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Performance of heat transfer in a porous square cavity filled with TiO2–H2O nanofluid by considering the impacts of magnetic field and heat absorption/generation with shape effects

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International Journal of Ambient Energy 2025年第1期46卷

作者： Santhosh, N. Subramanyam Reddy, A. Sivaraj, R. Rushi Kumar, B. Department of Mathematics School of Advanced Sciences Vellore Institute of Technology Vellore India Department of Mathematics and Statistics School of Applied Science and Humanities Vignan's Foundation for Science Technology and Research Andhra Pradesh Guntur India Department of Mathematics and Computing Dr B R Ambedkar National Institute of Technology Punjab Jalandhar India

This research aims to optimise the fluid flow and heat transfer features of a porous square cavity filled with (Formula presented.) (titanium oxide-water) nanoliquid under the influence of magnetic field and the heat source or sink. The non-dimensional version of partial differential equations is solved using the marker-and-cell technique (MAC) and the finite difference methodology. The left and right walls are adiabatic. The top wall is cooled, and the bottom wall is heated completely. Spherical (Formula presented.) and non-spherical shapes (hexahedron, tetrahedron, column and lamina) nanoparticles are utilised to examine the optimal heat transference and fluid circulations within the enclosure. The impacts are graphically visualised and discussed with the following parameters nanoparticles volume fraction (Formula presented.), heat source or sink (Q), Darcy number (Da), Rayleigh number (Ra), and Hartmann number (Ha). Of the four non-spherical configurations of nanoparticles, lamina nanoparticles provide the best thermal transference and fluid velocity inside the cavity. The average heat transfer rate improved by (Formula presented.) when (Formula presented.) nanoparticles were added to the base fluid. The maximum heat transmission rate is provided by nanoparticles that are lamina-shaped. © 2025 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Rayleigh number

A SHORT PROOF OF ISSERLIS’ THEOREM

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arXiv 2025年

作者： Munthe-Kaas, Hans Z. Verdier, Olivier Vilmart, Gilles Department of Mathematics and Statistics UiT – The Arctic University of Norway Tromsø Norway Department of Mathematics University of Bergen Bergen Norway Department of Computing Electrical Engineering and Mathematical Sciences Western Norway Norway University of Applied Sciences Bergen Norway Section of Mathematics University of Geneva Switzerland

We show that Isserlis’ theorem follows as a corollary to the invariant tensor theorem for isotropic *** Codes Primary: 60C05, 15A72, Secondary: 41A58, 60H35 Copyright © 2025, The Authors. All rights reserved.

关键词： Tensors

Artificial intelligent approach for flow stability in Eyring Powell hybrid nanofluids via porous shrinking sheets

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Journal of Molecular Liquids 2025年 422卷

作者： Fatima, Nahid Kouki, Marouan Khan, Muhammad Imran Amjad, Arslan Bin Asghar, Zaheer Zeeshan, Ahmad Ijaz, Nouman Department of Mathematics and Sciences Prince Sultan University Riyadh11586 Saudi Arabia Department of Information System Faculty of Computing and Information Technology Northern Border University Rafha Saudi Arabia Department of Mathematics and Statistics International Islamic University Islamabad 44000 Pakistan Centre for Mathematical Sciences Pakistan Institute of Engineering and Applied Sciences Nilore Islamabad45650 Pakistan Department of Physics and Applied Mathematics Pakistan Institute of Engineering and Applied Sciences Nilore Islamabad45650 Pakistan Department of Mathematics College of Science Korea University 145 Anam-ro Seongbuk-gu Seoul02841 Korea Republic of Department of Mathematics and Statistics Punjab Group of Colleges G.T. Road Jada Jhelum49600 Pakistan

This study aims to analyze flow stability using a computational intelligence technique that integrates a Levenberg-Marquardt approach utilizing artificial intelligence implemented through a backpropagation neural network. AI-based LMS-BPNN approach is utilized to examine the flow behavior of Eyring Powell hybrid nanofluid over a porous shrinking sheet. By applying skillful transformations, a set of ordinary differential equations is obtained from the partial differential equations that describe the hybrid nanofluid. Scenarios 1–5 illustrate how the built-in MATLAB function, bvp4c, solves ordinary differential equations systems by carefully modifying input parameters to get the initial or reference solution. The numerical data was split into three groups: 10 % for testing, 10 % for validation, and 80 % for training. The LMS-BPNN was used to find approximate solutions for these scenarios. To verify the effectiveness and reliability of LMS-BPNN, we employed regression analysis, error metrics, and correlation index (R)-based fitness curves. In each scenario, the temperature and velocity profiles gradually approached the boundary conditions as expected. The flow performance outcomes for the dual solution (Cfx and Nux) are also analyzed using the LMS-BPNN method. The perturbation scheme is applied to the boundary layer problem to obtain the eigenvalues problem. The unsteady solution f(η,τ) converges to steady solution fo(η) for τ→∞ when γ≥0. However, an unsteady solution f(η,τ) diverges to a steady solution fo(η) for τ→∞ when γ © 2025 Elsevier B.V.

