Results 61 to 70 of about 40,161 (298)

Convergence Analysis of the Tau Method for Volterra–Fredholm Integrodifferential Equations With Weakly Singular Kernel

Journal of Applied Mathematics
This work focuses on the analysis of the Volterra–Fredholm integral equation (VFIE) with a weakly singular kernel, which is a transformed form of a partial integrodifferential equation (PIDE) with a weakly singular kernel. We present an approach based on
Javad Shokri, Saeed Pishbin, Ahmed M. Rajab   +2 more
doaj   +1 more source

Re-iterated approximation methods for nonlinear Volterra integral equations

Mathematical Modelling and Analysis
In this article, the Newton-iteration scheme based upon iterated Galerkin operator is applied for solving non-linear Volterra Urysohn integral equations of the second kind for smooth and weakly singular kernels. A one step of improvement by iteration to
Samiran Chakraborty, Kapil Kant, Ritu Nigam, Gnaneshwar Nelakanti   +3 more
doaj   +1 more source

Kneser’s theorem for weak solutions of an integral equation with weakly singular kernel [PDF]

Publications de l'Institut Mathematique, 2005
We prove that the set of all weak solutions of the Volterra integral equation (1) is nonempty, compact and connected.
Dutkiewicz, Aldona, Szufla, Stanisław
openaire   +2 more sources

Atomic Defects in Layered Transition Metal Dichalcogenides for Sustainable Energy Storage and the Intelligent Trends in Data Analytics

Advanced Science, EarlyView.
This review comprehensively summarizes the atomic defects in TMDs for their applications in sustainable energy storage devices, along with the latest progress in ML methodologies for high‐throughput TEM data analysis, offering insights on how ML‐empowered microscopy facilitates bridging structure–property correlation and inspires knowledge for precise ...
Zheng Luo, Ying Yang, Zizhen Fu, Fengqi Liu, Susu Fang, Kele Xu, Shanshan Wang   +6 more
wiley   +1 more source

A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel [PDF]

Journal of Sciences, Islamic Republic of Iran, 2017
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where .
J. Biazar, A. Aasaraai, M. B. Mehrlatifan   +2 more
doaj  

ML Workflows for Screening Degradation‐Relevant Properties of Forever Chemicals

Advanced Science, EarlyView.
The environmental persistence of per‐ and polyfluoroalkyl substances (PFAS) necessitates efficient remediation strategies. This study presents physics‐informed machine learning workflows that accurately predict critical degradation properties, including bond dissociation energies and polarizability.
Pranoy Ray, Andrew R. Castillo, Manoj Kolel‐Veetil, Surya R. Kalidindi   +3 more
wiley   +1 more source

A regularization–discretization strategy for weakly singular Fredholm integral equations: a Tikhonov–Legendre approach

Open Mathematics
This study presents a new computational technique for solving weakly singular Fredholm integral equations of the first kind, based on a regularization–discretization strategy that combines Tikhonov regularization with Legendre spectral projection methods.
Bechouat Tahar, Boussetila Nadjib, Bağlan İrem, Lakhdari Abdelghani, Abdeljawad Thabet   +4 more
doaj   +1 more source

Construction of maximum likelihood estimator in the mixed fractional–fractional Brownian motion model with double long-range dependence

Modern Stochastics: Theory and Applications, 2015
We construct an estimator of the unknown drift parameter $\theta \in \mathbb{R}$ in the linear model \[X_{t}=\theta t+\sigma _{1}{B}^{H_{1}}(t)+\sigma _{2}{B}^{H_{2}}(t),\hspace{0.2778em}t\in [0,T],\] where ${B}^{H_{1}}$ and ${B}^{H_{2}}$ are two ...
Yuliya Mishura, Ivan Voronov
doaj   +1 more source

Transferable Deep Reinforcement Learning With Edge‐Contour‐Depth Fusion for Autonomous Wireless Capsule Endoscopy Navigation

Advanced Science, EarlyView.
This study presents an anatomical landmark‐guided DRL framework for autonomous wireless capsule endoscopy navigation. Using a lightweight edge‐contour‐depth fusion module, it achieves over 97% coverage across diverse gastric anatomies. To ensure reliability, a two‐stage sim‐to‐real pipeline with an adaptive dynamic programming controller mitigates ...
Haoxuan Wu, Haitao Gao, Qingyang Liu, Sishen Yuan, Haiyang Fang, Mingwu Su, Baijia Liang, Yongzun Yang, Long Bai, Wenzhen Dong, Dihong Xie, Shijian Su, Jiewen Lai, Shing Shin Cheng, Zhen Li, Xiuli Zuo, Hongliang Ren   +16 more
wiley   +1 more source

An Extension of the Product Integration Method to L1 with Applications in Astrophysics

Mathematical Modelling and Analysis, 2016
A Fredholm integral equation of the second kind in L1([a, b], C) with a weakly singular kernel is considered. Sufficient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C0 ([a, b],
Laurence Grammont, Mario Ahues, Hanane Kaboul   +2 more
doaj   +1 more source