Mathematics

14 pages, 1238 KiB

Open AccessArticle

Semiparametric Analysis of Additive–Multiplicative Hazards Model with Interval-Censored Data and Panel Count Data

by Tong Wang, Yang Li, Jianguo Sun and Shuying Wang

Mathematics 2024, 12(23), 3667; https://doi.org/10.3390/math12233667 - 22 Nov 2024

In survival analysis, interval-censored data and panel count data represent two prevalent types of incomplete data. Given that, within certain research contexts, the events of interest may simultaneously involve both data types, it is imperative to perform a joint analysis of these data [...] Read more.

In survival analysis, interval-censored data and panel count data represent two prevalent types of incomplete data. Given that, within certain research contexts, the events of interest may simultaneously involve both data types, it is imperative to perform a joint analysis of these data to fully comprehend the occurrence process of the events being studied. In this paper, a novel semiparametric joint regression analysis framework is proposed for the analysis of interval-censored data and panel count data. It is hypothesized that the failure time follows an additive–multiplicative hazards model, while the recurrent events follow a nonhomogeneous Poisson process. Additionally, a gamma-distributed frailty is introduced to describe the correlation between the failure time and the count process of recurrent events. To estimate the model parameters, a sieve maximum likelihood estimation method based on Bernstein polynomials is proposed. The performance of this estimation method under finite sample conditions is evaluated through a series of simulation studies, and an empirical study is illustrated. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data)

15 pages, 355 KiB

Open AccessArticle

Statistical Modeling to Improve Time Series Forecasting Using Machine Learning, Time Series, and Hybrid Models: A Case Study of Bitcoin Price Forecasting

by Moiz Qureshi, Hasnain Iftikhar, Paulo Canas Rodrigues, Mohd Ziaur Rehman and S. A. Atif Salar

Mathematics 2024, 12(23), 3666; https://doi.org/10.3390/math12233666 - 22 Nov 2024

Abstract

Bitcoin (BTC-USD) is a virtual currency that has grown in popularity after its inception in 2008. BTC-USD is an internet communication network that makes using digital money, including digital payments, easy. It offers decentralized clearing of transactions and money supply. This study attempts [...] Read more.

Bitcoin (BTC-USD) is a virtual currency that has grown in popularity after its inception in 2008. BTC-USD is an internet communication network that makes using digital money, including digital payments, easy. It offers decentralized clearing of transactions and money supply. This study attempts to accurately anticipate the BTC-USD prices (Close) using data from September 2023 to September 2024, comprising 390 observations. Four machine learning models—Multi-layer Perceptron, Extreme Learning Machine, Neural Network AutoRegression, and Extreme-Gradient Boost—as well as four time series models—Auto-Regressive Integrated Moving Average, Auto-Regressive, Non-Parametric Auto-Regressive, and Simple Exponential Smoothing models—are used to achieve this end. Various hybrid models are then proposed utilizing these models, which are based on simple averaging of these models. The data-splitting technique, commonly used in comparative analysis, splits the data into training and testing data sets. Through comparison testing with training data sets consisting of 30%, 20%, and 10%, the present work demonstrated that the suggested hybrid model outperforms the individual approaches in terms of error metrics, such as the MAE, RMSE, MAPE, SMAPE, and direction accuracy, such as correlation and the MDA of BTC. Furthermore, the DM test is utilized in this study to measure the differences in model performance, and a graphical evaluation of the models is also provided. The practical implication of this study is that financial analysts have a tool (the proposed model) that can yield insightful information about potential investments. Full article

(This article belongs to the Special Issue Time Series Forecasting for Economic and Financial Phenomena)

33 pages, 522 KiB

Open AccessFeature PaperArticle

Monochromatic Graph Decompositions Inspired by Anti-Ramsey Theory and Parity Constraints

by Yair Caro and Zsolt Tuza

Mathematics 2024, 12(23), 3665; https://doi.org/10.3390/math12233665 - 22 Nov 2024

Abstract

We open here many new tracks of research in anti-Ramsey Theory, considering edge-coloring problems inspired by rainbow coloring and further by odd colorings and conflict-free colorings. Let G be a graph and

F

any given family of graphs. For every integer [...] Read more.

