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Mathematics
Volume 9
Issue 10
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Mathematics, Volume 9, Issue 10 (May-2 2021) – 85 articles

Cover Story (view full-size image): Splitting methods arise by splitting the vector field into two simpler parts that can be integrated, either exactly or very precisely. High order methods are obtained by composing several steps of these flows with suitable coefficients. In this work, we improve their efficiency when they are used as temporal integrators of spatial discretizations of initial boundary value problems. View this paper.
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29 pages, 390 KiB  
Article
Profitability Index Maximization in an Inventory Model with a Price- and Stock-Dependent Demand Rate in a Power-Form
by Valentín Pando, Luis A. San-José, Joaquín Sicilia and David Alcaide-López-de-Pablo
Mathematics 2021, 9(10), 1157; https://doi.org/10.3390/math9101157 - 20 May 2021
Cited by 7 | Viewed by 2604
Abstract
This paper presents the optimal policy for an inventory model where the demand rate potentially depends on both selling price and stock level. The goal is the maximization of the profitability index, defined as the ratio income/expense. A numerical algorithm is proposed to [...] Read more.
This paper presents the optimal policy for an inventory model where the demand rate potentially depends on both selling price and stock level. The goal is the maximization of the profitability index, defined as the ratio income/expense. A numerical algorithm is proposed to calculate the optimal selling price. The optimal values for the depletion time, the cycle time, the maximum profitability index, and the lot size are evaluated from the selling price. The solution shows that the inventory must be replenished when the stock is depleted, i.e., the depletion time is always equal to the cycle time. The optimal policy is obtained with a suitable balance between ordering cost and holding cost. A condition that ensures the profitability of the financial investment in the inventory is established from the initial parameters. Profitability thresholds for several parameters, including the scale and the non-centrality parameters, keeping all the others fixed, are evaluated. The model with an isoelastic price-dependent demand is solved as a particular case. In this last model, all the optimal values are given in a closed form, and a sensitivity analysis is performed for several parameters, including the scale parameter. The results are illustrated with numerical examples. 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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14 pages, 3223 KiB  
Article
Analytical Solutions of the Fractional Mathematical Model for the Concentration of Tumor Cells for Constant Killing Rate
by Najma Ahmed, Nehad Ali Shah, Farman Ali, Dumitru Vieru and F.D. Zaman
Mathematics 2021, 9(10), 1156; https://doi.org/10.3390/math9101156 - 20 May 2021
Cited by 4 | Viewed by 2631
Abstract
Two generalized mathematical models with memory for the concentration of tumor cells have been analytically studied using the cylindrical coordinate and the integral transform methods. The generalization consists of the formulating of two mathematical models with Caputo-time fractional derivative, models that are suitable [...] Read more.
Two generalized mathematical models with memory for the concentration of tumor cells have been analytically studied using the cylindrical coordinate and the integral transform methods. The generalization consists of the formulating of two mathematical models with Caputo-time fractional derivative, models that are suitable to highlight the influence of the history of tumor evolution on the present behavior of the concentration of cancer cells. The time-oscillating concentration of cancer cells has been considered on the boundary of the domain. Analytical solutions of the fractional differential equations of the mathematical models have been determined using the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The positive roots of the transcendental equation with Bessel function J0(r)=0, which are needed in our study, have been determined with the subroutine rn=root(J0(r),r,(2n−1)π/4,(2n+3)π/4),n=1,2,… of the Mathcad 15 software. It is found that the memory effects are stronger at small values of the time, t. This aspect is highlighted in the graphical illustrations that analyze the behavior of the concentration of tumor cells. Additionally, the concentration of cancer cells is symmetric with respect to radial angle, and its values tend to be zero for large values of the time, t. Full article
(This article belongs to the Special Issue Fractional Differential Equations and Control Problems)
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8 pages, 227 KiB  
Article
Generalization of Quantum Ostrowski-Type Integral Inequalities
by Muhammad Aamir Ali, Sotiris K. Ntouyas and Jessada Tariboon
Mathematics 2021, 9(10), 1155; https://doi.org/10.3390/math9101155 - 20 May 2021
Cited by 7 | Viewed by 2040
Abstract
In this paper, we prove some new Ostrowski-type integral inequalities for q-differentiable bounded functions. It is also shown that the results presented in this paper are a generalization of know results in the literarure. Applications to special means are also discussed. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
25 pages, 1928 KiB  
Article
A Generalized Quasi Cubic Trigonometric Bernstein Basis Functions and Its B-Spline Form
by Yunyi Fu and Yuanpeng Zhu
Mathematics 2021, 9(10), 1154; https://doi.org/10.3390/math9101154 - 20 May 2021
Cited by 3 | Viewed by 2327
Abstract
In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape functions α(t) and β(t) are constructed in a generalized quasi cubic trigonometric space span [...] Read more.