关键词： Eigenvalues and eigenfunctions

Learning with Noisy Labels: the Exploration of Error Bounds in Classification

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arXiv 2025年

作者： Liu, Haixia Li, Boxiao Yang, Can Wang, Yang School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan China Department of Mathematics The Hong Kong University of Science and Technology Clear Water Bay China

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the presence of noisy labels is of considerable practical significance. In this paper, we focus on the error bounds of excess risks for classification problems with noisy labels within deep learning frameworks. We begin by exploring loss functions with noise-tolerant properties, ensuring that the empirical minimizer on noisy data aligns with that on the true data. Next, we estimate the error bounds of the excess risks, expressed as a sum of statistical error and approximation error. We estimate the statistical error on a dependent (mixing) sequence, bounding it with the help of the associated independent block sequence. For the approximation error, we first express the classifiers as the composition of the softmax function and a continuous function from [0, 1]d to RK. The main task is then to estimate the approximation error for the continuous function from [0, 1]d to RK. Finally, we focus on the curse of dimensionality based on the low-dimensional manifold assumption. Copyright © 2025, The Authors. All rights reserved.

关键词： Risk assessment

Kink movement on a periodic background

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Physical Review E 2025年第2期111卷 024203-024203页

作者： Tomasz Dobrowolski Jacek Gatlik Panayotis G. Kevrekidis Department of Computer Physics and Quantum Computing University of the National Education Commission in Krakow Podchorążych 2 30-084 Cracow Poland AGH University of Krakow Faculty of Physics and Applied Computer Science 30-059 Krakow Poland Department of Mathematics and Statistics University of Massachusetts Amherst Massachusetts 01003-4515 USA

The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models featuring very good agreement with the original field-theoretic partial differential equation are constructed, including in the nonperturbative region and for relativistic velocities. The numerical solutions of the sG model describing the evolution of the kink in the presence of a barrier as well as in the case of a periodic heterogeneity under the potential additional influence of a switched bias current and/or dissipation were obtained. The results of the field equation and the effective models were favorably compared. The effect of the choice of initial conditions in the field model on the agreement of the results with the effective model is also discussed.

关键词： sine-Gordon equation

Subtree distances, tight spans and diversities

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arXiv 2025年

作者： Bryant, David Huber, Katharina T. Moulton, Vincent Spillner, Andreas Department of Mathematics and Statistics University of Otago Dunedin New Zealand School of Computing Sciences University of East Anglia NorwichNR4 7TJ United Kingdom Merseburg University of Applied Sciences Merseburg06217 Germany

Metric embeddings are central to metric theory and its applications. Here we consider embeddings of a different sort: maps from a set to subsets of a metric space so that distances between points are approximated by minimal distances between subsets. Our main result is a characterization of when a set of distances d(x, y) between elements in a set X have a subtree representation, a real tree T and a collection {Sx}x-X of subtrees of T such that d(x, y) equals the length of the shortest path in T from a point in Sx to a point in Sy for all x, y ∈ X. The characterization was first established for finite X by Hirai (2006) using a tight span construction defined for distance spaces, metric spaces without the triangle inequality. To extend Hirai's result beyond finite X we establish fundamental results of tight span theory for general distance spaces, including the surprising observation that the tight span of a distance space is hyperconvex. We apply the results to obtain the first characterization of when a diversity - a generalization of a metric space which assigns values to all finite subsets of X, not just to pairs - has a tight span which is *** Codes 05C12, 54E35 © 2025, CC BY.