We open here many new tracks of research in anti-Ramsey Theory, considering edge-coloring problems inspired by rainbow coloring and further by odd colorings and conflict-free colorings. Let G be a graph and

F

any given family of graphs. For every integer

n \geq | G |

, let

f (n, G | F)

denote the smallest integer k such that any edge coloring of

K_{n}

with at least k colors forces a copy of G in which each color class induces a member of

F

. Observe that in anti-Ramsey problems, each color class is a single edge, i.e.,

F = {K_{2}}

. Among the many results introduced in this paper, we mention the following. (1) For every graph G, there exists a constant

c = c (G)

such that in any edge coloring of

K_{n}

with at least

c n

colors there is a copy of G in which every vertex v is incident with an edge whose color appears only once among all edges incident with v. (2) In sharp contrast to the above result we prove that if

F

is the class of all odd graphs (having vertices with odd degrees only) then

f (n, K_{k} | F) = (1 + o (1)) ex (n, K_{⌈ k / 2 ⌉})

, which is quadratic for

k \geq 5

. (3) We exactly determine

f (n, G | F)

for small graphs when

F

belongs to several families representing various odd/even coloring constraints. Full article

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

18 pages, 634 KiB

Open AccessArticle

An Efficient Simulated Annealing Algorithm for the Vehicle Routing Problem in Omnichannel Distribution

by Vincent F. Yu, Ching-Hsuan Lin, Renan S. Maglasang, Shih-Wei Lin and Kuan-Fu Chen

Mathematics 2024, 12(23), 3664; https://doi.org/10.3390/math12233664 - 22 Nov 2024

Abstract

A variant of the vehicle routing problem (VRP) known as the Vehicle Routing Problem in Omnichannel Retailing Distribution Systems (VRPO) has recently been introduced in the literature, driven by the increasing adoption of omnichannel logistics in practice. The VRPO scenario involves a large [...] Read more.

A variant of the vehicle routing problem (VRP) known as the Vehicle Routing Problem in Omnichannel Retailing Distribution Systems (VRPO) has recently been introduced in the literature, driven by the increasing adoption of omnichannel logistics in practice. The VRPO scenario involves a large retailer managing several stores, a depot, and a homogenous fleet of vehicles to meet the demands of both stores and online customers. This variant falls within the class of VRPs that consider precedence constraints. Although the vehicle routing problem in omnichannel retailing distribution (VRPO) has been addressed using a few heuristic and metaheuristic approaches, the use of Simulated Annealing (SA) remains largely unexplored in the pickup and delivery problem (PDP) literature, both before and after the rise of omnichannel logistics. This article introduces the Efficient Simulated Annealing (ESA) algorithm, demonstrating its suitability in generating new benchmark solutions for the VRPO. In experiments with sixty large instances, ESA significantly outperformed two previous algorithms, discovering new best-known solutions (BKSs) in fifty-nine out of sixty cases. Additionally, ESA demonstrated superior efficiency in 68.3% of the test cases in terms of reduced computational times, showcasing its higher effectiveness in handling complex VRPO instances Full article

(This article belongs to the Section Engineering Mathematics)

20 pages, 2676 KiB

Open AccessArticle

A Parallel-GPU DGTD Algorithm with a Third-Order LTS Scheme for Solving Multi-Scale Electromagnetic Problems

by Marlon J. Lizarazo and Elson J. Silva

Mathematics 2024, 12(23), 3663; https://doi.org/10.3390/math12233663 - 22 Nov 2024

Abstract

This paper presents a novel parallel-GPU discontinuous Galerkin time domain (DGTD) method with a third-order local time stepping (LTS) scheme for the solution of multi-scale electromagnetic problems. The parallel-GPU implementations were developed based on NVIDIA’s recommendations to guarantee the optimal GPU performance, and [...] Read more.

