete Information Fusion and Its Application in Sensor Data-Based Fault Diagnosis

by Yutong Chen and Yongchuan Tang

Mathematics 2021, 9(11), 1292; https://doi.org/10.3390/math9111292 - 04 Jun 2021

Cited by 7 | Viewed by 1944

Abstract

The Dempster–Shafer evidence theory has been widely used in the field of data fusion. However, with further research, incomplete information under the open world assumption has been discovered as a new type of uncertain information. The classical Dempster’s combination rules are difficult to [...] Read more.

The Dempster–Shafer evidence theory has been widely used in the field of data fusion. However, with further research, incomplete information under the open world assumption has been discovered as a new type of uncertain information. The classical Dempster’s combination rules are difficult to solve the related problems of incomplete information under the open world assumption. At the same time, partial information entropy, such as the Deng entropy is also not applicable to deal with problems under the open world assumption. Therefore, this paper proposes a new method framework to process uncertain information and fuse incomplete data. This method is based on an extension to the Deng entropy in the open world assumption, negation of basic probability assignment (BPA), and the generalized combination rule. The proposed method can solve the problem of incomplete information under the open world assumption, and obtain more uncertain information through the negative processing of BPA, which improves the accuracy of the results. The results of applying this method to fault diagnosis of electronic rotor examples show that, compared with the other uncertain information processing and fusion methods, the proposed method has wider adaptability and higher accuracy, and is more conducive to practical engineering applications. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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14 pages, 581 KiB

Open AccessArticle

Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method

by Jie Pan and Lianglin Xiong

Mathematics 2021, 9(11), 1291; https://doi.org/10.3390/math9111291 - 04 Jun 2021

Cited by 2 | Viewed by 1500

Abstract

In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural [...] Read more.

In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural networks (QNNs). The existence and uniqueness of the equilibrium solution (ES) for MQNN are concluded by exploiting the fixed-point theorem. Then a derivative formula of the quaternionic function’s norm is received. By utilizing the formula, the M-matrix theory, and the inequality techniques, some algebraic standards are gained to affirm the global exponential stability (GES) of the ES for the MQNN. Notably, compared to the existing work on QNN, our direct quaternionic method operates QNN as a whole and markedly reduces computing complexity and the gained results are more apt to be verified. The two numerical simulation instances are provided to evidence the merits of the theoretical results. Full article

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

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14 pages, 286 KiB

Open AccessArticle

A Perov Version of Fuzzy Metric Spaces and Common Fixed Points for Compatible Mappings

by Juan Martínez-Moreno and Dhananjay Gopal

Mathematics 2021, 9(11), 1290; https://doi.org/10.3390/math9111290 - 04 Jun 2021

Cited by 1 | Viewed by 1755

Abstract

In this paper, we define and study the Perov fuzzy metric space and the topology induced by this space. We prove Banach contraction theorems. Moreover, we devised new results for Kramosil and Michálek fuzzy metric spaces. In the process, some results about multidimensional [...] Read more.

In this paper, we define and study the Perov fuzzy metric space and the topology induced by this space. We prove Banach contraction theorems. Moreover, we devised new results for Kramosil and Michálek fuzzy metric spaces. In the process, some results about multidimensional common fixed points as coupled/tripled common fixed point results are derived from our main results. Full article

(This article belongs to the Special Issue Abstract Metric Spaces: Usefulness in Statistics and Fixed Point Theory)

2 pages, 178 KiB

Open AccessCorrection

Correction: Bustamante et al. Determining When an Algebra Is an Evolution Algebra. Mathematics 2020, 8, 1349

by Miguel D. Bustamante, Pauline Mellon and M. Victoria Velasco

Mathematics 2021, 9(11), 1289; https://doi.org/10.3390/math9111289 - 04 Jun 2021

Viewed by 1767

Abstract

The authors wish to make the following corrections to this paper [1] (see corrected version in postprint [2]):On page 2, paragraph 4, complete the first sentence ‘In Theorem 2 we show that if A is a real algebra and B is a basis [...] Read more.

