Mathematics

44 pages, 630 KiB

Open AccessReview

Partial Inverse Sturm-Liouville Problems

by Natalia P. Bondarenko

Mathematics 2023, 11(10), 2408; https://doi.org/10.3390/math11102408 - 22 May 2023

Cited by 2 | Viewed by 981

This paper presents a review of both classical and modern results pertaining to partial inverse spectral problems for differential operators. Such problems consist in the recovery of differential expression coefficients in some part of the domain (a finite interval or a geometric graph) [...] Read more.

This paper presents a review of both classical and modern results pertaining to partial inverse spectral problems for differential operators. Such problems consist in the recovery of differential expression coefficients in some part of the domain (a finite interval or a geometric graph) from spectral characteristics, while the coefficients in the remaining part of the domain are known a priori. Usually, partial inverse problems require less spectral data than complete inverse problems. In this review, we pay considerable attention to partial inverse problems on graphs and to the unified approach based on the reduction of partial inverse problems to Sturm-Liouville problems with entire analytic functions in a boundary condition. We not only describe the results of selected studies but also compare them with each other and establish interconnections. Full article

(This article belongs to the Special Issue Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators)

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26 pages, 7875 KiB

Open AccessArticle

A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

by Emad E. Ghandourah, Ahmed Amine Daikh, Samir Khatir, Abdulsalam M. Alhawsawi, Essam M. Banoqitah and Mohamed A. Eltaher

Mathematics 2023, 11(10), 2407; https://doi.org/10.3390/math11102407 - 22 May 2023

Cited by 10 | Viewed by 1052

Abstract

Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to [...] Read more.

Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions. Full article

(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)

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17 pages, 3348 KiB

Open AccessArticle

Splines Parameterization of Planar Domains by Physics-Informed Neural Networks

by Antonella Falini, Giuseppe Alessio D’Inverno, Maria Lucia Sampoli and Francesca Mazzia

Mathematics 2023, 11(10), 2406; https://doi.org/10.3390/math11102406 - 22 May 2023

Cited by 2 | Viewed by 1244

Abstract

The generation of structured grids on bounded domains is a crucial issue in the development of numerical models for solving differential problems. In particular, the representation of the given computational domain through a regular parameterization allows us to define a univalent mapping, which [...] Read more.

The generation of structured grids on bounded domains is a crucial issue in the development of numerical models for solving differential problems. In particular, the representation of the given computational domain through a regular parameterization allows us to define a univalent mapping, which can be computed as the solution of an elliptic problem, equipped with suitable Dirichlet boundary conditions. In recent years, Physics-Informed Neural Networks (PINNs) have been proved to be a powerful tool to compute the solution of Partial Differential Equations (PDEs) replacing standard numerical models, based on Finite Element Methods and Finite Differences, with deep neural networks; PINNs can be used for predicting the values on simulation grids of different resolutions without the need to be retrained. In this work, we exploit the PINN model in order to solve the PDE associated to the differential problem of the parameterization on both convex and non-convex planar domains, for which the describing PDE is known. The final continuous model is then provided by applying a Hermite type quasi-interpolation operator, which can guarantee the desired smoothness of the sought parameterization. Finally, some numerical examples are presented, which show that the PINNs-based approach is robust. Indeed, the produced mapping does not exhibit folding or self-intersection at the interior of the domain and, also, for highly non convex shapes, despite few faulty points near the boundaries, has better shape-measures, e.g., lower values of the Winslow functional. Full article

(This article belongs to the Special Issue Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges-II)

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16 pages, 738 KiB

Open AccessArticle

Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

by Zhengqi Ma, Shoucheng Yuan, Kexin Meng and Shuli Mei

Mathematics 2023, 11(10), 2405; https://doi.org/10.3390/math11102405 - 22 May 2023

Cited by 12 | Viewed by 884

Abstract

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii [...] Read more.

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering, 2nd Edition)

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17 pages, 5207 KiB

Open AccessArticle

Adaptive Enhanced Detection Network for Low Illumination Object Detection

by Hanting Wei, Bo Yu, Wei Wang and Chenghong Zhang

Mathematics 2023, 11(10), 2404; https://doi.org/10.3390/math11102404 - 22 May 2023

Cited by 1 | Viewed by 1004

Abstract

Any small environmental changes in the driving environment of a traffic vehicle can become a risk factor directly leading to major safety incidents. Therefore, it is necessary to assist drivers in automatically detecting risk factors during the driving process using algorithms. However, besides [...] Read more.