This paper presents a novel parallel-GPU discontinuous Galerkin time domain (DGTD) method with a third-order local time stepping (LTS) scheme for the solution of multi-scale electromagnetic problems. The parallel-GPU implementations were developed based on NVIDIA’s recommendations to guarantee the optimal GPU performance, and an LTS scheme based on the third-order Runge–Kutta (RK3) method was used to accelerate the solution of multi-scale problems further. This LTS scheme used third-order interpolation polynomials to ensure the continuity of the time solution. The numerical results indicate that the strategy with the parallel-GPU DGTD and LTS maintains the order of precision of standard global time stepping (GTS) and reduces the execution time by about 78% for a complex multi-scale electromagnetic scattering problem. Full article

(This article belongs to the Special Issue Advances in Computational Electromagnetics and Its Applications)

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13 pages, 245 KiB

Open AccessArticle

Strong Convergence of Truncated EM Method for Stochastic Volterra Integral Differential Equations with Hölder Diffusion Coefficients

by Juanting Feng and Qimin Zhang

Mathematics 2024, 12(23), 3662; https://doi.org/10.3390/math12233662 - 22 Nov 2024

Abstract

The strong convergence of numerical solutions is studied in this paper for stochastic Volterra integral differential equations (SVIDEs) with a Hölder diffusion coefficient using the truncated Euler–Maruyama method. Firstly, the numerical solutions of SVIDEs are obtained based on the Euler–Maruyama method. Then, the [...] Read more.

The strong convergence of numerical solutions is studied in this paper for stochastic Volterra integral differential equations (SVIDEs) with a Hölder diffusion coefficient using the truncated Euler–Maruyama method. Firstly, the numerical solutions of SVIDEs are obtained based on the Euler–Maruyama method. Then, the pth moment boundedness and strong convergence of truncated the Euler–Maruyama numerical solutions are proven under the local Lipschitz condition and the Khasminskii-type condition. Finally, the convergence rate of the truncated Euler–Maruyama method of the numerical solutions is also discussed under some suitable assumptions. Full article

17 pages, 823 KiB

Open AccessArticle

Feature Optimization and Dropout in Genetic Programming for Data-Limited Image Classification

by Chan Min Lee, Chang Wook Ahn and Man-Je Kim

Mathematics 2024, 12(23), 3661; https://doi.org/10.3390/math12233661 - 22 Nov 2024

Abstract

Image classification in data-limited environments presents a significant challenge, as collecting and labeling large image datasets in real-world applications is often costly and time-consuming. This has led to increasing interest in developing models under data-constrained conditions. This paper introduces the Feature Optimization and [...] Read more.

Image classification in data-limited environments presents a significant challenge, as collecting and labeling large image datasets in real-world applications is often costly and time-consuming. This has led to increasing interest in developing models under data-constrained conditions. This paper introduces the Feature Optimization and Dropout in Genetic Programming (FOD-GP) framework, which addresses this issue by leveraging Genetic Programming (GP) to evolve models automatically. FOD-GP incorporates feature optimization and adaptive dropout techniques to improve overall performance. Experimental evaluations on benchmark datasets, including CIFAR10, FMNIST, and SVHN, demonstrate that FOD-GP improves training efficiency. In particular, FOD-GP achieves up to a 12% increase in classification accuracy over traditional methods. The effectiveness of the proposed framework is validated through statistical analysis, confirming its practicality for image classification. These findings establish a foundation for future advancements in data-limited and interpretable machine learning, offering a scalable solution for complex classification tasks. Full article

(This article belongs to the Special Issue Evolutionary Computation for Feature Selection and Dimensionality Reduction)

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33 pages, 368 KiB

Open AccessArticle

Embedding the Different Families of Fuzzy Sets into Banach Spaces by Using Cauchy Sequences

by Hsien-Chung Wu

Mathematics 2024, 12(23), 3660; https://doi.org/10.3390/math12233660 - 22 Nov 2024

Abstract

The family

F (U)

of all fuzzy sets in a normed space cannot be a vector space. This deficiency affects its application to practical problems. The topics of functional analysis and nonlinear analysis in mathematics are based on vector spaces. Since [...] Read more.

