Mathematics

2 pages, 172 KiB

Open AccessEditorial

Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering

by Quanxin Zhu

Mathematics 2022, 10(24), 4837; https://doi.org/10.3390/math10244837 - 19 Dec 2022

Cited by 2 | Viewed by 1173

Nonlinear phenomena frequently occur in many fields, such as physics, biology, and engineering [...] Full article

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

16 pages, 960 KiB

Open AccessArticle

Event-Based Impulsive Control for Heterogeneous Neural Networks with Communication Delays

by Yilin Li, Chengbo Yi, Jianwen Feng and Jingyi Wang

Mathematics 2022, 10(24), 4836; https://doi.org/10.3390/math10244836 - 19 Dec 2022

Viewed by 1062

Abstract

The quasi-synchronization for a class of general heterogeneous neural networks is explored by event-based impulsive control strategy. Compared with the traditional average impulsive interval (AII) method, instead, an event-triggered mechanism (ETM) is employed to determine the impulsive instants, in which case the subjectivity [...] Read more.

The quasi-synchronization for a class of general heterogeneous neural networks is explored by event-based impulsive control strategy. Compared with the traditional average impulsive interval (AII) method, instead, an event-triggered mechanism (ETM) is employed to determine the impulsive instants, in which case the subjectivity of selecting the controlling sequence can be eliminated. In addition, considering the fact that communication delay is inevitable between the allocation and execution of instructions in practice, we further nominate an ETM centered on communication delays and aperiodic sampling, which is more accessible and affordable, yet can straightforwardly avoid Zeno behavior. Hence, on the basis of the novel event-triggered impulsive control strategy, quasi-synchronization of heterogeneous neural network model is investigated and some general conditions are also achieved. Finally, two numerical simulations are afforded to validate the efficacy of theoretical results. Full article

(This article belongs to the Special Issue Chaotic Systems and Their Applications)

► Show Figures

Figure 1

52 pages, 24566 KiB

Open AccessArticle

Interval Fuzzy Type-2 Sliding Mode Control Design of Six-DOF Robotic Manipulator

by Yassine Bouteraa, Khalid A. Alattas, Obaid Alshammari, Sondess Ben Aoun, Mohamed Amin Regaieg and Saleh Mobayen

Mathematics 2022, 10(24), 4835; https://doi.org/10.3390/math10244835 - 19 Dec 2022

Viewed by 1377

Abstract

The remarkable features of hybrid SMC assisted with fuzzy systems supplying parameters of the controller have led to significant success of these control approaches, especially in the control of multi-input and multi-output nonlinear systems. The development of type-1 fuzzy systems to type-2 fuzzy [...] Read more.

The remarkable features of hybrid SMC assisted with fuzzy systems supplying parameters of the controller have led to significant success of these control approaches, especially in the control of multi-input and multi-output nonlinear systems. The development of type-1 fuzzy systems to type-2 fuzzy systems has improved the performance of fuzzy systems due to the ability to model uncertainties in the expression of expert knowledge. Accordingly, in this paper, the basic approach of designing and implementing the interval type-2 fuzzy sliding mode control was proposed. According to the introduced systematic design procedure, complete optimal design of a type-2 fuzzy system structure was presented in providing sliding mode control parameters by minimizing tracking error and control energy. Based on the proposed method, the need for expert knowledge as the main challenge in designing fuzzy systems was eliminated. In addition, the possibility to limit the control outputs to deal with actuators’ saturation was made available. The control method was implemented on a six-degree-of-freedom robot manipulator that was exposed to severe external disturbances, and its performance was compared to a type-1 fuzzy system as well as to the conventional SMC. The achievements revealed improved performance of the combined control system of fuzzy sliding mode type-2 in comparison with its control counterparts. Full article

► Show Figures

Figure 1

13 pages, 805 KiB

Open AccessArticle

Graph Learning for Attributed Graph Clustering

by Xiaoran Zhang, Xuanting Xie and Zhao Kang

Mathematics 2022, 10(24), 4834; https://doi.org/10.3390/math10244834 - 19 Dec 2022

Viewed by 2388

Abstract

Due to the explosive growth of graph data, attributed graph clustering has received increasing attention recently. Although deep neural networks based graph clustering methods have achieved impressive performance, the huge amount of training parameters make them time-consuming and memory- intensive. Moreover, real-world graphs [...] Read more.

Due to the explosive growth of graph data, attributed graph clustering has received increasing attention recently. Although deep neural networks based graph clustering methods have achieved impressive performance, the huge amount of training parameters make them time-consuming and memory- intensive. Moreover, real-world graphs are often noisy or incomplete and are not optimal for the clustering task. To solve these problems, we design a graph learning framework for the attributed graph clustering task in this study. We firstly develop a shallow model for learning a fine-grained graph from smoothed data, which sufficiently exploits both node attributes and topology information. A regularizer is also designed to flexibly explore the high-order information hidden in the data. To further reduce the computation complexity, we then propose a linear method with respect to node number n, where a smaller graph is learned based on importance sampling strategy to select m

(m ≪ n)

anchors. Extensive experiments on six benchmark datasets demonstrate that our proposed methods are not only effective but also more efficient than state-of-the-art techniques. In particular, our method surpasses many recent deep learning approaches. Full article

(This article belongs to the Special Issue Trustworthy Graph Neural Networks: Models and Applications)

► Show Figures

Figure 1

20 pages, 3130 KiB

Open AccessArticle

Investigation of Mixed Convection in Spinning Nanofluid over Rotating Cone Using Artificial Neural Networks and BVP-4C Technique

by Ali Hassan, Qusain Haider, Najah Alsubaie, Fahad M. Alharbi, Abdullah Alhushaybari and Ahmed M. Galal

Mathematics 2022, 10(24), 4833; https://doi.org/10.3390/math10244833 - 19 Dec 2022

Cited by 2 | Viewed by 1372

Abstract

The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) [...] Read more.