Any small environmental changes in the driving environment of a traffic vehicle can become a risk factor directly leading to major safety incidents. Therefore, it is necessary to assist drivers in automatically detecting risk factors during the driving process using algorithms. However, besides making it more difficult for drivers to judge environmental changes, the performance of automatic detection networks in low illumination scenarios can also be greatly affected and cannot be used directly. In this paper, we propose a risk factor detection model based on deep learning in low illumination scenarios and test the optimization of low illumination image enhancement problems. The overall structure of this model includes dual discriminators, encoder–decoders, etc. The model consists of two main stages. In the first stage, the input low illumination scene image is adaptively converted into a standard illumination image through a lighting conversion module. In the second stage, the converted standard illumination image is automatically assessed for risk factors. The experiments show that the detection network can overcome the impact of low lighting and has high detection accuracy. Full article

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

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13 pages, 1203 KiB

Open AccessArticle

Rethinking the Role of Organizational Reflex in Maintaining a Company’s Sustainability

by Sigitas Vaitkevicius, Ojaras Purvinis, Leonidas Sakalauskas and Palmira Papsiene

Mathematics 2023, 11(10), 2403; https://doi.org/10.3390/math11102403 - 22 May 2023

Cited by 1 | Viewed by 960

Abstract

The organizational reflex in relation to the company is considered to be an instinctive reaction of its employees to an external stimulus that has arisen or, in other words, the ability of the employee to spontaneously generate a competitive response of the company [...] Read more.

The organizational reflex in relation to the company is considered to be an instinctive reaction of its employees to an external stimulus that has arisen or, in other words, the ability of the employee to spontaneously generate a competitive response of the company based on the information received from the global environment. It is an intentional algorithm that enables employees to know how and when to react as quickly as possible, according to the signal from the global environment received, within the limits of their area of expertise. This response phenomenon comes forth in the context of the functioning of a sustainable organization and highlights the coherence of the performance of a human resource. In order to maintain its competitiveness, each organization learns to react to the ongoing changes in the dynamic environment as quickly as possible and, in this process, develops action algorithms similar to human reflexes in structure. Modern science makes a great contribution to the longevity of the company by creating activity models for the organization and performing simulations in the digital space. In this paper, the simulation model of a company’s competitive human resource response to global changes, which is used for the description of organizational reflex, is present. The model reflects the human reflex arc in a company’s decision-making process, whose effectiveness depends on the coherence of its human resources and its ability to sustain an effective organizational reflex. The purpose of the developed model is to simulate the employee’s response to the signals incoming from the global environment and to describe the development process of the organizational reflex that is leading to the longevity of the company and the sustainability of its market leadership. Full article

(This article belongs to the Special Issue Modeling and Simulation of Social-Behavioral Phenomena)

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11 pages, 1784 KiB

Open AccessArticle

Mathematical Physics of Time Dilation through Curved Trajectories with Applications

by Ayman Kamel, Abdelhalim Ebaid, Essam R. El-Zahar, Riadh Chteoui and Laila F. Seddek

Mathematics 2023, 11(10), 2402; https://doi.org/10.3390/math11102402 - 22 May 2023

Cited by 1 | Viewed by 2283

Abstract

In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas [...] Read more.

In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas of time dilation for several trajectories of particle such as parabolic, elliptic, and circular and finds a relatively accurate trajectory. The obtained formulas are employed in order to analyze the time dilation of the muon particles decay. In this paper, it is found that the time dilation of the parabolic and the elliptical trajectories exceed the corresponding results utilizing the standard Lorentz-Einstein time dilation formula. Consequently, if we are able to control the trajectory of unstable particles by some external forces, then their life-times might be increased. Probably, the increase in lifetime via a curved trajectory occurs at lower relative velocity & acceleration energy if compared to the straight line trajectory. In addition, the circular trajectory leads to multiple values of time dilation at certain velocities of an observer in motion, which may give an interpretation of fluctuations of time dilation in quantum mechanics. The result arises from the present relatively accurate formula of time dilation that is very close to the experimental data of muon decay (CERN experiment) when it is compared to the result obtained by the Lorentz-Einstein formula. Finally, it may be concluded that the time dilation not only depends on relative velocity and acceleration energy of particles but also on curved trajectories. The present work may attract other researchers to study different trajectories. Full article

(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)

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26 pages, 18006 KiB

Open AccessArticle

Stochastic Levenberg–Marquardt Neural Network Implementation for Analyzing the Convective Heat Transfer in a Wavy Fin

by R. S. Varun Kumar, M. D. Alsulami, I. E. Sarris, G. Sowmya and Fehmi Gamaoun

Mathematics 2023, 11(10), 2401; https://doi.org/10.3390/math11102401 - 22 May 2023

Cited by 13 | Viewed by 1305

Abstract

The present research examines the steady, one-dimensional thermal distribution and heat transfer of a wavy fin. This heat transfer analysis considers convective effects as well as temperature-dependent thermal conductivity. Furthermore, a novel implementation of a neural network with backpropagated Levenberg–Marquardt algorithm (NN-BLMA)-based machine [...] Read more.

