Mathematics

16 pages, 341 KiB

Open AccessArticle

On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case

by Roberto S. Costas-Santos, Anier Soria-Lorente and Jean-Marie Vilaire

Mathematics 2022, 10(11), 1952; https://doi.org/10.3390/math10111952 - 6 Jun 2022

Cited by 4 | Viewed by 1890

In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product

⟨f, g⟩ = ⟨ u^{M}, f g ⟩ + λ T^{j} f (α) T^{j} g (α),

[...] Read more.

In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product

⟨f, g⟩ = ⟨ u^{M}, f g ⟩ + λ T^{j} f (α) T^{j} g (α),

where

u^{M}

is the Meixner linear operator,

λ \in R_{+}

,

j \in N

,

α \leq 0

, and

T

is the forward difference operator

Δ

or the backward difference operator ∇. Moreover, we derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of the second order is also given. In addition, for these polynomials, we derive a

(2 j + 3)

-term recurrence relation. Finally, we find the Mehler–Heine type formula for the particular case

α = 0

. Full article

(This article belongs to the Section Difference and Differential Equations)

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11 pages, 1044 KiB

Open AccessArticle

A Note on the Laguerre-Type Appell and Hypergeometric Polynomials

by Paolo Emilio Ricci and Rekha Srivastava

Mathematics 2022, 10(11), 1951; https://doi.org/10.3390/math10111951 - 6 Jun 2022

Cited by 5 | Viewed by 1797

Abstract

The Laguerre derivative and its iterations have been used to define new sets of special functions, showing the possibility of generating a kind of parallel universe for mathematical entities of this kind. In this paper, we introduce the Laguerre-type Appell polynomials, in particular, [...] Read more.

The Laguerre derivative and its iterations have been used to define new sets of special functions, showing the possibility of generating a kind of parallel universe for mathematical entities of this kind. In this paper, we introduce the Laguerre-type Appell polynomials, in particular, the Bernoulli and Euler case, and we examine a set of hypergeometric Laguerre–Bernoulli polynomials. We show their main properties and indicate their possible extensions. Full article

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13 pages, 906 KiB

Open AccessArticle

Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation

by Wendong Jiang, Chia-Liang Lin, Vasilios N. Katsikis, Spyridon D. Mourtas, Predrag S. Stanimirović and Theodore E. Simos

Mathematics 2022, 10(11), 1950; https://doi.org/10.3390/math10111950 - 6 Jun 2022

Cited by 15 | Viewed by 1950

Abstract

This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved [...] Read more.

This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME. Full article

(This article belongs to the Special Issue Selected Papers from the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM))

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26 pages, 383 KiB

Open AccessArticle

Modified Mann-Type Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points Implicating Countably Many Nonexpansive Operators

by Yun-Ling Cui, Lu-Chuan Ceng, Fang-Fei Zhang, Cong-Shan Wang, Jian-Ye Li, Hui-Ying Hu and Long He

Mathematics 2022, 10(11), 1949; https://doi.org/10.3390/math10111949 - 6 Jun 2022

Viewed by 1514

Abstract

In a real Hilbert space, let the CFPP, VIP, and HFPP denote the common fixed-point problem of countable nonexpansive operators and asymptotically nonexpansive operator, variational inequality problem, and hierarchical fixed point problem, respectively. With the help of the Mann iteration method, a subgradient [...] Read more.

In a real Hilbert space, let the CFPP, VIP, and HFPP denote the common fixed-point problem of countable nonexpansive operators and asymptotically nonexpansive operator, variational inequality problem, and hierarchical fixed point problem, respectively. With the help of the Mann iteration method, a subgradient extragradient approach with a linear-search process, and a hybrid deepest-descent technique, we construct two modified Mann-type subgradient extragradient rules with a linear-search process for finding a common solution of the CFPP and VIP. Under suitable assumptions, we demonstrate the strong convergence of the suggested rules to a common solution of the CFPP and VIP, which is only a solution of a certain HFPP. Full article

(This article belongs to the Special Issue Applied Functional Analysis and Applications)

19 pages, 2020 KiB

Open AccessArticle

Optimal Pricing Policies with an Allowable Discount for Perishable Items under Time-Dependent Sales Price and Trade Credit

by Mrudul Y. Jani, Manish R. Betheja, Amrita Bhadoriya, Urmila Chaudhari, Mohamed Abbas and Malak S. Alqahtani

Mathematics 2022, 10(11), 1948; https://doi.org/10.3390/math10111948 - 6 Jun 2022

Cited by 7 | Viewed by 2133

Abstract

Trade credit is generally used by businesses to obtain external funds. This article demonstrates an inventory system from the retailer’s point of view in which (1) the influence of trade credit on expanding small businesses and their consumers is the focus of this [...] Read more.

Trade credit is generally used by businesses to obtain external funds. This article demonstrates an inventory system from the retailer’s point of view in which (1) the influence of trade credit on expanding small businesses and their consumers is the focus of this research, and (2) the retailer’s on-hand inventory follows the non-instantaneous deterioration. (3) To maximize profit, the demand is disclosed, which is based on not just the sales price, but also on cumulative demand, which indicates saturation and diffusion. (4) The product’s initial price and the permitted discount rate at the time of deterioration are considered to be time-dependent functions of the sales price. In the absence of deterioration, the item is sold at a constant rate, and whenever deterioration occurs, the sales price is assumed to be an exponential function of the discount variable. The main aim is to optimize the total profit of the retailer in terms of cycle time and sales price. The traditional algorithm of optimization is used to address the optimization problem. Finally, the theoretical results are validated by solving three numerical illustrations and conducting a sensitivity analysis of the main factors resulting from the following managerial implications: (1) credit period provides the maximum profit margin of any financing method, and (2) an increase in the initial rate of demand raises sales price while increasing overall profit significantly. Full article

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9 pages, 266 KiB

Open AccessArticle

Ćirić-Type Operators and Common Fixed Point Theorems

by Claudia Luminiţa Mihiţ, Ghiocel Moţ and Gabriela Petruşel

Mathematics 2022, 10(11), 1947; https://doi.org/10.3390/math10111947 - 6 Jun 2022

Cited by 1 | Viewed by 1530

Abstract

In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we [...] Read more.