The authors wish to make the following corrections to this paper [1] (see corrected version in postprint [2]):On page 2, paragraph 4, complete the first sentence ‘In Theorem 2 we show that if A is a real algebra and B is a basis of A then B also is a basis of

A_{ℂ}

, the complexification of A (with the same multiplication structure matrices) and that A is an evolution algebra if, and only if,

A_{ℂ}

is an evolution algebra’ with the phrase ‘and has a natural basis consisting of elements of A’ [...] Full article

26 pages, 2083 KiB

Open AccessArticle

Anomaly Detection in Multichannel Data Using Sparse Representation in RADWT Frames

by Daniela De Canditiis and Italia De Feis

Mathematics 2021, 9(11), 1288; https://doi.org/10.3390/math9111288 - 03 Jun 2021

Cited by 2 | Viewed by 2090

Abstract

We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with [...] Read more.

We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. Under the standard hypothesis of Gaussian additive noise, we model the signals by the RADWT and the anomalies as additive in each signal. Then we perform AD imposing a double penalty on the multiple regression model we obtained, promoting group sparsity both on the regression coefficients and on the anomalies. The first constraint preserves a common structure on the underlying signal components; the second one aims to identify the presence/absence of anomalies. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case. Full article

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

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21 pages, 3282 KiB

Open AccessArticle

Model of Evaluation and Selection of Expert Group Members for Smart Cities, Green Transportation and Mobility: From Safe Times to Pandemic Times

by Miroslav Kelemen, Volodymyr Polishchuk, Beáta Gavurová, Róbert Rozenberg, Juraj Bartok, Ladislav Gaál, Martin Gera and Martin Kelemen, Jr.

Mathematics 2021, 9(11), 1287; https://doi.org/10.3390/math9111287 - 03 Jun 2021

Cited by 21 | Viewed by 3076

Abstract

This paper presents the development of technologies to support the decision-making of local government executives and smart city concept managers in selecting and evaluating the competencies of new members for advisory groups for solving problems that are implemented in safe times in individual [...] Read more.

This paper presents the development of technologies to support the decision-making of local government executives and smart city concept managers in selecting and evaluating the competencies of new members for advisory groups for solving problems that are implemented in safe times in individual areas or in crises, such as pandemics. The reason for developing effective urban transformation strategies and for the transparent selection of independent experts (non-politicians) for policymaking, decision-making, and implementation teams is not only the heterogeneity of smart city dimensions together with the necessary complexity and systems approach, but also the nature of the capacities and tools needed for smart city concepts. The innovative hybrid competency assessment model is based on fuzzy logic and a network for neuro-fuzzy assessment. It is a technological model for evaluating the competencies of specialists, taking into account the influence of human factors on the processes of personnel selection and system management. An innovative web platform named “Smart City Concept Personnel Selection” has been designed, which can be adapted to various users of municipalities or regional institutions for the transparent selection of qualified personnel for effective decision-making and the use of public funds during safe times or emergencies, such as the COVID-19 pandemic. Full article

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

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24 pages, 2040 KiB

Open AccessArticle

Generalization of the Modigliani–Miller Theory for the Case of Variable Profit

by Peter Brusov, Tatiana Filatova, Natali Orekhova, Veniamin Kulik, She-I Chang and George Lin

Mathematics 2021, 9(11), 1286; https://doi.org/10.3390/math9111286 - 03 Jun 2021

Cited by 12 | Viewed by 4773

Abstract

For the first time we have generalized the world-famous theory by Nobel Prize winners Modigliani and Miller for the case of variable profit, which significantly extends the application of the theory in practice, specifically in business valuation, ratings, corporate finance, etc. We demonstrate [...] Read more.

