Results 41 to 50 of about 888,449 (207)

Riemannian Geometry for the Classification of Brain States with Intracortical Brain Recordings

Advanced Intelligent Systems
This study investigates the application of Riemannian geometry‐based methods for brain decoding using invasive electrophysiological recordings. While Riemannian geometry has been successfully applied in noninvasive settings, its utility for invasive ...
Arnau Marin‐Llobet, Sergio Sánchez‐Manso, Arnau Manasanch, Lluc Tresserras, Xinhe Zhang, Yining Hua, Hao Zhao, Melody Torao‐Angosto, Maria V Sanchez‐Vives, Leonardo Dalla Porta   +9 more
doaj   +1 more source

Purely Coclosed G2‐Structures on Nilmanifolds—II

Mathematische Nachrichten, EarlyView.
ABSTRACT This paper completes the classification of seven‐dimensional nilpotent Lie groups endowed with a left‐invariant purely coclosed G2$\text{G}_2$‐structure, initiated in Bazzoni et al. [Mathematische Nachrichten 296 no. 6 (2023): 2236–2257], the authors provided the classification of decomposable seven‐dimensional nilpotent Lie groups and of the ...
Giovanni Bazzoni, Giorgia Petracci
wiley   +1 more source

Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry

Advanced Nonlinear Studies, 2022
In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa, Tesi Maria Carla, Tripaldi Francesca   +2 more
doaj   +1 more source

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
A. Paliathanasis, S. Moyo, P. G. L. Leach   +2 more
wiley   +1 more source

To geometric aspects of in nite-dimensional dynamical systems

Современная математика: Фундаментальные направления
The main goal of the work is to construct analogues of Christoffel symbols for infinitedimensional systems and on this basis to obtain geodesic equations for such systems.
V. M. Savchin
doaj   +1 more source

The Information Geometry of Sensor Configuration

Sensors, 2021
In problems of parameter estimation from sensor data, the Fisher information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the measurements ...
Simon Williams, Arthur George Suvorov, Zengfu Wang, Bill Moran   +3 more
doaj   +1 more source

On Geometric Phase Model in the Theory of Curves With Myller Configuration

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we introduce a linearly polarized light wave in an optical fiber and rotation of the polarization plane through the Frenet‐type frame with Myller configuration. Since the geometric evaluation and interpretations of a polarized light wave are associated with geometric phase, a new type of geometric phase model has been ...
Zehra İşbilir, Bahar Doğan Yazıcı, Murat Tosun   +2 more
wiley   +1 more source

Riemannian Maps To Almost Hermitian Manifolds

, 2017
In this chapter, we study Riemannian maps from Riemannian manifolds to almost Hermitian manifolds. In section 1, we study invariant Riemannian maps, that is, the image of derivative map is invariant under the almost complex structure of the base manifold.
Sahin, Bayram, Bayram Şahin
core   +1 more source

LARGE SOLUTIONS FOR YAMABE AND SIMILAR PROBLEMS ON DOMAINS IN RIEMANNIAN MANIFOLDS [PDF]

, 2011
We present a unified approach to study large positive solutions (i.e., u(x) -> infinity as x -> partial derivative Omega) of the equation Delta u + hu - k psi(u) = -f in an arbitrary domain Omega.
Martin Dindoš, Dindos, Martin; id_orcid
core   +1 more source

The infinity(x)-Laplace equation in Riemannian vector fields

Electronic Journal of Differential Equations, 2015
We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of viscosity solutions to the infinity(x)-Laplace equation in Riemannian vector fields.
Thomas Bieske
doaj