The present research examines the steady, one-dimensional thermal distribution and heat transfer of a wavy fin. This heat transfer analysis considers convective effects as well as temperature-dependent thermal conductivity. Furthermore, a novel implementation of a neural network with backpropagated Levenberg–Marquardt algorithm (NN-BLMA)-based machine learning intelligent strategies is provided to interpret the heat transfer analysis of a convective wavy fin. The non-linear ordinary differential equation (ODE) of the study problem is converted into its non-dimensional form using the similarity transformation technique. The dimensionless equation obtained is then numerically explored via the Runge–Kutta–Fehlberg scheme. A data set for varying the pertinent parameters is generated, and an artificial neural network model is designed to estimate the heat transfer behavior of the wavy fin. The effectiveness of the proposed NN-BLMA is subsequently endorsed by analyses using a regression model, mean square error, and histograms. The findings of comprehensive computational parametric studies illustrate that the presented technique, NN-BLMA is an effective convergent stochastic numerical solver employed for the heat transfer model of the convective wavy fin. The wavy fin’s temperature dispersion optimizes as the thermal conductivity parameter rises. Heat transfer rate is higher in wavy fin compared to rectangular fin. Full article

(This article belongs to the Special Issue Application of Mathematical Modeling, Optimization, Artificial Intelligence in Chemical Engineering)

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29 pages, 22885 KiB

Open AccessArticle

An FW–GA Hybrid Algorithm Combined with Clustering for UAV Forest Fire Reconnaissance Task Assignment

by Xinlin Liu, Tian Jing and Linyi Hou

Mathematics 2023, 11(10), 2400; https://doi.org/10.3390/math11102400 - 22 May 2023

Cited by 5 | Viewed by 1097

Abstract

The assignment of tasks for unmanned aerial vehicles (UAVs) during forest fire reconnaissance is a highly complex and large-scale problem. Current task allocation methods struggle to strike a balance between solution speed and effectiveness. In this paper, a two-phase centralized UAV task assignment [...] Read more.

The assignment of tasks for unmanned aerial vehicles (UAVs) during forest fire reconnaissance is a highly complex and large-scale problem. Current task allocation methods struggle to strike a balance between solution speed and effectiveness. In this paper, a two-phase centralized UAV task assignment model based on expectation maximization (EM) clustering and the multidimensional knapsack model (MKP) is proposed for the forest fire reconnaissance task assignment. The fire situation information is acquired using the sensors carried by satellites at first. Then, the EM algorithm based on the Gaussian mixture model (GMM) is applied to get the initial position of every UAV. In the end, the MKP is applied for UAV task assignment based on the initial positions of the UAVs. An improved genetic algorithm (GA) based on the fireworks algorithm (FWA) is proposed for faster iteration speed. A simulation was carried out against the background of forest fires in Liangshan Prefecture, Sichuan Province, and the simulation’s results demonstrate that the task assignment model can quickly and effectively address task allocation problems on a large scale. In addition, the FW–GA hybrid algorithm has great advantages over the traditional GA, particularly in solving time, iteration convergence speed, and solution effectiveness. It can reduce up to 556% of the iteration time and increase objective function value by 1.7% compared to the standard GA. Furthermore, compared to the GA–SA algorithm, its solving time is up to 60 times lower. This paper provides a new idea for future large-scale UAV task assignment problems. Full article

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14 pages, 302 KiB

Open AccessArticle

Fixed Point Results in

F

-Bipolar Metric Spaces with Applications

by Badriah Alamri

Mathematics 2023, 11(10), 2399; https://doi.org/10.3390/math11102399 - 22 May 2023

Cited by 1 | Viewed by 839

Abstract

The aim of this research article is to obtain fixed point results in the context of

F

-bipolar metric spaces. The obtained results extend some fixed point theorems in the existing literature. We also provide a non-trivial example to validate our claims. The [...] Read more.

The aim of this research article is to obtain fixed point results in the context of

F

-bipolar metric spaces. The obtained results extend some fixed point theorems in the existing literature. We also provide a non-trivial example to validate our claims. The existence and uniqueness of the solution of the integral equation are proved as applications of our leading results. Furthermore, the existence of the unique solution in homotopy theory is also investigated. Full article

21 pages, 463 KiB

Open AccessArticle

Quantile-Composited Feature Screening for Ultrahigh-Dimensional Data

by Shuaishuai Chen and Jun Lu

Mathematics 2023, 11(10), 2398; https://doi.org/10.3390/math11102398 - 22 May 2023

Viewed by 872

Abstract

Ultrahigh-dimensional grouped data are frequently encountered by biostatisticians working on multi-class categorical problems. To rapidly screen out the null predictors, this paper proposes a quantile-composited feature screening procedure. The new method first transforms the continuous predictor to a Bernoulli variable, by thresholding the [...] Read more.

Ultrahigh-dimensional grouped data are frequently encountered by biostatisticians working on multi-class categorical problems. To rapidly screen out the null predictors, this paper proposes a quantile-composited feature screening procedure. The new method first transforms the continuous predictor to a Bernoulli variable, by thresholding the predictor at a certain quantile. Consequently, the independence between the response and each predictor is easy to judge, by employing the Pearson chi-square statistic. The newly proposed method has the following salient features: (1) it is robust against high-dimensional heterogeneous data; (2) it is model-free, without specifying any regression structure between the covariate and outcome variable; (3) it enjoys a low computational cost, with the computational complexity controlled at the sample size level. Under some mild conditions, the new method was shown to achieve the sure screening property without imposing any moment condition on the predictors. Numerical studies and real data analyses further confirmed the effectiveness of the new screening procedure. Full article

(This article belongs to the Special Issue Methods and Applications in Multivariate Statistics)

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4 pages, 184 KiB

Open AccessEditorial

Advances in Mathematical Inequalities and Applications

by Milica Klaričić Bakula

Mathematics 2023, 11(10), 2397; https://doi.org/10.3390/math11102397 - 22 May 2023

Viewed by 1030

Abstract

Why do we study inequalities [...] Full article

(This article belongs to the Special Issue Advances in Mathematical Inequalities and Applications)

35 pages, 19835 KiB

Open AccessArticle

Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant

by Ernesto Moya-Albor, Andrés Romero-Arellano, Jorge Brieva and Sandra L. Gomez-Coronel

Mathematics 2023, 11(10), 2396; https://doi.org/10.3390/math11102396 - 22 May 2023

Cited by 7 | Viewed by 1790

Abstract

In this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional [...] Read more.