In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape functions α(t) and β(t) are constructed in a generalized quasi cubic trigonometric space span{1,sin2t,(1−sint)2α(t),(1−cost)2β(t)}, which includes lots of previous work as special cases. Sufficient conditions concerning the two shape functions to guarantee the new construction of Bernstein basis functions are given, and three specific examples of the shape functions and the related applications are shown. The corresponding generalized quasi cubic trigonometric Bézier curves and the corner cutting algorithm are also given. Based on the new constructed generalized quasi cubic trigonometric Bernstein basis functions, a kind of new generalized quasi cubic trigonometric B-spline basis functions with two local shape functions αi(t) and βi(t) is also constructed in detail. Some important properties of the new generalized quasi cubic trigonometric B-spline basis functions are proven, including partition of unity, nonnegativity, linear independence, total positivity and C2 continuity. The shape of the parametric curves generated by the new proposed B-spline basis functions can be adjusted flexibly. Full article
(This article belongs to the Special Issue Computer Aided Geometric Design)
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24 pages, 9716 KiB  
Article
Non-Isothermal Hydrodynamic Characteristics of a Nanofluid in a Fin-Attached Rotating Tube Bundle
by Mashhour A. Alazwari and Mohammad Reza Safaei
Mathematics 2021, 9(10), 1153; https://doi.org/10.3390/math9101153 - 20 May 2021
Cited by 35 | Viewed by 2269
Abstract
In the present study, a novel configuration of a rotating tube bundle was simulated under non-isothermal hydrodynamic conditions using a mixture model. Eight fins were considered in this study, which targeted the hydrodynamics of the system. An aqueous copper nanofluid was used as [...] Read more.
In the present study, a novel configuration of a rotating tube bundle was simulated under non-isothermal hydrodynamic conditions using a mixture model. Eight fins were considered in this study, which targeted the hydrodynamics of the system. An aqueous copper nanofluid was used as the heat transfer fluid. Various operating factors, such as rotation speed (up to 500 rad/s), Reynolds number (10–80), and concentration of the nanofluid (0.0–4.0%) were applied, and the performance of the microchannel heat exchanger was assessed. It was found that the heat transfer coefficient of the system could be enhanced by increasing the Reynolds number, the concentration of the nanofluid, and the rotation speed. The maximum enhancement in the heat transfer coefficient (HTC) was 258% after adding a 4% volumetric nanoparticle concentration to the base fluid and increasing Re from 10 to 80 and ω from 0 to 500 rad/s. Furthermore, at Re = 80 and ω = 500 rad/s, the HTC values measured for the nanofluid were 42.3% higher than those calculated for water, showing the nanoparticles’ positive impact on the heat transfer paradigm. Moreover, it was identified that copper nanoparticles’ presence had no significant effect on the system’s pressure drop. This was attributed to the interaction of the fluid flow and circulated flow around the tubes. Finally, the heat transfer coefficient and pressure drop had no considerable changes when augmenting the rotation speed at high Reynolds numbers. Full article
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)
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20 pages, 665 KiB  
Article
Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates
by Flavia Antonacci, Cristina Costantini and Marco Papi
Mathematics 2021, 9(10), 1152; https://doi.org/10.3390/math9101152 - 20 May 2021
Cited by 2 | Viewed by 2432
Abstract
We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank [...] Read more.
We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation formula for contingent derivatives, in particular for Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, we implement the Kalman filter and obtain a dynamical estimate of the short-term interest rate. In turn, by this estimate, at each time step, we calibrate the model parameters under the risk-neutral measure and the coefficient of the risk premium. We compare the market values of German interest rate yields for several maturities with the corresponding values predicted by our model, from 2007 to 2015. The numerical results validate both our model and our numerical procedure. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
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17 pages, 275 KiB  
Article
Inequalities on the Generalized ABC Index
by Paul Bosch, Edil D. Molina, José M. Rodríguez and José M. Sigarreta
Mathematics 2021, 9(10), 1151; https://doi.org/10.3390/math9101151 - 20 May 2021
Cited by 6 | Viewed by 1897
Abstract
In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. [...] Read more.
In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own. Full article
(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory)
11 pages, 281 KiB  
Article
Fractional Line Integral
by Gabriel Bengochea and Manuel Ortigueira
Mathematics 2021, 9(10), 1150; https://doi.org/10.3390/math9101150 - 20 May 2021
Viewed by 2102
Abstract
This paper proposed a definition of the fractional line integral, generalising the concept of the fractional definite integral. The proposal replicated the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It was based on the concept of the [...] Read more.
