Mathematics

12 pages, 285 KiB

Open AccessArticle

New Monotonic Properties of Positive Solutions of Higher-Order Delay Differential Equations and Their Applications

by Ali Muhib, Osama Moaaz, Clemente Cesarano, Shami A. M. Alsallami, Sayed Abdel-Khalek and Abd Elmotaleb A. M. A. Elamin

Mathematics 2022, 10(10), 1786; https://doi.org/10.3390/math10101786 - 23 May 2022

Cited by 7 | Viewed by 1967

Abstract

In this work, new criteria were established for testing the oscillatory behavior of solutions of a class of even-order delay differential equations. We follow an approach that depends on obtaining new monotonic properties for the decreasing positive solutions of the studied equation. Moreover, [...] Read more.

In this work, new criteria were established for testing the oscillatory behavior of solutions of a class of even-order delay differential equations. We follow an approach that depends on obtaining new monotonic properties for the decreasing positive solutions of the studied equation. Moreover, we use these properties to provide new oscillation criteria of an iterative nature. We provide an example to support the significance of the results and compare them with the related previous work. Full article

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

17 pages, 384 KiB

Open AccessArticle

On Robustness for Spatio-Temporal Data

by Alfonso García-Pérez

Mathematics 2022, 10(10), 1785; https://doi.org/10.3390/math10101785 - 23 May 2022

Cited by 2 | Viewed by 2515

Abstract

The spatio-temporal variogram is an important factor in spatio-temporal prediction through kriging, especially in fields such as environmental sustainability or climate change, where spatio-temporal data analysis is based on this concept. However, the traditional spatio-temporal variogram estimator, which is commonly employed for these [...] Read more.

The spatio-temporal variogram is an important factor in spatio-temporal prediction through kriging, especially in fields such as environmental sustainability or climate change, where spatio-temporal data analysis is based on this concept. However, the traditional spatio-temporal variogram estimator, which is commonly employed for these purposes, is extremely sensitive to outliers. We approach this problem in two ways in the paper. First, new robust spatio-temporal variogram estimators are introduced, which are defined as M-estimators of an original data transformation. Second, we compare the classical estimate against a robust one, identifying spatio-temporal outliers in this way. To accomplish this, we use a multivariate scale-contaminated normal model to produce reliable approximations for the sample distribution of these new estimators. In addition, we define and study a new class of M-estimators in this paper, including real-world applications, in order to determine whether there are any significant differences in the spatio-temporal variogram between two temporal lags and, if so, whether we can reduce the number of lags considered in the spatio-temporal analysis. Full article

(This article belongs to the Special Issue Probability Theory and Stochastic Modeling with Applications)

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17 pages, 1314 KiB

Open AccessArticle

Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method

by Mohammad Shqair, Emad A. M. Farrag and Mohammed Al-Smadi

Mathematics 2022, 10(10), 1784; https://doi.org/10.3390/math10101784 - 23 May 2022

Cited by 6 | Viewed by 2003

Abstract

The solution of the complex neutron diffusion equations system of equations in a spherical nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remarkable approximation method that successfully solves different systems of diffusion equations, and in this work, [...] Read more.

The solution of the complex neutron diffusion equations system of equations in a spherical nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remarkable approximation method that successfully solves different systems of diffusion equations, and in this work, the system is solved for the first time using the approximation method. The considered system of neutron diffusion equations consists of two consistent subsystems, where the first studies the reactor and the multi-group subsystem of equations in the reactor core, and the other studies the multi-group subsystem of equations in the reactor reflector; each subsystem can deal with any finite number of neutron energy groups. The system is simplified numerically to a one-group bare and reflected reactor, which is compared with the modified differential transform method; a two-group bare reactor, which is compared with the residual power series method; a two-group reflected reactor, which is compared with the classical method; and a four-group bare reactor compared with the residual power series. Full article

(This article belongs to the Topic Multi-Energy Systems)

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12 pages, 320 KiB

Open AccessFeature PaperArticle

A Note on the Strong Predictable Representation Property and Enlargement of Filtration

by Antonella Calzolari and Barbara Torti

Mathematics 2022, 10(10), 1783; https://doi.org/10.3390/math10101783 - 23 May 2022

Cited by 1 | Viewed by 1850

Abstract

The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable [...] Read more.

The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable martingale representations for filtrations enlarged by means of a full process, possibly with accessible components in its jump times. The emphasis is on the non-uniqueness of the martingale enjoying the strong predictable representation property with respect to the same enlarged filtration. Full article

(This article belongs to the Special Issue Information in Economics, Finance and Insurance: Modelling and Applications)

15 pages, 5070 KiB

Open AccessArticle

RST Digital Robust Control for DC/DC Buck Converter Feeding Constant Power Load

by Akram M. Abdurraqeeb, Abdullrahman A. Al-Shamma’a, Abdulaziz Alkuhayli, Abdullah M. Noman and Khaled E. Addoweesh

Mathematics 2022, 10(10), 1782; https://doi.org/10.3390/math10101782 - 23 May 2022

Cited by 11 | Viewed by 2405

Abstract

The instability of DC microgrids is the most prominent problem that limits the expansion of their use, and one of the most important causes of instability is constant power load CPLs. In this paper, a robust RST digital feedback controller is proposed to [...] Read more.