In this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional universal Turing machine with a high key space, is used. Moreover, a deterministic noise technique that adds security to the MDD is utilized. The proposed hybrid scheme exploits the advantages of MDD and Langton’s ant, generating a very secure and reliable encryption algorithm. In this proposal, if the key is known, the original image is recovered without loss. The method has demonstrated high performance through various tests, including statistical analysis (histograms and correlation distributions), entropy, texture analysis, encryption quality, key space assessment, key sensitivity analysis, and robustness to differential attack. The proposed method highlights obtaining chi-square values between

233.951

and

281.687

, entropy values between

7.9999225223

and

7.9999355791

, PSNR values (in the original and encrypted images) between

8.134

and

9.957

, the number of pixel change rate (NPCR) values between

99.60851796 %

and

99.61054611 %

, unified average changing intensity (UACI) values between

33.44672377 %

and

33.47430379 %

, and a vast range of possible keys

> 5.8459 \times 10^{72}

. On the other hand, an analysis of the sensitivity of the key shows that slight changes to the key do not generate any additional information to decrypt the image. In addition, the proposed method shows a competitive performance against recent works found in the literature. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography)

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3 pages, 210 KiB

Open AccessCorrection

Correction: Tolmachev et al. Algorithmic Aspects of Simulation of Magnetic Field Generation by Thermal Convection in a Plane Layer of Fluid. Mathematics 2023, 11, 808

by Daniil Tolmachev, Roman Chertovskih and Vladislav Zheligovsky

Mathematics 2023, 11(10), 2395; https://doi.org/10.3390/math11102395 - 22 May 2023

Viewed by 538

Abstract

There was an error in the original publication [...] Full article

(This article belongs to the Special Issue Numerical Analysis and Scientific Computing II)

11 pages, 253 KiB

Open AccessArticle

Mathematical Modeling of Mechanical Forces and Power Balance in Electromechanical Energy Converter

by Boris V. Malozyomov, Nikita V. Martyushev, Svetlana N. Sorokova, Egor A. Efremenkov and Mengxu Qi

Mathematics 2023, 11(10), 2394; https://doi.org/10.3390/math11102394 - 22 May 2023

Cited by 17 | Viewed by 1133

Abstract

This article proposes a calculation method for mechanical (electromagnetic) forces arising in an electromechanical energy converter acting on current circuits in a magnetic field, or on capacitor plates in an electric one. Transformations were performed on the basis of the principle of possible [...] Read more.

This article proposes a calculation method for mechanical (electromagnetic) forces arising in an electromechanical energy converter acting on current circuits in a magnetic field, or on capacitor plates in an electric one. Transformations were performed on the basis of the principle of possible displacements involving the apparatus of partial derivatives. It was found that the power converted into mechanical power is partially spent on changing the energy of the electromagnetic field, and the remaining power, determined by the co-energy, is converted into mechanical power. Expressions for the mechanical (electromagnetic) forces were obtained based on the power balance. The reliability of the obtained results was compared with the known results. Of these, one can observe the well-known 50/50 principle, which states that only part of the power associated with the movement of the circuits is converted into mechanical power, while the rest is intended for changing the energy of the magnetic field. Full article

(This article belongs to the Section Engineering Mathematics)

13 pages, 340 KiB

Open AccessArticle

Coexistence and Replacement of Two Different Maturation Strategies Adopted by a Stage-Structured Population

by Shuyang Xue

Mathematics 2023, 11(10), 2393; https://doi.org/10.3390/math11102393 - 22 May 2023

Viewed by 656

Abstract

Maturation strategies play a key role in the survival and development of populations. In response to changes in the external environment and human interventions, populations adopt appropriate maturation strategies. Different maturation strategies can lead to different birth and mortality rates. In this paper, [...] Read more.

Maturation strategies play a key role in the survival and development of populations. In response to changes in the external environment and human interventions, populations adopt appropriate maturation strategies. Different maturation strategies can lead to different birth and mortality rates. In this paper, we develop and analyze a stage-structured population model with two maturation strategies to obtain conditions for the coexistence of two maturation strategies and conditions for competitive exclusion. Our results also show that equality of fitness—represented by basic reproductive numbers being greater than 1 under different maturation strategies—promotes the coexistence of the two strategies. The reason why a strategy is replaced by another one is that the population adopting this strategy has weak fitness, which is measured by the basic reproductive number. Full article

(This article belongs to the Special Issue Applications of Differential Equations to Mathematical Biology)

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21 pages, 643 KiB

Open AccessArticle

Quality Assessment Assistance of Lateral Knee X-rays: A Hybrid Convolutional Neural Network Approach

by Simon Lysdahlgaard, Sandi Baressi Šegota, Søren Hess, Ronald Antulov, Martin Weber Kusk and Zlatan Car

Mathematics 2023, 11(10), 2392; https://doi.org/10.3390/math11102392 - 22 May 2023

Viewed by 1631

Abstract

A common issue with X-ray examinations (XE) is the erroneous quality classification of the XE, implying that the process needs to be repeated, thus delaying the diagnostic assessment of the XE and increasing the amount of radiation the patient receives. The authors propose [...] Read more.