The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) are employed to study heat transmission by using a trained artificial neural network. The system of highly non-linear flow governing partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) which is taken as a system model. This achieved system model is utilized to generate data set using the “Adams” method for distinct scenarios of heat transmission investigation in a spinning nanofluid over a rotating system for the implementation of the proposed ANNLMB. Additionally, with the help of training, testing, and validation, the approximate solution of heat transmission in a spinning nanofluid in a rotating system is obtained using a BNN-based solver. The generated reference data achieved employing the proposed artificial neural network based on a Levenberg–Marquardt intelligent network is distributed in the following manner: training at 82%, testing at 9%, and validation at 9%. Furthermore, MSE, histograms, and regression analyses are performed to depict and discuss the impact of the varying influence of key parameters, such as unsteadiness “s” in spinning flow, Prandtl number effect “pr”, the rotational ratio of nanofluid and cone

α_{1}

and buoyancy effect

γ_{1}

on velocities

F^{'} G

and temperature

Θ

profiles. The mean square error confirms the accuracy of the achieved results. Prandtl number and unsteadiness decrease the temperature profile and thermal boundary layer of the rotating nanofluid. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

► Show Figures

Figure 1

15 pages, 309 KiB

Open AccessArticle

Coefficient Inequalities for Biholomorphic Mappings on the Unit Ball of a Complex Banach Space

by Hidetaka Hamada, Gabriela Kohr and Mirela Kohr

Mathematics 2022, 10(24), 4832; https://doi.org/10.3390/math10244832 - 19 Dec 2022

Viewed by 991

Abstract

In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. [...] Read more.

In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. Hamada, G. Kohr and M. Kohr. We obtain the Fekete–Szegö inequalities using the norm under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. In the second part of this paper, we give the estimation of the difference of the moduli of successive coefficients for the first elements of g-Loewner chains on the unit disc. We also give the estimation of the difference of the moduli of successive coefficients for the first elements F of g-Loewner chains on the unit ball of a complex Banach space under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. Full article

(This article belongs to the Special Issue New Trends in Complex Analysis Researches)

13 pages, 1305 KiB

Open AccessArticle

Entropies Via Various Molecular Descriptors of Layer Structure of H₃BO₃

by Muhammad Usman Ghani, Muhammad Kashif Maqbool, Reny George, Austine Efut Ofem and Murat Cancan

Mathematics 2022, 10(24), 4831; https://doi.org/10.3390/math10244831 - 19 Dec 2022

Cited by 11 | Viewed by 1377

Abstract

Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, since work is produced by organized molecular motion. Entropy theory offers a profound understanding of the direction of spontaneous change for many commonplace events. A formal definition of a [...] Read more.

Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, since work is produced by organized molecular motion. Entropy theory offers a profound understanding of the direction of spontaneous change for many commonplace events. A formal definition of a random graph exists. It deals with relational data’s probabilistic and structural properties. The lower-order distribution of an ensemble of attributed graphs may be used to describe the ensemble by considering it to be the results of a random graph. Shannon’s entropy metric is applied to represent a random graph’s variability. A structural or physicochemical characteristic of a molecule or component of a molecule is known as a molecular descriptor. A mathematical correlation between a chemical’s quantitative molecular descriptors and its toxicological endpoint is known as a QSAR model for predictive toxicology. Numerous physicochemical, toxicological, and pharmacological characteristics of chemical substances help to foretell their type and mode of action. Topological indices were developed some 150 years ago as an alternative to the Herculean, and arduous testing is needed to examine these features. This article uses various computational and mathematical techniques to calculate atom–bond connectivity entropy, atom–bond sum connectivity entropy, the newly defined Albertson entropy using the Albertson index, and the IRM entropy using the IRM index. We use the subdivision and line graph of the

H_{3} B O_{3}

layer structure, which contains one boron atom and three oxygen atoms to form the chemical boric acid. Full article

(This article belongs to the Special Issue Mathematical and Molecular Topology)

► Show Figures

Figure 1

22 pages, 918 KiB

Open AccessArticle

Subgraph Query Matching in Multi-Graphs Based on Node Embedding

by Muhammad Anwar, Aboul Ella Hassanien, Václav Snás̃el and Sameh H. Basha

Mathematics 2022, 10(24), 4830; https://doi.org/10.3390/math10244830 - 19 Dec 2022

Viewed by 1944

Abstract

This paper presents an efficient algorithm for matching subgraph queries in a multi-graph based on features-based indexing techniques. The KD-tree data structure represents these nodes’ features, while the set-trie index data structure represents the multi-edges to make queries effectively. The vertex core number, [...] Read more.