In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature. Full article

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)

20 pages, 6025 KiB

Open AccessArticle

Symmetric Diffeomorphic Image Registration with Multi-Label Segmentation Masks

by Chenwei Cai, Lvda Wang and Shihui Ying

Mathematics 2022, 10(11), 1946; https://doi.org/10.3390/math10111946 - 6 Jun 2022

Cited by 2 | Viewed by 2013

Abstract

Image registration aims to align two images through a spatial transformation. It plays a significant role in brain imaging analysis. In this research, we propose a symmetric diffeomorphic image registration model based on multi-label segmentation masks to solve the problems in brain MRI [...] Read more.

Image registration aims to align two images through a spatial transformation. It plays a significant role in brain imaging analysis. In this research, we propose a symmetric diffeomorphic image registration model based on multi-label segmentation masks to solve the problems in brain MRI registration. We first introduce the similarity metric of the multi-label masks to the energy function, which improves the alignment of the brain region boundaries and the robustness to the noise. Next, we establish the model on the diffeomorphism group through the relaxation method and the inverse consistent constraint. The algorithm is designed through the local linearization and least-squares method. We then give spatially adaptive parameters to coordinate the descent of the energy function in different regions. The results show that our approach, compared with the mainstream methods, has better accuracy and noise resistance, and the transformations are more smooth and more reasonable. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)

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15 pages, 313 KiB

Open AccessArticle

Supplements Related to Normal π-Projective Hypermodules

by Burcu Nişancı Türkmen, Hashem Bordbar and Irina Cristea

Mathematics 2022, 10(11), 1945; https://doi.org/10.3390/math10111945 - 6 Jun 2022

Cited by 2 | Viewed by 1462

Abstract

In this study, the role of supplements in Krasner hypermodules is examined and related to normal

π

-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we give characterizations of finitely generated supplemented [...] Read more.

In this study, the role of supplements in Krasner hypermodules is examined and related to normal

π

-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we give characterizations of finitely generated supplemented and amply supplemented Krasner hypermodules. In the second part of the paper we relate the normal projectivity to direct summands and supplements in Krasner hypermodules. Full article

(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)

19 pages, 4592 KiB

Open AccessArticle

Improved Deep Neural Network (IDNN) with SMO Algorithm for Enhancement of Third Zone Distance Relay under Power Swing Condition

by Cholleti Sriram, Jarupula Somlal, B. Srikanth Goud, Mohit Bajaj, Mohamed F. Elnaggar and Salah Kamel

Mathematics 2022, 10(11), 1944; https://doi.org/10.3390/math10111944 - 6 Jun 2022

Cited by 4 | Viewed by 1978

Abstract

A zone 3 distance relay is utilized to provide remote backup protection in the event that the primary protection fails. However, under stressful situations such as severe loads, voltage, and transient instability, the danger of malfunction in distance relay is relatively high since [...] Read more.

A zone 3 distance relay is utilized to provide remote backup protection in the event that the primary protection fails. However, under stressful situations such as severe loads, voltage, and transient instability, the danger of malfunction in distance relay is relatively high since it collapses the system’s stability and reliability. During maloperation, the relay does not function properly to operate the transmission line. To overcome this problem, an advanced power swing blocking scheme has been developed. An improved DNN-based power swing blocking system is proposed to avoid the maloperation of the distance relay and improve the system’s reliability. The current and voltage signal of the system is sensed, and the sensed data is fed into the Improved Discrete Wavelet Transform (IMDWT). The IMDWT generates the coefficient value of the sensed data and further computes the standard deviation (SD) from the coefficient, which is used to detect the condition of a system, such as normal or stressed. The SD value is given to the most valuable algorithm for the improved Deep Neural Network (IDNN). In the proposed work, the improved DNN operates in two modes, the first mode is RDL-1 (normal condition), and the second mode is RDL-2 (power swing condition). The performance of the IDNN is enhanced by using the threshold-based blocking approach. Based on the threshold value, the proposed method detects an appropriate condition of the system. The proposed method is implemented in the Western System Coordinating Council (WSCC) IEEE 9 bus system, and the results are validated in MATLAB/Simulink software. The overall accuracy of the proposed method is 97%. The proposed method provides rapid operation and detects the power swing condition to trip the distance relay. Full article

(This article belongs to the Special Issue Advanced Aspects of Computational Intelligence with Its Applications)

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16 pages, 3135 KiB

Open AccessArticle

Wind Speed Prediction via Collaborative Filtering on Virtual Edge Expanding Graphs

by Xiang Ying, Keke Zhao, Zhiqiang Liu, Jie Gao, Dongxiao He, Xuewei Li and Wei Xiong

Mathematics 2022, 10(11), 1943; https://doi.org/10.3390/math10111943 - 6 Jun 2022

Cited by 4 | Viewed by 1839

Abstract

Accurate and stable wind speed prediction is crucial for the safe operation of large-scale wind power grid connections. Existing methods are typically limited to a certain fixed area when learning the information of the wind speed sequence, which cannot make full use of [...] Read more.