The family

F (U)

of all fuzzy sets in a normed space cannot be a vector space. This deficiency affects its application to practical problems. The topics of functional analysis and nonlinear analysis in mathematics are based on vector spaces. Since these two topics have been well developed such that their tools can be used to solve practical economics and engineering problems, lacking a vector structure for the family

F (U)

diminishes its applications to these kinds of practical problems when fuzzy uncertainty has been detected in a real environment. Embedding the whole family

F (U)

into a Banach space is still not possible. However, it is possible to embed some interesting and important subfamilies of

F (U)

into some suitable Banach spaces. This paper presents the concrete and detailed structures of these kinds of Banach spaces such that their mathematical structures can penetrate the core of practical economics and engineering problems in fuzzy environments. The important issue of uniqueness for these Banach spaces is also addressed via the concept of isometry. Full article

(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)

10 pages, 241 KiB

Open AccessArticle

Disaffinity Vectors on a Riemannian Manifold and Their Applications

by Sharief Deshmukh, Amira Ishan and Bang-Yen Chen

Mathematics 2024, 12(23), 3659; https://doi.org/10.3390/math12233659 - 22 Nov 2024

Abstract

A disaffinity vector on a Riemannian manifold

(M, g)

is a vector field whose affinity tensor vanishes. In this paper, we observe that nontrivial disaffinity functions offer obstruction to the topology of M and show that the existence of a [...] Read more.

A disaffinity vector on a Riemannian manifold

(M, g)

is a vector field whose affinity tensor vanishes. In this paper, we observe that nontrivial disaffinity functions offer obstruction to the topology of M and show that the existence of a nontrivial disaffinity function on M does not allow M to be compact. A characterization of the Euclidean space is also obtained by using nontrivial disaffinity functions. Further, we study properties of disaffinity vectors on M and prove that every Killing vector field is a disaffinity vector. Then, we prove that if the potential field

ζ

of a Ricci soliton

(M, g, ζ, λ)

is a disaffinity vector, then the scalar curvature is constant. As an application, we obtain conditions under which a Ricci soliton

(M, g, ζ, λ)

is trivial. Finally, we prove that a Yamabe soliton

(M, g, ξ, λ)

with a disaffinity potential field

ξ

is trivial. Full article

(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications)

12 pages, 365 KiB

Open AccessArticle

On Unicyclic Graphs with a Given Number of Pendent Vertices or Matching Number and Their Graphical Edge-Weight-Function Indices

by Akbar Ali, Abdulaziz M. Alanazi, Taher S. Hassan and Yilun Shang

Mathematics 2024, 12(23), 3658; https://doi.org/10.3390/math12233658 - 22 Nov 2024

Abstract

Consider a unicyclic graph G with edge set

E (G)

. Let

f

be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G [...] Read more.

Consider a unicyclic graph G with edge set

E (G)

. Let

f

be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G is defined as

I_{f} (G) = \sum_{x y \in E (G)} f (d_{G} (x), d_{G} (y))

, where

d_{G} (x)

denotes the degree a vertex x in G. This paper determines optimal bounds for

I_{f} (G)

in terms of the order of G and a parameter

z

, where

z

is either the number of pendent vertices of G or the matching number of G. The paper also fully characterizes all unicyclic graphs that achieve these bounds. The function

f

must satisfy specific requirements, which are met by several popular indices, including the Sombor index (and its reduced version), arithmetic–geometric index, sigma index, and symmetric division degree index. Consequently, the general results obtained provide bounds for several well-known indices. Full article

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11 pages, 292 KiB

Open AccessArticle

Cyclic Structure, Vertex Degree and Number of Linear Vertices in Minimal Strong Digraphs

by Miguel Arcos-Argudo, Jesús Lacalle and Luis M. Pozo-Coronado

Mathematics 2024, 12(23), 3657; https://doi.org/10.3390/math12233657 - 22 Nov 2024

Abstract

Minimal Strong Digraphs (MSDs) can be regarded as a generalization of the concept of tree to directed graphs. Their cyclic structure and some spectral properties have been studied in several articles. In this work, we further study some properties of MSDs that have [...] Read more.

Minimal Strong Digraphs (MSDs) can be regarded as a generalization of the concept of tree to directed graphs. Their cyclic structure and some spectral properties have been studied in several articles. In this work, we further study some properties of MSDs that have to do with bounding the length of the longest cycle (regarding the number of linear vertices, or the maximal in- or outdegree of vertices); studying whatever consequences from the spectral point of view; and giving some insight about the circumstances in which an efficient algorithm to find the longest cycle contained in an MSD can be formulated. Among other properties, we show that the number of linear vertices contained in an MSD is greater than or equal to the maximal (respectively minimal) in- or outdegree of any vertex of the MSD and that the maximal length of a cycle contained in an MSD is lesser than or equal to