The instability of DC microgrids is the most prominent problem that limits the expansion of their use, and one of the most important causes of instability is constant power load CPLs. In this paper, a robust RST digital feedback controller is proposed to overcome the instability issues caused by the negative-resistance effect of CPLs and to improve robustness against the perturbations of power load and input voltage fluctuations, as well as to achieve a good tracking performance. To develop the proposed controller, it is necessary to first identify the dynamic model of the DC/DC buck converter with CPL. Second, based on the pole placement and sensitivity function shaping technique, a controller is designed and applied to the buck converter system. Then, validation of the proposed controller using Matlab/Simulink was achieved. Finally, the experimental validation of the RST controller was performed on a DC/DC buck converter with CPL using a real-time Hardware-in-the-loop (HIL). The OPAL-RT OP4510 RCP/HIL and dSPACE DS1104 controller board are used to model the DC/DC buck converter and to implement the suggested RST controller, respectively. The simulation and HIL experimental results indicate that the suggested RST controller has high efficiency. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems)

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19 pages, 1640 KiB

Open AccessFeature PaperArticle

Fast Summarization of Long Time Series with Graphics Processor

by Mikhail Zymbler and Andrey Goglachev

Mathematics 2022, 10(10), 1781; https://doi.org/10.3390/math10101781 - 23 May 2022

Cited by 3 | Viewed by 1694

Abstract

Summarization of a long time series often occurs in analytical applications related to decision-making, modeling, planning, and so on. Informally, summarization aims at discovering a small-sized set of typical patterns (subsequences) to briefly represent the long time series. Apparent approaches to summarization like [...] Read more.

Summarization of a long time series often occurs in analytical applications related to decision-making, modeling, planning, and so on. Informally, summarization aims at discovering a small-sized set of typical patterns (subsequences) to briefly represent the long time series. Apparent approaches to summarization like motifs, shapelets, cluster centroids, and so on, either require training data or do not provide an analyst with information regarding the fraction of the time series that a typical subsequence found corresponds to. Recently introduced, the time series snippet concept overcomes the above-mentioned limitations. A snippet is a subsequence that is similar to many other subsequences of the time series with respect to a specially defined similarity measure based on the Euclidean distance. However, the original Snippet-Finder algorithm has cubic time complexity concerning the lengths of the time series and the snippet. In this article, we propose the PSF (Parallel Snippet-Finder) algorithm that accelerates the original snippet discovery schema with GPU and ensures acceptable performance over very long time series. As opposed to the original algorithm, PSF splits the calculation of the similarity of all the time series subsequences to a snippet into several steps, each of which is performed in parallel. Experimental evaluation over real-world time series shows that PSF outruns both the original algorithm and a straightforward parallelization. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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15 pages, 3713 KiB

Open AccessArticle

Advanced Control Algorithm for FADEC Systems in the Next Generation of Turbofan Engines to Minimize Emission Levels

by Majid Aghasharifian Esfahani, Mohammadmehdi Namazi, Theoklis Nikolaidis and Soheil Jafari

Mathematics 2022, 10(10), 1780; https://doi.org/10.3390/math10101780 - 23 May 2022

Cited by 1 | Viewed by 3440

Abstract

New propulsion systems in aircrafts must meet strict regulations and emission limitations. The Flightpath 2050 goals set by the Advisory Council for Aviation Research and Innovation in Europe (ACARE) include reductions of 75%, 90%, and 65% in CO₂, NO_x, [...] Read more.

New propulsion systems in aircrafts must meet strict regulations and emission limitations. The Flightpath 2050 goals set by the Advisory Council for Aviation Research and Innovation in Europe (ACARE) include reductions of 75%, 90%, and 65% in CO₂, NO_x, and noise, respectively. These goals are not fully satisfied by marginal improvements in gas turbine technology or aircraft design. A novel control design procedure for the next generation of turbofan engines is proposed in this paper to improve Full Authority Digital Engine Control (FADEC) systems and reduce the emission levels to meet the Flightpath 2050 regulations. Hence, an Adaptive Network–based Fuzzy Inference System (ANFIS), nonlinear autoregressive network with exogenous inputs (NARX) techniques, and the block-structure Hammerstein–Wiener approach are used to develop a model for a turbofan engine. The Min–Max control structure is chosen as the most widely used practical control algorithm for gas turbine aero engines. The objective function is considered to minimize the emission level for the engine in a pre-defined maneuver while keeping the engine performance in different aspects. The Genetic Algorithm (GA) is applied to find the optimized control structure. The results confirm the effectiveness of the proposed approach in emission reduction for the next generation of turbofan engines. Full article

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Graphical abstract

17 pages, 2381 KiB

Open AccessFeature PaperArticle

Multicriteria Analytical Model for Mechanical Integrity Prognostics of Reactor Pressure Vessels Manufactured from Forged and Rolled Steels

by Alvaro Rodríguez-Prieto, Manuel Callejas, Ernesto Primera, Guglielmo Lomonaco and Ana María Camacho

Mathematics 2022, 10(10), 1779; https://doi.org/10.3390/math10101779 - 23 May 2022

Cited by 1 | Viewed by 2207

Abstract

The aim of this work is to present a new analytical model to evaluate jointly the mechanical integrity and the fitness-for-service of nuclear reactor pressure-vessels steels. This new methodology integrates a robust and regulated irradiation embrittlement prediction model such as the ASTM E-900 [...] Read more.

