Mathematics

10 pages, 265 KiB

Open AccessArticle

On a Certain Functional Equation and Its Application to the Schwarz Problem

by Vladimir Nikolaev and Vladimir Vasilyev

Mathematics 2023, 11(12), 2789; https://doi.org/10.3390/math11122789 - 20 Jun 2023

Cited by 2 | Viewed by 1100

The Schwarz problem for J-analytic functions in an ellipse is considered. In this case, the matrix J is assumed to be two-dimensional with different eigenvalues located above the real axis. The Schwarz problem is reduced to an equivalent boundary value problem for [...] Read more.

The Schwarz problem for J-analytic functions in an ellipse is considered. In this case, the matrix J is assumed to be two-dimensional with different eigenvalues located above the real axis. The Schwarz problem is reduced to an equivalent boundary value problem for the scalar functional equation depending on the real parameter l. This parameter is determined by the Jordan basis of the matrix

J .

An analysis of the functional equation was performed. It is shown that for

l \in [0, 1]

, the solution of the Schwarz problem with matrix J exists uniquely in the Hölder classes in an arbitrary ellipse. Full article

18 pages, 1067 KiB

Open AccessArticle

A Finite-Time Sliding Mode Control Approach for Constrained Euler–Lagrange System

by Guhao Sun and Qingshuang Zeng

Mathematics 2023, 11(12), 2788; https://doi.org/10.3390/math11122788 - 20 Jun 2023

Viewed by 1491

Abstract

This paper investigates a general control strategy to track the reference trajectory for the constrained Euler–Lagrange system with model uncertainties and unknown external disturbances. Unlike the disturbances assumed to be upper-bounded by a constant in other papers, we consider the disturbances to be [...] Read more.

This paper investigates a general control strategy to track the reference trajectory for the constrained Euler–Lagrange system with model uncertainties and unknown external disturbances. Unlike the disturbances assumed to be upper-bounded by a constant in other papers, we consider the disturbances to be bounded by a function of the system states, which are more realistic. First, the nominal controller was designed based on the nonsingular fast terminal sliding mode control, and global fast finite-time convergence to the sliding surface was guaranteed. As the system is state-constrained in this paper, we introduce the control barrier function approach to formulate the constraints and ensure the system does not break the restrictions. The proposed control strategy was numerically assessed on a two-link robot manipulator system, and the simulation results illustrate the effectiveness of the proposed control strategy. Full article

(This article belongs to the Special Issue Advanced Control Theory with Applications)

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15 pages, 284 KiB

Open AccessArticle

Higher Monotonicity Properties for Zeros of Certain Sturm-Liouville Functions

by Tzong-Mo Tsai

Mathematics 2023, 11(12), 2787; https://doi.org/10.3390/math11122787 - 20 Jun 2023

Viewed by 950

Abstract

In this paper, we consider the differential equation

y^{″} + ω^{2} ρ (x) y = 0

, where

ω

is a positive parameter. The principal concern here is to find conditions on the function [...] Read more.

In this paper, we consider the differential equation

y^{″} + ω^{2} ρ (x) y = 0

, where

ω

is a positive parameter. The principal concern here is to find conditions on the function

ρ^{- 1 / 2} (x)

which ensure that the consecutive differences of sequences constructed from the zeros of a nontrivial solution of the equation are regular in sign for sufficiently large

ω

. In particular, if

c_{ν k} (α)

denotes the kth positive zero of the general Bessel (cylinder) function

C_{ν} (x; α) = J_{ν} (x) cos α - Y_{ν} (x) sin α

of order

ν

and if

| ν | < 1 / 2

, we prove that

{(- 1)}^{m} Δ^{m + 2} c_{ν k} (α) > 0 (m = 0, 1, 2, \dots; k = 1, 2, \dots),

where

Δ a_{k} = a_{k + 1} - a_{k} .

This type of inequalities was conjectured by Lorch and Szego in 1963. In addition, we show that the differences of the zeros of various orthogonal polynomials with higher degrees possess sign regularity. Full article

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

20 pages, 5750 KiB

Open AccessArticle

An Ensemble Deep Learning Model for Provincial Load Forecasting Based on Reduced Dimensional Clustering and Decomposition Strategies

by Kaiyan Wang, Haodong Du, Jiao Wang, Rong Jia and Zhenyu Zong

Mathematics 2023, 11(12), 2786; https://doi.org/10.3390/math11122786 - 20 Jun 2023

Cited by 1 | Viewed by 1555

Abstract

The accurate prediction of short-term load is crucial for the grid dispatching department in developing power generation plans, regulating unit output, and minimizing economic losses. However, due to the variability in customers’ electricity consumption behaviour and the randomness of load fluctuations, it is [...] Read more.