A common issue with X-ray examinations (XE) is the erroneous quality classification of the XE, implying that the process needs to be repeated, thus delaying the diagnostic assessment of the XE and increasing the amount of radiation the patient receives. The authors propose a system for automatic quality classification of XE based on convolutional neural networks (CNN) that would simplify this process and significantly decrease erroneous quality classification. The data used for CNN training consist of 4000 knee images obtained via radiography procedure (KXE) in total, with 2000 KXE labeled as acceptable and 2000 as unacceptable. Additionally, half of the KXE belonging to each label are right knees and left knees. Due to the sensitivity to image orientation of some CNNs, three approaches are discussed: (1) Left-right-knee (LRK) classifies XE based just on their label, without taking into consideration their orientation; (2) Orientation discriminator (OD) for the left knee (LK) and right knee (RK) analyses images based on their orientation and inserts them into two separate models regarding orientation; (3) Orientation discriminator combined with knee XRs flipped to the left or right (OD-LFK)/OD-RFK trains the models with all images being horizontally flipped to the same orientation and uses the aforementioned OD to determine whether the image needs to be flipped or not. All the approaches are tested with five CNNs (AlexNet, ResNet50, ResNet101, ResNet152, and Xception), with grid search and k-fold cross-validation. The best results are achieved using the OD-RFK hybrid approach with the Xception network architecture as the classifier and ResNet152 as the OD, with an average AUC of 0.97 (±0.01). Full article

(This article belongs to the Special Issue Applications of Artificial Intelligence in Biomedical Image Processing)

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11 pages, 5750 KiB

Open AccessArticle

Surface Family Pair with Bertrand Pair as Common Geodesic Curves in Galilean 3-Space 𝔾₃

by Areej A. Almoneef and Rashad A. Abdel-Baky

Mathematics 2023, 11(10), 2391; https://doi.org/10.3390/math11102391 - 22 May 2023

Cited by 2 | Viewed by 828

Abstract

This paper is about deriving the necessary and sufficient conditions of a surface family pair with a Bertrand pair as common geodesic curves in Galilean 3-space

G_{3}

. Thereafter, the consequence for the ruled surface family pair is also deduced. Meanwhile, some [...] Read more.

This paper is about deriving the necessary and sufficient conditions of a surface family pair with a Bertrand pair as common geodesic curves in Galilean 3-space

G_{3}

. Thereafter, the consequence for the ruled surface family pair is also deduced. Meanwhile, some examples are provided to show the surfaces family with common Bertrand geodesic curves. Full article

(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)

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9 pages, 862 KiB

Open AccessArticle

On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid

by Wael W. Mohammed, Farah M. Al-Askar, Clemente Cesarano and M. El-Morshedy

Mathematics 2023, 11(10), 2390; https://doi.org/10.3390/math11102390 - 22 May 2023

Cited by 2 | Viewed by 1051

Abstract

We take into account the stochastic Boiti–Leon–Manna–Pempinelli equation (SBLMPE), which is perturbed by a multiplicative Brownian motion. By applying He’s semi-inverse method and the Riccati equation mapping method, we can acquire the solutions of the SBLMPE. Since the Boiti–Leon–Manna–Pempinelli equation is utilized to [...] Read more.

We take into account the stochastic Boiti–Leon–Manna–Pempinelli equation (SBLMPE), which is perturbed by a multiplicative Brownian motion. By applying He’s semi-inverse method and the Riccati equation mapping method, we can acquire the solutions of the SBLMPE. Since the Boiti–Leon–Manna–Pempinelli equation is utilized to explain incompressible liquid in fluid mechanics, the acquired solutions may be applied to explain a lot of fascinating physical phenomena. To address how Brownian motion effects the exact solutions of the SBLMPE, we present some 2D and 3D diagrams. Full article

(This article belongs to the Special Issue Spectral Theory and Its Applications in Problems of Mathematical Physics)

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14 pages, 10412 KiB

Open AccessArticle

Overlapping Domain Decomposition Method with Cascadic Multigrid for Image Restoration

by Zhaoteng Chu and Chenliang Li

Mathematics 2023, 11(10), 2389; https://doi.org/10.3390/math11102389 - 22 May 2023

Viewed by 1063

Abstract

In the process of image restoration, it is usually necessary to solve large-scale inverse problems, where the computational cost is very high for large or high-resolution images. The domain decomposition method is one of the most effective algorithms to solve large-scale problems, which [...] Read more.