The aim of this work is to present a new analytical model to evaluate jointly the mechanical integrity and the fitness-for-service of nuclear reactor pressure-vessels steels. This new methodology integrates a robust and regulated irradiation embrittlement prediction model such as the ASTM E-900 with the ASME Fitness-for-Service code used widely in other demanding industries, such as oil and gas, to evaluate, among others, the risk of experiencing degradation mechanisms such as the brittle fracture (generated, in this case, due to the irradiation embrittlement). This multicriteria analytical model, which is based on a new formulation of the brittle fracture criterion, allows an adequate prediction of the irradiation effect on the fracture toughness of reactor pressure-vessel steels, letting us jointly evaluate the mechanical integrity and the fitness-for-service of the vessel by using standardized limit conditions. This allows making decisions during the design, manufacturing and in-service of reactor pressure vessels. The results obtained by the application of the methodology are coherent with several historical experimental works. Full article

(This article belongs to the Special Issue Mathematical Modelling and Multi-Criteria Optimisation in Engineering)

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17 pages, 2172 KiB

Open AccessArticle

Application of HMM and Ensemble Learning in Intelligent Tunneling

by Yongbo Pan and Xunlin Zhu

Mathematics 2022, 10(10), 1778; https://doi.org/10.3390/math10101778 - 23 May 2022

Cited by 2 | Viewed by 1777

Abstract

The cutterhead torque and thrust, reflecting the obstruction degree of the geological environment and the behavior of excavation, are the key operating parameters for the tunneling of tunnel boring machines (TBMs). In this paper, a hybrid hidden Markov model (HMM) combined with ensemble [...] Read more.

The cutterhead torque and thrust, reflecting the obstruction degree of the geological environment and the behavior of excavation, are the key operating parameters for the tunneling of tunnel boring machines (TBMs). In this paper, a hybrid hidden Markov model (HMM) combined with ensemble learning is proposed to predict the value intervals of the cutterhead torque and thrust based on the historical tunneling data. First, the target variables are encoded into discrete states by means of HMM. Then, ensemble learning models including AdaBoost, random forest (RF), and extreme random tree (ERT) are employed to predict the discrete states. On this basis, the performances of those models are compared under different forms of the same input parameters. Moreover, to further validate the effectiveness and superiority of the proposed method, two excavation datasets including Beijing and Zhengzhou from the actual project under different geological conditions are utilized for comparison. The results show that the ERT outperforms the other models and the corresponding prediction accuracies are up to 0.93 and 0.99 for the cutterhead torque and thrust, respectively. Therefore, the ERT combined with HMM can be used as a valuable prediction tool for predicting the cutterhead torque and thrust, which is of positive significance to alert the operator to judge whether the excavation is normal and assist the intelligent tunneling. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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18 pages, 1906 KiB

Open AccessArticle

Bayesian Networks for Preprocessing Water Management Data

by Rosa Fernández Ropero, María Julia Flores and Rafael Rumí

Mathematics 2022, 10(10), 1777; https://doi.org/10.3390/math10101777 - 23 May 2022

Cited by 2 | Viewed by 1792

Abstract

Environmental data often present inconveniences that make modeling tasks difficult. During the phase of data collection, two problems were found: (i) a block of five months of data was unavailable, and (ii) no information was collected from the coastal area, which made flood-risk [...] Read more.

Environmental data often present inconveniences that make modeling tasks difficult. During the phase of data collection, two problems were found: (i) a block of five months of data was unavailable, and (ii) no information was collected from the coastal area, which made flood-risk estimation difficult. Thus, our aim is to explore and provide possible solutions to both issues. To avoid removing a variable (or those missing months), the proposed solution is a BN-based regression model using fixed probabilistic graphical structures to impute the missing variable as accurately as possible. For the second problem, the lack of information, an unsupervised classification method based on BN was developed to predict flood risk in the coastal area. Results showed that the proposed regression solution could predict the behavior of the continuous missing variable, avoiding the initial drawback of rejecting it. Moreover, the unsupervised classifier could classify all observations into a set of groups according to upstream river behavior and rainfall information, and return the probability of belonging to each group, providing appropriate predictions about the risk of flood in the coastal area. Full article

(This article belongs to the Section Probability and Statistics)

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23 pages, 2919 KiB

Open AccessArticle

DEA and Machine Learning for Performance Prediction

by Zhishuo Zhang, Yao Xiao and Huayong Niu

Mathematics 2022, 10(10), 1776; https://doi.org/10.3390/math10101776 - 23 May 2022

Cited by 14 | Viewed by 4562

Abstract

Data envelopment analysis (DEA) has been widely applied to evaluate the performance of banks, enterprises, governments, research institutions, hospitals, and other fields as a non-parametric estimation method for evaluating the relative effectiveness of research objects. However, the composition of its effective frontier surface [...] Read more.

Data envelopment analysis (DEA) has been widely applied to evaluate the performance of banks, enterprises, governments, research institutions, hospitals, and other fields as a non-parametric estimation method for evaluating the relative effectiveness of research objects. However, the composition of its effective frontier surface is based on the input-output data of existing decision units, which makes it challenging to apply the method to predict the future performance level of other decision units. In this paper, the Slack Based Measure (SBM) model in DEA method is used to measure the relative efficiency values of decision units, and then, eleven machine learning models are used to train the absolute efficient frontier to be applied to the performance prediction of new decisions units. To further improve the prediction effect of the models, this paper proposes a training set under the DEA classification method, starting from the training-set sample selection and input feature indicators. In this paper, regression prediction of test set performance based on the training set under different classification combinations is performed, and the prediction effects of proportional relative indicators and absolute number indicators as machine-learning input features are explored. The robustness of the effective frontier surface under the integrated model is verified. An integrated models of DEA and machine learning with better prediction effects is proposed, taking China’s regional carbon-dioxide emission (carbon emission) performance prediction as an example. The novelty of this work is mainly as follows: firstly, the integrated model can achieve performance prediction by constructing an effective frontier surface, and the empirical results show that this is a feasible methodological technique. Secondly, two schemes to improve the prediction effectiveness of integrated models are discussed in terms of training set partitioning and feature selection, and the effectiveness of the schemes is demonstrated by using carbon-emission performance prediction as an example. This study has some application value and is a complement to the existing literature. Full article

