scholarly journals An Operator Approach to Tangent Vector Field Processing

2013 ◽  
Vol 32 (5) ◽  
pp. 73-82 ◽  
Author(s):  
Omri Azencot ◽  
Mirela Ben-Chen ◽  
Frédéric Chazal ◽  
Maks Ovsjanikov
Keyword(s):  
Vector Field ◽  
Tangent Vector ◽  
Tangent Vector Field ◽  
Operator Approach

scholarly journals A Set of Axioms for the Degree of a Tangent Vector Field on Differentiable Manifolds

2010 ◽  
Vol 2010 (1) ◽  
pp. 845631 ◽  
Author(s):  
Massimo Furi ◽  
MariaPatrizia Pera ◽  
Marco Spadini
Keyword(s):  
Vector Field ◽  
Tangent Vector ◽  
Tangent Vector Field ◽  
Differentiable Manifolds

scholarly journals Branches of Forced Oscillations Induced by a Delayed Periodic Force

2019 ◽  
Vol 19 (1) ◽  
pp. 149-163 ◽  
Author(s):  
Alessandro Calamai ◽  
Maria Patrizia Pera ◽  
Marco Spadini
Keyword(s):  
Vector Field ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Time Lag ◽  
Tangent Vector ◽  
Forced Oscillations ◽  
Tangent Vector Field ◽  
Periodic Force ◽  
Topological Approach ◽  
Delay Differential

Abstract We study global continuation properties of the set of T-periodic solutions of parameterized second order delay differential equations with constant time lag on smooth manifolds. We apply our results to get multiplicity of T-periodic solutions. Our topological approach is mainly based on the notion of degree of a tangent vector field.

scholarly journals A Riemannian derivative-free Polak–Ribiére–Polyak method for tangent vector field

2020 ◽  
Vol 86 (1) ◽  
pp. 325-355 ◽  
Author(s):  
Teng-Teng Yao ◽  
Zhi Zhao ◽  
Zheng-Jian Bai ◽  
Xiao-Qing Jin
Keyword(s):  
Vector Field ◽  
Tangent Vector ◽  
Tangent Vector Field ◽  
Derivative Free

On some notions of tangent space to a measure

1999 ◽  
Vol 129 (2) ◽  
pp. 331-342 ◽  
Author(s):  
Ilaria Fragalà ◽  
Carlo Mantegazza
Keyword(s):  
Vector Field ◽  
Radon Measure ◽  
Tangent Space ◽  
Blow Up ◽  
Measure Theory ◽  
Tangent Vector ◽  
Geometric Measure Theory ◽  
Tangent Vector Field ◽  
Geometric Measure ◽  
Variable Dimension

We consider some definitions of tangent space to a Radon measure μ on ℝn that have been given in the literature. In particular, we focus our attention on a recent distributional notion of tangent vector field to a measure and we compare it to other definitions coming from ‘geometric measure theory’, based on the idea of blow-up. After showing some classes of examples, we prove an estimate from above for the dimension of the tangent spaces and a rectifiability theorem which also includes the case of measures supported on sets of variable dimension.

Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic Transforms

2021 ◽  
Vol 47 (4) ◽  
pp. 1-24
Author(s):  
Quoc T. Le Gia ◽  
Ming Li ◽  
Yu Guang Wang
Keyword(s):  
Spherical Harmonics ◽  
Spherical Harmonic ◽  
Fourier Coefficients ◽  
Computational Cost ◽  
Tangent Vector ◽  
Tangent Vector Field ◽  
Vector Spherical Harmonics ◽  
Numerical Examples ◽  
Vector Spherical Harmonic ◽  
Tangent Fields

Vector spherical harmonics on the unit sphere of ℝ 3 have broad applications in geophysics, quantum mechanics, and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this article, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to N log √ N for N number of evaluation points. The adjoint FaVeST, which evaluates a linear combination of vector spherical harmonics with a degree up to ⊡ M for M evaluation points, has cost proportional to M log √ M . Numerical examples of simulated tangent fields illustrate the accuracy, efficiency, and stability of FaVeST.

scholarly journals On Copula-Itô processes

2019 ◽  
Vol 7 (1) ◽  
pp. 322-347
Author(s):  
Piotr Jaworski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Infinitesimal Generator ◽  
Continuous Semigroup ◽  
Tangent Vector ◽  
Parabolic Partial Differential Equation ◽  
Strongly Continuous Semigroup ◽  
Tangent Vector Field ◽  
The Family ◽  
Semigroup Of Transformations

AbstractWe study the dynamics of the family of copulas {Ct}t≥0 of a pair of stochastic processes given by stochastic differential equations (SDE). We associate to it a parabolic partial differential equation (PDE). Having embedded the set of bivariate copulas in a dual of a Sobolev Hilbert space H1 (ℝ2)* we calculate the derivative with respect to t and the *weak topology i.e. the tangent vector field to the image of the curve t → Ct. Furthermore we show that the family {Ct}t≥0 is an orbit of a strongly continuous semigroup of transformations and provide the infinitesimal generator of this semigroup.

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces
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