In the process of image restoration, it is usually necessary to solve large-scale inverse problems, where the computational cost is very high for large or high-resolution images. The domain decomposition method is one of the most effective algorithms to solve large-scale problems, which can effectively decrease the computational cost. The cascadic multigrid method has a good effect on the linear model of image restoration and can obtain high quality restored images. In this paper, the overlapping domain decomposition method (DDM) with the cascadic multigrid method (CMG) and the DDM with new extrapolation cascadic multigrid method (NECMG) are presented to solve the image restoration problems of denoising and deblurring. We first divide the image problem into some overlapping and independent subproblems. Then, each subproblem is solved independently by CMG or NECMG with the edge-preserving operator. Numerical experiments show that the new method is effective. Full article

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

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19 pages, 3347 KiB

Open AccessArticle

Mathematical Analysis of an Anthroponotic Cutaneous Leishmaniasis Model with Asymptomatic Infection

by Muntaser Safan and Alhanouf Altheyabi

Mathematics 2023, 11(10), 2388; https://doi.org/10.3390/math11102388 - 21 May 2023

Cited by 2 | Viewed by 971

Abstract

This work aims mainly to study the impact of experiencing asymptomatic anthroponotic cutaneous leishmaniasis (ACL) infection on the overall dynamics and outcomes of the disease. Therefore, a deterministic model for the transmission dynamics of ACL of type SEAIS in the human host and [...] Read more.

This work aims mainly to study the impact of experiencing asymptomatic anthroponotic cutaneous leishmaniasis (ACL) infection on the overall dynamics and outcomes of the disease. Therefore, a deterministic model for the transmission dynamics of ACL of type SEAIS in the human host and SI in sandfly populations is proposed and mathematically analyzed. The model is shown to be well-posed. Its equilibrium and stability analyses are shown. The equilibrium analysis shows that the model has an ACL-free equilibrium that is proven to be locally and globally asymptotically stable if and only if

R_{0} < 1

. In addition, the model has a unique ACL-endemic equilibrium that is shown to exist and be locally asymptotically stable if and only if

R_{0} > 1

. Numerical simulations are performed to show the asymptotic stability of these equilibriums. In addition, the effect of ignoring asymptomatic infections is studied and the analysis shows that ignoring the development of asymptomatic infections overestimates the effort required to eliminate the infection. Moreover, it implies inaccurate measures of controlling ACL infection, especially those based on either using insecticide sprays or bednets. Full article

(This article belongs to the Special Issue Mathematical Methods and Models in Epidemiology)

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14 pages, 2384 KiB

Open AccessArticle

Dynamic Pricing with Parametric Demand Learning and Reference-Price Effects

by Bing Wang, Wenjie Bi and Haiying Liu

Mathematics 2023, 11(10), 2387; https://doi.org/10.3390/math11102387 - 21 May 2023

Viewed by 1716

Abstract

In reality, sellers face challenges in obtaining perfect demand information. Demand is influenced not only by price but also by behavioral factors such as reference effects, which complicate optimal pricing for enterprises. To address this problem, we propose a dynamic pricing model that [...] Read more.

In reality, sellers face challenges in obtaining perfect demand information. Demand is influenced not only by price but also by behavioral factors such as reference effects, which complicate optimal pricing for enterprises. To address this problem, we propose a dynamic pricing model that incorporates demand learning and considers consumer reference effects. Using the Bayesian method and based on historical sales and prices, sellers can learn about demand patterns. We analyze the model to determine the existence of an optimal solution and provide an algorithm to solve it. Our numerical simulation demonstrates that the total consumer demand and the impact of price on demand remain relatively stable over time. However, the factors influencing the reference effects exhibit greater variability. Sellers can also gain insights into market demand through their learning behavior in each phase and adjust production based on market size. For instance, our simulation shows an increase in market demand over time, allowing the seller to adjust the production plan according to the demand change. Full article

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21 pages, 996 KiB

Open AccessArticle

Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q-Trigonometric Functions with Applications in Computer Modeling

by Yongsheng Rao, Waseem Ahmad Khan, Serkan Araci and Cheon Seoung Ryoo

Mathematics 2023, 11(10), 2386; https://doi.org/10.3390/math11102386 - 20 May 2023

Cited by 2 | Viewed by 886

Abstract

In this article, we define q-cosine and q-sine Apostol-type Frobenius–Euler polynomials and derive interesting relations. We also obtain new properties by making use of power series expansions of q-trigonometric functions, properties of q-exponential functions, and q-analogues of the [...] Read more.

In this article, we define q-cosine and q-sine Apostol-type Frobenius–Euler polynomials and derive interesting relations. We also obtain new properties by making use of power series expansions of q-trigonometric functions, properties of q-exponential functions, and q-analogues of the binomial theorem. By using the Mathematica program, the computational formulae and graphical representation for the aforementioned polynomials are obtained. By making use of a partial derivative operator, we derived some interesting finite combinatorial sums. Finally, we detail some special cases for these results. Full article

(This article belongs to the Special Issue Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms)

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22 pages, 3481 KiB

Open AccessArticle

FedISM: Enhancing Data Imbalance via Shared Model in Federated Learning

by Wu-Chun Chung, Yan-Hui Lin and Sih-Han Fang

Mathematics 2023, 11(10), 2385; https://doi.org/10.3390/math11102385 - 20 May 2023

Viewed by 1530

Abstract

Considering the sensitivity of data in medical scenarios, federated learning (FL) is suitable for applications that require data privacy. Medical personnel can use the FL framework for machine learning to assist in analyzing large-scale data that are protected within the institution. However, not [...] Read more.

