Results 71 to 80 of about 54,244 (231)

Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems

International Journal for Numerical Methods in Engineering, Volume 126, Issue 12, 30 June 2025.
ABSTRACT Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous‐time analog to discrete neural networks. Despite their promise, deploying neural ODEs in practical applications often encounters the challenge of stiffness, a condition where ...
Matteo Caldana, Jan S. Hesthaven
wiley   +1 more source

Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumps

Қарағанды университетінің хабаршысы. Математика сериясы, 2018
The article is devoted to study of boundary value problem with boundary jumps for third order linear integro-differential equation with a small parameter at the highest derivatives, provided that additional characteristic equation’s roots have opposite ...
A.E. Mirzakulova, N. Atakhan, N. Asset, A. Rysbek   +3 more
doaj   +1 more source

Singularly perturbed elliptic problems in exterior domains

Differential and Integral Equations, 2000
The paper deals with the following problem: \[ -\varepsilon^2\Delta u+u=u^{p-1},\quad u>0\text{ in }\Omega,\quad u\in H^1_0 (\Omega) \tag{1} \] where \(\Omega\) is a domain in \(\mathbb{R}^N\) such that \(\mathbb{R}^N \setminus \Omega\) is a bounded open set ...
Dancer, E. N., Yan, Shusen
openaire   +3 more sources

Scaling Exponents of Turbulent Static Pressure Structure Function in the Inertial Subrange

Geophysical Research Letters, Volume 52, Issue 11, 16 June 2025.
Abstract The measured variations in the turbulent static pressure structure function Dpp(r) ${D}_{pp}(r)$ with scale r $r$ in the roughness sublayer above a subarctic forest are empirically shown to exhibit exponents that are smaller than r4/3 ${r}^{4/3}$ predicted for the inertial subrange (ISR).
Gabriel G. Katul, Toprak Aslan, Mika Aurela   +2 more
wiley   +1 more source

The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits

Discrete Dynamics in Nature and Society, 2016
Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed.
Han Xu, Yinlai Jin
doaj   +1 more source

Singularly Perturbed Control Systems with Noncompact Fast Variable

, 2015
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in the sense of ...
Nguyen, Thuong, Siconolfi, Antonio
core   +1 more source

Extracellular Vesicle Lipids and Their Role in Delivery

Journal of Extracellular Biology, Volume 4, Issue 6, June 2025.
ABSTRACT Small extracellular vesicles (sEVs) possess many advantageous characteristics which highlight their potential as nanocarriers for biomedical applications, including the ability to cross the blood brain barrier, improved biocompatibility and exhibit tissue tropism.
Austin Brent, Paniz Shirmast, Nigel A. J. McMillan   +2 more
wiley   +1 more source

Boundary-layers for a Neumann problem at higher critical exponents

, 2016
We consider the Neumann problem $$(P)\qquad - \Delta v + v= v^{q-1} \ \text{in }\ \mathcal{D}, \ v > 0 \ \text{in } \ \mathcal{D},\ \partial_\nu v = 0 \ \text{on } \partial\mathcal{D} ,$$ where $\mathcal{D} $ is an open bounded domain in $\mathbb{R}^N,$ $
Manna, Bhakti B., Pistoia, Angela
core   +1 more source

Rectifiability, finite Hausdorff measure, and compactness for non‐minimizing Bernoulli free boundaries

Communications on Pure and Applied Mathematics, Volume 78, Issue 3, Page 545-591, March 2025.
Abstract While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent ...
Dennis Kriventsov, Georg S. Weiss
wiley   +1 more source

Acute and non‐acute decompensation of liver cirrhosis

Liver International, Volume 45, Issue 3, March 2025.
Abstract In the traditional view, the occurrence of cirrhosis‐related complications, such as hepatic encephalopathy, formation of ascites or variceal haemorrhage, marks the transition to the decompensated stage of cirrhosis. Although the dichotomous stratification into a compensated and decompensated state reflects a prognostic water‐shed moment and ...
Martin S. McCoy, Paolo Angeli, Jonel Trebicka   +2 more
wiley   +1 more source