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arXiv 2025年

作者： Zhang, Hao Wang, Qi Sun, Jian Wen, Zhijie Shi, Jun Ying, Shihui The Department of Mathematics School of Science Shanghai University Shanghai200444 China Shanghai Institute of Applied Mathematics and Mechanics The School of Mechanics and Engineering Science Shanghai University Shanghai200072 China The School of Mathematics and Statistics Xi'an Jiaotong University Shaanxi Xi’an710049 China The School of Communication and Information Engineering Shanghai University Shanghai200444 China

Magnetic Resonance Imaging (MRI) is widely used in clinical practice, but suffered from prolonged acquisition time. Although deep learning methods have been proposed to accelerate acquisition and demonstrate promising performance, they rely on high-quality fully-sampled datasets for training in a supervised manner. However, such datasets are time-consuming and expensive-to-collect, which constrains their broader applications. On the other hand, self-supervised methods offer an alternative by enabling learning from under-sampled data alone, but most existing methods rely on further partitioned under-sampled k-space data as model's input for training, resulting in a loss of valuable information. Additionally, their models have not fully incorporated image priors, leading to degraded reconstruction performance. In this paper, we propose a novel re-visible dual-domain self-supervised deep unfolding network to address these issues when only undersampled datasets are available. Specifically, by incorporating re-visible dual-domain loss, all under-sampled k-space data are utilized during training to mitigate information loss caused by further partitioning. This design enables the model to implicitly adapt to all under-sampled k-space data as input. Additionally, we design a deep unfolding network based on Chambolle and Pock Proximal Point Algorithm (DUN-CP-PPA) to achieve end-to-end reconstruction, incorporating imaging physics and image priors to guide the reconstruction process. By employing a Spatial-Frequency Feature Extraction (SFFE) block to capture global and local feature representation, we enhance the model's efficiency to learn comprehensive image priors. Experiments conducted on the fastMRI and IXI datasets demonstrate that our method significantly outperforms state-of-the-art approaches in terms of reconstruction performance. Copyright © 2025, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

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Some fractional-order modeling and analysis of the transmission dynamics together with prevention controls

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The European Physical Journal Special Topics 2024年 1-25页

作者： Guirao, Juan L. G. Jan, Rashid Baleanu, Dumitru Mohammed, Pshtiwan Othman Abdullah, Farah Aini Chorfi, Nejmeddine Department of Applied Mathematics and Statistics Technical University of Cartagena Hospital de Marina Cartagena Spain Department of Civil Engineering Institute of Energy Infrastructure (IEI) College of Engineering Universiti Tenaga Nasional (UNITEN) Kajang Malaysia Mathematics Research Center Near East University TRNC Nicosia Turkey Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Institute of Space Science-Subsidiary of INFLPR Magurele-Bucharest Romania Department of Mathematics College of Education University of Sulaimani Sulaimani Iraq Research and Development Center University of Sulaimani Sulaymaniyah Iraq School of Mathematical Sciences Universiti Sains Malaysia USM Penang Malaysia Department of Mathematics College of Science King Saud University Riyadh Saudi Arabia

The purpose of the present research is to improve our understanding of how coronavirus infection spreads by creating an epidemic model that incorporates isolation and quarantine measures. The dynamics of this viral spread are represented using the Caputo–Fabrizio operator. By analyzing the equilibria of the model and utilizing the next-generation matrix method, we determine the endemic indicator, $${\mathcal {R}}_0$$ . The main findings demonstrate that the equilibrium without infection is locally stable when $${\mathcal {R}}_0$$ is less than one and unstable otherwise. Also, we demonstrate the existence and uniqueness of the solution of our recommended model. In addition to this, we interrogate the solution pathways of the system by varying different factors, aiming to comprehend the intricate transmission of COVID-19 and visualize the crucial factors of the system that can aid public health officials in the control of the spread of infection.