This paper presents an efficient algorithm for matching subgraph queries in a multi-graph based on features-based indexing techniques. The KD-tree data structure represents these nodes’ features, while the set-trie index data structure represents the multi-edges to make queries effectively. The vertex core number, triangle number, and vertex degree are the eight features’ main features. The densest vertex in the query graph is extracted based on these main features. The proposed model consists of two phases. The first phase’s main idea is that, for the densest extracted vertex in the query graph, find the density similar neighborhood structure in the data graph. Then find the k-nearest neighborhood query to obtain the densest subgraph. The second phase for each layer graph, mapping the vertex to feature vector (Vertex Embedding), improves the proposed model. To reduce the node-embedding size to be efficient with the KD-tree, indexing a dimension reduction, the principal component analysis (PCA) method is used. Furthermore, symmetry-breaking conditions will remove the redundancy in the generated pattern matching with the query graph. In both phases, the filtering process is applied to minimize the number of candidate data nodes of the initiate query vertex. The filtering process is applied to minimize the number of candidate data nodes of the initiate query vertex. Finally, testing the effect of the concatenation of the structural features (orbits features) with the meta-features (summary of general, statistical, information-theoretic, etc.) for signatures of nodes on the model performance. The proposed model is tested over three real benchmarks, multi-graph datasets, and two randomly generated multi-graph datasets. The results agree with the theoretical study in both random cliques and Erdos random graph. The experiments showed that the time efficiency and the scalability results of the proposed model are acceptable. Full article

► Show Figures

Figure 1

24 pages, 4135 KiB

Open AccessArticle

Modeling the Operation of Signal-Controlled Intersections with Different Lane Occupancy

by Viacheslav Morozov, Vladimir Shepelev and Viktor Kostyrchenko

Mathematics 2022, 10(24), 4829; https://doi.org/10.3390/math10244829 - 19 Dec 2022

Cited by 8 | Viewed by 1703

Abstract

In many cities of the world, the problem of traffic congestion on the roads remains relevant and unresolved. It is especially noticeable at signal-controlled intersections, since traffic signalization is among the most important factors that reduce the maximum possible value of the traffic [...] Read more.

In many cities of the world, the problem of traffic congestion on the roads remains relevant and unresolved. It is especially noticeable at signal-controlled intersections, since traffic signalization is among the most important factors that reduce the maximum possible value of the traffic flow rate at the exit of a street intersection. Therefore, the development of a methodology aimed at reducing transport losses when pedestrians move through signal-controlled intersections is a joint task for the research and engineering community and municipalities. This paper is a continuation of a study wherein the results produced a mathematical model of the influence of lane occupancy and traffic signalization on the traffic flow rate. These results were then experimentally confirmed. The purpose of this work is to develop a method for the practical application of the mathematical model thus obtained. Together with the obtained results of the previous study, as well as a systems approach, traffic flow theory, impulses, probabilities and mathematical statistics form the methodological basis of this work. This paper established possible areas for the practical application of the previously obtained mathematical model. To collect the initial experimental data, open-street video surveillance cameras were used as vehicle detectors, the image streams of which were processed in real time using neural network technologies. Based on the results of this work, a new method was developed that allows for the adjustment of the traffic signal cycle, considering the influence of lane occupancy. In addition, the technological, economic and environmental effects were calculated, which was achieved through the application of the proposed method. Full article

(This article belongs to the Special Issue Mathematical Modeling of Engineering and Socio-Economic Processes and Systems)

► Show Figures

Figure 1

17 pages, 1010 KiB

Open AccessArticle

Zeroing Neural Networks Combined with Gradient for Solving Time-Varying Linear Matrix Equations in Finite Time with Noise Resistance

by Jun Cai, Wenlong Dai, Jingjing Chen and Chenfu Yi

Mathematics 2022, 10(24), 4828; https://doi.org/10.3390/math10244828 - 19 Dec 2022

Viewed by 1147

Abstract

Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks [...] Read more.

Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks (ZNN), we propose an integration-enhanced combined accelerating zeroing neural network (IEAZNN) model to solve LME problem accurately and efficiently. Different from most of the existing ZNNs research, there are two error functions combined in the IEAZNN model, among which the gradient of the energy function is the first design for the purpose of decreasing the norm-based error to zero and the second one is adding an integral term to resist additive noise. On the strength of novel combination in two error functions, the IEAZNN model is capable of converging in finite time and resisting noise at the same time. Moreover, theoretical proof and numerical verification results show that the IEAZNN model can achieve high accuracy and fast convergence speed in solving time-varying LME problems compared with the conventional ZNN (CZNN) and integration-enhanced ZNN (IEZNN) models, even in various kinds of noise environments. Full article

(This article belongs to the Special Issue AI Algorithm Design and Application)

► Show Figures

Figure 1

24 pages, 381 KiB

Open AccessFeature PaperArticle

Rolling Geodesics, Mechanical Systems and Elastic Curves

by Velimir Jurdjevic

Mathematics 2022, 10(24), 4827; https://doi.org/10.3390/math10244827 - 19 Dec 2022

Cited by 3 | Viewed by 1011

Abstract

This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem. We show remarkable connections between these two problems manifested by the associated Hamiltonians obtained by the Maximum Principle of optimal control. We also [...] Read more.