The accurate prediction of short-term load is crucial for the grid dispatching department in developing power generation plans, regulating unit output, and minimizing economic losses. However, due to the variability in customers’ electricity consumption behaviour and the randomness of load fluctuations, it is challenging to achieve high prediction accuracy. To address this issue, we propose an ensemble deep learning model that utilizes reduced dimensional clustering and decomposition strategies to mitigate large prediction errors caused by non-linearity and unsteadiness of load sequences. The proposed model consists of three steps: Firstly, the selected load features are dimensionally reduced using singular value decomposition (SVD), and the principal features are used for clustering different loads. Secondly, variable mode decomposition (VMD) is applied to decompose the total load of each class into intrinsic mode functions of different frequencies. Finally, an ensemble deep learning model is developed by combining the strengths of LSTM and CNN-GRU deep learning algorithms to achieve accurate load forecasting. To validate the effectiveness of our proposed model, we employ actual residential electricity load data from a province in northwest China. The results demonstrate that the proposed algorithm performs better than existing methods in terms of predictive accuracy. Full article

(This article belongs to the Special Issue Modeling and Simulation for the Electrical Power System)

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20 pages, 16324 KiB

Open AccessArticle

Adaptive Super-Twisting Sliding Mode Control of Active Power Filter Using Interval Type-2-Fuzzy Neural Networks

by Jiacheng Wang, Yunmei Fang and Juntao Fei

Mathematics 2023, 11(12), 2785; https://doi.org/10.3390/math11122785 - 20 Jun 2023

Cited by 6 | Viewed by 1209

Abstract

Aiming at the unknown uncertainty of an active power filter system in practical operation, combining the advantages of self-feedback structure, interval type-2 fuzzy neural network, and super-twisting sliding mode, an adaptive super-twisting sliding mode control method of interval type-2 fuzzy neural network with [...] Read more.

Aiming at the unknown uncertainty of an active power filter system in practical operation, combining the advantages of self-feedback structure, interval type-2 fuzzy neural network, and super-twisting sliding mode, an adaptive super-twisting sliding mode control method of interval type-2 fuzzy neural network with self-feedback recursive structure (IT2FNN-SFR STSMC) is proposed in this paper. IT2FNN has an uncertain membership function, which can enhance the nonlinear ability and robustness of the network. The historical information will be stored and utilized by the self-feedback recursive structure (SFR) at runtime. Therefore, the novel IT2FNN-SFR is designed to improve the dynamic approximation effect of the neural network and reduce the dependence of the controller on the actual mathematical model. The adaptive rate of each weight of the neural network is designed by the Lyapunov method and gradient descent (GD) algorithm to ensure the convergence and stability of the system. Super-twisting sliding mode control (STSMC) has strong robustness, which can effectively reduce system chattering, and improve control accuracy and system performance. The gain of the integral term in the STSMC is set as a constant, and the other gain is changed adaptively whose adaptive rate is deduced through the stability proof of the neural network, which greatly reduces the difficulty of parameter adjustment. The harmonic suppression ability of the designed control strategy is verified by simulation experiments. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 2nd Edition)

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14 pages, 297 KiB

Open AccessArticle

Some Further Coefficient Bounds on a New Subclass of Analytic Functions

by Yue-Juan Sun, Muhammad Arif, Lei Shi and Muhammad Imran Faisal

Mathematics 2023, 11(12), 2784; https://doi.org/10.3390/math11122784 - 20 Jun 2023

Viewed by 976

Abstract

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass

SQ

of analytic functions with

f^{'} (z)

subordinated to

1 / {(1 - z)}^{2}

[...] Read more.

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass

SQ

of analytic functions with

f^{'} (z)

subordinated to

1 / {(1 - z)}^{2}

in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant

H_{2, 3} (f)

and the third Hankel determinant

H_{3, 1} (f)

for

f \in SQ

. This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions. Full article

(This article belongs to the Special Issue New Trends in Complex Analysis Research, 2nd Edition)

19 pages, 6195 KiB

Open AccessArticle

A New Visualization and Analysis Method for a Convolved Representation of Mass Computational Experiments with Biological Models

by Alexandra I. Klimenko, Diana A. Vorobeva and Sergey A. Lashin

Mathematics 2023, 11(12), 2783; https://doi.org/10.3390/math11122783 - 20 Jun 2023

Viewed by 1200

Abstract

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties [...] Read more.

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics. Full article

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

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11 pages, 288 KiB

Open AccessArticle

Oscillation Criteria for Qusilinear Even-Order Differential Equations

by Mnaouer Kachout, Clemente Cesarano, Amir Abdel Menaem, Taher S. Hassan and Belal A. Glalah

Mathematics 2023, 11(12), 2782; https://doi.org/10.3390/math11122782 - 20 Jun 2023

Viewed by 1237

Abstract

In this study, we extended and improved the oscillation criteria previously established for second-order differential equations to even-order differential equations. Some examples are given to demonstrate the significance of the results accomplished. Full article

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

16 pages, 6206 KiB

Open AccessArticle

by Raoul R. Nigmatullin and YangQuan Chen

Mathematics 2023, 11(12), 2781; https://doi.org/10.3390/math11122781 - 20 Jun 2023

Cited by 2 | Viewed by 1211

Abstract

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and includes previously unknown but [...] Read more.

