Results 71 to 80 of about 3,057 (193)

Two theorems on (ϵ)-Sasakian manifolds

International Journal of Mathematics and Mathematical Sciences, 1998
In this paper, We prove that every (ϵ)-sasakian manifold is a hypersurface of an indefinite kaehlerian manifold, and give a necessary and sufficient condition for a Riemannian manifold to be an (ϵ)-sasakian manifold.
Xu Xufeng, Chao Xiaoli
doaj   +1 more source

Strain‐Space Hyperreduction Using Empirically Corrected Cluster Cubature With Linear and Quadratic Approximation Spaces

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT Strain‐space reduced cubature techniques such as the Empirically Corrected Cluster Cubature (E3C) considerably reduce the integration effort incurred in computational homogenisation problems. In this work, we apply E3C in tandem with projection‐based model reduction techniques utilising both linear and quadratic approximation spaces.
Erik Faust, Dong Zhao, Lisa Scheunemann
wiley   +1 more source

A Spike‐Based Graph Surrogate for Modeling Finite Element Structures

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT The use of Artificial Intelligence (AI) in structural mechanics has grown substantially in the recent years, with diverse applications ranging from constitutive laws and Gauss‐point‐level enhancements to the complete replacement of classical Finite Element Methods (FEM) with surrogate models.
Vaishnav Bhaskaran, Rutwik Gulakala, Marcus Stoffel   +2 more
wiley   +1 more source

Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson, Janne Nurminen, Mikko Salo   +2 more
wiley   +1 more source

Stochastic Approximation on Riemannian Manifolds [PDF]

Applied Mathematics & Optimization, 2019
The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a manifold using a retraction mapping. In addition, for submanifolds of a Euclidean space, a framework is developed
openaire   +3 more sources

The mod 2 Seiberg–Witten invariants of spin structures and spin families

Journal of Topology, Volume 19, Issue 4, December 2026.
Abstract We completely determine the mod 2 Seiberg–Witten invariants for any spin structure on any closed, oriented, smooth 4‐manifold X$X$. Our computation confirms the validity of the simple‐type conjecture mod 2 for spin structures. Our proof also works for families of spin 4‐manifolds and thus computes the mod 2 Seiberg–Witten invariants for spin ...
David Baraglia
wiley   +1 more source

Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA

Communications on Pure and Applied Mathematics, Volume 79, Issue 10, Page 2291-2369, October 2026.
ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo   +2 more
wiley   +1 more source

Conformal quasi-hemi-slant $\xi^{\perp}$-Riemannian submersions from Sasakian manifolds [PDF]

Mathematica Bohemica
We introduce some geometric properties of a horizontally conformal quasi-hemi-slant Riemannian submersion from a Sasakian manifold, normal to the characteristic vector field, supported by an example.
Fortuné Massamba, Pontsho Moile
doaj   +1 more source

Mirror descent on Riemannian manifolds

Analysis and Applications
Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian manifolds. In particular, we develop a Riemannian Mirror Descent (RMD) framework via reparameterization and further
Jiaxin Jiang, Lei Shi, Jiyuan Tan
openaire   +2 more sources

Hearing the Serre Invariant of a Compact p‐Adic Analytic Manifold

Mathematische Nachrichten, Volume 299, Issue 10, Page 3126-3138, October 2026.
ABSTRACT Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact p$p$‐adic analytic manifold X$X$, one such operator Δ0s$\Delta _0^s$ with s∈R$s\in \mathbb {R}$ is applied to hearing the Serre invariant i(X)$i(X)$ by showing that a wavelet eigenvalue (with the wavelet having small support) is always ...
Patrick Erik Bradley, Ángel Morán Ledezma   +1 more
wiley   +1 more source