For the first time we have generalized the world-famous theory by Nobel Prize winners Modigliani and Miller for the case of variable profit, which significantly extends the application of the theory in practice, specifically in business valuation, ratings, corporate finance, etc. We demonstrate that all the theorems, statements and formulae of Modigliani and Miller are changed significantly. We combine theoretical and numerical (by MS Excel) considerations. The following results are obtained: (1) Discount rate for leverage company changes from the weighted average cost of capital, WACC, to WACC–g (where g is growing rate), for a financially independent company from k₀ to k₀–g. This means that WACC and k₀ are no longer the discount rates as it takes place in case of classical Modigliani–Miller theory with constant profit. WACC grows with g, while real discount rates WACC–g and k₀–g decrease with g. This leads to an increase of company capitalization with g. (2) The tilt angle of the equity cost k_e(L) grows with g. This should change the dividend policy of the company, because the economically justified value of dividends is equal to equity cost. (3) A qualitatively new effect in corporate finance has been discovered: at rate g < g* the slope of the curve k_e(L) turns out to be negative, which could significantly alter the principles of the company’s dividend policy. Full article

(This article belongs to the Section Financial Mathematics)

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13 pages, 289 KiB

Open AccessArticle

Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds

by Hülya Aytimur, Adela Mihai and Cihan Özgür

Mathematics 2021, 9(11), 1285; https://doi.org/10.3390/math9111285 - 03 Jun 2021

Cited by 6 | Viewed by 2000

Abstract

The Chen first inequality and a Chen inequality for the

δ (2, 2)

-invariant on statistical submanifolds of Sasaki-like statistical manifolds, under a curvature condition, are obtained. Full article

9 pages, 269 KiB

Open AccessArticle

Minimally Supported Frequency (MSF) d-Dilation Wavelets

by Aparna Vyas and Gibak Kim

Mathematics 2021, 9(11), 1284; https://doi.org/10.3390/math9111284 - 03 Jun 2021

Cited by 1 | Viewed by 1759

Abstract

In this paper, we provide a geometric construction of a symmetric

2 n

-interval minimally supported frequency (MSF) d-dilation wavelet set with

d \in (1, \infty)

and characterize all symmetric d-dilation wavelet sets. We also provide two special [...] Read more.

In this paper, we provide a geometric construction of a symmetric

2 n

-interval minimally supported frequency (MSF) d-dilation wavelet set with

d \in (1, \infty)

and characterize all symmetric d-dilation wavelet sets. We also provide two special kinds of symmetric d-dilation wavelet sets, one of which has

4 m

-intervals whereas the other has

(4 m + 2)

-intervals, for

m \in N

. In addition, we construct a family of d-dilation wavelet sets that has an infinite number of components. Full article

27 pages, 737 KiB

Open AccessArticle

A Global Analysis of Delayed SARS-CoV-2/Cancer Model with Immune Response

by Afnan Al Agha, Safiya Alshehaiween, Ahmed Elaiw and Matuka Alshaikh

Mathematics 2021, 9(11), 1283; https://doi.org/10.3390/math9111283 - 03 Jun 2021

Cited by 6 | Viewed by 1721

Abstract

Coronavirus disease 2019 (COVID-19) is a respiratory disease caused by SARS-CoV-2. It appeared in China in late 2019 and rapidly spread to most countries of the world. Cancer patients infected with SARS-CoV-2 are at higher risk of developing severe infection and death. This [...] Read more.

Coronavirus disease 2019 (COVID-19) is a respiratory disease caused by SARS-CoV-2. It appeared in China in late 2019 and rapidly spread to most countries of the world. Cancer patients infected with SARS-CoV-2 are at higher risk of developing severe infection and death. This risk increases further in the presence of lymphopenia affecting the lymphocytes count. Here, we develop a delayed within-host SARS-CoV-2/cancer model. The model describes the occurrence of SARS-CoV-2 infection in cancer patients and its effect on the functionality of immune responses. The model considers the time delays that affect the growth rates of healthy epithelial cells and cancer cells. We provide a detailed analysis of the model by proving the nonnegativity and boundedness of the solutions, finding steady states, and showing the global stability of the different steady states. We perform numerical simulations to highlight some important observations. The results indicate that increasing the time delay in the growth rate of cancer cells reduced the size of tumors and decreased the likelihood of deterioration in the condition of SARS-CoV-2/cancer patients. On the other hand, lymphopenia increased the concentrations of SARS-CoV-2 particles and cancer cells, which worsened the condition of the patient. Full article

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Mathematics, Volume 9, Issue 11 (June-1 2021) – 155 articles

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