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and includes previously unknown but crucial adjustments. These new discoveries have the potential to significantly alter the preexisting theory and create new connections between it and its experimental support, particularly when it comes to measurements of the impedances of diverse metamaterials. It is now easy to demonstrate that any random curve with a clearly stated tendency in a specific range of scales is self-similar using the method involving reduction to three invariant points (Ymx, Ymn, and Ymin). This useful procedure indicates that the chosen random curve, even after being compressed a certain number of times, still resembles the original curve. Based on this common peculiarity, it is now possible to derive “a universal” fitting function that can be used in a variety of applied sciences, particularly those that deal with complex systems, to parametrize many initial curves when a model fitting function derived from a simple model is not present. This self-similarity principle-derived function demonstrates its effectiveness in data linked to photodiode noise and the smoothed integral curves produced from well-known transcendental numbers E and Pi, which are considered in the paper as an example. Full article

(This article belongs to the Section Dynamical Systems)

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16 pages, 941 KiB

Open AccessArticle

Continual Pre-Training of Language Models for Concept Prerequisite Learning with Graph Neural Networks

by Xin Tang, Kunjia Liu, Hao Xu, Weidong Xiao and Zhen Tan

Mathematics 2023, 11(12), 2780; https://doi.org/10.3390/math11122780 - 20 Jun 2023

Cited by 1 | Viewed by 2091

Abstract

Prerequisite chains are crucial to acquiring new knowledge efficiently. Many studies have been devoted to automatically identifying the prerequisite relationships between concepts from educational data. Though effective to some extent, these methods have neglected two key factors: most works have failed to utilize [...] Read more.

Prerequisite chains are crucial to acquiring new knowledge efficiently. Many studies have been devoted to automatically identifying the prerequisite relationships between concepts from educational data. Though effective to some extent, these methods have neglected two key factors: most works have failed to utilize domain-related knowledge to enhance pre-trained language models, thus making the textual representation of concepts less effective; they also ignore the fusion of semantic information and structural information formed by existing prerequisites. We propose a two-stage concept prerequisite learning model (TCPL), to integrate the above factors. In the first stage, we designed two continual pre-training tasks for domain-adaptive and task-specific enhancement, to obtain better textual representation. In the second stage, to leverage the complementary effects of the semantic and structural information, we optimized the encoder of the resource–concept graph and the pre-trained language model simultaneously, with hinge loss as an auxiliary training objective. Extensive experiments conducted on three public datasets demonstrated the effectiveness of the proposed approach. Our proposed model improved by 7.9%, 6.7%, 5.6%, and 8.4% on ACC, F1, AP, and AUC on average, compared to the state-of-the-art methods. Full article

(This article belongs to the Topic Data Science and Knowledge Discovery)

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25 pages, 24986 KiB

Open AccessArticle

A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE² Method

by Ang Zhao, Vincent Beng Chye Tan, Pei Li, Kui Liu and Zhendong Hu

Mathematics 2023, 11(12), 2779; https://doi.org/10.3390/math11122779 - 20 Jun 2023

Viewed by 1613

Abstract

The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE² method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order [...] Read more.

The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE² method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE² model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results. Full article

(This article belongs to the Special Issue Applied Mathematics and Continuum Mechanics)

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25 pages, 450 KiB

Open AccessArticle

Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations

by L. Chitra, K. Alagesan, Vediyappan Govindan, Salman Saleem, A. Al-Zubaidi and C. Vimala

Mathematics 2023, 11(12), 2778; https://doi.org/10.3390/math11122778 - 20 Jun 2023

Cited by 1 | Viewed by 1118

Abstract

In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the [...] Read more.

In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the Tarig transform to show that linear and nonlinear differential equations are stable. This study also demonstrates that the Tarig transform method is more effective for analyzing the stability issue for differential equations with constant coefficients. A discussion of applications follows, to illustrate our approach. This research also presents a novel approach to studying the stability of differential equations. Furthermore, this study demonstrates that Tarig transform analysis is more practical for examining stability issues in linear differential equations with constant coefficients. In addition, we examine some applications of linear, nonlinear, and fractional differential equations, by using the Tarig integral transform. Full article

(This article belongs to the Special Issue Advances in Integral Equations and Transforms: Theory and Applications in Science and Engineering)

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15 pages, 838 KiB

Open AccessArticle

Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches

by Ervin Kaminski Lenzi, Luiz Roberto Evangelista and Luciano Rodrigues da Silva

Mathematics 2023, 11(12), 2777; https://doi.org/10.3390/math11122777 - 20 Jun 2023

Viewed by 1149

Abstract

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of [...] Read more.

