Results 41 to 50 of about 550,253 (159)

Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications

Mathematics, 2023
The method of gradient estimation for the heat-type equation using the Harnack quantity is a classical approach used for understanding the nature of the solution of these heat-type equations. Most of the studies in this field involve the Laplace–Beltrami
Yanlin Li, Sujit Bhattacharyya, Shahroud Azami, Apurba Saha, Shyamal Kumar Hui   +4 more
doaj   +1 more source

Attention Based Optimization for 3D Shape Registration

Computer Graphics Forum, EarlyView.
Abstract Transformers are sequence‐to‐sequence architectures originally designed to handle structurally rigid and order‐sensitive data, such as text and images. At their core, they exploit the attention mechanism, which is permutation‐equivariant and relies on computing token‐to‐token relationships.
A. Riva, L. Olearo, S. Melzi
wiley   +1 more source

Minimizers of the dynamical Boulatov model

European Physical Journal C: Particles and Fields, 2018
We study the Euler–Lagrange equation of the dynamical Boulatov model which is a simplicial model for 3d Euclidean quantum gravity augmented by a Laplace–Beltrami operator.
Joseph Ben Geloun, Alexander Kegeles, Andreas G. A. Pithis   +2 more
doaj   +1 more source

Comparative multimodal calibration of patient‐specific atrial fibrillation models: Impact of imaging and electrophysiology data on arrhythmogenic substrate identification

The Journal of Physiology, EarlyView.
Abstract figure legend Comparative multimodal calibration of patient‐specific left atrial (LA) models to identify arrhythmogenic substrates in atrial fibrillation (AF). A, LA models shown in posterior and anterior views, calibrated separately using: late gadolinium enhancement magnetic resonance imaging (LGE‐MRI) image intensity ratio (IIR; blue–red ...
Mahmoud Ehnesh, Haseeb Valli, Ovais A. Jaffery, Sam Coveney, Alexander Zolotarev, Zhong Chen, Wajid Hussain, David G. Jones, Raad Mohiaddin, Tom Wong, Gregory Slabaugh, Steven A. Niederer, Edward Vigmond, Shouvik Haldar, Caroline Roney   +14 more
wiley   +1 more source

Accurate and Efficient Data‐Driven Partitioned Scheme for Coupled Heterogeneous Numerical Models

Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.
ABSTRACT Heterogeneous numerical models (HNMs) combine conventional discretization modules such as finite elements with nonconventional data‐driven and reduced‐order modules. HNMs can improve computational efficiency and enable simulations of multi‐physics systems in which one or more constituent components lack first‐principles descriptions and must ...
Edward Huynh, Justin Owen, Paul Kuberry, Pavel Bochev   +3 more
wiley   +1 more source

The Spectrum of the Laplace-Beltrami Operator on NoncompactManifolds

In this thesis we introduce the Laplace-Beltrami operator on Riemannian manifolds and study its spectrum on noncompact manifolds. For compact connected manifolds it is known that the Laplace-Beltrami operator has a discrete spectrum consisting of real ...
Backman, Elliot
core   +3 more sources

Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

International Journal of Mathematics and Mathematical Sciences, 1997
The spectral function Θ(t)=∑i=1∞exp(−tλj), where {λj}j=1∞ are the eigenvalues of the negative Laplace-Beltrami operator −Δ, is studied for a compact Riemannian manifold Ω of dimension “k” with a smooth boundary ∂Ω, where a finite number of piecewise ...
E. M. E. Zayed
doaj   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Linear Toroidal‐Inertial Waves on A Differentially Rotating Sphere with Application to Helioseismology: Modeling, Forward and Inverse Problems

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 14122-14148, August 2026.
ABSTRACT This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth‐order scalar equation.
Tram Thi Ngoc Nguyen, Damien Fournier, Laurent Gizon, Thorsten Hohage   +3 more
wiley   +1 more source

The Laplace-Beltrami Operator on the Surface of the Ellipsoid [PDF]

The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is reduced to a ...
Volkmer, Hans
core   +1 more source