2 n - m

where

n, m

are the order and the size of the MSD, respectively; we find a bound for the coefficients of the characteristic polynomial of an MSD, and finally, we prove that computing the longest cycle contained in an MSD is an NP-hard problem. Full article

(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)

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32 pages, 6565 KiB

Open AccessArticle

Sparse Feature-Weighted Double Laplacian Rank Constraint Non-Negative Matrix Factorization for Image Clustering

by Hu Ma, Ziping Ma, Huirong Li and Jingyu Wang

Mathematics 2024, 12(23), 3656; https://doi.org/10.3390/math12233656 - 22 Nov 2024

Abstract

As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide [...] Read more.

As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide the decomposition process, using fixed data graphs and feature graphs to capture relationships between data points and features. However, these fixed graphs may limit the model’s expressiveness. Additionally, many NMF variants face challenges when dealing with complex data distributions and are vulnerable to noise and outliers. To overcome these challenges, we propose a novel method called sparse feature-weighted double Laplacian rank constraint non-negative matrix factorization (SFLRNMF), along with its extended version, SFLRNMTF. These methods adaptively construct more accurate data similarity and feature similarity graphs, while imposing rank constraints on the Laplacian matrices of these graphs. This rank constraint ensures that the resulting matrix ranks reflect the true number of clusters, thereby improving clustering performance. Moreover, we introduce a feature weighting matrix into the original data matrix to reduce the influence of irrelevant features and apply an

L_{2,1 / 2}

norm sparsity constraint in the basis matrix to encourage sparse representations. An orthogonal constraint is also enforced on the coefficient matrix to ensure interpretability of the dimensionality reduction results. In the extended model (SFLRNMTF), we introduce a double orthogonal constraint on the basis matrix and coefficient matrix to enhance the uniqueness and interpretability of the decomposition, thereby facilitating clearer clustering results for both rows and columns. However, enforcing double orthogonal constraints can reduce approximation accuracy, especially with low-rank matrices, as it restricts the model’s flexibility. To address this limitation, we introduce an additional factor matrix R, which acts as an adaptive component that balances the trade-off between constraint enforcement and approximation accuracy. This adjustment allows the model to achieve greater representational flexibility, improving reconstruction accuracy while preserving the interpretability and clustering clarity provided by the double orthogonality constraints. Consequently, the SFLRNMTF approach becomes more robust in capturing data patterns and achieving high-quality clustering results in complex datasets. We also propose an efficient alternating iterative update algorithm to optimize the proposed model and provide a theoretical analysis of its performance. Clustering results on four benchmark datasets demonstrate that our method outperforms competing approaches. Full article

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14 pages, 1614 KiB

Open AccessArticle

Solving Nonlinear Equation Systems via a Steffensen-Type Higher-Order Method with Memory

by Shuai Wang, Haomiao Xian, Tao Liu and Stanford Shateyi

Mathematics 2024, 12(23), 3655; https://doi.org/10.3390/math12233655 - 22 Nov 2024

Abstract

This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The [...] Read more.

This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The resulting order is

\sqrt{5} + 2

, utilizing the identical number of functional evaluations as the solver without memory, thereby demonstrating a higher computational index of efficiency. Finally, we illustrate the advantages of the proposed scheme with memory through various test problems. Full article

(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)

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31 pages, 11738 KiB

Open AccessArticle

Computational Evaluation of Heat and Mass Transfer in Cylindrical Flow of Unsteady Fractional Maxwell Fluid Using Backpropagation Neural Networks and LMS

by Waqar Ul Hassan, Khurram Shabbir, Muhammad Imran Khan and Liliana Guran

Mathematics 2024, 12(23), 3654; https://doi.org/10.3390/math12233654 - 21 Nov 2024

Abstract

Fractional calculus plays a pivotal role in modern scientific and engineering disciplines, providing more accurate solutions for complex fluid dynamics phenomena due to its non-locality and inherent memory characteristics. In this study, Caputo’s time fractional derivative operator approach is employed for heat and [...] Read more.