Accurate and stable wind speed prediction is crucial for the safe operation of large-scale wind power grid connections. Existing methods are typically limited to a certain fixed area when learning the information of the wind speed sequence, which cannot make full use of the spatiotemporal correlation of the wind speed sequence. To address this problem, in this paper we propose a new wind speed prediction method based on collaborative filtering against a virtual edge expansion graph structure in which virtual edges enrich the semantics that the graph can express. It is an effective extension of the dataset, connecting wind turbines of different wind farms through virtual edges to ensure that the spatial correlation of wind speed sequences can be effectively learned and utilized. The new collaborative filtering on the graph is reflected in the processing of the wind speed sequence. The wind speed is preprocessed from the perspective of pattern mining to effectively integrate various information, and the k-d tree is used to match the wind speed sequence to achieve the purpose of collaborative filtering. Finally, a model with long short-term memory (LSTM) as the main body is constructed for wind speed prediction. By taking the wind speed of the actual wind farm as the research object, we compare the new approach with four typical wind speed prediction methods. The mean square error is reduced by 16.40%, 11.78%, 9.57%, and 18.36%, respectively, which demonstrates the superiority of the proposed new method. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Graph Machine Learning)

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18 pages, 1362 KiB

Open AccessArticle

A Two-Step Data Normalization Approach for Improving Classification Accuracy in the Medical Diagnosis Domain

by Ivan Izonin, Roman Tkachenko, Nataliya Shakhovska, Bohdan Ilchyshyn and Krishna Kant Singh

Mathematics 2022, 10(11), 1942; https://doi.org/10.3390/math10111942 - 6 Jun 2022

Cited by 41 | Viewed by 5725

Abstract

Data normalization is a data preprocessing task and one of the first to be performed during intellectual analysis, particularly in the case of tabular data. The importance of its implementation is determined by the need to reduce the sensitivity of the artificial intelligence [...] Read more.

Data normalization is a data preprocessing task and one of the first to be performed during intellectual analysis, particularly in the case of tabular data. The importance of its implementation is determined by the need to reduce the sensitivity of the artificial intelligence model to the values of the features in the dataset to increase the studied model’s adequacy. This paper focuses on the problem of effectively preprocessing data to improve the accuracy of intellectual analysis in the case of performing medical diagnostic tasks. We developed a new two-step method for data normalization of numerical medical datasets. It is based on the possibility of considering both the interdependencies between the features of each observation from the dataset and their absolute values to improve the accuracy when performing medical data mining tasks. We describe and substantiate each step of the algorithmic implementation of the method. We also visualize the results of the proposed method. The proposed method was modeled using six different machine learning methods based on decision trees when performing binary and multiclass classification tasks. We used six real-world, freely available medical datasets with different numbers of vectors, attributes, and classes to conduct experiments. A comparison between the effectiveness of the developed method and that of five existing data normalization methods was carried out. It was experimentally established that the developed method increases the accuracy of the Decision Tree and Extra Trees Classifier by 1–5% in the case of performing the binary classification task and the accuracy of the Bagging, Decision Tree, and Extra Trees Classifier by 1–6% in the case of performing the multiclass classification task. Increasing the accuracy of these classifiers only by using the new data normalization method satisfies all the prerequisites for its application in practice when performing various medical data mining tasks. Full article

(This article belongs to the Special Issue Computational Approaches for Data Inspection in Biomedicine)

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24 pages, 3361 KiB

Open AccessArticle

Design and Operation of Multipurpose Production Facilities Using Solar Energy Sources for Heat Integration Sustainable Strategies

by Pedro Simão, Miguel Vieira, Telmo Pinto and Tânia Pinto-Varela

Mathematics 2022, 10(11), 1941; https://doi.org/10.3390/math10111941 - 6 Jun 2022

Viewed by 1968

Abstract

Industrial production facilities have been facing the requirement to optimise resource efficiency, while considering sustainable goals. This paper addresses the introduction of renewable energies in production by exploring the combined design and scheduling of a multipurpose batch facility, with innovative consideration of direct/indirect [...] Read more.

Industrial production facilities have been facing the requirement to optimise resource efficiency, while considering sustainable goals. This paper addresses the introduction of renewable energies in production by exploring the combined design and scheduling of a multipurpose batch facility, with innovative consideration of direct/indirect heat integration using a solar energy source for thermal energy storage. A mixed-integer linear programming model is formulated to support decisions on scheduling and design selection of storage and processing units, heat exchange components, collector systems, and energy storage units. The results show the minimisation of utilities consumption, with an increase in the operational profit using combined heat integration strategies for the production schedule. A set of illustrative case-study examples highlight the advantages of the solar-based heat storage integration, assessing optimal decision support in the strategic and operational management of these facilities. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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17 pages, 803 KiB

Open AccessArticle

Stability Results of Quadratic-Additive Functional Equation Based on Hyers Technique in Matrix Paranormed Spaces

by Kandhasamy Tamilvanan, Yahya Almalki, Syed Abdul Mohiuddine and Ravi P. Agarwal

Mathematics 2022, 10(11), 1940; https://doi.org/10.3390/math10111940 - 6 Jun 2022

Cited by 2 | Viewed by 1387

Abstract

In this work, we introduce a mixed type of quadratic-additive (QA) functional equation and obtain its general solution. The objective of this work is to investigate the Ulam–Hyers stability of this quadratic-additive (QA) functional equation in matrix paranormed spaces (briefly, MP spaces) using [...] Read more.