关键词： Trees (mathematics)

Automated Ensemble Multimodal Machine Learning for Healthcare

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IEEE Journal of Biomedical and Health Informatics 2025年 PP卷 PP页

作者： Imrie, Fergus Denner, Stefan Brunschwig, Lucas S. Maier-Hein, Klaus Van Der Schaar, Mihaela University of Oxford Department of Statistics Oxford United Kingdom Heidelberg University Faculty of Mathematics and Computer Science Germany École Polytechnique Fédérale de Lausanne Switzerland Division of Medical Image Computing Germany Heidelberg University Hospital Pattern Analysis and Learning Group Department of Radiation Oncology Germany Heidelberg Germany University of Cambridge Department of Applied Mathematics and Theoretical Physics United Kingdom

The application of machine learning in medicine and healthcare has led to the creation of numerous diagnostic and prognostic models. However, despite their success, current approaches generally issue predictions using data from a single modality. This stands in stark contrast with clinician decision-making which employs diverse information from multiple sources. While several multimodal machine learning approaches exist, significant challenges in developing multimodal systems remain that are hindering clinical adoption. In this paper, we introduce a multimodal framework, AutoPrognosis-M, that enables the integration of structured clinical (tabular) data and medical imaging using automated machine learning. AutoPrognosis-M incorporates 17 imaging models, including convolutional neural networks and vision transformers, and three distinct multimodal fusion strategies. In an illustrative application using a multimodal skin lesion dataset, we highlight the importance of multimodal machine learning and the power of combining multiple fusion strategies using ensemble learning. We have open-sourced our framework as a tool for the community and hope it will accelerate the uptake of multimodal machine learning in healthcare and spur further innovation. © 2013 IEEE.

关键词： Adversarial machine learning

A FOUR-FIELD MIXED FORMULATION FOR INCOMPRESSIBLE FINITE ELASTICITY

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arXiv 2025年

作者： Fu, Guosheng Neunteufel, Michael Schöberl, Joachim Zdunek, Adam Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Fariborz Maseeh Department of Mathematics and Statistics Portland State University 1825 SW Broadway PortlandOR97201 United States Institute of Analysis and Scientific Computing TU Wien Wiedner Hauptstr. 8-10 WienA-1040 Austria HB Berrit Solhemsbackarna 73 Spånga SE-163 56 Sweden

In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations [12], involving normal velocity and tangential-normal stress continuous fields, to incompressible finite elasticity. By means of the three-field Hu–Washizu principle, introducing the displacement gradient and 1st Piola–Kirchhoff stress tensor as additional fields, we circumvent the inversion of the constitutive law. We lift the arising distributional derivatives of the displacement gradient to a regular auxiliary displacement gradient field. Static condensation can be applied at the element level, providing a global pure displacement problem to be solved. We present a stabilization motivated by Hybrid Discontinuous Galerkin methods. A solving algorithm is discussed, which asserts the solvability of the arising linearized subproblems for problems with physically positive eigenvalues. The excellent performance of the proposed method is corroborated by several numerical *** Codes 74S05 (Primary) 74B20 (Secondary) Copyright © 2025, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

An Inertial Spectral Conjugate Gradient Method for Monotone Nonlinear Equations With Applications

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Mathematical Methods in the applied Sciences 2025年

作者： Abdullahi, Muhammad Pan, Kejia Bala Abubakar, Auwal Sani Halilu, Abubakar School of Mathematics and Statistics HNP-LAMA Central South University Hunan Changsha China Mathematical Innovation and Applications Research Group Department of Mathematics Sule Lamido University Jigawa State Kafin Hausa Nigeria Department of Art and Science George Mason University Incheon Yeonsu-gu Korea Republic of Numerical Optimization Research Group Department of Mathematical Sciences Faculty of Physical Sciences Bayero University Kano Nigeria Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Medunsa Pretoria South Africa Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Kuala Terengganu Malaysia

This paper introduces an inertial spectral algorithm for solving monotone nonlinear equations, building upon prior developments in spectral methods for unconstrained optimization problems. Previous approaches introduced new spectral parameters and addressed such problems using a modified secant condition and quasi-Newton directions. We modify the search direction and integrates an inertial technique to improve numerical efficiency. The proposed method consistently ensures that the search direction satisfies the sufficient descent property independent of the method's line-search. We establish global convergence and a linear convergence rate under some standard assumptions. Extensive numerical experiments demonstrate the algorithm's strong performance, especially for large-scale problems. We also showcase its practical applications in logistic regression, a key model in data analysis, and sparse signal recovery, a prominent area in signal processing. The results emphasize the method's superior efficiency and effectiveness in these fields. © 2025 John Wiley & Sons Ltd.

关键词： Nonlinear equations