Fractional calculus plays a pivotal role in modern scientific and engineering disciplines, providing more accurate solutions for complex fluid dynamics phenomena due to its non-locality and inherent memory characteristics. In this study, Caputo’s time fractional derivative operator approach is employed for heat and mass transfer modeling in unsteady Maxwell fluid within a cylinder. Governing equations within a cylinder involve a system of coupled, nonlinear fractional partial differential equations (PDEs). A machine learning technique based on the Levenberg–Marquardt scheme with a backpropagation neural network (LMS-BPNN) is employed to evaluate the predicted solution of governing flow equations up to the required level of accuracy. The numerical data sheet is obtained using series solution approach Homotopy perturbation methods. The data sheet is divided into three portions i.e.,

80 %

is used for training,

10 %

for validation, and

10 %

for testing. The mean-squared error (MSE), error histograms, correlation coefficient (R), and function fitting are computed to examine the effectiveness and consistency of the proposed machine learning technique i.e., LMS-BPNN. Moreover, additional error metrics, such as R-squared, residual plots, and confidence intervals, are incorporated to provide a more comprehensive evaluation of model accuracy. The comparison of predicted solutions with LMS-BPNN and an approximate series solution are compared and the goodness of fit is found. The momentum boundary layer became higher and higher as there was an enhancement in the value of Caputo, fractional order α = 0.5 to α = 0.9. Higher thermal boundary layer (TBL) profiles were observed with the rising value of the heat source. Full article

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

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22 pages, 7564 KiB

Open AccessArticle

Computational Modeling of Natural Convection in Nanofluid-Saturated Porous Media: An Investigation into Heat Transfer Phenomena

by Janja Kramer Stajnko, Jure Ravnik, Renata Jecl and Matjaž Nekrep Perc

Mathematics 2024, 12(23), 3653; https://doi.org/10.3390/math12233653 - 21 Nov 2024

Abstract

A numerical study was carried out to analyze the phenomenon of natural convection in a porous medium saturated with nanofluid. In the study, the boundary element method was used for computational modeling. The fluid flow through a porous matrix is described using the [...] Read more.

A numerical study was carried out to analyze the phenomenon of natural convection in a porous medium saturated with nanofluid. In the study, the boundary element method was used for computational modeling. The fluid flow through a porous matrix is described using the Darcy–Brinkman–Forchheimer momentum equation. In addition, a mathematical model for nanofluids was used, which follows a single-phase approach and assumes that the nanoparticles within a fluid can be treated as an independent fluid with effective properties. A combination of single- and sub-domain boundary element methods was used to solve the relevant set of partial differential equations. The method was originally developed for pure flow scenarios, but also proves to be effective in the context of fluid flow through porous media. The results are calculated for the case of two- and three-dimensional square cavities. In addition to various values of dimensionless control parameters, including the porous Rayleigh number (Ra_p), Darcy number (Da), porosity (ϕ) and nanoparticle volume fractions (φ), the effects of the inclination angle of the cavity on the overall heat transfer (expressed by the Nusselt number (Nu)) and fluid flow characteristics were investigated. The results indicate a pronounced dependence of the overall heat transfer on the introduction of nanoparticles and inclination angle. The heat transfer in a two-dimensional cavity is increased for higher values of Darcy number in the conduction flow regime, while it is suppressed for lower values of Darcy number in the Darcy flow regime. In the case of a three-dimensional cavity, increasing the volume fraction of nanoparticles leads to a decrease in heat transfer, and furthermore, increasing the inclination angle of the cavity considerably weakens the buoyancy flow. Full article

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

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55 pages, 4094 KiB

Open AccessFeature PaperArticle

A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions V: The Case of the Open Newton–Cotes Differential Formulae

by Theodore E. Simos

Mathematics 2024, 12(23), 3652; https://doi.org/10.3390/math12233652 - 21 Nov 2024

Abstract

The author has just published a theory on first-order differential equations that accounts for the phase-lag and amplification-factor calculations using explicit, implicit, and backward differentiation multistep methods. Eliminating the phase-lag and amplification-factor derivatives, his presentation delves into how the techniques’ effectiveness changes. The [...] Read more.

