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Using the embedded gradient vector field method (see P. Birtea, D. Comanescu, Hessian operators on constraint manifolds, J. Nonlinear Science 25, 2015), we present a general formula for the Laplace-Beltrami operator defined on a constraint manifold,
Externí odkaz:
http://arxiv.org/abs/2206.06790
We develop the embedded gradient vector field method, introduced in [8] and [9], for the case of the special unitary group $\mathcal{SU}(N)$ regarded as a constraint submanifold of the unitary group $\mathcal{U}(N)$. The optimization problem associat
Externí odkaz:
http://arxiv.org/abs/2103.11132
Publikováno v:
University Lecture Series, 74. American Mathematical Society, Providence, RI, 2020. 128 pp. ISBN:978-1-4704-5495-1
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions with geometry
Externí odkaz:
http://arxiv.org/abs/1904.04044
We regard the real symplectic group $Sp(2n,\mathbb{R})$ as a constraint submanifold of the $2n\times 2n$ real matrices $\mathcal{M}_{2n}(\mathbb{R})$ endowed with the Euclidean (Frobenius) metric, respectively as a submanifold of the general linear g
Externí odkaz:
http://arxiv.org/abs/1811.07345
The main tool to study a second order optimality problem is the Hessian operator associated to the cost function that defines the optimization problem. By regarding an orthogonal Stiefel manifold as a constraint manifold embedded in an Euclidean spac
Externí odkaz:
http://arxiv.org/abs/1802.05469
Homotopy probability theory is a version of probability theory in which the vector space of random variables is replaced with a chain complex. A natural example extends ordinary probability theory on a finite volume Riemannian manifold M. In this exa
Externí odkaz:
http://arxiv.org/abs/1608.00141
Autor:
León, Joel García
Publikováno v:
Proceedings of the American Mathematical Society, 2008 Dec 01. 136(12), 4445-4452.
Externí odkaz:
http://dx.doi.org/10.1090/S0002-9939-08-08824-2
The main tool to study a second order optimality problem is the Hessian operator associated to the cost function that defines the optimization problem. By regarding an orthogonal Stiefel manifold as a constraint manifold embedded in an Euclidean spac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a04025659130ae0f8cb26412412497c
http://arxiv.org/abs/1802.05469
http://arxiv.org/abs/1802.05469
Autor:
Emmanuel Giner, Jean-Paul Penot
We examine how the subdi¤erentials of nonconvex integral functionals can be deduced from the subdi¤erentials of the corresponding integrand or at least be estimated with the help of them. In fact, assuming some regularity properties of the integran
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e23d5058032a125d5364fa52c0bd5dd
https://hal.sorbonne-universite.fr/hal-01450022
https://hal.sorbonne-universite.fr/hal-01450022
Autor:
Tunçel, Levent
Publikováno v:
Mathematics of Computation, 2009 Apr 01. 78(266), 1233-1236.
Externí odkaz:
https://www.jstor.org/stable/40234655