This paper proposed a definition of the fractional line integral, generalising the concept of the fractional definite integral. The proposal replicated the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It was based on the concept of the fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integral, the Grünwald–Letnikov and Liouville directional derivatives were introduced and their properties described. The integral was defined for a piecewise linear path first and, from it, for any regular curve. Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems)
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13 pages, 260 KiB  
Article
Existence and Symmetry of Solutions for a Class of Fractional Schrödinger–Poisson Systems
by Yongzhen Yun, Tianqing An and Guoju Ye
Mathematics 2021, 9(10), 1149; https://doi.org/10.3390/math9101149 - 20 May 2021
Viewed by 1557
Abstract
In this paper, we investigate a class of Schrödinger–Poisson systems with critical growth. By the principle of concentration compactness and variational methods, we prove that the system has radially symmetric solutions, which improve the related results on this topic. Full article
38 pages, 558 KiB  
Article
Current Trends in Random Walks on Random Lattices
by Jewgeni H. Dshalalow and Ryan T. White
Mathematics 2021, 9(10), 1148; https://doi.org/10.3390/math9101148 - 19 May 2021
Cited by 9 | Viewed by 4989
Abstract
In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice [...] Read more.
In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing. Full article
(This article belongs to the Special Issue Latest Advances in Random Walks Dating Back to One Hundred Years)
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25 pages, 1014 KiB  
Article
The Optimal Mechanism Design of Retail Prices in the Electricity Market for Several Types of Consumers
by Natalia Aizenberg and Nikolai Voropai
Mathematics 2021, 9(10), 1147; https://doi.org/10.3390/math9101147 - 19 May 2021
Cited by 4 | Viewed by 1971
Abstract
In this paper, we discuss the demand side management (DSM) problem: how to incentivize a consumer to equalize the load during the day through price-dependent demand. Traditionally, the retail market offers several electricity payment schemes. A scheme is effective when the different tariffs [...] Read more.
In this paper, we discuss the demand side management (DSM) problem: how to incentivize a consumer to equalize the load during the day through price-dependent demand. Traditionally, the retail market offers several electricity payment schemes. A scheme is effective when the different tariffs satisfy different consumers. At the same time, the existing and generally accepted retail pricing schemes can lead to an "adverse selection" problem when all consumers choose the same price, thereby, reducing the possible general welfare. We propose an optimal design of pricing mechanisms, taking into account the interests of the electricity supplier and different types of consumers. The results of our work are that the optimal mechanism is implemented simultaneously for several periods, including the case when the ratio of types of consumers in periods changes. In addition, the mechanism proposed by us, in contrast to the studies of other researchers, provides an equilibrium close to the socially optimal maximum. We describe the implementation algorithm of the mechanism and provide examples of its action in the electric power system with different types and numbers of consumers. Full article
(This article belongs to the Special Issue Numerical Simulation and Control in Energy Systems)
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12 pages, 2013 KiB  
Article
On the Existence and Uniqueness of the ODE Solution and Its Approximation Using the Means Averaging Approach for the Class of Power Electronic Converters
by Santolo Meo and Luisa Toscano
Mathematics 2021, 9(10), 1146; https://doi.org/10.3390/math9101146 - 19 May 2021
Cited by 8 | Viewed by 2034
Abstract
Power electronic converters are mathematically represented by a system of ordinary differential equations discontinuous right-hand side that does not verify the conditions of the Cauchy-Lipschitz Theorem. More generally, for the properties that characterize their discontinuous behavior, they represent a particular class of systems [...] Read more.
Power electronic converters are mathematically represented by a system of ordinary differential equations discontinuous right-hand side that does not verify the conditions of the Cauchy-Lipschitz Theorem. More generally, for the properties that characterize their discontinuous behavior, they represent a particular class of systems on which little has been investigated over the years. The purpose of the paper is to prove the existence of at least one global solution in Filippov’s sense to the Cauchy problem related to the mathematical model of a power converter and also to calculate the error in norm between this solution and the integral of its averaged approximation. The main results are the proof of this theorem and the analytical formulation that provides to calculate the cited error. The demonstration starts by a proof of local existence provided by Filippov himself and already present in the literature for a particular class of systems and this demonstration is generalized to the class of electronic power converters, exploiting the non-chattering property of this class of systems. The obtained results are extremely useful for estimating the accuracy of the averaged model used for analysis or control of the effective system. In the paper, the goodness of the analytical proof is supported by experimental tests carried out on a converter prototype representing the class of power electronics converter. Full article
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13 pages, 956 KiB  
Review
The FMM Approach to Analyze Biomedical Signals: Theory, Software, Applications and Future
by Cristina Rueda, Itziar Fernández, Yolanda Larriba and Alejandro Rodríguez-Collado
Mathematics 2021, 9(10), 1145; https://doi.org/10.3390/math9101145 - 19 May 2021
Cited by 2 | Viewed by 2999
Abstract
Oscillatory systems arise in the different biological and medical fields. Mathematical and statistical approaches are fundamental to deal with these processes. The Frequency Modulated Mobiüs approach (FMM), reviewed in this paper, is one of these approaches. Little known as it has been recently [...] Read more.