Considering the sensitivity of data in medical scenarios, federated learning (FL) is suitable for applications that require data privacy. Medical personnel can use the FL framework for machine learning to assist in analyzing large-scale data that are protected within the institution. However, not all clients have the same distribution of datasets, so data imbalance problems occur among clients. The main challenge is to overcome the performance degradation caused by low accuracy and the inability to converge the model. This paper proposes a FedISM method to enhance performance in the case of Non-Independent Identically Distribution (Non-IID). FedISM exploits a shared model trained on a candidate dataset before performing FL among clients. The Candidate Selection Mechanism (CSM) was proposed to effectively select the most suitable candidate among clients for training the shared model. Based on the proposed approaches, FedISM not only trains the shared model without sharing any raw data, but it also provides an optimal solution through the selection of the best shared model. To evaluate performance, the proposed FedISM was applied to classify coronavirus disease (COVID), pneumonia, normal, and viral pneumonia in the experiments. The Dirichlet process was also used to simulate a variety of imbalanced data distributions. Experimental results show that FedISM improves accuracy by up to 25% when privacy concerns regarding patient data are rising among medical institutions. Full article

(This article belongs to the Special Issue New Trends in Machine Learning and Medical Imaging and Applications)

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16 pages, 14385 KiB

Open AccessArticle

Matlab-Based Design Consideration of Series ZVS Single-Ended Resonant DC-DC Converter

by Nikolay Hinov and Bogdan Gilev

Mathematics 2023, 11(10), 2384; https://doi.org/10.3390/math11102384 - 20 May 2023

Cited by 1 | Viewed by 820

Abstract

The paper presents a model-based design consideration of a series single-ended transistor resonant DC-DC converter with zero voltage switching (ZVS). A characteristic of this converter is that it is highly efficient due to the resonant nature of electromagnetic processes in the power circuit [...] Read more.

The paper presents a model-based design consideration of a series single-ended transistor resonant DC-DC converter with zero voltage switching (ZVS). A characteristic of this converter is that it is highly efficient due to the resonant nature of electromagnetic processes in the power circuit and operation with soft commutations. The manuscript proposes that the determination of some of the circuit elements of the device be carried out with optimization procedures based on the application of artificial intelligence techniques. For this purpose, an objective function is used with additional constraints, such as equalities and inequalities, for both the optimization parameters and the state variables. The use of the proposed method is justified in cases where there is no methodology for the design of the specific power electronic device or there is, but it is too complicated to apply. This is usually due to the increasing complexity of power circuits and their possible modes of operation and the inevitable assumptions and limitations in the analysis and the relevant methodologies based on that analysis. In this way, a natural combination, complement and development of classical design methods with innovative ones based on the application of artificial intelligence techniques is carried out. Full article

(This article belongs to the Special Issue Control, Optimization and Intelligent Computing in Energy)

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18 pages, 1951 KiB

Open AccessArticle

Novel Method for Estimating Time-Varying COVID-19 Transmission Rate

by Hongfei Xiao, Deqin Lin and Shiyu Li

Mathematics 2023, 11(10), 2383; https://doi.org/10.3390/math11102383 - 20 May 2023

Viewed by 989

Abstract

The transmission rate is an important indicator for characterizing a virus and estimating the risk of its outbreak in a certain area, but it is hard to measure. COVID-19, for instance, has greatly affected the world for more than 3 years since early [...] Read more.

The transmission rate is an important indicator for characterizing a virus and estimating the risk of its outbreak in a certain area, but it is hard to measure. COVID-19, for instance, has greatly affected the world for more than 3 years since early 2020, but scholars have not yet found an effective method to obtain its timely transmission rate due to the fact that the value of COVID-19 transmission rate is not constant but dynamic, always changing over time and places. Therefore, in order to estimate the timely dynamic transmission rate of COVID-19, we performed the following: first, we utilized a rolling time series to construct a time-varying transmission rate model and, based on the model, managed to obtain the dynamic value of COVID-19 transmission rate in mainland China; second, to verify the result, we used the obtained COVID-19 transmission rate as the explanatory variable to conduct empirical research on the impact of the COVID-19 pandemic on China’s stock markets. Eventually, the result revealed that the COVID-19 transmission rate had a significant negative impact on China’s stock markets, which, to some extent, confirms the validity of the used measurement method in this paper. Notably, the model constructed in this paper, combined with local conditions, can not only be used to estimate the COVID-19 transmission rate in mainland China but also in other affected countries or regions and would be applicable to calculate the transmission rate of other pathogens, not limited to COVID-19, which coincidently fills the gaps in the research. Furthermore, the research based on this model might play a part in regulating anti-pandemic governmental policies and could also help investors and stakeholders to make decisions in a pandemic setting. Full article

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17 pages, 387 KiB

Open AccessArticle

On Matrices with Only One Non-SDD Row

by Ksenija Doroslovački and Dragana Cvetković

Mathematics 2023, 11(10), 2382; https://doi.org/10.3390/math11102382 - 20 May 2023

Viewed by 905

Abstract

The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas of applied linear algebra, as well as in a wide range of applications, such as in dynamical analysis of complex networks that arise in [...] Read more.