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of the main properties of these approaches and used the thermal Green function formalism to perform the developments, simultaneously allowing us to analyze each case’s dynamics and thermodynamics aspects. In particular, the results allow us to understand how the extensions change the behavior of some quantities, particularly fluctuations related to the system. Full article

(This article belongs to the Section Mathematical Physics)

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Graphical abstract

18 pages, 2961 KiB

Open AccessArticle

Evaluating Economy Hotel Website Service Quality: A Hybrid Bounded Rationality Behavioral Decision Support Model

by Zhiping Hou, Sangsang He, Ruxia Liang, Junbo Li, Ruilu Huang and Jianqiang Wang

Mathematics 2023, 11(12), 2776; https://doi.org/10.3390/math11122776 - 20 Jun 2023

Cited by 1 | Viewed by 1194

Abstract

Hotel website service quality evaluation has gained extensive attention. However, previous studies have given little concern about human hesitance and uncertainty in judgments. Moreover, they do not consider hotel managers and customers’ psychological behaviors simultaneously. This study explores criteria for evaluating hotel performance [...] Read more.

Hotel website service quality evaluation has gained extensive attention. However, previous studies have given little concern about human hesitance and uncertainty in judgments. Moreover, they do not consider hotel managers and customers’ psychological behaviors simultaneously. This study explores criteria for evaluating hotel performance and proposes a hybrid evaluation model for the hesitation and uncertainty in the service quality evaluation of economy hotel websites, and applied to the actual economy hotel websites. The model introduces the probabilistic linguistic term sets to describe customers and managers’ qualitative assessments and use analytical network process to prioritize hotel website features. Then, it develops an integrated TODIM-PROMETHEE II method to rank alternatives considering both hotel managers and customers’ psychological factors. Furthermore, we illustrate the effectiveness of the hybrid evaluation model through a case of economy hotel websites in China. Service competence and customer relationship are the two most important performance features for economy hotel websites. Finally, conclusions and implications are drawn from the results of case study. Full article

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4 pages, 193 KiB

Open AccessEditorial

Special Issue “Statistical Data Modeling and Machine Learning with Applications II”

by Snezhana Gocheva-Ilieva, Atanas Ivanov and Hristina Kulina

Mathematics 2023, 11(12), 2775; https://doi.org/10.3390/math11122775 - 20 Jun 2023

Viewed by 1444

Abstract

Currently, we are witnessing rapid progress and synergy between mathematics and computer science [...] Full article

(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications II)

11 pages, 275 KiB

Open AccessArticle

Connections between Linear Complementary Dual Codes, Permanents and Geometry

by Adel N. Alahmadi, Husain S. Alhazmi, Hatoon Shoaib, David G. Glynn, Saeed Ur Rehman and Patrick Solé

Mathematics 2023, 11(12), 2774; https://doi.org/10.3390/math11122774 - 20 Jun 2023

Viewed by 1370

Abstract

Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, [...] Read more.

Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, the matroid represented by the columns of the matrix has an odd number of bases. We explain how Grassmannian varieties as well as linear and quadratic complexes are connected with LCD codes. Accessing the classification of polarities, we relate the binary LCD codes of dimension k to the two kinds of symmetric non-singular binary matrices, to certain truncated Reed–Muller codes, and to the geometric codes of planes in finite projective space via the self-orthogonal codes of dimension k. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

17 pages, 1426 KiB

Open AccessArticle

Efficient Index Modulation-Based MIMO OFDM Data Transmission and Detection for V2V Highly Dispersive Channels

by J. Alberto Del Puerto-Flores, Francisco R. Castillo-Soria, Carlos A. Gutiérrez and Fernando Peña-Campos

Mathematics 2023, 11(12), 2773; https://doi.org/10.3390/math11122773 - 20 Jun 2023

Cited by 3 | Viewed by 1859

Abstract

Vehicle-to-vehicle (V2V) communication networks are based on vehicles that wirelessly exchange data, traffic congestion, and safety warnings between them. The design of new V2V systems requires increasingly energetically and spectrally efficient systems. Conventional multiple-input–multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems have been [...] Read more.

Vehicle-to-vehicle (V2V) communication networks are based on vehicles that wirelessly exchange data, traffic congestion, and safety warnings between them. The design of new V2V systems requires increasingly energetically and spectrally efficient systems. Conventional multiple-input–multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems have been used successfully for the last decade. However, MIMO-OFDM systems need to be improved to face future communication networks in high-mobility environments. This article proposes an efficient index modulation (IM)-based MIMO-OFDM system for V2V channels. The proposed transmission system is evaluated in high Doppler-spread channels. The results demonstrate that the proposed scheme reduces the required computational complexity in data detection and exhibits gains of up to 3 dB in bit error rate (BER) performance when compared to the conventional MIMO-OFDM system under the same conditions and parameters, along with achieving superior spectral efficiency. The results show the viability of implementing the proposed system in practical applications for high-transmission-rate V2V channels. Full article

(This article belongs to the Special Issue Advances in Communication Systems, IoT and Blockchain)

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19 pages, 27566 KiB

Open AccessArticle

NSNet: An N-Shaped Convolutional Neural Network with Multi-Scale Information for Image Denoising

by Yifen Li and Yuanyang Chen

Mathematics 2023, 11(12), 2772; https://doi.org/10.3390/math11122772 - 19 Jun 2023

Viewed by 1578

Abstract

Deep learning models with convolutional operators have received widespread attention for their good image denoising performance. However, since the convolutional operation prefers to extract local features, the extracted features may lose some global information, such as texture, structure, and color characteristics, when the [...] Read more.