This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem. We show remarkable connections between these two problems manifested by the associated Hamiltonians obtained by the Maximum Principle of optimal control. We also show that each of these Hamiltonians is completely intergrable, in the sense of Liouville. Finally we demonstrate the significance of these results for the theory of mechanical systems. Full article

(This article belongs to the Special Issue Variational Methods on Riemannian Manifolds: Theory and Applications)

27 pages, 657 KiB

Open AccessArticle

The E-Bayesian Methods for the Inverse Weibull Distribution Rate Parameter Based on Two Types of Error Loss Functions

by Hassan M. Okasha, Abdulkareem M. Basheer and Yuhlong Lio

Mathematics 2022, 10(24), 4826; https://doi.org/10.3390/math10244826 - 19 Dec 2022

Viewed by 1233

Abstract

Given a sample, E-Bayesian estimates, which are the expected Bayesian estimators over the joint distributions of two hyperparameters in the prior distribution, are developed for the inverse Weibull distribution rate parameter under the scaled squared error and linear exponential error loss functions, respectively. [...] Read more.

Given a sample, E-Bayesian estimates, which are the expected Bayesian estimators over the joint distributions of two hyperparameters in the prior distribution, are developed for the inverse Weibull distribution rate parameter under the scaled squared error and linear exponential error loss functions, respectively. The corresponding expected mean square errors, EMSEs, of E-Bayesian estimators based on the sample are derived. Moreover, the theoretical properties of EMSEs are established. A Monte Carlo simulation study is conducted for the performance comparison. Finally, three data sets are given for illustration. Full article

► Show Figures

Figure 1

14 pages, 336 KiB

Open AccessArticle

About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals

by Ion Mierluș-Mazilu and Lucian Niță

Mathematics 2022, 10(24), 4825; https://doi.org/10.3390/math10244825 - 19 Dec 2022

Viewed by 816

Abstract

If X is a Hilbert space, one can consider the space

cabv (X)

of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich [...] Read more.

If X is a Hilbert space, one can consider the space

cabv (X)

of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich type norm. Our first goal was to introduce a Monge–Kantorovich type norm on

cabv (X)

, where X is a Banach space, but not necessarily a Hilbert space. Thus, we introduced here the Monge–Kantorovich type norm on

cabv (L^{q} ([0, 1])), (1 < q < \infty)

. We obtained some properties of this norm and provided some examples. Then, we used the Monge–Kantorovich norm on

cabv (K^{n}) (K

being

R

or

C)

to obtain convergence properties for sequences of fractal sets and fractal vector measures associated to a sequence of iterated function systems. Full article

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

13 pages, 1034 KiB

Open AccessArticle

Dynamic ILC for Linear Repetitive Processes Based on Different Relative Degrees

by Lei Wang, Liangxin Dong, Ruitian Yang and Yiyang Chen

Mathematics 2022, 10(24), 4824; https://doi.org/10.3390/math10244824 - 19 Dec 2022

Viewed by 1084

Abstract

The current research on iterative learning control focuses on the condition where the system relative degree is equal to 1, while the condition where the system relative degree is equal to 0 or greater than 1 is not considered. Therefore, this paper studies [...] Read more.

The current research on iterative learning control focuses on the condition where the system relative degree is equal to 1, while the condition where the system relative degree is equal to 0 or greater than 1 is not considered. Therefore, this paper studies the monotonic convergence of the corresponding dynamic iterative learning controller systematically for discrete linear repetitive processes with different relative degrees. First, a 2D discrete Roesser model of the iterative learning control system is presented by means of 2D systems theory. Then, the monotonic convergence condition of the controlled system is analyzed according to the stability theory of linear repetitive process. Furthermore, the sufficient conditions of the controller existence are given in linear matrix inequality format under different relative degrees, which guarantees the system dynamic performance. Finally, through comparison with static controllers under different relative degrees, the simulation results show that the designed schemes are effective and feasible. Full article

► Show Figures

Figure 1

23 pages, 3224 KiB

Open AccessArticle

Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach

by Hualin Song, Cheng Hu and Juan Yu

Mathematics 2022, 10(24), 4823; https://doi.org/10.3390/math10244823 - 19 Dec 2022

Cited by 4 | Viewed by 1206

Abstract

This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the [...] Read more.

This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria are derived. In synchronization analysis, unlike the existing control schemes for reduced-order subsystems, some feedback and adaptive control schemes, formed by the linear part and the fractional derivative part, are directly designed for the response fractional inertial neural networks, and some synchronization conditions are derived using the established fractional inequality. Finally, the theoretical analysis is supported via two numerical examples. Full article

(This article belongs to the Special Issue Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value)

► Show Figures

Figure 1

15 pages, 293 KiB

Open AccessArticle

On Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity

by Luyang Li, Linhui Wang, Qinglan Zhao and Dong Zheng

Mathematics 2022, 10(24), 4822; https://doi.org/10.3390/math10244822 - 19 Dec 2022

Viewed by 1088

Abstract

Boolean functions and vectorial Boolean functions are the most important nonlinear components of stream ciphers. They should satisfy several criteria such as high nonlinearity, proper resiliency and so on to guarantee the security of the whole system. However, there are some constraints among [...] Read more.