(This article belongs to the Special Issue Quantitative Analysis and DEA Modeling in Applied Economics)

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21 pages, 5271 KiB

Open AccessArticle

Mathematical Simulation of Heat Transfer in Thermally Magnetised Oldroyd-B Fluid in Sakiadis Rheology with a Heat Reservoir

by Zeeshan, Rasool Shah, Waris Khan, Essam R. El-Zahar, Se-Jin Yook and Nehad Ali Shah

Mathematics 2022, 10(10), 1775; https://doi.org/10.3390/math10101775 - 23 May 2022

Cited by 1 | Viewed by 1747

Abstract

Sakiadis rheology of a generalised polymeric material, as well as a heat source or sink and a magnetic field, are all part of this study. Thermal radiations have been introduced into the convective heating process. The translation of a physical situation into a [...] Read more.

Sakiadis rheology of a generalised polymeric material, as well as a heat source or sink and a magnetic field, are all part of this study. Thermal radiations have been introduced into the convective heating process. The translation of a physical situation into a set of nonlinear equations was achieved through mathematical modelling. To convert the resulting partial differential equation into a set of nonlinear ordinary differential equations, appropriate transformations have been used. The velocity and temperature profiles are generated both analytically by HAM and numerically by the Runge–Kutta method (RK-4). In order to analyse the behaviour of the physical quantities involved, numerical and graphical depictions have been offered. To show that the acquired findings are correct, a nonlinear system error analysis has been offered. The heat flux study has been shown using bar charts. For the essential factors involved, the local Nusselt number and local Skin friction are calculated in tabular form. The fluid particles’ molecular mobility was slowed due to the magnetic field and porosity, and the heat transfer rates were demonstrated to be lowered when magnetic and porosity effects are present. This magnetic field and porosity effects regulating property has applications in MHD ion propulsion and power production, the electromagnetic casting of metals, etc. Furthermore, internal heat absorption and generation have diametrically opposed impacts on fluid temperature. The novelty of the present study is that no one has investigated the Sakiadis flow of thermal convection magnetised Oldroyd-B fluid in terms of a heat reservoir across a porous sheet. In limited circumstances, a satisfactory match is revealed when the collected values are compared to the existing work published corroborating the current attempt. The findings of this study are expected to be applicable to a wide range of technical and industrial processes, including steel extrusion, wire protective layers, fiber rolling, fabrication, polythene stuff such as broadsheet, fiber, and stainless steel sheets, and even the process of depositing a thin layer where the sheet is squeezed. Full article

(This article belongs to the Special Issue Mathematics and Engineering II)

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14 pages, 12502 KiB

Open AccessArticle

A Discrete Dynamics Approach to a Tumor System

by Tareq Saeed, Kamel Djeddi, Juan L. G. Guirao, Hamed H. Alsulami and Mohammed Sh. Alhodaly

Mathematics 2022, 10(10), 1774; https://doi.org/10.3390/math10101774 - 23 May 2022

Cited by 5 | Viewed by 1901

Abstract

In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We [...] Read more.

In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We studied the stability of the fixed points in the discrete cancer system using the new version of Marotto’s theorem at a fixed point; we prove that the discrete cancer system is chaotic. Finally, we present numerical simulations, e.g., Lyapunov exponents and bifurcations diagrams. Full article

(This article belongs to the Special Issue Mathematical Models and Applications in Cancer)

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32 pages, 12618 KiB

Open AccessArticle

Estimating Structural Shocks with the GVAR-DSGE Model: Pre- and Post-Pandemic

by Chunyeung Kwok

Mathematics 2022, 10(10), 1773; https://doi.org/10.3390/math10101773 - 23 May 2022

Cited by 2 | Viewed by 2305

Abstract

This paper investigates the possibility of using the global VAR (GVAR) model to estimate a simple New Keynesian DSGE-type multi-country model. The long-run forecasts from an estimated GVAR model were used to calculate the steady-states of macro variables as differences. The deviations from [...] Read more.

This paper investigates the possibility of using the global VAR (GVAR) model to estimate a simple New Keynesian DSGE-type multi-country model. The long-run forecasts from an estimated GVAR model were used to calculate the steady-states of macro variables as differences. The deviations from the long-run forecasts were taken as the deviation from the steady-states and were used to estimate a simple NK open economy model with an IS curve, Philips curve, Taylor rule, and an exchange rate equation. The shocks to these equations were taken as the demand shock, supply shock, monetary shock, and exchange rate shock, respectively. An alternative model was constructed to compare the results from GVAR long-run forecasts. The alternative model used a Hodrick–Prescott (HP) filter to derive deviations from the steady-states. The impulsive response functions from the shocks were then compared to results from other DSGE models in the literature. Both GVAR and HP estimates produced dissimilar results, although the GVAR managed to capture more from the data, given the explicit co-integration relationships. For the IRFs, both GVAR and HP estimated DSGE models appeared to be as expected before the pandemic; however, if we include the pandemic data, i.e., 2020, the IRFs are very different, due to the nature of the policy actions. In general, DSGE–GVAR models appear to be much more versatile, and are able to capture dynamics that HP filters are not. Full article

(This article belongs to the Special Issue Mathematical Financial Econometrics: Non-normal Distributions and Risk Forecasting)

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27 pages, 740 KiB

Open AccessArticle

Stability and Numerical Simulations of a New SVIR Model with Two Delays on COVID-19 Booster Vaccination

by Xinyu Liu and Yuting Ding

Mathematics 2022, 10(10), 1772; https://doi.org/10.3390/math10101772 - 23 May 2022

Cited by 6 | Viewed by 2147

Abstract

As COVID-19 continues to threaten public health around the world, research on specific vaccines has been underway. In this paper, we establish an SVIR model on booster vaccination with two time delays. The time delays represent the time of booster vaccination and the [...] Read more.