In this work, we introduce a mixed type of quadratic-additive (QA) functional equation and obtain its general solution. The objective of this work is to investigate the Ulam–Hyers stability of this quadratic-additive (QA) functional equation in matrix paranormed spaces (briefly, MP spaces) using the Hyers method for the factor sum of norms. Full article

(This article belongs to the Section Difference and Differential Equations)

19 pages, 333 KiB

Open AccessArticle

Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions of Bounded Turning Associated with Petal-Shaped Domain

by Lei Shi, Muhammad Arif, Ayesha Rafiq, Muhammad Abbas and Javed Iqbal

Mathematics 2022, 10(11), 1939; https://doi.org/10.3390/math10111939 - 6 Jun 2022

Cited by 12 | Viewed by 1561

Abstract

The purpose of this article is to obtain the sharp estimates of the first four initial logarithmic coefficients for the class

{BT}_{s}

of bounded turning functions associated with a petal-shaped domain. Further, we investigate the sharp estimate of Fekete-Szegö inequality, Zalcman inequality [...] Read more.

The purpose of this article is to obtain the sharp estimates of the first four initial logarithmic coefficients for the class

{BT}_{s}

of bounded turning functions associated with a petal-shaped domain. Further, we investigate the sharp estimate of Fekete-Szegö inequality, Zalcman inequality on the logarithmic coefficients and the Hankel determinant

H_{2, 1} (F_{f} / 2)

and

H_{2, 2} (F_{f} / 2)

for the class

{BT}_{s}

with the determinant entry of logarithmic coefficients. Full article

(This article belongs to the Special Issue Advances on Complex Analysis)

22 pages, 333 KiB

Open AccessArticle

Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods

by Syed Abdul Mohiuddine, Kandhasamy Tamilvanan, Mohammad Mursaleen and Trad Alotaibi

Mathematics 2022, 10(11), 1938; https://doi.org/10.3390/math10111938 - 6 Jun 2022

Cited by 6 | Viewed by 1760

Abstract

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate the stability results by using the Hyers method in modular space for quartic functional equations without using the Fatou property, without using [...] Read more.

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate the stability results by using the Hyers method in modular space for quartic functional equations without using the Fatou property, without using the

Δ_{b}

-condition and without using both the

Δ_{b}

-condition and the Fatou property. Moreover, we investigate the stability results for this functional equation with the help of a fixed-point technique involving the idea of the Fatou property in modular spaces. Furthermore, a suitable counter example is also demonstrated to prove the non-stability of a singular case. Full article

19 pages, 623 KiB

Open AccessArticle

Estimation of Error Variance in Regularized Regression Models via Adaptive Lasso

by Xin Wang, Lingchen Kong and Liqun Wang

Mathematics 2022, 10(11), 1937; https://doi.org/10.3390/math10111937 - 6 Jun 2022

Cited by 5 | Viewed by 2639

Abstract

Estimation of error variance in a regression model is a fundamental problem in statistical modeling and inference. In high-dimensional linear models, variance estimation is a difficult problem, due to the issue of model selection. In this paper, we propose a novel approach for [...] Read more.

Estimation of error variance in a regression model is a fundamental problem in statistical modeling and inference. In high-dimensional linear models, variance estimation is a difficult problem, due to the issue of model selection. In this paper, we propose a novel approach for variance estimation that combines the reparameterization technique and the adaptive lasso, which is called the natural adaptive lasso. This method can, simultaneously, select and estimate the regression and variance parameters. Moreover, we show that the natural adaptive lasso, for regression parameters, is equivalent to the adaptive lasso. We establish the asymptotic properties of the natural adaptive lasso, for regression parameters, and derive the mean squared error bound for the variance estimator. Our theoretical results show that under appropriate regularity conditions, the natural adaptive lasso for error variance is closer to the so-called oracle estimator than some other existing methods. Finally, Monte Carlo simulations are presented, to demonstrate the superiority of the proposed method. Full article

(This article belongs to the Special Issue Statistical Methods for High-Dimensional and Massive Datasets)

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6 pages, 242 KiB

Open AccessArticle

Solution Spaces Associated to Continuous or Numerical Models for Which Integrable Functions Are Bounded

by Brian Villegas-Villalpando, Jorge E. Macías-Díaz and Qin Sheng

Mathematics 2022, 10(11), 1936; https://doi.org/10.3390/math10111936 - 6 Jun 2022

Viewed by 1438

Abstract

Boundedness is an essential feature of the solutions for various mathematical and numerical models in the natural sciences, especially those systems in which linear or nonlinear preservation or stability features are fundamental. In those cases, the boundedness of the solutions outside a set [...] Read more.

Boundedness is an essential feature of the solutions for various mathematical and numerical models in the natural sciences, especially those systems in which linear or nonlinear preservation or stability features are fundamental. In those cases, the boundedness of the solutions outside a set of zero measures is not enough to guarantee that the solutions are physically relevant. In this note, we will establish a criterion for the boundedness of integrable solutions of general continuous and numerical systems. More precisely, we establish a characterization of those measures over arbitrary spaces for which real-valued integrable functions are necessarily bounded at every point of the domain. The main result states that the collection of measures for which all integrable functions are everywhere bounded are exactly all of those measures for which the infimum of the measures for nonempty sets is a positive extended real number. Full article

(This article belongs to the Special Issue Numerical Methods for Solving Differential Problems-II)

21 pages, 3629 KiB

Open AccessArticle

Sliding Mode Control of Manipulator Based on Improved Reaching Law and Sliding Surface

by Peng Ji, Chenglong Li and Fengying Ma

Mathematics 2022, 10(11), 1935; https://doi.org/10.3390/math10111935 - 5 Jun 2022

Cited by 16 | Viewed by 3218

Abstract

Aiming at the problem of convergence speed and chattering in sliding mode variable structure control of manipulator, an improved exponential reaching law and nonlinear sliding surface are proposed, and the Lyapunov function is used to analyze its stability. According to the dynamic model [...] Read more.