Oscillatory systems arise in the different biological and medical fields. Mathematical and statistical approaches are fundamental to deal with these processes. The Frequency Modulated Mobiüs approach (FMM), reviewed in this paper, is one of these approaches. Little known as it has been recently developed, it solves a variety of exciting questions with real data; some of them, such as the decomposition of the signal into components and their multiple uses, are of general application, others are specific. Among the exciting specific applications is the automatic interpretation of the electrocardiogram signal. In this paper, a summary of the theoretical, statistical and computational properties of the FMM approach are revised. Additionally, as a novelty, the FMM approach’s usefulness for the analysis of blood pressure signals is shown. For the latter, a new robust estimation algorithm is proposed using FMM models with restrictions. The paper ends with a view about challenges for the future. Full article
(This article belongs to the Special Issue Models and Methods in Bioinformatics: Theory and Applications)
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23 pages, 7682 KiB  
Article
Nonlinear-Observer-Based Design Approach for Adaptive Event-Driven Tracking of Uncertain Underactuated Underwater Vehicles
by Jin Hoe Kim and Sung Jin Yoo
Mathematics 2021, 9(10), 1144; https://doi.org/10.3390/math9101144 - 19 May 2021
Cited by 5 | Viewed by 1824
Abstract
A nonlinear-observer-based design methodology is proposed for an adaptive event-driven output-feedback tracking problem with guaranteed performance of uncertain underactuated underwater vehicles (UUVs) in six-degrees-of-freedom (6-DOF). A nonlinear observer using adaptive neural networks is presented to estimate the velocity information in the presence of [...] Read more.
A nonlinear-observer-based design methodology is proposed for an adaptive event-driven output-feedback tracking problem with guaranteed performance of uncertain underactuated underwater vehicles (UUVs) in six-degrees-of-freedom (6-DOF). A nonlinear observer using adaptive neural networks is presented to estimate the velocity information in the presence of unknown nonlinearities in the dynamics of 6-DOF UUVs where a state transformation approach using a time-varying scaling factor is introduced. Then, an output-feedback tracker using a nonlinear error function and estimated states is recursively designed to overcome the underactuated problem of the system dynamics and to guarantee preselected control performance in three-dimensional space. It is shown that the tracking error of the nonlinear-observer-based output-feedback control system exponentially converges a small neighbourhood around the zero. Efficiency of the resulting output-feedback strategy is verified through a simulation. Full article
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29 pages, 679 KiB  
Article
Residue Sum Formula for Pricing Options under the Variance Gamma Model
by Pedro Febrer and João Guerra
Mathematics 2021, 9(10), 1143; https://doi.org/10.3390/math9101143 - 18 May 2021
Cited by 3 | Viewed by 2167
Abstract
We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties [...] Read more.
We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties of multidimensional complex analysis, with particular emphasis on the multidimensional Jordan Lemma and the application of residue calculus to a Mellin–Barnes integral representation in C3, for the call option price. Moreover, we derive triple sum series formulas for some of the Greeks associated to the call option and we discuss the numerical accuracy and convergence of the main pricing formula. Full article
(This article belongs to the Special Issue Recent Advances on Nonlinear Models in Mathematical Finance)
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19 pages, 3134 KiB  
Article
Applied Machine Learning Algorithms for Courtyards Thermal Patterns Accurate Prediction
by Eduardo Diz-Mellado, Samuele Rubino, Soledad Fernández-García, Macarena Gómez-Mármol, Carlos Rivera-Gómez and Carmen Galán-Marín
Mathematics 2021, 9(10), 1142; https://doi.org/10.3390/math9101142 - 18 May 2021
Cited by 21 | Viewed by 2856
Abstract
Currently, there is a lack of accurate simulation tools for the thermal performance modeling of courtyards due to their intricate thermodynamics. Machine Learning (ML) models have previously been used to predict and evaluate the structural performance of buildings as a means of solving [...] Read more.