As COVID-19 continues to threaten public health around the world, research on specific vaccines has been underway. In this paper, we establish an SVIR model on booster vaccination with two time delays. The time delays represent the time of booster vaccination and the time of booster vaccine invalidation, respectively. Second, we investigate the impact of delay on the stability of non-negative equilibria for the model by considering the duration of the vaccine, and the system undergoes Hopf bifurcation when the duration of the vaccine passes through some critical values. We obtain the normal form of Hopf bifurcation by applying the multiple time scales method. Then, we study the model with two delays and show the conditions under which the nontrivial equilibria are locally asymptotically stable. Finally, through analysis of official data, we select two groups of parameters to simulate the actual epidemic situation of countries with low vaccination rates and countries with high vaccination rates. On this basis, we select the third group of parameters to simulate the ideal situation in which the epidemic can be well controlled. Through comparative analysis of the numerical simulations, we concluded that the most appropriate time for vaccination is to vaccinate with the booster shot 6 months after the basic vaccine. The priority for countries with low vaccination rates is to increase vaccination rates; otherwise, outbreaks will continue. Countries with high vaccination rates need to develop more effective vaccines while maintaining their coverage rates. When the vaccine lasts longer and the failure rate is lower, the epidemic can be well controlled within 20 years. Full article

(This article belongs to the Special Issue Recent Advances in Theory and Application of Dynamical Systems)

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17 pages, 328 KiB

Open AccessArticle

A New Look at the Initial Condition Problem

by Manuel D. Ortigueira

Mathematics 2022, 10(10), 1771; https://doi.org/10.3390/math10101771 - 23 May 2022

Cited by 18 | Viewed by 2123

Abstract

In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved [...] Read more.

In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generality as well as applied to continuous-time fractional autoregressive-moving average systems. Full article

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

13 pages, 3201 KiB

Open AccessArticle

Introducing a Precise System for Determining Volume Percentages Independent of Scale Thickness and Type of Flow Regime

by Abdulilah Mohammad Mayet, Seyed Mehdi Alizadeh, Zana Azeez Kakarash, Ali Awadh Al-Qahtani, Abdullah K. Alanazi, Hala H. Alhashimi, Ehsan Eftekhari-Zadeh and Ehsan Nazemi

Mathematics 2022, 10(10), 1770; https://doi.org/10.3390/math10101770 - 23 May 2022

Cited by 20 | Viewed by 2098

Abstract

When fluids flow into the pipes, the materials in them cause deposits to form inside the pipes over time, which is a threat to the efficiency of the equipment and their depreciation. In the present study, a method for detecting the volume percentage [...] Read more.

When fluids flow into the pipes, the materials in them cause deposits to form inside the pipes over time, which is a threat to the efficiency of the equipment and their depreciation. In the present study, a method for detecting the volume percentage of two-phase flow by considering the presence of scale inside the test pipe is presented using artificial intelligence networks. The method is non-invasive and works in such a way that the detector located on one side of the pipe absorbs the photons that have passed through the other side of the pipe. These photons are emitted to the pipe by a dual source of the isotopes barium-133 and cesium-137. The Monte Carlo N Particle Code (MCNP) simulates the structure, and wavelet features are extracted from the data recorded by the detector. These features are considered Group methods of data handling (GMDH) inputs. A neural network is trained to determine the volume percentage with high accuracy independent of the thickness of the scale in the pipe. In this research, to implement a precise system for working in operating conditions, different conditions, including different flow regimes and different scale thickness values as well as different volume percentages, are simulated. The proposed system is able to determine the volume percentages with high accuracy, regardless of the type of flow regime and the amount of scale inside the pipe. The use of feature extraction techniques in the implementation of the proposed detection system not only reduces the number of detectors, reduces costs, and simplifies the system but also increases the accuracy to a good extent. Full article

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

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10 pages, 246 KiB

Open AccessArticle

The Best Ulam Constant of the Fréchet Functional Equation

by Irina Opraie, Dorian Popa and Liana Timboş

Mathematics 2022, 10(10), 1769; https://doi.org/10.3390/math10101769 - 22 May 2022

Viewed by 1587

Abstract

In this paper, we prove the Ulam stability of the Fréchet functional equation [...] Read more.

In this paper, we prove the Ulam stability of the Fréchet functional equation

f (x + y + z) + f (x) + f (y) + f (z) = f (x + y) + f (y + z) + f (z + x)

arising from the characterization of inner product spaces and we determine its best Ulam constant. Using this result, we give a stability result for a pexiderized version of the Fréchet functional equation. Full article

(This article belongs to the Special Issue Mathematical Inequalities, Models and Applications)

15 pages, 1522 KiB

Open AccessArticle

An Approach to Assessing Spatial Coherence of Current and Voltage Signals in Electrical Networks

by Pavel Ilyushin, Aleksandr Kulikov, Konstantin Suslov and Sergey Filippov

Mathematics 2022, 10(10), 1768; https://doi.org/10.3390/math10101768 - 22 May 2022

Cited by 2 | Viewed by 1429

Abstract

In the context of energy industry decentralization, electrical networks encounter deviations of power quality indices (PQI), including violations of the sinusoidality of current and voltage signals, which increase errors in the joint digital processing of spatially separated signals in digital devices. This paper [...] Read more.

In the context of energy industry decentralization, electrical networks encounter deviations of power quality indices (PQI), including violations of the sinusoidality of current and voltage signals, which increase errors in the joint digital processing of spatially separated signals in digital devices. This paper addresses specific features of using the concept of spatial coherence in the measurement and digital processing of current and voltage signals. Methods for assessing the coherence of current and voltage signals during synchronized measurements are considered for the case of PQI deviation. The example of a double-ended transmission line fault location (hereafter, DTLFL) demonstrates that the lower the cross-correlation coefficient, the higher the error and the lower the accuracy of calculating the distance to the fault site. The nature of the influence of spatial coherence violations on errors in DTLFL depends on the expression used to calculate the distance to the fault point. The application of a normalized cross-correlation coefficient for finding errors in the digital processing of current and voltage signals, in the case of spatial coherence violation, was substantiated. The influence of interharmonics and noise on errors in DTLFL, in the case of violations of spatial coherence of signals, was investigated. The magnitude of distortions and error in estimating the current and voltage amplitude depends on the ratio between the amplitudes and phases of the fundamental and distorting interharmonics. Filtration of the original and decimated signals based on the discrete Fourier transform eliminates the noise components of the power frequency harmonics. Full article

(This article belongs to the Special Issue Model Predictive Control and Optimization for Cyber-Physical Systems)

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20 pages, 334 KiB

Open AccessArticle

Prediction of Medical Conditions Using Machine Learning Approaches: Alzheimer’s Case Study

by Georgiana Ingrid Stoleru and Adrian Iftene

Mathematics 2022, 10(10), 1767; https://doi.org/10.3390/math10101767 - 22 May 2022

Cited by 3 | Viewed by 2973

Abstract

Alzheimer’s Disease (AD) is a highly prevalent condition and most of the people suffering from it receive the diagnosis late in the process. The diagnosis is currently established following an evaluation of the protein biomarkers in cerebrospinal fluid (CSF), brain imaging, cognitive tests, [...] Read more.

Alzheimer’s Disease (AD) is a highly prevalent condition and most of the people suffering from it receive the diagnosis late in the process. The diagnosis is currently established following an evaluation of the protein biomarkers in cerebrospinal fluid (CSF), brain imaging, cognitive tests, and the medical history of the individuals. While diagnostic tools based on CSF collections are invasive, the tools used for acquiring brain scans are expensive. Taking these into account, an early predictive system, based on Artificial Intelligence (AI) approaches, targeting the diagnosis of this condition, as well as the identification of lead biomarkers becomes an important research direction. In this survey, we review the state-of-the-art research on machine learning (ML) techniques used for the detection of AD and Mild Cognitive Impairment (MCI). We attempt to identify the most accurate and efficient diagnostic approaches, which employ ML techniques and therefore, the ones most suitable to be used in practice. Research is still ongoing to determine the best biomarkers for the task of AD classification. At the beginning of this survey, after an introductory part, we enumerate several available resources, which can be used to build ML models targeting the diagnosis and classification of AD, as well as their main characteristics. After that, we discuss the candidate markers which were used to build AI models with the best results in terms of diagnostic accuracy, as well as their limitations. Full article

(This article belongs to the Special Issue Application of Advanced Computing and Artificial Intelligence in Engineering and Science)

32 pages, 507 KiB

Open AccessArticle

State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations

by Jun Moon

Mathematics 2022, 10(10), 1766; https://doi.org/10.3390/math10101766 - 22 May 2022

Cited by 2 | Viewed by 2000

Abstract

In this paper, we consider the two-player state and control path-dependent stochastic zero-sum differential game. In our problem setup, the state process, which is controlled by the players, is dependent on (current and past) paths of state and control processes of the players. [...] Read more.

In this paper, we consider the two-player state and control path-dependent stochastic zero-sum differential game. In our problem setup, the state process, which is controlled by the players, is dependent on (current and past) paths of state and control processes of the players. Furthermore, the running cost of the objective functional depends on both state and control paths of the players. We use the notion of non-anticipative strategies to define lower and upper value functionals of the game, where unlike the existing literature, these value functions are dependent on the initial states and control paths of the players. In the first main result of this paper, we prove that the (lower and upper) value functionals satisfy the dynamic programming principle (DPP), for which unlike the existing literature, the Skorohod metric is necessary to maintain the separability of càdlàg (state and control) spaces. We introduce the lower and upper Hamilton–Jacobi–Isaacs (HJI) equations from the DPP, which correspond to the state and control path-dependent nonlinear second-order partial differential equations. In the second main result of this paper, we show that by using the functional Itô calculus, the lower and upper value functionals are viscosity solutions of (lower and upper) state and control path-dependent HJI equations, where the notion of viscosity solutions is defined on a compact

κ

-Hölder space to use several important estimates and to guarantee the existence of minimum and maximum points between the (lower and upper) value functionals and the test functions. Based on these two main results, we also show that the Isaacs condition and the uniqueness of viscosity solutions imply the existence of the game value. Finally, we prove the uniqueness of classical solutions for the (state path-dependent) HJI equations in the state path-dependent case, where its proof requires establishing an equivalent classical solution structure as well as an appropriate contradiction argument. Full article

(This article belongs to the Special Issue Stochastic Processes and Their Applications)

19 pages, 416 KiB

Open AccessArticle

Optimal H₂ Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization

by Ion Necoara and Tudor-Corneliu Ionescu

Mathematics 2022, 10(10), 1765; https://doi.org/10.3390/math10101765 - 22 May 2022

Viewed by 1992

Abstract

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free [...] Read more.