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INVERSION SETS AND QUOTIENT ROOT SYSTEMS

arXiv

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arXiv 2023年

作者： Dimitrov, Ivan Gigliotti, Cole Ossip, Etan Paquette, Charles Wehlau, David Department of Mathematics and Statistics Queen’s University United Kingdom Department of Mathematics University of British Columbia Canada Faculty of Engineering and Applied Science Queen’s University United Kingdom Department of Mathematics and Computer Science Royal Military College of Canada Canada

We provide a recursive description of all decompositions of the positive roots R+ of a quotient root system R into disjoint unions of inversion sets. Our description is type-independent and generalizes the analogous result for type A root systems in [USRA]. The main tool is the notion of an inflation of a subset of a quotient root system. This new notion allows us to treat all root systems (and their quotients) uniformly. We also obtain some numerical results about the number of special decompositions. The new sequences we obtain may be considered as extensions of Catalan *** Codes 17B22 © 2023, CC BY.

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Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference *** II:Higher-Order Schemes

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Numerical mathematics(Theory,Methods and Applications) 2022年第3期15卷 819-850页

作者： M.Esmaeilzadeh R.M.Barron Department of Mechanical Automotive&Materials EngineeringUniversity of WindsorWindsorOntarioN9B 3P4Canada Department of Mathematics&Statistics University of WindsorWindsorOntarioN9B 3P4Canada Department of Mechanical Engineering South Tehran BranchIslamic Azad UniversityTehranP.C:***Iran

Compact higher-order(HO)schemes for a new finite difference method,referred to as the Cartesian cut-stencil FD method,for the numerical solution of the convection-diffusion equation in complex shaped domains have been addressed in this *** Cartesian cut-stencil FD method,which employs 1-D quadratic transformation functions to map a non-uniform(uncut or cut)physical stencil to a uniform computational stencil,can be combined with compact HO Pad´e-Hermitian formulations to produce HO cut-stencil *** modified partial differential equation technique is used to develop formulas for the local truncation error for the cut-stencil HO *** effect of various HO approximations for Neumann boundary conditions on the solution accuracy and global order of convergence are *** numerical results for second-order and compact HO formulations of the Cartesian cut-stencil FD method have been compared for test problems using the method of manufactured solutions.

关键词： Cartesian cut-stencil finite difference method compact higher-order formulation irregular domain Neumann boundary conditions local truncation error

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A study of Cu/Ag nanoparticle shape-augmented heat transfer in Darcy–Brinkman–Forchheimer flow in a square cavity

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Waves in Random and Complex Media 2023年

作者： Mallikarjuna, B. Rathish Kumar, B.V. TEQIP IIT Kanpur Kanpur India Department of Mathematics BMS College of Engineering Bangalore Affiliated to Visvesvaraya Technological University Belaaum India Department of Mathematics and Statistics IIT Kanpur Kanpur India

The present work is an analysis of heat transfer flow phenomena due to the natural convection process in a square enclosure filled with a porous medium containing Cu/Ag water-based nanofluid. Multiphysics faceted Darcy–Brinkman–Forchheimer model is used to govern the flow in a porous medium. Different shapes (sphere, blades, bricks, cylinders, and platelets) of the nanoparticles are considered to examine their influence on heat transfer. The model has been solved by the finite element method. The numerical results have been validated against results from the literature. Computed results have been presented graphically by streamlines, isotherms, local and cumulative Nusselt number plots for various physical parameters, Rayleigh number (Ra), inverse Darcy number ((Formula presented.)), Brinkman effect (Λ), the porosity of the porous medium (Formula presented.) and solid volume fraction of the nanoparticles (Formula presented.). The study pioneers the investigation on the significance of the combined influence of effective viscosity and nanofluid viscosity through the Brinkman effect and reports its importance on nanoparticle shape-based heat transfer augmentation. Cost-effective Cu nanoparticles are shown to augment the heat transfer as achieved by the conventionally preferred Ag nanoparticles. While spherical nanoparticles outperform other shapes in heat transfer augmentation for Brinkman effect (Formula presented.), the blade-shaped nanoparticles dominate when Brinkman effect (Formula presented.). Higher heat transfer rates are noticed for lesser values of the Brinkman effect, high porosity, the maximum volume fraction of the nanoparticles, high Rayleigh number, and low permeability with spherical-shaped nanoparticles than blade-shaped nanoparticles. © 2023 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Silver nanoparticles