The author has just published a theory on first-order differential equations that accounts for the phase-lag and amplification-factor calculations using explicit, implicit, and backward differentiation multistep methods. Eliminating the phase-lag and amplification-factor derivatives, his presentation delves into how the techniques’ effectiveness changes. The theory for determining the phase lag and amplification factor, initially established for explicit multistep techniques, will be extended to the Open Newton–Cotes Differential Formulae in this work. The effect of the derivatives of these variables on the efficiency of these calculations will be studied. The novel discovered approach’s symplectic form will be considered next. The discussion of numerical experiment findings and some conclusions on the existing methodologies will conclude in this section. Full article

(This article belongs to the Section Mathematical Physics)

18 pages, 346 KiB

Open AccessFeature PaperArticle

Pinching Results for Submanifolds in Lorentzian–Sasakian Manifolds Endowed with a Semi-Symmetric Non-Metric Connection

by Mohammed Mohammed, Ion Mihai and Andreea Olteanu

Mathematics 2024, 12(23), 3651; https://doi.org/10.3390/math12233651 - 21 Nov 2024

Abstract

We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space [...] Read more.

We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space form. Full article

(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)

17 pages, 3307 KiB

Open AccessArticle

MCADNet: A Multi-Scale Cross-Attention Network for Remote Sensing Image Dehazing

by Tao Tao, Haoran Xu, Xin Guan and Hao Zhou

Mathematics 2024, 12(23), 3650; https://doi.org/10.3390/math12233650 - 21 Nov 2024

Abstract

Remote sensing image dehazing (RSID) aims to remove haze from remote sensing images to enhance their quality. Although existing deep learning-based dehazing methods have made significant progress, it is still difficult to completely remove the uneven haze, which often leads to color or [...] Read more.

Remote sensing image dehazing (RSID) aims to remove haze from remote sensing images to enhance their quality. Although existing deep learning-based dehazing methods have made significant progress, it is still difficult to completely remove the uneven haze, which often leads to color or structural differences between the dehazed image and the original image. In order to overcome this difficulty, we propose the multi-scale cross-attention dehazing network (MCADNet), which offers a powerful solution for RSID. MCADNet integrates multi-kernel convolution and a multi-head attention mechanism into the U-Net architecture, enabling effective multi-scale information extraction. Additionally, we replace traditional skip connections with a cross-attention-based gating module, enhancing feature extraction and fusion across different scales. This synergy enables the network to maximize the overall similarity between the restored image and the real image while also restoring the details of the complex texture areas in the image. We evaluate MCADNet on two benchmark datasets, Haze1K and RICE, demonstrating its superior performance. Ablation experiments further verify the importance of our key design choices in enhancing dehazing effectiveness. Full article

(This article belongs to the Special Issue Image Processing and Machine Learning with Applications)

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19 pages, 1774 KiB

Open AccessArticle

Solution of Internal Forces in Statically Indeterminate Structures Under Localized Distributed Moments

by Pengyun Wei, Junhong Hu, Haizhong Man and Shunjun Hong

Mathematics 2024, 12(23), 3649; https://doi.org/10.3390/math12233649 - 21 Nov 2024

Abstract

Classical methods for manually solving internal forces in statically indeterminate structures mainly include force and displacement methods. While the force method involves substantial work when solving the internal forces of structures with higher degrees of indeterminacy, the displacement method offers a fixed and [...] Read more.

Classical methods for manually solving internal forces in statically indeterminate structures mainly include force and displacement methods. While the force method involves substantial work when solving the internal forces of structures with higher degrees of indeterminacy, the displacement method offers a fixed and easily understood approach. However, the displacement method requires prior knowledge of load constant formulas. Common methods for deriving load constant formulas include the force method, virtual beam method, and energy method. Nevertheless, deriving load constant formulas for localized distributed moments using these methods proves to be highly challenging. This study aims to derive load constant formulas for localized distributed moments. Firstly, the load constant formula for a single concentrated moment is derived using the formula for a single concentrated force. Then, the load constant formulas for localized uniform moments and localized linearly distributed moments are derived via the integral method, leveraging the load constant formula for a single concentrated moment. This approach addresses the problem of solving internal forces in statically indeterminate structures under distributed moments via the displacement method. Finally, the proposed approach is verified using three typical examples. The promotion of the research results in this article in teaching can deepen students’ understanding of load constants and the displacement method, enrich teaching content, and have certain engineering applications and teaching practical significance. Full article

(This article belongs to the Special Issue Progress in Computational and Applied Mechanics)

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