Deep learning models with convolutional operators have received widespread attention for their good image denoising performance. However, since the convolutional operation prefers to extract local features, the extracted features may lose some global information, such as texture, structure, and color characteristics, when the object in the image is large. To address this issue, this paper proposes an N-shaped convolutional neural network with the ability to extract multi-scale features to capture more useful information and alleviate the problem of global information loss. The proposed network has two main parts: a multi-scale input layer and a multi-scale feature extraction layer. The former uses a two-dimensional Haar wavelet to create an image pyramid, which contains the corrupted image’s high- and low-frequency components at different scales. The latter uses a U-shaped convolutional network to extract features at different scales from this image pyramid. The method sets the mean-squared error as the loss function and uses the residual learning strategy to learn the image noise directly. Compared with some existing image denoising methods, the proposed method shows good performance in gray and color image denoising, especially in textures and contours. Full article

(This article belongs to the Special Issue Data Mining and Machine Learning with Applications)

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29 pages, 587 KiB

Open AccessArticle

Study of Dynamic Solutions for Human–Machine System with Human Error and Common-Cause Failure

by Juan Zhao and Ehmet Kasim

Mathematics 2023, 11(12), 2771; https://doi.org/10.3390/math11122771 - 19 Jun 2023

Viewed by 1021

Abstract

This work investigates a dynamic solution of human–machine systems with human error and common-cause failure. By means of functional analysis, it is proved that the semigroup generated by the underlying operator converges exponentially to a projection operator by analyzing the spectral property of [...] Read more.

This work investigates a dynamic solution of human–machine systems with human error and common-cause failure. By means of functional analysis, it is proved that the semigroup generated by the underlying operator converges exponentially to a projection operator by analyzing the spectral property of the underlying operator, and the asymptotic expressions of the system’s time-dependent solutions are presented. We also provide numerical examples to illustrate the effects of different parameters on the system and the theoretical analysis’s validity. Full article

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16 pages, 822 KiB

Open AccessArticle

Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property

by Md. Sahidul Islam, Masato Kimura and Hisanori Miyata

Mathematics 2023, 11(12), 2770; https://doi.org/10.3390/math11122770 - 19 Jun 2023

Cited by 1 | Viewed by 1499 | Correction

Abstract

In this paper, we develop a generalized moment method with a continuous weight function for the Smoluchowski coagulation equation in its continuous form to study the mass conservation property of this equation. We first establish some basic inequalities for the generalized moment and [...] Read more.

In this paper, we develop a generalized moment method with a continuous weight function for the Smoluchowski coagulation equation in its continuous form to study the mass conservation property of this equation. We first establish some basic inequalities for the generalized moment and prove the mass conservation property under a sufficient condition on the kernel and an initial condition, utilizing these inequalities. Additionally, we provide some concrete examples of coagulation kernels that exhibit mass conservation properties and show that these kernels exhibit either polynomial or exponential growth along specific particular curves. Full article

(This article belongs to the Special Issue Differential and Integro–Differential Equations: Theory and Applications)

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18 pages, 6571 KiB

Open AccessArticle

A Novel Data-Driven Feature Extraction Strategy and Its Application in Looseness Detection of Rotor-Bearing System

by Yulai Zhao, Junzhe Lin, Xiaowei Wang, Qingkai Han and Yang Liu

Mathematics 2023, 11(12), 2769; https://doi.org/10.3390/math11122769 - 19 Jun 2023

Cited by 2 | Viewed by 1173

Abstract

During the service of rotating machinery, the pedestal bolts are prone to looseness due to the vibration environment, which affects the performance of rotating machinery and generate potential safety hazard. To monitor the occurrence and deterioration of the pedestal looseness in time, this [...] Read more.