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On Multiparameter Spectral Theory of 3-Parameter Aeroelastic Flutter Problems

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IAENG International Journal of Applied mathematics 2023年第4期53卷 1页

作者： Bora, N. Chutia, B. Bhattacharyya, S. Department of Mathematics Dibrugarh University Institute of Engineering and Technology Dibrugarh University Assam Dibrugarh786004 India Department of Mathematics Dibrugarh University Assam Dibrugarh786004 India Department of Agricultural Statistics Biswanath College of Agriculture Assam Biswanath784176 India

In this paper, we consider the aeroelastic flutter problem (AEFP) in terms of matrix equations. We provide a general framework on the spectral theory of three parameter AEFP in tensor product space under the auspices of the techniques of multiparameter eigenvalue problems (MEP) in matrix form. It is to noted that, the AEFP of an undamped system can be converted to a linear singular two parameter eigenvalue problem (2PEP) in double dimension and by quasilinearization technique it can be converted to a linear three parameter eigenvalue problem (3PEP) of the same dimension. The de-facto way to find the numeric of MEP is by solving associated joint generalised eigenvalue problem (GEP) using conventional numerical method, provided the problem being nonsingular. Since the transformed version of AEFP in matrix form is singular, so the usual solution techniques for MEP can not be applied to address AEFP and it necessitates to adopt alternate numerical techniques for the same. In the current paper, it is intended to address singular AEFP under certain assumptions. The paper also serves as a report on the Kronecker product method, so called Delta method developed by Atkinson for finding finite eigenvalues of singular three parameter AEFP. © (2023), (International Association of Engineers). All Rights Reserved.

关键词： Numerical methods

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Trends in citizen influencing willingness to participate in marine debris management and social well-being in Bali metropolitan, Indonesia

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Urban Governance 2024年第4期4卷 362-373页

作者： Suhardono, Sapta Lee, Chun-Hung Suryawan, I Wayan Koko Environmental Sciences Study Program Faculty of Mathematics and Natural Sciences Universitas Sebelas Maret Surakarta 57126 Indonesia Department of Natural Resources and Environmental Studies College of Environmental Studies and Oceanography National Dong Hwa University Taiwan Hualien 97401 Taiwan Department of Environmental Engineering Faculty of Infrastructure Planning Universitas Pertamina Jakarta 12220 Indonesia

In Bali, the high volume of tourists significantly contributes to marine debris, particularly plastics, which threatens the ecological health of beaches and marine life, impacting both tourism and local livelihoods. Effective management is crucial to preserve Bali's natural beauty and sustainability. This study explores the factors influencing the willingness to participate (WTP) in marine debris management among urban communities in the Bali metropolitan area, Indonesia. Utilizing a binary logistic regression model, we examine the impact of key elements for effective marine debris management, risk awareness, learning performance, and higher monthly income and geographic differences between inland and coastal communities. The findings reveal that effective management practices significantly enhance community participation, highlighting the importance of transparency, accountability, and well-organized efforts. Educational initiatives also play a crucial role, with performance in risk awareness and learning showing a marginally significant positive effect on WTP. Conversely, higher income levels negatively influence participation, suggesting a preference for institutional funding over personal contributions. Geographic differences indicate that coastal communities are more inclined to participate than inland communities. These insights provide valuable guidance for policymakers and practitioners in developing strategies to mobilize volunteers, enhance urban resilience, and promote social well-being. By implementing effective management practices, comprehensive educational programs, tailored engagement strategies, and fostering partnerships, urban communities in Bali can become more resilient and actively address environmental challenges. © 2024 The Authors

关键词： Community engagement Debris management Marine sustainability Social well-being Urban resilience

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Young measure relaxation gaps for controllable systems with smooth state constraints

arXiv

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arXiv 2025年

作者： Augier, Nicolas Korda, Milan Rios-Zertuche, Rodolfo LAAS-CNRS Toulouse France Faculty of Electrical Engineering Czech Technical University Prague Czech Republic Department of Mathematics and Statistics UiT The Arctic University Norway

