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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 +2 more
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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 +2 more
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The χ-Hessian Quotient for Riemannian Metrics
Axioms, 2021 Pseudo-Riemannian geometry and Hilbert–Schmidt norms are two important fields of research in applied mathematics. One of the main goals of this paper will be to find a link between these two research fields. In this respect, in the present paper, we will
Pişcoran Laurian-Ioan +3 more
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International Journal of Mechanical System Dynamics, EarlyView.ABSTRACT Modern engineering systems require advanced uncertainty‐aware model updating methods that address parameter correlations beyond conventional interval analysis. This paper proposes a novel framework integrating Riemannian manifold theory with Gaussian Process Regression (GPR) for systems governed by Symmetric Positive‐Definite (SPD) matrix ...
Yanhe Tao +3 more
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To geometric aspects of in nite-dimensional dynamical systems
Современная математика: Фундаментальные направленияThe 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
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Fractons, non-Riemannian geometry, and double field theory
Physical Review Research, 2022 We initiate a systematic study of fracton physics within the geometric framework of double field theory. We ascribe the immobility and large degeneracy of the former to the non-Riemannian backgrounds of the latter, in terms of generalized geodesics and ...
Stephen Angus +2 more
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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 +3 more
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Initial State Privacy of Nonlinear Systems on Riemannian Manifolds
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
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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
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Induced geometry from disformal transformation
Physics Letters B, 2015 In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry.
Fang-Fang Yuan, Peng Huang
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