The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas of applied linear algebra, as well as in a wide range of applications, such as in dynamical analysis of complex networks that arise in ecology, epidemiology, infectology, neurology, engineering, economy, opinion dynamics, and many other fields. To conclude that the particular dynamical system is (locally) stable, it is sufficient to prove that the corresponding (Jacobian) matrix is an H-matrix with negative diagonal entries. In practice, however, it is very difficult to determine whether a matrix is a non-singular H-matrix or not, so it is valuable to investigate subclasses of H-matrices which are defined by relatively simple and practical criteria. Many subclasses of H-matrices have recently been discussed in detail demonstrating the many benefits they can provide, though one particular subclass has not been fully exploited until now. The aim of this paper is to attract attention to this class and discuss its relation with other more investigated classes, while showing its main advantage, based on its simplicity and elegance. This new approach, which we are presenting in this paper, will be compared with the existing ones, in three possible areas of applications, spectrum localization; maximum norm estimation of the inverse matrix in the point, as well as the block case; and error estimation for LCP problems. The main conclusion is that the importance of our approach grows with the matrix dimension. Full article

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

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24 pages, 3088 KiB

Open AccessArticle

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

by Yuanyuan Shi, Qibai Huang and Jiangying Peng

Mathematics 2023, 11(10), 2381; https://doi.org/10.3390/math11102381 - 19 May 2023

Viewed by 948

Abstract

The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters [...] Read more.

The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures. Full article

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16 pages, 512 KiB

Open AccessArticle

Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

by Agassi Melikov, Laman Poladova, Sandhya Edayapurath and Janos Sztrik

Mathematics 2023, 11(10), 2380; https://doi.org/10.3390/math11102380 - 19 May 2023

Cited by 4 | Viewed by 1092

Abstract

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) in service facility. Consumer customers (c-customers) that arrived to buy inventory can be queued in an infinite buffer. [...] Read more.

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) in service facility. Consumer customers (c-customers) that arrived to buy inventory can be queued in an infinite buffer. Under catastrophes, all inventory of the system is destroyed but customers in the system (on server or in buffer) are still waiting for replenishment of stocks. Upon arrival of n-customer one c-customer is pushed out, if any. One of two replenishment policies (RP) can be used in the system: either

(s, S)

or randomized. In the investigated QISs, a hybrid service scheme was used: if upon arrival of the c-customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or joining the queue (backorder scheme). Mathematical models of the investigated QISs were constructed as two-dimensional Markov chains (2D MC). Ergodicity conditions of the investigated QISs were obtained, and the matrix-analytic method (MAM) was used to calculate the steady-state probabilities of the constructed 2D MCs. Formulas for performance measures were found and the results of numerical experiments are presented. Full article

(This article belongs to the Special Issue Advances in Queueing Theory)

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18 pages, 2638 KiB

Open AccessArticle

A Multi-Agent Adaptive Co-Evolution Method in Dynamic Environments

by Yan Li, Huazhi Zhang, Weiming Xu, Jianan Wang, Jialu Wang and Suyu Wang

Mathematics 2023, 11(10), 2379; https://doi.org/10.3390/math11102379 - 19 May 2023

Viewed by 935

Abstract

It is challenging to ensure satisfying co-evolution efficiency for the multi-agents in dynamic environments since during Actor-Critic training there is a high probability of falling into local optimality, failing to adapt to the suddenly changed environment quickly. To solve this problem, this paper [...] Read more.

It is challenging to ensure satisfying co-evolution efficiency for the multi-agents in dynamic environments since during Actor-Critic training there is a high probability of falling into local optimality, failing to adapt to the suddenly changed environment quickly. To solve this problem, this paper proposes a multi-agent adaptive co-evolution method in dynamic environments (ACE-D) based on the classical multi-agent reinforcement learning method MADDPG, which effectively realizes self-adaptive new environments and co-evolution in dynamic environments. First, an experience screening policy is introduced based on the MADDPG method to reduce the negative influence of original environment experience on exploring new environments. Then, an adaptive weighting policy is applied to the policy network, which accordingly generates benchmarks for varying environments and assigns higher weights to those policies that are more beneficial for new environments exploration, so that to save time while promoting adaptability of the agents. Finally, different types of dynamic environments with complexity at different levels are built to verify the co-evolutionary effects of the two policies separately and the ACE-D method comprehensively. The experimental results demonstrate that, compared with a range of other methods, the ACE-D method has obvious advantages helping multi-agent adapt to dynamic environments and preventing them from falling into local optima, with more than 25% improvement in stable reward and more than 23% improvement in training efficiency. The ACE-D method is valuable and commendable to promote the co-evolutionary effect of multi-agent in dynamic environments. Full article

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