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free parameters. Based on the parametrization and using the

H_{2}

-norm of the approximation error as the objective function, we derive a nonconvex optimization problem, i.e., we search for the optimal free parameters to determine the model yielding the minimal

H_{2}

-norm of the approximation error. Furthermore, we provide the necessary first-order optimality conditions in terms of the controllability and the observability Gramians of a minimal realization of the error system. We then propose two gradient-type algorithms to compute the (local) optimal models, with mathematical guarantees on the convergence. We also derive convex semidefinite programming relaxations for the nonconvex Problem, under the assumption that the error system admits block-diagonal Gramians, and derive sufficient conditions to guarantee the block diagonalization. The solutions resulting at each step of the proposed algorithms guarantee the achievement of the imposed moment matching conditions. The second gradient-based algorithm exhibits the additional property that, when stopped, yields a stable approximation with a reduced

H_{2}

-error norm. We illustrate the theory on a CD-player and on a discretized heat equation. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

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16 pages, 1125 KiB

Open AccessArticle

Analysis of Industrial Engineering Students’ Perception after a Multiple Integrals-Based Activity with a Fourth-Year Student

by Anuar R. Giménez, Jesús Martín-Vaquero and Manuel Rodríguez-Martín

Mathematics 2022, 10(10), 1764; https://doi.org/10.3390/math10101764 - 21 May 2022

Cited by 2 | Viewed by 2611

Abstract

In industrial engineering degrees in Spain, mathematics subjects are usually taught during the first two academic years. Consequently, it is often the case that students sometimes do not feel motivated to learn subjects such as Mathematics II (calculus). Nevertheless, this subject is fundamental [...] Read more.

In industrial engineering degrees in Spain, mathematics subjects are usually taught during the first two academic years. Consequently, it is often the case that students sometimes do not feel motivated to learn subjects such as Mathematics II (calculus). Nevertheless, this subject is fundamental for understanding other subjects in the degree study plan, as well as for the graduate’s future professional career as an engineer. To address this, a problem-based teaching methodology was carried out with the help of a fourth-year student who explained an activity to first-year students in a manner which was both friendly and approachable. In this experiment, the student went through a series of practical problems taken from different engineering subjects, which required multivariable integrals to be calculated and which he had learned in mathematics as a first-year student. In addition, a method based on pre-test and post-test assessments was applied. From this work, various benefits were observed in terms of learning, as well as an increase in the level of motivation of first-year students. There was a greater appreciation of the usefulness of calculus and computer programs to solve real-life problems, and the students generally responded positively to this type of activity. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)

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17 pages, 1163 KiB

Open AccessArticle

Intent-Controllable Citation Text Generation

by Shing-Yun Jung, Ting-Han Lin, Chia-Hung Liao, Shyan-Ming Yuan and Chuen-Tsai Sun

Mathematics 2022, 10(10), 1763; https://doi.org/10.3390/math10101763 - 21 May 2022

Cited by 5 | Viewed by 2360

Abstract

We study the problem of controllable citation text generation by introducing a new concept to generate citation texts. Citation text generation, as an assistive writing approach, has drawn a number of researchers’ attention. However, current research related to citation text generation rarely addresses [...] Read more.

We study the problem of controllable citation text generation by introducing a new concept to generate citation texts. Citation text generation, as an assistive writing approach, has drawn a number of researchers’ attention. However, current research related to citation text generation rarely addresses how to generate the citation texts that satisfy the specified citation intents by the paper’s authors, especially at the beginning of paper writing. We propose a controllable citation text generation model that extends a pre-trained sequence to sequence models, namely, BART and T5, by using the citation intent as the control code to generate the citation text, meeting the paper authors’ citation intent. Experimental results demonstrate that our model can generate citation texts semantically similar to the reference citation texts and satisfy the given citation intent. Additionally, the results from human evaluation also indicate that incorporating the citation intent may enable the models to generate relevant citation texts almost as scientific paper authors do, even when only a little information from the citing paper is available. Full article

(This article belongs to the Special Issue Advances in Machine Learning Methods for Natural Language Processing and Computational Linguistics)

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22 pages, 2997 KiB

Open AccessArticle

Simulation and State Feedback Control of a Pressure Swing Adsorption Process to Produce Hydrogen

by Mario Martínez García, Jesse Y. Rumbo Morales, Gerardo Ortiz Torres, Salvador A. Rodríguez Paredes, Sebastián Vázquez Reyes, Felipe de J. Sorcia Vázquez, Alan F. Pérez Vidal, Jorge S. Valdez Martínez, Ricardo Pérez Zúñiga and Erasmo M. Renteria Vargas

Mathematics 2022, 10(10), 1762; https://doi.org/10.3390/math10101762 - 21 May 2022

Cited by 16 | Viewed by 3109

Abstract

One of the separation processes used for the production and purification of hydrogen is molecular sieve adsorption using the Pressure Swing Adsorption (PSA) method. The process uses two beds containing activated carbon and a sequence of four steps (adsorption, depressurization, purge, and repressurization) [...] Read more.

One of the separation processes used for the production and purification of hydrogen is molecular sieve adsorption using the Pressure Swing Adsorption (PSA) method. The process uses two beds containing activated carbon and a sequence of four steps (adsorption, depressurization, purge, and repressurization) for hydrogen production and purification. The initial composition is 0.11 CO, 0.61 H₂, and 0.28 CH₄ in molar fractions. The aim of this work is to bring the purity of hydrogen to 0.99 in molar fraction and implement controllers that can maintain the desired purity even in the presence of the disturbances that occur in the PSA process. The controller design (discrete PID and state feedback control) was based on the Hammerstein–Wiener model, which had an 80% fit over the rigorous PSA model. Both controllers were validated on a virtual plant of the PSA process, showing great performance and robustness against disturbances. The results obtained show that it is possible to follow the desired trajectory and attenuate double disturbances, while managing to maintain the purity of hydrogen at a value of 0.99 in molar fraction, which meets the international standards to be used as a biofuel. Full article

(This article belongs to the Special Issue Numerical Simulation and Control in Energy Systems)

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14 pages, 3760 KiB

Open AccessEditor’s ChoiceArticle

An Efficient Computational Technique for the Electromagnetic Scattering by Prolate Spheroids

by Ludovica Tognolatti, Cristina Ponti, Massimo Santarsiero and Giuseppe Schettini

Mathematics 2022, 10(10), 1761; https://doi.org/10.3390/math10101761 - 21 May 2022

Cited by 3 | Viewed by 2289

Abstract

In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one [...] Read more.

In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one of its axes, which is also known as a spheroid. We have developed a fast and ad hoc code to solve the electromagnetic scattering problem, using spheroidal vector wave functions, which are special functions used to describe physical problems in which a prolate or oblate spheroidal reference system is considered. Numerical results are presented, both for TE and TM polarization of the incident wave, and are validated by a comparison with results obtained by a commercial electromagnetic simulator. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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17 pages, 623 KiB

Open AccessArticle

A Fuzzy Simheuristic for the Permutation Flow Shop Problem under Stochastic and Fuzzy Uncertainty

by Juliana Castaneda, Xabier A. Martin, Majsa Ammouriova, Javier Panadero and Angel A. Juan

Mathematics 2022, 10(10), 1760; https://doi.org/10.3390/math10101760 - 21 May 2022

Cited by 7 | Viewed by 1927

Abstract

Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper, we analyze the permutation flow shop problem (PFSP) with both stochastic and fuzzy processing times. The [...] Read more.

Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper, we analyze the permutation flow shop problem (PFSP) with both stochastic and fuzzy processing times. The main goal is to find the solution (permutation of jobs) that minimizes the expected makespan. However, due to the existence of uncertainty, other characteristics of the solution are also taken into account. In particular, we illustrate how survival analysis can be employed to enrich the probabilistic information given to decision-makers. To solve the aforementioned optimization problem, we extend the concept of a simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated in the PFSP. In order to test our approach, classical PFSP instances have been adapted and extended, so that processing times become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones. Full article

(This article belongs to the Special Issue Applications of Mathematical Methods and Fuzzy Techniques in Decision Making)

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15 pages, 323 KiB

Open AccessArticle

Exact Solvability Conditions for the Non-Local Initial Value Problem for Systems of Linear Fractional Functional Differential Equations

by Natalia Dilna and Michal Fečkan

Mathematics 2022, 10(10), 1759; https://doi.org/10.3390/math10101759 - 21 May 2022

Cited by 3 | Viewed by 1360

Abstract

The exact conditions sufficient for the unique solvability of the initial value problem for a system of linear fractional functional differential equations determined by isotone operators are established. In a sense, the conditions obtained are optimal. The method of the test elements intended [...] Read more.

The exact conditions sufficient for the unique solvability of the initial value problem for a system of linear fractional functional differential equations determined by isotone operators are established. In a sense, the conditions obtained are optimal. The method of the test elements intended for the estimation of the spectral radius of a linear operator is used. The unique solution is presented by the Neumann’s series. All theoretical investigations are shown in the examples. A pantograph-type model from electrodynamics is studied. Full article

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)

20 pages, 340 KiB

Open AccessArticle

A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

by Long-Sheng Liu, Qing-Wen Wang and Mahmoud Saad Mehany

Mathematics 2022, 10(10), 1758; https://doi.org/10.3390/math10101758 - 21 May 2022

Cited by 13 | Viewed by 1850

Abstract

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves

η

-Hermicity. We [...] Read more.

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves

η

-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper. Full article

(This article belongs to the Special Issue Selected Papers from The China-Korea-USA International Conference on Matrix Theory with Applications)

15 pages, 2212 KiB

Open AccessArticle

Modeling Electricity Price Dynamics Using Flexible Distributions

by Sherzod N. Tashpulatov

Mathematics 2022, 10(10), 1757; https://doi.org/10.3390/math10101757 - 21 May 2022

Cited by 1 | Viewed by 2056

Abstract

We consider the wholesale electricity market prices in England and Wales during its complete history, where price-cap regulation and divestment series were introduced at different points in time. We compare the impact of these regulatory reforms on the dynamics of electricity prices. For [...] Read more.

We consider the wholesale electricity market prices in England and Wales during its complete history, where price-cap regulation and divestment series were introduced at different points in time. We compare the impact of these regulatory reforms on the dynamics of electricity prices. For this purpose, we apply flexible distributions that account for asymmetry, heavy tails, and excess kurtosis usually observed in data or model residuals. The application of skew generalized error distribution is appropriate for our case study. We find that after the second series of divestments, price level and volatility are lower than during price-cap regulation and after the first series of divestments. This finding implies that a sufficient horizontal restructuring through divestment series may be superior to price-cap regulation. The conclusion could be interesting to other countries because the England and Wales electricity market served as the benchmark model for liberalizing energy markets worldwide. Full article

(This article belongs to the Special Issue Probability Distributions and Their Applications)

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