Aiming at the problem of convergence speed and chattering in sliding mode variable structure control of manipulator, an improved exponential reaching law and nonlinear sliding surface are proposed, and the Lyapunov function is used to analyze its stability. According to the dynamic model of the 6-DOF UR5 manipulator and the proposed reaching law and sliding surface, the corresponding control scheme is designed. The control performance of the proposed control scheme is verified by tracking the end trajectory of the manipulator on the MATLAB and CoppeliaSim robot simulation platform. The experimental results show that the proposed control scheme can not only significantly improve the convergence speed and make the system converge quickly, but also can effectively reduce the chattering of the system. Even in the presence of disturbance signals, fast and stable tracking can be achieved while ensuring the robustness of the system, and the chattering of the robotic arm system can be weakened to a certain extent. Compared with the classical control method based on the computational torque method and the traditional sliding mode control scheme based on the exponential reaching law, the proposed scheme has certain advantages in terms of tracking accuracy, convergence speed, and reducing system chattering, and effectively improves the overall control performance of the system. Full article

(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)

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10 pages, 3064 KiB

Open AccessArticle

Deep Learning Approaches for the Segmentation of Glomeruli in Kidney Histopathological Images

by Giovanna Maria Dimitri, Paolo Andreini, Simone Bonechi, Monica Bianchini, Alessandro Mecocci, Franco Scarselli, Alberto Zacchi, Guido Garosi, Thomas Marcuzzo and Sergio Antonio Tripodi

Mathematics 2022, 10(11), 1934; https://doi.org/10.3390/math10111934 - 5 Jun 2022

Cited by 10 | Viewed by 2541

Abstract

Deep learning is widely applied in bioinformatics and biomedical imaging, due to its ability to perform various clinical tasks automatically and accurately. In particular, the application of deep learning techniques for the automatic identification of glomeruli in histopathological kidney images can play a [...] Read more.

Deep learning is widely applied in bioinformatics and biomedical imaging, due to its ability to perform various clinical tasks automatically and accurately. In particular, the application of deep learning techniques for the automatic identification of glomeruli in histopathological kidney images can play a fundamental role, offering a valid decision support system tool for the automatic evaluation of the Karpinski metric. This will help clinicians in detecting the presence of sclerotic glomeruli in order to decide whether the kidney is transplantable or not. In this work, we implemented a deep learning framework to identify and segment sclerotic and non-sclerotic glomeruli from scanned Whole Slide Images (WSIs) of human kidney biopsies. The experiments were conducted on a new dataset collected by both the Siena and Trieste hospitals. The images were segmented using the DeepLab V2 model, with a pre-trained ResNet101 encoder, applied to 512 × 512 patches extracted from the original WSIs. The results obtained are promising and show a good performance in the segmentation task and a good generalization capacity, despite the different coloring and typology of the histopathological images. Moreover, we present a novel use of the CD10 staining procedure, which gives promising results when applied to the segmentation of sclerotic glomeruli in kidney tissues. Full article

(This article belongs to the Special Issue Neural Networks and Learning Systems II)

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18 pages, 3645 KiB

Open AccessArticle

Unsteady Separated Stagnation-Point Flow Past a Moving Plate with Suction Effect in Hybrid Nanofluid

by Nurul Amira Zainal, Roslinda Nazar, Kohilavani Naganthran and Ioan Pop

Mathematics 2022, 10(11), 1933; https://doi.org/10.3390/math10111933 - 5 Jun 2022

Cited by 3 | Viewed by 2253

Abstract

Previous research has shown that incorporating stagnation-point flow in diverse manufacturing industries is beneficial due to its importance in thermal potency. Consequently, this research investigates the thermophysical properties of the unsteady separated stagnation-point flow past a moving plate by utilising a dual-type nanoparticle, [...] Read more.

Previous research has shown that incorporating stagnation-point flow in diverse manufacturing industries is beneficial due to its importance in thermal potency. Consequently, this research investigates the thermophysical properties of the unsteady separated stagnation-point flow past a moving plate by utilising a dual-type nanoparticle, namely a hybrid nanofluid. The impact of suction imposition on the entire hydrodynamic flow and heat transfer as well as the growth of boundary layers was also taken into account. A new mathematical hybrid nanofluid model is developed, and similarity solutions are obtained in the form of ordinary differential equations (ODEs). The bvp4c approach in MATLAB determines the reduced ODEs estimated solutions. The results show that increasing the stagnation strength parameters expands the skin friction coefficient and heat transfer rate. The addition of the suction parameter also resulted in an augmentation of thermal conductivity. Interestingly, reducing the unsteadiness parameter proportionately promotes heat-transfer performance. This significant involvement is noticeable in advancing industrial development, specifically in the manufacturing industries and operations systems. Full article

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

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15 pages, 10771 KiB

Open AccessArticle

Wave Loss: A Topographic Metric for Image Segmentation

by Ákos Kovács, Jalal Al-Afandi, Csaba Botos and András Horváth

Mathematics 2022, 10(11), 1932; https://doi.org/10.3390/math10111932 - 4 Jun 2022

Viewed by 2166

Abstract

The solution of segmentation problems with deep neural networks requires a well-defined loss function for comparison and network training. In most network training approaches, only area-based differences that are of differing pixel matter are considered; the distribution is not. Our brain can compare [...] Read more.

The solution of segmentation problems with deep neural networks requires a well-defined loss function for comparison and network training. In most network training approaches, only area-based differences that are of differing pixel matter are considered; the distribution is not. Our brain can compare complex objects with ease and considers both pixel level and topological differences simultaneously and comparison between objects requires a properly defined metric that determines similarity between them considering changes both in shape and values. In past years, topographic aspects were incorporated in loss functions where either boundary pixels or the ratio of the areas were employed in difference calculation. In this paper we will show how the application of a topographic metric, called wave loss, can be applied in neural network training and increase the accuracy of traditional segmentation algorithms. Our method has increased segmentation accuracy by 3% on both the Cityscapes and Ms-Coco datasets, using various network architectures. Full article

(This article belongs to the Special Issue Neural Networks and Learning Systems II)

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15 pages, 2668 KiB

Open AccessArticle

Agglomeration Regimes of Particles under a Linear Laminar Flow: A Numerical Study

by Yunzhou Qian, Shane P. Usher, Peter J. Scales, Anthony D. Stickland and Alessio Alexiadis

Mathematics 2022, 10(11), 1931; https://doi.org/10.3390/math10111931 - 4 Jun 2022

Cited by 2 | Viewed by 2583

Abstract

In this work, a combined smoothed particle hydrodynamics and discrete element method (SPH-DEM) model was proposed to model particle agglomeration in a shear flow. The fluid was modeled with the SPH method and the solid particles with DEM. The system was governed by [...] Read more.

In this work, a combined smoothed particle hydrodynamics and discrete element method (SPH-DEM) model was proposed to model particle agglomeration in a shear flow. The fluid was modeled with the SPH method and the solid particles with DEM. The system was governed by three fundamental dimensionless groups: the Reynolds number Re (1.5~150), which measured the effect of the hydrodynamics; the adhesion number Ad (6 × 10⁻⁵~6 × 10⁻³), which measured the inter-particle attraction; and the solid fraction α, which measured the concentration of particles. Based on these three dimensionless groups, several agglomeration regimes were found. Within these regimes, the aggregates could have different sizes and shapes that went from long thread-like structures to compact spheroids. The effect of the particle–particle interaction model was also investigated. The results were combined into ‘agglomeration maps’ that allowed for a quick determination of the agglomerate type once α, Re, Ad were known. Full article

(This article belongs to the Special Issue Computational Fluid Dynamics II)

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16 pages, 1611 KiB

Open AccessArticle

Relational Structure-Aware Knowledge Graph Representation in Complex Space

by Ke Sun, Shuo Yu, Ciyuan Peng, Yueru Wang, Osama Alfarraj, Amr Tolba and Feng Xia

Mathematics 2022, 10(11), 1930; https://doi.org/10.3390/math10111930 - 4 Jun 2022

Cited by 3 | Viewed by 2943

Abstract

Relations in knowledge graphs have rich relational structures and various binary relational patterns. Various relation modelling strategies are proposed for embedding knowledge graphs, but they fail to fully capture both features of relations, rich relational structures and various binary relational patterns. To address [...] Read more.

Relations in knowledge graphs have rich relational structures and various binary relational patterns. Various relation modelling strategies are proposed for embedding knowledge graphs, but they fail to fully capture both features of relations, rich relational structures and various binary relational patterns. To address the problem of insufficient embedding due to the complexity of the relations, we propose a novel knowledge graph representation model in complex space, namely MARS, to exploit complex relations to embed knowledge graphs. MARS takes the mechanisms of complex numbers and message-passing and then embeds triplets into relation-specific complex hyperplanes. Thus, MARS can well preserve various relation patterns, as well as structural information in knowledge graphs. In addition, we find that the scores generated from the score function approximate a Gaussian distribution. The scores in the tail cannot effectively represent triplets. To address this particular issue and improve the precision of embeddings, we use the standard deviation to limit the dispersion of the score distribution, resulting in more accurate embeddings of triplets. Comprehensive experiments on multiple benchmarks demonstrate that our model significantly outperforms existing state-of-the-art models for link prediction and triple classification. Full article

(This article belongs to the Special Issue New Trends in Graph and Complexity Based Data Analysis and Processing)

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24 pages, 1978 KiB

Open AccessArticle

Binary Aquila Optimizer for Selecting Effective Features from Medical Data: A COVID-19 Case Study

by Mohammad H. Nadimi-Shahraki, Shokooh Taghian, Seyedali Mirjalili and Laith Abualigah

Mathematics 2022, 10(11), 1929; https://doi.org/10.3390/math10111929 - 4 Jun 2022

Cited by 50 | Viewed by 3095

Abstract

Medical technological advancements have led to the creation of various large datasets with numerous attributes. The presence of redundant and irrelevant features in datasets negatively influences algorithms and leads to decreases in the performance of the algorithms. Using effective features in data mining [...] Read more.

Medical technological advancements have led to the creation of various large datasets with numerous attributes. The presence of redundant and irrelevant features in datasets negatively influences algorithms and leads to decreases in the performance of the algorithms. Using effective features in data mining and analyzing tasks such as classification can increase the accuracy of the results and relevant decisions made by decision-makers using them. This increase can become more acute when dealing with challenging, large-scale problems in medical applications. Nature-inspired metaheuristics show superior performance in finding optimal feature subsets in the literature. As a seminal attempt, a wrapper feature selection approach is presented on the basis of the newly proposed Aquila optimizer (AO) in this work. In this regard, the wrapper approach uses AO as a search algorithm in order to discover the most effective feature subset. S-shaped binary Aquila optimizer (SBAO) and V-shaped binary Aquila optimizer (VBAO) are two binary algorithms suggested for feature selection in medical datasets. Binary position vectors are generated utilizing S- and V-shaped transfer functions while the search space stays continuous. The suggested algorithms are compared to six recent binary optimization algorithms on seven benchmark medical datasets. In comparison to the comparative algorithms, the gained results demonstrate that using both proposed BAO variants can improve the classification accuracy on these medical datasets. The proposed algorithm is also tested on the real-dataset COVID-19. The findings testified that SBAO outperforms comparative algorithms regarding the least number of selected features with the highest accuracy. Full article

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22 pages, 929 KiB

Open AccessArticle

Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes

by Yifan Zhang, Tianzeng Li, Zhiming Zhang and Yu Wang

Mathematics 2022, 10(11), 1928; https://doi.org/10.3390/math10111928 - 4 Jun 2022

Viewed by 1631

Abstract

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the [...] Read more.

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the relation of the fractional derivatives. Then, the new feedback controllers are proposed to achieve synchronization between the complex networks with the fractional-order chaotic nodes based on feedback control. We propose some new sufficient synchronous criteria based on the Lyapunov stability and a simple Lyapunov function. By the numerical simulations of the complex networks, we find that these synchronous criteria can apply to the arbitrary complex dynamical networks with arbitrary fractional-order chaotic nodes. Numerical simulations of synchronization between two complex dynamical networks with the fractional-order chaotic nodes are given by the GMMP method and the Newton method, and the results of numerical simulation demonstrate that the proposed method is universal and effective. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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15 pages, 1324 KiB

Open AccessArticle

An Active Learning Algorithm Based on the Distribution Principle of Bhattacharyya Distance

by He Xu, Chunyue Ding, Peng Li and Yimu Ji

Mathematics 2022, 10(11), 1927; https://doi.org/10.3390/math10111927 - 4 Jun 2022

Cited by 1 | Viewed by 1764

Abstract

Active learning is a method that can actively select examples with much information from a large number of unlabeled samples to query labeled by experts, so as to obtain a high-precision classifier with a small number of samples. Most of the current research [...] Read more.

Active learning is a method that can actively select examples with much information from a large number of unlabeled samples to query labeled by experts, so as to obtain a high-precision classifier with a small number of samples. Most of the current research uses the basic principles to optimize the classifier at each iteration, but the batch query with the largest amount of information in each round does not represent the overall distribution of the sample, that is, it may fall into partial optimization and ignore the whole, which will may affect or reduce its accuracy. In order to solve this problem, a special distance measurement method—Bhattacharyya Distance—is used in this paper. By using this distance and designing a new set of query decision logic, we can improve the accuracy of the model. Our method embodies the query of the samples with the most representative distribution and the largest amount of information to realize the classification task based on a small number of samples. We perform theoretical proofs and experimental analysis. Finally, we use different data sets and compare them with other classification algorithms to evaluate the performance and efficiency of our algorithm. Full article

(This article belongs to the Topic Machine and Deep Learning)

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22 pages, 2685 KiB

Open AccessArticle

Analysis of Dipolar Sources in the Solution of the Electroencephalographic Inverse Problem

by María Monserrat Morín-Castillo, Jesús Arriaga-Hernández, Bolivia Cuevas-Otahola and José Jacobo Oliveros-Oliveros

Mathematics 2022, 10(11), 1926; https://doi.org/10.3390/math10111926 - 4 Jun 2022

Cited by 5 | Viewed by 2003

Abstract

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving [...] Read more.

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving the inverse problem from the EEG measurements, the so-called Electroencephalographic Inverse Problem (EIP), which is ill-posed in the Hadamard sense since the problem has numerical instability. We focus on the identification of volumetric dipolar sources of the EEG by constructing and modeling a simplification to reduce the multilayer conductive medium (two layers or regions

Ω_{1}

and

Ω_{2}

) to a problem of a single layer of a homogeneous medium with a null Neumann condition on the boundary. For this simplification purpose, we consider the Cauchy problem to be solved at each time. We compare the results we obtained solving the multiple layers problem with those obtained by our simplification proposal. In both cases, we solve the direct and inverse problems for two different sources, as synthetic results for dipolar sources resembling epileptic foci, and a similar case with an external stimulus (intense light, skin stimuli, sleep problems, etc). For the inverse problem, we use the Tikhonov regularization method to handle its numerical instability. Additionally, we build an algorithm to solve both models (multiple layers problem and our simplification) in time, showing optimization of the problem when considering 128 divisions in the time interval

[0, 1]

s, solving the inverse problem at each time (interval division) and comparing the recovered source with the initial one in the algorithm. We observed a significant decrease in the computation times when simplifying the numerical calculations, resulting in a decrease up to

50 %

in the execution times, between the EIP multilayer model and our simplification proposal, to a single layer homogeneous problem of a homogeneous medium, which translates into a numerical efficiency in this type of problem. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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21 pages, 3146 KiB

Open AccessArticle

Multicompartmental Mathematical Model of SARS-CoV-2 Distribution in Human Organs and Their Treatment

by Vasiliy N. Afonyushkin, Ilya R. Akberdin, Yulia N. Kozlova, Ivan A. Schukin, Tatyana E. Mironova, Anna S. Bobikova, Viktoriya S. Cherepushkina, Nikolaj A. Donchenko, Yulia E. Poletaeva and Fedor A. Kolpakov

Mathematics 2022, 10(11), 1925; https://doi.org/10.3390/math10111925 - 4 Jun 2022

Cited by 7 | Viewed by 2831

Abstract

Patients with COVID-19 can develop pneumonia, severe symptoms of acute respiratory distress syndrome, and multiple organ failure. Nevertheless, the variety of forms of this disease requires further research on the pathogenesis of this disease. Based on the analysis of published data and original [...] Read more.

Patients with COVID-19 can develop pneumonia, severe symptoms of acute respiratory distress syndrome, and multiple organ failure. Nevertheless, the variety of forms of this disease requires further research on the pathogenesis of this disease. Based on the analysis of published data and original experiments on the concentrations of SARS-CoV-2 in biological fluids of the nasopharynx, lungs, and intestines and using a developed modular model of the virus distribution in human tissue and organs, an assessment of the SARS-CoV-2 reproduction in various compartments of the body is presented. Most of the viral particles can transport to the esophagus from the nasopharynx. The viral particles entering the gastrointestinal tract will obviously be accompanied by the infection of the intestinal epithelium and accumulation of the virus in the intestinal lumen in an amount proportional to their secretory and protein-synthetic activities. The relatively low concentration of SARS-CoV-2 in tissues implies an essential role of transport processes and redistribution of the virus from the nasopharynx and intestines to the lungs. The model simulations also suppose that sanitation of the nasopharynx mucosa at the initial stage of the infectious process has prospects for the use in medical practice. Full article

(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)

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18 pages, 29860 KiB

Open AccessArticle

Design of a Thermal Measurement System with Vandal Protection Used for the Characterization of New Asphalt Pavements through Discriminated Dimensionless Analysis

by Juan Francisco Sánchez-Pérez, Gloria Motos-Cascales, Manuel Conesa, Francisco Moral-Moreno, Enrique Castro and Gonzalo García-Ros

Mathematics 2022, 10(11), 1924; https://doi.org/10.3390/math10111924 - 3 Jun 2022

Cited by 2 | Viewed by 1985

Abstract

This work focuses on the protection of measurement sensors against accidents, vandalism, or theft and on the improvement of the data collected due to the interference produced by these protections. These sensors are part of a larger study, within the framework of a [...] Read more.

This work focuses on the protection of measurement sensors against accidents, vandalism, or theft and on the improvement of the data collected due to the interference produced by these protections. These sensors are part of a larger study, within the framework of a LIFE Heatland project, carried out in a Spanish city, Murcia, with the fundamental objective of minimizing the urban heat island effect using pavements with lower solar energy storage than traditional ones. The study presented here has been carried out through the implementation of aluminum tubes that protect the sensors installed in the street. Once the problem of sensor protection had been solved, the problem of thermal interference in the measurements due to overheating inside the tubes had to be overcome by means of discriminated dimensionless analysis techniques, focusing on heat transfer by convection of the air flow in the inner part of the tube, by finding the most suitable size and materials to complement the outer aluminum coating. In particular, the search for the critical radius of the tubes was essential since it allowed the insulator size to be optimized. Derived from the study carried out to avoid the overheating of the tube, a small part was covered with a dark material and holes were made to improve air circulation inside the tube, allowing adequate measurement results to be obtained. Finally, the results showed that the designed device was suitable for temperature measurement, since small variations were observed with respect to the control device. Full article

(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications)

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24 pages, 3849 KiB

Open AccessArticle

Emergent Intelligence in Smart Ecosystems: Conflicts Resolution by Reaching Consensus in Resource Management

by George Rzevski, Petr Skobelev and Alexey Zhilyaev

Mathematics 2022, 10(11), 1923; https://doi.org/10.3390/math10111923 - 3 Jun 2022

Cited by 9 | Viewed by 2415

Abstract

A new emergent intelligence approach to the design of smart ecosystems, based on the complexity science principles, is introduced and discussed. The smart ecosystem for resource management is defined as a system of autonomous decision-making multi-agent systems capable to allocate resources, plan orders [...] Read more.

A new emergent intelligence approach to the design of smart ecosystems, based on the complexity science principles, is introduced and discussed. The smart ecosystem for resource management is defined as a system of autonomous decision-making multi-agent systems capable to allocate resources, plan orders for resources, and to optimize, coordinate, monitor, and control the execution of plans in real time. The emergent intelligence enables software agents to collectively resolve conflicts arising in resource management decisions by reaching a consensus through a process of detecting conflicts and negotiation for finding trade-offs. The key feature of the proposed approach is the ontological model of the enterprise and the method of collective decision-making by software agents that compete or cooperate with each other on the virtual market of the digital ecosystem. Emergent intelligent systems do not require extensive training using a large quantity of data, like conventional artificial intelligence/machine learning systems. The developed model, method, and tool were applied for managing the resources of a factory workshop, a group of small satellites, and some other applications. A comparison of the developed and traditional tools is given. The new metric for measuring the adaptability of emergent intelligence is introduced. The performance of the new model and method are validated by constructing and evaluating large-scale resource management solutions for commercial clients. As demonstrated, the essential benefit is the high adaptability and efficiency of the resource management systems when operating under complex and dynamic market conditions. Full article

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

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