During the service of rotating machinery, the pedestal bolts are prone to looseness due to the vibration environment, which affects the performance of rotating machinery and generate potential safety hazard. To monitor the occurrence and deterioration of the pedestal looseness in time, this paper proposes a data-driven diagnosis strategy for the rotor-bearing system. Firstly, the finite element model of a rotor-bearing system is established, which considers the piecewise nonlinear force caused by pedestal looseness. Taking the vibration response as output and periodic unbalanced force as input, the system’s NARX (Nonlinear Auto-Regressive with exogenous inputs) model is identified. Then GALEs (Generalized Associated Linear Equations) are used to evaluate NOFRFs (Nonlinear Output Frequency Response Functions) of the NARX model. Based on the first three-order NOFRFs, the analytical expression of the second-order optimal weighted contribution rate is derived and used as a new health indicator. The simulation results show that compared with the conventional NOFRFs-based health indicator, the new indicator is more sensitive to weak looseness. Finally, a rotor-bearing test rig was built, and the pedestal looseness was performed. The experiment results show that as the degree of looseness increases, the new indicator SRm shows a monotonous upward trend, increasing from 0.48 in no looseness to 0.90 in severe looseness, a rise of 89.7%. However, the traditional indicator Fe2 has no monotonicity, which further verifies the sensitivity of the first three-order NOFRFs-based second-order optimal weighted contribution rate and the effectiveness of the proposed data-driven feature extraction strategy. Full article

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22 pages, 2186 KiB

Open AccessArticle

An Innovative Decision Model Utilizing Intuitionistic Hesitant Fuzzy Aczel-Alsina Aggregation Operators and Its Application

by Wajid Ali, Tanzeela Shaheen, Hamza Ghazanfar Toor, Faraz Akram, Md. Zia Uddin and Mohammad Mehedi Hassan

Mathematics 2023, 11(12), 2768; https://doi.org/10.3390/math11122768 - 19 Jun 2023

Cited by 5 | Viewed by 1603

Abstract

The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to [...] Read more.

The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to introduce two novel approaches. Firstly, we propose a three-way model for investors in the business domain, which utilizes interval-valued equivalence classes under the framework of intuitionistic hesitant fuzzy information. Secondly, we present a multiple-attribute decision-making (MADM) method using various aggregation operators for intuitionistic hesitant fuzzy sets (IHFSs). These operators include the IHF Aczel–Alsina average

(I H F A_{A} A)

operator, the IHF Aczel–Alsina weighted average

(I H F A_{A} W A_{ϣ})

operator, and the IHF Aczel–Alsina ordered weighted average

(I H F A_{A} O W A_{ϣ})

operator and the IHF Aczel–Alsina hybrid average

(I H F A_{A} H A_{ϣ})

operators. We demonstrate the properties of idempotency, boundedness, and monotonicity for these newly established aggregation operators. Additionally, we provide a detailed technique for three-way decision-making using intuitionistic hesitant fuzzy Aczel–Alsina aggregation operators. Furthermore, we present a numerical case analysis to illustrate the pertinency and authority of the esteblished model for investment in business. In conclusion, we highlight that the developed approach is highly suitable for investment selection policies, and we anticipate its extension to other fuzzy information domains. Full article

(This article belongs to the Special Issue Hesitant Fuzzy Set and Its Variants for Multi-Attribute Decision-Making)

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18 pages, 331 KiB

Open AccessArticle

Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions

by Dan Zhu, Ming Zhou and Chuancun Yin

Mathematics 2023, 11(12), 2767; https://doi.org/10.3390/math11122767 - 19 Jun 2023

Viewed by 1108

Abstract

The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions. Under the condition that the two Brownian motions

{B_{1} (t), t \geq 0}

and [...] Read more.

The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions. Under the condition that the two Brownian motions

{B_{1} (t), t \geq 0}

and

{B_{2} (t), t \geq 0}

are correlated, we establish new results for the finite-time ruin probabilities. Our research enriches the development of the ruin theory with heavy tails in unidimensional risk models and the dependence theory of stochastic processes. Full article

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

26 pages, 5886 KiB

Open AccessReview

Progress in Blind Image Quality Assessment: A Brief Review

by Pei Yang, Jordan Sturtz and Letu Qingge

Mathematics 2023, 11(12), 2766; https://doi.org/10.3390/math11122766 - 19 Jun 2023

Cited by 5 | Viewed by 2369

Abstract

As a fundamental research problem, blind image quality assessment (BIQA) has attracted increasing interest in recent years. Although great progress has been made, BIQA still remains a challenge. To better understand the research progress and challenges in this field, we review BIQA methods [...] Read more.

As a fundamental research problem, blind image quality assessment (BIQA) has attracted increasing interest in recent years. Although great progress has been made, BIQA still remains a challenge. To better understand the research progress and challenges in this field, we review BIQA methods in this paper. First, we introduce the BIQA problem definition and related methods. Second, we provide a detailed review of the existing BIQA methods in terms of representative hand-crafted features, learning-based features and quality regressors for two-stage methods, as well as one-stage DNN models with various architectures. Moreover, we also present and analyze the performance of competing BIQA methods on six public IQA datasets. Finally, we conclude our paper with possible future research directions based on a performance analysis of the BIQA methods. This review will provide valuable references for researchers interested in the BIQA problem. Full article

(This article belongs to the Special Issue New Advances and Applications in Image Processing and Computer Vision)

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14 pages, 667 KiB

Open AccessArticle

Mathematical Optimization of Carbon Storage and Transport Problem for Carbon Capture, Use, and Storage Chain

by Yiwei Wu, Hongyu Zhang, Shuaian Wang and Lu Zhen

Mathematics 2023, 11(12), 2765; https://doi.org/10.3390/math11122765 - 19 Jun 2023

Cited by 2 | Viewed by 2049

Abstract

The greenhouse effect caused by carbon dioxide (

{C O}_{2}

) emissions has forced the shipping industry to actively reduce the amount of

{C O}_{2}

emissions emitted directly into the atmosphere over the past few years. Carbon capture, utilization, and storage [...] Read more.