Boolean functions and vectorial Boolean functions are the most important nonlinear components of stream ciphers. They should satisfy several criteria such as high nonlinearity, proper resiliency and so on to guarantee the security of the whole system. However, there are some constraints among the criteria, and how to achieve a trade-off between them is an important issue. In this paper, some nonlinear Boolean functions possessing simple algebraic normal form with special Walsh spectrum are proposed. By using these functions, we provide two construction methods on balanced and resilient Boolean functions with high nonlinearity. In addition, based on the disjoint linear codes and vector matrices with special properties, some resilient vectorial Boolean functions with currently best-known nonlinearity have also been given. Full article

(This article belongs to the Special Issue Advances in Algebraic Coding Theory and Cryptography)

20 pages, 357 KiB

Open AccessArticle

On Impulsive Implicit ψ-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation

by Abdelkrim Salim, Jehad Alzabut, Weerawat Sudsutad and Chatthai Thaiprayoon

Mathematics 2022, 10(24), 4821; https://doi.org/10.3390/math10244821 - 19 Dec 2022

Cited by 3 | Viewed by 890

Abstract

In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit

ψ

-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle [...] Read more.

In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit

ψ

-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle and Krasnoselskii’s fixed point theorem. In addition, the Ulam–Hyers–Rassias stability result is proved using the nonlinear functional analysis technique. Finally, illustrative examples are given to validate our main results. Full article

(This article belongs to the Special Issue Theory and Applications of Fractional Equations and Calculus)

16 pages, 11065 KiB

Open AccessArticle

A Memristor-Based Colpitts Oscillator Circuit

by Ling Zhou, Zhenzhen You, Xiaolin Liang and Xiaowu Li

Mathematics 2022, 10(24), 4820; https://doi.org/10.3390/math10244820 - 19 Dec 2022

Cited by 3 | Viewed by 1486

Abstract

This paper investigates a simple memristor emulator consisting of a diode bridge and a capacitor. It exhibits pinched hysteresis loops, and what is more striking is the higher frequency, as it operates up to greater than 5 MHz. Based on the proposed memristor, [...] Read more.

This paper investigates a simple memristor emulator consisting of a diode bridge and a capacitor. It exhibits pinched hysteresis loops, and what is more striking is the higher frequency, as it operates up to greater than 5 MHz. Based on the proposed memristor, a higher-frequency Colpitts circuit was established. According to the mathematical model of the system, the system only possesses one unstable equilibrium point. Period doubling bifurcation, reverse periodic doubling bifurcation, different types of periodic and chaotic orbits, transient chaos, coexisting bifurcations and offset boosting are depicted. More interestingly, it has coexisting multiple attractors with different topologies, such as a chaotic attractor accompanied with periodic orbits, period-1 orbits with bicuspid structure and periodic-2 orbits with tridentate structure. Moreover, a hardware circuit using discrete components was fabricated and experimental measurements were consistent with the MATLAB numerical results, further confirming the real feasibility of the proposed circuit. Full article

(This article belongs to the Special Issue Chaotic Systems and Their Applications)

► Show Figures

Figure 1

14 pages, 331 KiB

Open AccessArticle

Pre-Hausdorffness and Hausdorffness in Quantale-Valued Gauge Spaces

by Samed Özkan, Samirah Alsulami, Tesnim Meryem Baran and Muhammad Qasim

Mathematics 2022, 10(24), 4819; https://doi.org/10.3390/math10244819 - 19 Dec 2022

Cited by 1 | Viewed by 945

Abstract

In this paper, we characterize each of

T_{0}

,

T_{1}

, Pre-Hausdorff and Hausdorff separation properties for the category

L - GS

of quantale-valued gauge spaces and

L

-gauge morphisms. Moreover, we investigate how these concepts are related to each other [...] Read more.

In this paper, we characterize each of

T_{0}

,

T_{1}

, Pre-Hausdorff and Hausdorff separation properties for the category

L - GS

of quantale-valued gauge spaces and

L

-gauge morphisms. Moreover, we investigate how these concepts are related to each other in this category. We show that

T_{0}

,

T_{1}

and

T_{2}

are equivalent in the realm of Pre-Hausdorff quantale-valued gauge spaces. Finally, we compare our results with the ones in some other categories. Full article

(This article belongs to the Special Issue New Progress in General Topology and Its Applications)

9 pages, 545 KiB

Open AccessArticle

The Point of No Return: Evolution of Excess Mutation Rate Is Possible Even for Simple Mutation Models

by Brian Mintz and Feng Fu

Mathematics 2022, 10(24), 4818; https://doi.org/10.3390/math10244818 - 19 Dec 2022

Cited by 1 | Viewed by 1128

Abstract

Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore, it is reasonable to expect that mutation rates will evolve downwards. However, we find that this need not be the case, [...] Read more.

Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore, it is reasonable to expect that mutation rates will evolve downwards. However, we find that this need not be the case, examining several models of mutation. While upwards evolution of the mutation rate has been found with frequency- or time-dependent fitness, we demonstrate its possibility in a much simpler context. This work uses adaptive dynamics to study the evolution of the mutation rate, and the replicator–mutator equation to model trait evolution. Our approach differs from previous studies by considering a wide variety of methods to represent mutation. We use a finite string approach inspired by genetics as well as a model of local mutation on a discretization of the unit intervals, handling mutation beyond the endpoints in three ways. The main contribution of this work is a demonstration that the evolution of the mutation rate can be significantly more complicated than what is usually expected in relatively simple models. Full article

(This article belongs to the Special Issue Mathematics: 10th Anniversary)

► Show Figures

Figure 1

10 pages, 324 KiB

Open AccessArticle

A Refined Jensen Inequality Connected to an Arbitrary Positive Finite Sequence

by Shanhe Wu, Muhammad Adil Khan, Tareq Saeed and Zaid Mohammed Mohammed Mahdi Sayed

Mathematics 2022, 10(24), 4817; https://doi.org/10.3390/math10244817 - 18 Dec 2022

Cited by 1 | Viewed by 1219

Abstract

The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s [...] Read more.

The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s inequality. As results, we obtain refinements of the quasi-arithmetic and power mean inequalities. Finally, several results are obtained in information theory with the help of the main results. Full article

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

21 pages, 738 KiB

Open AccessFeature PaperArticle

A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

by Melkamu Molla Ferede, Samuel Mwalili, Getachew Dagne, Simon Karanja, Workagegnehu Hailu, Mahmoud El-Morshedy and Afrah Al-Bossly

Mathematics 2022, 10(24), 4816; https://doi.org/10.3390/math10244816 - 18 Dec 2022

Cited by 1 | Viewed by 1376

Abstract

In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may [...] Read more.

In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may be exposed to more than one type of failure event (competing risks). Considering the competing event as an independent censoring of the time-to-event process may underestimate the true survival probability and give biased results. Within the joint model, longitudinal outcomes may have nonlinear (irregular) trajectories over time and exhibit skewness with heavy tails. Accordingly, fully parametric mixed-effect models may not be flexible enough to model this type of complex longitudinal data. In addition, assuming a Gaussian distribution for model errors may be too restrictive to adequately represent within-individual variations and may lack robustness against deviation from distributional assumptions. To simultaneously overcome these issues, in this paper, we presented semiparametric joint models for competing risks failure time and skewed-longitudinal data by using a smoothing spline approach and a multivariate skew-t distribution. We also considered different parameterization approaches in the formulation of joint models and used a Bayesian approach to make the statistical inference. We illustrated the proposed methods by analyzing real data on a chronic kidney disease. To evaluate the performance of the methods, we also carried out simulation studies. The results of both the application and simulation studies revealed that the joint modelling approach proposed in this study performed well when the semiparametric, random-effects parameterization, and skew-t distribution specifications were taken into account. Full article

(This article belongs to the Special Issue Current Developments in Theoretical and Applied Statistics)

► Show Figures

Figure 1

25 pages, 5639 KiB

Open AccessArticle

A New Text-Mining–Bayesian Network Approach for Identifying Chemical Safety Risk Factors

by Zhiyong Zhou, Jianhui Huang, Yao Lu, Hongcai Ma, Wenwen Li and Jianhong Chen

Mathematics 2022, 10(24), 4815; https://doi.org/10.3390/math10244815 - 18 Dec 2022

Cited by 3 | Viewed by 1802

Abstract

The frequent occurrence of accidents in the chemical industry has caused serious economic loss and negative social impact. The chemical accident investigation report is of great value for analyzing the risk factors involved. However, traditional manual analysis is time-consuming and labor-intensive, while existing [...] Read more.

The frequent occurrence of accidents in the chemical industry has caused serious economic loss and negative social impact. The chemical accident investigation report is of great value for analyzing the risk factors involved. However, traditional manual analysis is time-consuming and labor-intensive, while existing keyword extraction methods still need to be improved. This study aims to propose an improved text-mining method to analyze a large number of chemical accident reports. A workflow was designed for building and updating lexicons of word segmentation. An improved keyword extraction algorithm was proposed to extract the top 100 keywords from 330 incident reports. A total of 51 safety risk factors was obtained by standardizing these keywords. In all, 294 strong association rules were obtained by Apriori. Based on these rules, a Bayesian network was built to analyze safety risk factors. The mean accuracy and mean recall of the BM25 model in the comparison experiments were 10.5% and 14.38% higher than those of TF-IDF, respectively. The results of association-rule mining and Bayesian network analysis can clearly demonstrate the interrelationship between the safety risk factors. The methodology of this study can quickly and efficiently extract key information from incident reports which can provide managers with new insights and suggestions. Full article

(This article belongs to the Special Issue Data Analysis and Domain Knowledge)

► Show Figures

Figure 1

18 pages, 4575 KiB

Open AccessArticle

Physics-Based Observers for Measurement-While-Drilling System in Down-the-Hole Drills

by Gabriel Bout, Diego Brito, René Gómez, Gonzalo Carvajal and Guillermo Ramírez

Mathematics 2022, 10(24), 4814; https://doi.org/10.3390/math10244814 - 18 Dec 2022

Cited by 5 | Viewed by 2046

Abstract

Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this [...] Read more.

Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this context must be designed and conditioned for operating in harsh conditions, imposing trade-offs between the complexity, cost, and reliability of the measurement system. This paper presents a methodology for integrating physics-based observers into an MWD system as an alternative to complement or replace traditional physical sensors. The proposed observers leverage mathematical models of the drill’s electrical motor and its interaction with dynamic loads to estimate the bit speed and torque in a Down-the-Hole rig using current and voltage measurements taken from the motor power line. Experiments using data collected from four test samples with different rock strengths show a consistent correlation between the rate of penetration and specific energy derived from the observed drilling variables with the ones obtained from standardized tests of uniaxial compressive strength. The simplicity of the setup and results validate the feasibility of the proposed approach to be evaluated as an alternative to reduce the complexity and increase the reliability of MWD systems. Full article

(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)

► Show Figures

Figure 1

16 pages, 340 KiB

Open AccessFeature PaperArticle

Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems

by Touria Karite, Adil Khazari and Delfim F. M. Torres

Mathematics 2022, 10(24), 4813; https://doi.org/10.3390/math10244813 - 18 Dec 2022

Viewed by 1134

Abstract

We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for [...] Read more.

We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results. Full article

(This article belongs to the Special Issue Dynamical Systems and Their Applications (DSTA) — In Memory of Prof. Dr. José A. Tenreiro Machado)

19 pages, 4113 KiB

Open AccessArticle

Edge Computing Offloading Method Based on Deep Reinforcement Learning for Gas Pipeline Leak Detection

by Dong Wei, Renjun Wang, Changqing Xia, Tianhao Xia, Xi Jin and Chi Xu

Mathematics 2022, 10(24), 4812; https://doi.org/10.3390/math10244812 - 18 Dec 2022

Cited by 3 | Viewed by 1485

Abstract

Traditional gas pipeline leak detection methods require task offload decisions in the cloud, which has low real time performance. The emergence of edge computing provides a solution by enabling offload decisions directly at the edge server, improving real-time performance; however, energy is the [...] Read more.

Traditional gas pipeline leak detection methods require task offload decisions in the cloud, which has low real time performance. The emergence of edge computing provides a solution by enabling offload decisions directly at the edge server, improving real-time performance; however, energy is the new bottleneck. Therefore, focusing on the gas transmission pipeline leakage detection scenario in real time, a novel detection algorithm that combines the benefits of both the heuristic algorithm and the advantage actor critic (AAC) algorithm is proposed in this paper. It aims at optimization with the goal of real-time guarantee of pipeline mapping analysis tasks and maximizing the survival time of portable gas leak detectors. Since the computing power of portable detection devices is limited, as they are powered by batteries, the main problem to be solved in this study is how to take into account the node energy overhead while guaranteeing the system performance requirements. By introducing the idea of edge computing and taking the mapping relationship between resource occupation and energy consumption as the starting point, the optimization model is established, with the goal to optimize the total system cost (TSC). This is composed of the node’s transmission energy consumption, local computing energy consumption, and residual electricity weight. In order to minimize TSC, the algorithm uses the AAC network to make task scheduling decisions and judge whether tasks need to be offloaded, and uses heuristic strategies and the Cauchy–Buniakowsky–Schwarz inequality to determine the allocation of communication resources. The experiments show that the proposed algorithm in this paper can meet the real-time requirements of the detector, and achieve lower energy consumption. The proposed algorithm saves approximately 56% of the system energy compared to the Deep Q Network (DQN) algorithm. Compared with the artificial gorilla troops Optimizer (GTO), the black widow optimization algorithm (BWOA), the exploration-enhanced grey wolf optimizer (EEGWO), the African vultures optimization algorithm (AVOA), and the driving training-based optimization (DTBO), it saves 21%, 38%, 30%, 31%, and 44% of energy consumption, respectively. Compared to the fully local computing and fully offloading algorithms, it saves 50% and 30%, respectively. Meanwhile, the task completion rate of this algorithm reaches 96.3%, which is the best real-time performance among these algorithms. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Mathematical Modeling for Optimization Problems)

► Show Figures

Figure 1

34 pages, 9230 KiB

Open AccessArticle

Higher Moments Actually Matter: Spillover Approach for Case of CESEE Stock Markets

by Tihana Škrinjarić

Mathematics 2022, 10(24), 4811; https://doi.org/10.3390/math10244811 - 18 Dec 2022

Cited by 2 | Viewed by 1118

Abstract

The interconnectedness of stock markets is an important topic in empirical research, as spillovers on financial markets matter for asset pricing, portfolio allocation, financial stability, and risk management. This research focuses on all four moments of return distributions on stock markets and their [...] Read more.