Currently, there is a lack of accurate simulation tools for the thermal performance modeling of courtyards due to their intricate thermodynamics. Machine Learning (ML) models have previously been used to predict and evaluate the structural performance of buildings as a means of solving complex mathematical problems. Nevertheless, the microclimatic conditions of the building surroundings have not been as thoroughly addressed by these methodologies. To this end, in this paper, the adaptation of ML techniques as a more comprehensive methodology to fill this research gap, covering not only the prediction of the courtyard microclimate but also the interpretation of experimental data and pattern recognition, is proposed. Accordingly, based on the climate zoning and aspect ratios of 32 monitored case studies located in the South of Spain, the Support Vector Regression (SVR) method was applied to predict the measured temperature inside the courtyard. The results provided by this strategy showed good accuracy when compared to monitored data. In particular, for two representative case studies, if the daytime slot with the highest urban overheating is considered, the relative error is almost below 0.05%. Additionally, values for statistical parameters are in good agreement with other studies in the literature, which use more computationally expensive CFD models and show more accuracy than existing commercial tools. Full article
(This article belongs to the Special Issue Mathematical Methods, Modelling and Applications)
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22 pages, 1526 KiB  
Article
The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression
by Helida Nurcahayani, I Nyoman Budiantara and Ismaini Zain
Mathematics 2021, 9(10), 1141; https://doi.org/10.3390/math9101141 - 18 May 2021
Cited by 8 | Viewed by 2336
Abstract
Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; [...] Read more.
Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation. Full article
(This article belongs to the Section Probability and Statistics)
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27 pages, 13133 KiB  
Article
An Adaptive Cuckoo Search-Based Optimization Model for Addressing Cyber-Physical Security Problems
by Mohamed Abdel-Basset, Reda Mohamed, Nazeeruddin Mohammad, Karam Sallam and Nour Moustafa
Mathematics 2021, 9(10), 1140; https://doi.org/10.3390/math9101140 - 18 May 2021
Cited by 4 | Viewed by 2075
Abstract
One of the key challenges in cyber-physical systems (CPS) is the dynamic fitting of data sources under multivariate or mixture distribution models to determine abnormalities. Equations of the models have been statistically characterized as nonlinear and non-Gaussian ones, where data have high variations [...] Read more.
One of the key challenges in cyber-physical systems (CPS) is the dynamic fitting of data sources under multivariate or mixture distribution models to determine abnormalities. Equations of the models have been statistically characterized as nonlinear and non-Gaussian ones, where data have high variations between normal and suspicious data distributions. To address nonlinear equations of these distributions, a cuckoo search algorithm is employed. In this paper, the cuckoo search algorithm is effectively improved with a novel strategy, known as a convergence speed strategy, to accelerate the convergence speed in the direction of the optimal solution for achieving better outcomes in a small number of iterations when solving systems of nonlinear equations. The proposed algorithm is named an improved cuckoo search algorithm (ICSA), which accelerates the convergence speed by improving the fitness values of function evaluations compared to the existing algorithms. To assess the efficacy of ICSA, 34 common nonlinear equations that fit the nature of cybersecurity models are adopted to show if ICSA can reach better outcomes with high convergence speed or not. ICSA has been compared with several well-known, well-established optimization algorithms, such as the slime mould optimizer, salp swarm, cuckoo search, marine predators, bat, and flower pollination algorithms. Experimental outcomes have revealed that ICSA is superior to the other in terms of the convergence speed and final accuracy, and this makes a promising alternative to the existing algorithm. Full article
(This article belongs to the Section Mathematics and Computer Science)
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17 pages, 1131 KiB  
Article
Reliability Properties of the NDL Family of Discrete Distributions with Its Inference
by Mohammed Mohammed Ahmed Almazah, Badr Alnssyan, Abdul Hadi N. Ahmed and Ahmed Z. Afify
Mathematics 2021, 9(10), 1139; https://doi.org/10.3390/math9101139 - 18 May 2021
Cited by 5 | Viewed by 2017
Abstract
The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In [...] Read more.
The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In the present article, we further investigate new results of value in the areas of both theoretical and applied reliability. To be specific, several closure properties of the NDL are proved. Among the results, sufficient conditions that maintain the preservation properties under useful partial orderings, convolution, and random sum of random variables are introduced. Eight different methods of estimation, including the maximum likelihood, least squares, weighted least squares, Cramér–von Mises, the maximum product of spacing, Anderson–Darling, right-tail Anderson–Darling, and percentiles, have been used to estimate the parameter of interest. The performance of these estimators has been evaluated through extensive simulation. We have also demonstrated two applications of NDL in modeling real-life problems, including count data. It is worth noting that almost all the methods have resulted in very satisfactory estimates on both simulated and real-world data. Full article
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
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19 pages, 2796 KiB  
Article
A New Class of Estimators Based on a General Relative Loss Function
by Tao Hu and Baosheng Liang
Mathematics 2021, 9(10), 1138; https://doi.org/10.3390/math9101138 - 18 May 2021
Cited by 1 | Viewed by 1867
Abstract
Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile [...] Read more.
Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making statistical inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided. Full article
(This article belongs to the Special Issue Advances in Mathematics and Statistics with Applications in Engineering and Industry)
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21 pages, 1131 KiB  
Article
Efficient Processing of All Nearest Neighbor Queries in Dynamic Road Networks
by Aavash Bhandari, Aziz Hasanov, Muhammad Attique, Hyung-Ju Cho and Tae-Sun Chung
Mathematics 2021, 9(10), 1137; https://doi.org/10.3390/math9101137 - 17 May 2021
Cited by 2 | Viewed by 2469
Abstract
The increasing trend of GPS-enabled smartphones has led to the tremendous usage of Location-Based Service applications. In the past few years, a significant amount of studies have been conducted to process All nearest neighbor (ANN) queries. An ANN query on a road network [...] Read more.
The increasing trend of GPS-enabled smartphones has led to the tremendous usage of Location-Based Service applications. In the past few years, a significant amount of studies have been conducted to process All nearest neighbor (ANN) queries. An ANN query on a road network extracts and returns all the closest data objects for all query objects. Most of the existing studies on ANN queries are performed either in Euclidean space or static road networks. Moreover, combining the nearest neighbor query and join operation is an expensive procedure because it requires computing the distance between each pair of query objects and data objects. This study considers the problem of processing the ANN queries on a dynamic road network where the weight, i.e., the traveling distance and time varies due to various traffic conditions. To address this problem, a shared execution-based approach called standard clustered loop (SCL) is proposed that allows efficient processing of ANN queries on a dynamic road network. The key concept behind the shared execution technique is to exploit the coherence property of road networks by clustering objects that share common paths and processing the cluster as a single path. In an empirical study, the SCL method achieves significantly better performance than competitive methods and efficiently reduces the computational cost to process ANN queries in various problem settings. Full article
(This article belongs to the Special Issue Information Systems Modeling Based on Graph Theory)
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24 pages, 6933 KiB  
Article
Q or R Factor Analysis for Subjectiveness Measurement in Consumer Behavior? A Study Case on Durable Goods Buying Behavior in Romania
by Manuela Rozalia Gabor and Nicoleta Cristache
Mathematics 2021, 9(10), 1136; https://doi.org/10.3390/math9101136 - 17 May 2021
Cited by 4 | Viewed by 3262
Abstract
The complexity of consumer behavior requires new research methods to overcome the limitations of conventional evident-based research. The aim of this paper is the comparison between two types of factor analyses, Q and R (PCA and cluster analysis) for subjectiveness measurement in the [...] Read more.
The complexity of consumer behavior requires new research methods to overcome the limitations of conventional evident-based research. The aim of this paper is the comparison between two types of factor analyses, Q and R (PCA and cluster analysis) for subjectiveness measurement in the case of durable goods buying behavior in Romanian households with different levels of education and occupancy. Our study explores different subjective patterns of stimulus of 30 statements (Q-sample) by 30 Romanian households (P-sample) using the Q-sort method for collecting data. For the Q-sample inputs, results from the literature were used. Based on the 30 Q-sorts, we discovered four factors for both Q and R factor analysis, mostly different according to specific results from different methods. For the Q method, we used the labels “pragmatic”, “modern”, “traditionalist”, and “innovator. For R factor analysis and cluster, we used “traditional Romanian brands”, “real needs and power purchasing”, “sceptic versus optimistic subjectiveness”, and “negative subjectiveness”. This paper suggests the Q methodology as a structured and transparent approach to consumer behavior research by combining the in-depth subjectivity of qualitative methods and statistical rigor of factor analysis to identify groups in consumers. The research provides useful suggestions for selecting and approaching target consumer segments in the Romanian durable goods industry. Full article
(This article belongs to the Special Issue Analysis and Mathematical Modeling of Economic - Related Data)
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10 pages, 252 KiB  
Article
On the Paired-Domination Subdivision Number of Trees
by Shouliu Wei, Guoliang Hao, Seyed Mahmoud Sheikholeslami, Rana Khoeilar and Hossein Karami
Mathematics 2021, 9(10), 1135; https://doi.org/10.3390/math9101135 - 17 May 2021
Cited by 3 | Viewed by 1648
Abstract
A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G [...] Read more.
A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G. The paired-domination subdivision number sdγpr(G) of G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the paired-domination number. Here, we show that, for each tree T ≠ P5 of order n ≥ 3 and each edge e ∉ E(T), sdγpr(T) + sdγpr(T + e) ≤ n + 2. Full article
(This article belongs to the Special Issue Graphs, Metrics and Models)
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16 pages, 269 KiB  
Article
On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique
by Ahmed Refice, Mohammed Said Souid and Ivanka Stamova
Mathematics 2021, 9(10), 1134; https://doi.org/10.3390/math9101134 - 17 May 2021
Cited by 27 | Viewed by 2628
Abstract
In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with [...] Read more.
In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of the observed results. Full article
(This article belongs to the Section Mathematical Physics)
15 pages, 2335 KiB  
Article
A Residual-Learning-Based Multi-Scale Parallel-Convolutions- Assisted Efficient CAD System for Liver Tumor Detection
by Muazzam Maqsood, Maryam Bukhari, Zeeshan Ali, Saira Gillani, Irfan Mehmood, Seungmin Rho and Young-Ae Jung
Mathematics 2021, 9(10), 1133; https://doi.org/10.3390/math9101133 - 17 May 2021
Cited by 22 | Viewed by 3000
Abstract
Smart multimedia-based medical analytics and decision-making systems are of prime importance in the healthcare sector. Liver cancer is commonly stated to be the sixth most widely diagnosed cancer and requires an early diagnosis to help with treatment planning. Liver tumors have similar intensity [...] Read more.
Smart multimedia-based medical analytics and decision-making systems are of prime importance in the healthcare sector. Liver cancer is commonly stated to be the sixth most widely diagnosed cancer and requires an early diagnosis to help with treatment planning. Liver tumors have similar intensity levels and contrast as compared to neighboring tissues. Similarly, irregular tumor shapes are another major issue that depends on the cancer stage and tumor type. Generally, liver tumor segmentation comprises two steps: the first one involves liver identification, and the second stage involves tumor segmentation. This research work performed tumor segmentation directly from a CT scan, which tends to be more difficult and important. We propose an efficient algorithm that employs multi-scale parallel convolution blocks (MPCs) and Res blocks based on residual learning. The fundamental idea of utilizing multi-scale parallel convolutions of varying filter sizes in MPCs is to extract multi-scale features for different tumor sizes. Moreover, the utilization of residual connections and residual blocks helps to extract rich features with a reduced number of parameters. Moreover, the proposed work requires no post-processing techniques to refine the segmentation. The proposed work was evaluated using the 3DIRCADb dataset and achieved a Dice score of 77.15% and 93% accuracy. Full article
(This article belongs to the Special Issue Machine Learning in Image Processing and Pattern Recognition: Modern Methods and Applications)
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21 pages, 512 KiB  
Article
Modeling COVID-19 with Uncertainty in Granada, Spain. Intra-Hospitalary Circuit and Expectations over the Next Months
by José M. Garrido, David Martínez-Rodríguez, Fernando Rodríguez-Serrano, Sorina-M. Sferle and Rafael-J. Villanueva
Mathematics 2021, 9(10), 1132; https://doi.org/10.3390/math9101132 - 17 May 2021
Cited by 2 | Viewed by 2543
Abstract
Mathematical models have been remarkable tools for knowing in advance the appropriate time to enforce population restrictions and distribute hospital resources. Here, we present a mathematical Susceptible-Exposed-Infectious-Recovered (SEIR) model to study the transmission dynamics of COVID-19 in Granada, Spain, taking into account the [...] Read more.
Mathematical models have been remarkable tools for knowing in advance the appropriate time to enforce population restrictions and distribute hospital resources. Here, we present a mathematical Susceptible-Exposed-Infectious-Recovered (SEIR) model to study the transmission dynamics of COVID-19 in Granada, Spain, taking into account the uncertainty of the phenomenon. In the model, the patients moving throughout the hospital’s departments (intra-hospitalary circuit) are considered in order to help to optimize the use of a hospital’s resources in the future. Two main seasons, September–April (autumn-winter) and May–August (summer), where the hospital pressure is significantly different, have been included. The model is calibrated and validated with data obtained from the hospitals in Granada. Possible future scenarios have been simulated. The model is able to capture the history of the pandemic in Granada. It provides predictions about the intra-hospitalary COVID-19 circuit over time and shows that the number of infected is expected to decline continuously from May without an increase next autumn–winter if population measures continue to be satisfied. The model strongly suggests that the number of infected cases will reduce rapidly with aggressive vaccination policies. The proposed study is being used in Granada to design public health policies and perform wise re-distribution of hospital resources in advance. Full article
(This article belongs to the Special Issue Advances on Uncertainty Quantification: Theory and Modelling)
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7 pages, 623 KiB  
Article
A Novel Analysis of the Smooth Curve with Constant Width Based on a Time Delay System
by Teng Fu and Yusheng Zhou
Mathematics 2021, 9(10), 1131; https://doi.org/10.3390/math9101131 - 17 May 2021
Cited by 1 | Viewed by 1964
Abstract
In this paper, we analyze the C∞ smooth curve of constant width using the characteristic equation of a time delay system. We prove that a closed convex curve must be a circle if it is still a smooth curve of constant width [...] Read more.
In this paper, we analyze the C∞ smooth curve of constant width using the characteristic equation of a time delay system. We prove that a closed convex curve must be a circle if it is still a smooth curve of constant width after taking any number of derivatives. Finally, the simulation results are presented for analyzing the influence of derivative orders on a smooth non-circular curve of constant width. Full article
(This article belongs to the Special Issue Differential Geometry of Spaces with Special Structures)
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12 pages, 4960 KiB  
Article
Image Denoising Using Adaptive and Overlapped Average Filtering and Mixed-Pooling Attention Refinement Networks
by Ming-Hao Lin, Zhi-Xiang Hou, Kai-Han Cheng, Chin-Hsien Wu and Yan-Tsung Peng
Mathematics 2021, 9(10), 1130; https://doi.org/10.3390/math9101130 - 17 May 2021
Cited by 3 | Viewed by 2344
Abstract
Cameras are essential parts of portable devices, such as smartphones and tablets. Most people have a smartphone and can take pictures anywhere and anytime to record their lives. However, these pictures captured by cameras may suffer from noise contamination, causing issues for subsequent [...] Read more.
Cameras are essential parts of portable devices, such as smartphones and tablets. Most people have a smartphone and can take pictures anywhere and anytime to record their lives. However, these pictures captured by cameras may suffer from noise contamination, causing issues for subsequent image analysis, such as image recognition, object tracking, and classification of an object in the image. This paper develops an effective combinational denoising framework based on the proposed Adaptive and Overlapped Average Filtering (AOAF) and Mixed-pooling Attention Refinement Networks (MARNs). First, we apply AOAF to the noisy input image to obtain a preliminarily denoised result, where noisy pixels are removed and recovered. Next, MARNs take the preliminary result as the input and output a refined image where details and edges are better reconstructed. The experimental results demonstrate that our method performs favorably against state-of-the-art denoising methods. Full article
(This article belongs to the Special Issue Artificial Intelligence and Big Data Computing)
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11 pages, 1033 KiB  
Article
Long Text QA Matching Model Based on BiGRU–DAttention–DSSM
by Shihong Chen and Tianjiao Xu
Mathematics 2021, 9(10), 1129; https://doi.org/10.3390/math9101129 - 17 May 2021
Cited by 5 | Viewed by 2656
Abstract
QA matching is a very important task in natural language processing, but current research on text matching focuses more on short text matching rather than long text matching. Compared with short text matching, long text matching is rich in information, but distracting information [...] Read more.
QA matching is a very important task in natural language processing, but current research on text matching focuses more on short text matching rather than long text matching. Compared with short text matching, long text matching is rich in information, but distracting information is frequent. This paper extracted question-and-answer pairs about psychological counseling to research long text QA-matching technology based on deep learning. We adjusted DSSM (Deep Structured Semantic Model) to make it suitable for the QA-matching task. Moreover, for better extraction of long text features, we also improved DSSM by enriching the text representation layer, using a bidirectional neural network and attention mechanism. The experimental results show that BiGRU–Dattention–DSSM performs better at matching questions and answers. Full article
(This article belongs to the Section Mathematics and Computer Science)
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15 pages, 3262 KiB  
Article
LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation
by Hamede Karami, Saleh Mobayen, Marzieh Lashkari, Farhad Bayat and Arthur Chang
Mathematics 2021, 9(10), 1128; https://doi.org/10.3390/math9101128 - 16 May 2021
Cited by 22 | Viewed by 3336
Abstract
In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear [...] Read more.
In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches. Full article
(This article belongs to the Special Issue Nonlinear Dynamics)
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