In this article, we tackle the problem of the existence of a gap corresponding to Young measure relaxations for state-constrained optimal control problems. We provide a counterexample proving that a gap may occur in a very regular setting, namely for a smooth controllable system state-constrained to the closed unit ball, provided that the Lagrangian density (i.e., the running cost) is non-convex in the control variables. The example is constructed in the setting of sub-Riemannian geometry with the core ingredient being an unusual admissible curve that exhibits a certain form of resistance to state-constrained approximation. Specifically, this curve cannot be approximated by neighboring admissible curves while obeying the state constraint due to the intricate nature of the dynamics near the boundary of the constraint set. Our example also presents an occupation measure relaxation *** Codes 49Q15 (Primary) Copyright © 2025, The Authors. All rights reserved.

关键词： Constrained optimization

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Exploring the Potential of the Machine Learning Techniques in the Water Quality Assessment: A Review of Applications and Performance

Exploring the Potential of the Machine Learning Techniques i...

引用

International Conference on Advanced engineering, Technology and Applications, ICAETA 2024

作者： Márquez, Fausto Pedro García Al-taie, Ali Hussein Shuaa Zakur, Yahya Asmar Alsadoon, Abeer Flaih, Laith R. Zakoor, Yousif Asmar Ingenium Research Group Universidad Castilla-La Mancha Ciudad Real13071 Spain Department of Mathematics Faculty of Education for Pure Sciences Wasit University Wasit Iraq Department of Statistics Faculty of Mathematical Science University of Mazandaran Babolsar Iran Sydney Australia Sydney Australia Department of Computer Science College of Science Cihan University-Erbil Erbil Iraq Department of Civil Engineering College of Engineering Wasit University Wasit Iraq

ISBN: (纸本)9783031709234

In this review, the application of machine learning (ML) algorithms in water environment research is proficiently explored. The quick increase in data size related to the water environment has necessitated the use of ML for data analysis, classification, and forecasting. Unlike classical models, machine learning models excel in solving complex problems. They have been successfully applied to various aspects of water management and treatment systems, such as construction, simulation, evaluation, water pollution surveillance, controlling, water quality amelioration, and watershed environmental security management. The survey specifically focuses on the evaluation of water quality in diverse water environments, including surface water, drinking water, groundwater, sewage, and seawater. Moreover, potential future implementations of machine learning in water environments are proposed. ML facilitates the detection and prediction of water contamination events, as well as the provision of decision support systems for water resource management. Real-time monitoring of water quality, anomaly detection, and prediction of potential contamination events are among the specific applications of machine learning high-lighted. The review covers the advantages and disadvantages of generally used ML algorithms, with a particular emphasis on new ML techniques that surpass classical methods. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Sewage

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Reproducing kernels and new approaches in compositional data analysis

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 15560-15593页

作者： Binglin Li Changwon Yoon Jeongyoun Ahn Department of Mathematics and Statistics North Carolina A&T State University Greensboro NC Department of Industrial and Systems Engineering Korea Advanced Institute of Science and Technology Daejeon Korea

Compositional data, such as human gut microbiomes, consist of non-negative variables where only the relative values of these variables are available. Analyzing compositional data requires careful treatment of the geometry of the data. A common geometrical approach to understanding such data is through a regular simplex. The majority of existing approaches rely on log-ratio or power transformations to address the inherent simplicial geometry. In this work, based on the key observation that compositional data are projective, we reinterpret the compositional domain as a group quotient of a sphere, leveraging the intrinsic connection between projective and spherical geometry. This interpretation enables us to understand the function spaces on the compositional domain in terms of those on a sphere, and furthermore, to utilize spherical harmonics theory for constructing a compositional Reproducing Kernel Hilbert Space (RKHS). The construction of RKHS for compositional data opens up new research avenues for future methodology developments, particularly introducing well-developed kernel methods to compositional data analysis. We demonstrate the wide applicability of the proposed theoretical framework with examples of nonparametric density estimation, kernel exponential family, and support vector machine for compositional data.

关键词： directional statistics group invariance homogeneous polynomials kernel methods spherical harmonics

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