The interconnectedness of stock markets is an important topic in empirical research, as spillovers on financial markets matter for asset pricing, portfolio allocation, financial stability, and risk management. This research focuses on all four moments of return distributions on stock markets and their spillovers between CESEE (Central, Eastern, and South-Eastern Europe) stock markets. Higher moments analysis needs to be explored more deeply, but can provide detailed insights into distribution shifts of market returns due to shocks in other markets. This research fills such a gap in the literature by estimating spillover effects between the four moments of stock market return distributions. Based on data from January 2013 to September 2022, the VAR (vector autoregression) model is estimated for individual moments across stock markets as a base for the calculation of spillover indices. The main findings indicate that it is difficult to track all the spillovers at once as the net emitter of shocks to one or other of the countries involved often change to being a net receiver and vice versa. Moreover, higher moments spillovers matter for individual markets, which has important implications for dynamic portfolio selection. Full article

► Show Figures

Figure 1

25 pages, 7548 KiB

Open AccessArticle

Concrelife: A Software to Solve the Chloride Penetration in Saturated and Unsaturated Reinforced Concrete

by Juan Francisco Sánchez-Pérez, Pilar Hidalgo and Francisco Alhama

Mathematics 2022, 10(24), 4810; https://doi.org/10.3390/math10244810 - 17 Dec 2022

Cited by 2 | Viewed by 1336

Abstract

This paper presents new software (Concrelife) capable of reliably simulating chloride ions penetration in reinforced concrete from different environments in the most common 1-D rectangular geometry scenarios. Its numerical solution is obtained from the simulation of models whose structure is based on Network [...] Read more.

This paper presents new software (Concrelife) capable of reliably simulating chloride ions penetration in reinforced concrete from different environments in the most common 1-D rectangular geometry scenarios. Its numerical solution is obtained from the simulation of models whose structure is based on Network Simulation Method. These models are generated by the program itself and run in the powerful free code NgSpice. The mathematical model of the problem includes the formation of bound chloride, precipitated chloride, reduction of porosity, saturated and unsaturated conditions, etc. All this allows tackling all kinds of scenarios, such as successive changes in concentration and temperature at the boundary, wet-drying cycles, washing of structures, etc. Concrelife has been developed with a pleasant window environment, intuitive and easy for a user not expert in numerical techniques, both for the introduction of data and for the graphic representation of the results, which include the spatial and temporal concentration of all species of chloride, porosity, water content in pores etc. To test and verify the results of the software, applications are presented to real scenarios. Full article

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

► Show Figures

Figure 1

18 pages, 2602 KiB

Open AccessArticle

Advanced Algorithms in Automatic Generation Control of Hydroelectric Power Plants

by Yury V. Kazantsev, Gleb V. Glazyrin, Alexandra I. Khalyasmaa, Sergey M. Shayk and Mihail A. Kuparev

Mathematics 2022, 10(24), 4809; https://doi.org/10.3390/math10244809 - 17 Dec 2022

Cited by 3 | Viewed by 1630

Abstract

The problem of load distribution between hydraulic units at hydropower plants is a difficult task due to the nonlinearity of hydro turbine characteristics and individual peculiarities of the generation units, in which operating conditions are often different. It is necessary to apply the [...] Read more.

The problem of load distribution between hydraulic units at hydropower plants is a difficult task due to the nonlinearity of hydro turbine characteristics and individual peculiarities of the generation units, in which operating conditions are often different. It is necessary to apply the most up-to-date optimization methods that take into account the nonlinearity of the turbine characteristics. The methods must also consider strict constraints on the operation conditions of the power equipment when searching for the extremum of the objective function specified in the form of equalities and inequalities. When solving the aforementioned optimization problem, the constraints on computing capacities of the digital automatic generation control systems that must operate in real-time mode were taken into account. To solve the optimization task, the interior point method was analyzed and the method of Lagrange multipliers was modified so that it could minimize turbine discharge and active energy losses in the windings of the power generators and unit power transformers. The article presents the simulation results of the developed optimization algorithms and the results of the field tests of the automatic generation control system executing the proposed algorithms. All of the tests showed a fairly high efficiency of the proposed optimization methods in real operation conditions. Full article

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

► Show Figures

Figure 1

18 pages, 11411 KiB

Open AccessArticle

Fracture Process and Failure Mode of Brazilian Discs with Cracks of Different Angles: A Numerical Study

by Xiaoyan Luo, Guoyan Zhao, Peng Xiao and Wengang Zhao

Mathematics 2022, 10(24), 4808; https://doi.org/10.3390/math10244808 - 17 Dec 2022

Viewed by 1152

Abstract

In order to determine the effect of internal cracks on the tensile failure of materials, a hybrid finite–discrete element method was used to analyze the Brazilian disc test with cracks of different angles. When the pre-crack angle is between 0° and 60°, the [...] Read more.

In order to determine the effect of internal cracks on the tensile failure of materials, a hybrid finite–discrete element method was used to analyze the Brazilian disc test with cracks of different angles. When the pre-crack angle is between 0° and 60°, the wing crack is initiated from the pre-crack end. When the pre-crack is 90°, the crack initiated from the pre-crack center. When the pre-crack angle is between 0° and 60°, the maximum principal stress and plastic strain are concentrated at the pre-crack end. When the pre-crack angle is 90°, the maximum principal stress and plastic strain are concentrated in the pre-crack center. As the crack angle increased from 0° to 90°, the failure mode of Brazilian discs with cracks transits from splitting into two parts to splitting into four parts. The influence of crack length is further studied. When the crack length is less than 5 mm, the crack angle has little influence on the disc failure mode; Brazilian discs with cracks of different angles undergoes splitting failure along the loading axis. When the crack length is larger than 5 mm, the crack angle has a great effect on the disc failure mode. Full article

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

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematics, Volume 10, Issue 24 (December-2 2022) – 209 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI