Results 71 to 80 of about 29,805 (265)

The spectral Galerkin method for the differential operator eigenvalue problems based on a least-squares form and its Schur complement type implementation methods

Results in Applied Mathematics
The differential operator eigenvalue problems often arise in the field of physics and engineering, such as solid band structure, electron orbitals of atoms or molecules, and quantum bound states.
Jiaoxia Huang, Yonghui Qin
doaj   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Explaining the Origin of Negative Poisson's Ratio in Amorphous Networks With Machine Learning

Advanced Intelligent Discovery, EarlyView.
This review summarizes how machine learning (ML) breaks the “vicious cycle” in designing auxetic amorphous networks. By transitioning from traditional “black‐box” optimization to an interpretable “AI‐Physics” closed‐loop paradigm, ML is shown to not only discover highly optimized structures—such as all‐convex polygon networks—but also unveil hidden ...
Shengyu Lu, Xiangying Shen
wiley   +1 more source

On the Perturbed Eigenvalue Problem

Journal of Mathematical Analysis and Applications, 1995
The author considers the perturbed eigenvalue problem \(L(x) v(x)= \lambda(x) v(x)\) near \(0= x\in \mathbb{R}\) with \(L(x)\) a Fredholm operator of index zero. Using the implicit function theorem and the bordering lemma, he derives a necessary and sufficient smoothness condition for the characteristic pairs \((\lambda(x), v(x))\) with eigenvalue ...
openaire   +1 more source

Choptuik Spacetime as an Eigenvalue Problem [PDF]

Physical Review Letters, 1995
Review section rewritten; sign error in equation (4), error concerning non-minimally coupled scalar field, one typo in table corrected, references added. To be published in Phys.
openaire   +3 more sources

Deep Learning–Based Extraction of Promising Material Groups and Common Features from High‐Dimensional Data: A Case of Optical Spectra of Inorganic Crystals

Advanced Intelligent Discovery, EarlyView.
We report a novel interpretation method for deep learning models based on feature extraction and clustering. Applying this method to an atomistic line graph neural network (ALIGNN) model trained on optical absorption spectra of 2,681 inorganic compounds obtained from first‐principles calculations, we successfully identify key factors underlying ...
Akira Takahashi, Yu Kumagai, Arata Takamatsu, Fumiyasu Oba   +3 more
wiley   +1 more source

Robust Reinforcement Learning Control Framework for a Quadrotor Unmanned Aerial Vehicle Using Critic Neural Network

Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.
Quadrotor unmanned aerial vehicle control is critical to maintain flight safety and efficiency, especially when facing external disturbances and model uncertainties. This article presents a robust reinforcement learning control scheme to deal with these challenges.
Yu Cai, Yefeng Yang, Tao Huang, Boyang Li   +3 more
wiley   +1 more source

A one dimensional Hammerstein problem

Electronic Journal of Differential Equations, 1999
Nonlinear equations of the form $L[u]=lambda g(u)$ where $L$ is a linear operator on a function space and $g$ maps $u$ to the composition function $gcirc u$ arise in the theory of spontaneous combustion.
Jun Hua, James L. Moseley
doaj  

EIGENVALUE PROBLEMS FOR SINGULAR ODES [PDF]

Glasgow Mathematical Journal, 2010
AbstractWe investigate eigenvalue intervals for the Dirichlet problem when the nonlinearity may be singular at t = 0 or t = 1. Our approach is based on variational methods and cover both sublinear and superlinear cases. We also study the continuous dependence of solutions on functional parameters.
O'REGAN, DONAL, ORPEL, ALEKSANDRA
openaire   +3 more sources

Sound‐Based Assembly of Magnetically Actuated Soft Robots Toward Enhanced Release of Extracellular Vesicles

Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.
Magnetic soft robots offer promise in biomedicine due to their wireless actuation and rapid response, but current fabrication methods are complex and have limited cellular compatibility. A new, contactless bioassembly strategy using hydrodynamic instabilities is introduced, enabling customizable, centimeter‐scale robots.
Wei Gao, Riccardo Tognato, Micaela Natta, Elena Della Bella, Alessandro Cianciosi, Tiziano Serra   +5 more
wiley   +1 more source