The greenhouse effect caused by carbon dioxide (

{C O}_{2}

) emissions has forced the shipping industry to actively reduce the amount of

{C O}_{2}

emissions emitted directly into the atmosphere over the past few years. Carbon capture, utilization, and storage (CCUS) is one of the main technological methods for reducing the amount of

{C O}_{2}

emissions emitted directly into the atmosphere.

{C O}_{2}

transport, i.e., shipping

{C O}_{2}

to permanent or temporary storage sites, is a critical intermediate step in the CCUS chain. This study formulates a mixed-integer programming model for a carbon storage and transport problem in the CCUS chain to optimally determine ship allocation, ship departure scheduling, and

{C O}_{2}

storage and transport. Taking advantage of the structure of the problem, we transform the mixed-integer programming model into a simpler model that can be computed efficiently. To evaluate the performance of the simpler model, numerous computational experiments are conducted. The results show that all small-scale instances (each with 10 power plants) and medium-scale instances (each with 30 power plants) can be solved optimality by Gurobi within 14.33 s. For large-scale instances with 60 and 65 power plants, feasible solutions with average gap values of 0.06% and 6.93% can be obtained by Gurobi within one hour, which indicates that the proposed methodology can be efficiently applied to practical problems. In addition, important parameters, including the unit fuel price, the time-charter cost, and the ship sailing speed, are examined in sensitivity analyses to investigate the impacts of these factors on operations decisions. In summary, a lower fuel price, a lower charter cost, or a higher ship sailing speed can increase the profit of the CCUS chain. Full article

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18 pages, 326 KiB

Open AccessArticle

On Extendibility of Evolution Subalgebras Generated by Idempotents

by Farrukh Mukhamedov and Izzat Qaralleh

Mathematics 2023, 11(12), 2764; https://doi.org/10.3390/math11122764 - 19 Jun 2023

Cited by 1 | Viewed by 900

Abstract

In the present paper, we examined the extendibility of evolution subalgebras generated by idempotents of evolution algebras. The extendibility of the isomorphism of such subalgebras to the entire algebra was investigated. Moreover, the existence of an evolution algebra generated by arbitrary idempotents was [...] Read more.

In the present paper, we examined the extendibility of evolution subalgebras generated by idempotents of evolution algebras. The extendibility of the isomorphism of such subalgebras to the entire algebra was investigated. Moreover, the existence of an evolution algebra generated by arbitrary idempotents was also studied. Furthermore, we described the tensor product of algebras generated by arbitrary idempotents and found the conditions of the tensor decomposability of four-dimensional S-evolution algebras. This paper’s findings shed light on the field of algebraic structures, particularly in studying evolution algebras. By examining the extendibility of evolution subalgebras generated by idempotents, we provide insights into the structural properties and relationships within these algebras. Understanding the isomorphism of such subalgebras and their extension allows a deeper comprehension of the overall algebraic structure and its behaviour. Full article

(This article belongs to the Special Issue Non-associative Structures and Their Applications in Physics and Geometry)

14 pages, 1269 KiB

Open AccessArticle

Robust Tilt-Integral-Derivative Controllers for Fractional-Order Interval Systems

by Muhammad Zeeshan Malik, Shiqing Zhang, Guang Chen and Mamdouh L. Alghaythi

Mathematics 2023, 11(12), 2763; https://doi.org/10.3390/math11122763 - 19 Jun 2023

Cited by 2 | Viewed by 1362

Abstract

In this study, an innovative and sophisticated graphical tuning approach is postulated, aimed at the design of tilt-integral-derivative (TID) controllers that are specifically customized for fractional-order interval plants, whose numerators and denominators consist of fractional-order polynomials that are subjected to parametric uncertainties. By [...] Read more.

In this study, an innovative and sophisticated graphical tuning approach is postulated, aimed at the design of tilt-integral-derivative (TID) controllers that are specifically customized for fractional-order interval plants, whose numerators and denominators consist of fractional-order polynomials that are subjected to parametric uncertainties. By leveraging the powerful value set concept and the advanced D-composition technique, a comprehensive set of stabilizing TID controllers is obtained. The validity and effectiveness of the proposed methodology are demonstrated by some examples, which vividly illustrate its remarkable performance and potential. Full article

(This article belongs to the Section Engineering Mathematics)

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15 pages, 665 KiB

Open AccessArticle

Estimating Failure Probability with Neural Operator Hybrid Approach

by Mujing Li, Yani Feng and Guanjie Wang

Mathematics 2023, 11(12), 2762; https://doi.org/10.3390/math11122762 - 18 Jun 2023

Cited by 2 | Viewed by 1352

Abstract

Evaluating failure probability for complex engineering systems is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and, hence, requires numerous repeated simulations of a complex system to generate sufficient samples. To improve the efficiency, methods [...] Read more.

Evaluating failure probability for complex engineering systems is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and, hence, requires numerous repeated simulations of a complex system to generate sufficient samples. To improve the efficiency, methods based on surrogate models are proposed to approximate the limit state function. In this work, we reframe the approximation of the limit state function as an operator learning problem and utilize the DeepONet framework with a hybrid approach to estimate the failure probability. The numerical results show that our proposed method outperforms the prior neural hybrid method. Full article

(This article belongs to the Special Issue Advances in Numerical Linear Algebra and Its Applications)

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24 pages, 766 KiB

Open AccessArticle

Optimization of Asset and Liability Management of Banks with Minimum Possible Changes

by Pejman Peykani, Mostafa Sargolzaei, Mohammad Hashem Botshekan, Camelia Oprean-Stan and Amir Takaloo

Mathematics 2023, 11(12), 2761; https://doi.org/10.3390/math11122761 - 18 Jun 2023

Cited by 8 | Viewed by 4969

Abstract

Asset-Liability Management (ALM) of banks is defined as simultaneous planning of all bank assets and liabilities under different conditions and its purpose is to maximize profits and minimize the risks in banks by optimizing the parameters in the balance sheet. Most of the [...] Read more.

Asset-Liability Management (ALM) of banks is defined as simultaneous planning of all bank assets and liabilities under different conditions and its purpose is to maximize profits and minimize the risks in banks by optimizing the parameters in the balance sheet. Most of the studies `and proposed models in the ALM field are based on an objective function that maximizes bank profit. It is not easy to apply changes in these models in order to reach the optimal values of the parameters in the balance sheet. In this article, an attempt has been made to propose a linear model using constraints to achieve optimal values of balance sheet parameters using ALM objectives and considering balance sheet, system and regulatory constraints. It has also been tried to design the model according to the most possible mode and with the least changes and to minimize the size of the balance sheet. The analysis of the model presented in this article has been conducted using the parameters of the balance sheet and income statement of one of the famous Iranian banks. The results obtained from the proposed model show that the values of cash and receivables from banks and other credit institutions have decreased by 30% and increased by 200%, respectively, compared to the actual values of these parameters. Also, Total Income, Operating Income and Non-Operating Income have grown by 30% compared to the actual values of these parameters. Also, the values of a number of parameters are estimated to be zero after optimization. According to the results, it is obvious that the performance of bank managers, especially in the management of bank assets, is significantly different from the optimal values of the balance sheet, and the results obtained from the proposed model can help the management of banks as much as possible. Full article

(This article belongs to the Special Issue Statistical Methods of Analyzing Financial Equilibrium, Performance and Risk)

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16 pages, 1168 KiB

Open AccessArticle

An RNN-Based Performance Identification Model for Multi-Agent Containment Control Systems

by Wei Liu, Fei Teng, Xiaotian Fang, Yuan Liang and Shiliang Zhang

Mathematics 2023, 11(12), 2760; https://doi.org/10.3390/math11122760 - 18 Jun 2023

Cited by 2 | Viewed by 1279

Abstract

In the containment control problem of multi-agent systems (MASs), the convergence of followers is always a potential threat to the security of system operations. From the perspective of system topology, the inherently non-linear properties of the algebraic connectivity of the follower2follower (F2F) network, [...] Read more.

In the containment control problem of multi-agent systems (MASs), the convergence of followers is always a potential threat to the security of system operations. From the perspective of system topology, the inherently non-linear properties of the algebraic connectivity of the follower2follower (F2F) network, combined with the influence of the leader2follower (L2F) topology on the system, make it difficult to design the convergence positions of the followers through mere mathematical analysis. Therefore, in the background of temporary networking tasks for large-scale systems, to achieve the goal of forecasting the performance of the whole system when networking is only completed with local information, this paper investigates the application and effectiveness of recurrent neural networks (RNNs) in the containment control system performance identification, thus improving the efficiency of system networking while ensuring system security. Two types of identification models based on two types of neural networks (NNs), MLP and standard RNN are developed, according to the range of information required for performance identification. Evaluation of the models is carried out by means of the coefficient of determination (

R^{2}

) as well as the root-mean-square error (RMSE). The results show that each model may produce a better forecasting accuracy than the other models in specific cases, with models based on the standard RNN possessing smaller errors. With the proposed method, model identification can be achieved, but in-depth development of the model in further studies is still necessary to the extent the accuracy of the model. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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Mathematics, Volume 11, Issue 12 (June-2 2023) – 198 articles

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