Results 11 to 20 of about 24,975 (207)
Hessian Operators on Constraint Manifolds [PDF]
Journal of Nonlinear Science, 2015 On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for the case of the orthogonal group ${\bf O}(n)$ by using only Euclidean coordinates on $\mathbb{R}^{n^2}$.
Birtea, Petre, Comănescu, Dan
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Differential Geometry and its Applications, 1997 An affine manifold is Hessian if it possesses a Hessian metric, that is, a Riemannian metric which is locally the Hessian of a function. Hessian manifolds are the analogue of Kähler manifolds among affine manifolds and enjoy many strong properties. For example, the first theorem in the paper is that a simply connected affine manifold with a complete ...
Shima, Hirohiko, Yagi, Katsumi
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Complex Hessian Equation on Kähler Manifold [PDF]
International Mathematics Research Notices, 2009 12 ...
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Regularity of degenerate k-Hessian equations on closed Hermitian manifolds
Advanced Nonlinear Studies, 2022 In this article, we are concerned with the existence of weak C1,1{C}^{1,1} solution of the kk-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation.
Zhang Dekai
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Cancer Reports, EarlyView., 2023 Abstract Background A methodology to assess the immune microenvironment (IME) of non‐small cell lung cancer (NSCLC) has not been established, and the prognostic impact of IME factors is not yet clear. Aims This study aimed to assess the IME factors and evaluate their prognostic values. Methods and Results We assessed CD8+ tumor‐infiltrating lymphocyte (
Yukihiro Terada +16 more
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Hessian manifolds of nonpositive constant Hessian sectional curvature [PDF]
Tohoku Mathematical Journal, 2013 We classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.
Furuhata, Hitoshi, Kurose, Takashi
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On the Distributional Hessian of the Distance Function [PDF]
, 2014 We describe the precise structure of the distributional Hessian of the distance function from a point of a Riemannian manifold. In doing this we also discuss some geometrical properties of the cutlocus of a point and we compare some different weak ...
Mantegazza, Carlo +2 more
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Homogeneous hessian manifolds [PDF]
Annales de l'Institut Fourier, 1980 A flat affine manifold is said to Hessian if it is endowed with a Riemannian metric whose local expression has the form g ij =∂ 2 Φ ∂x i ∂x j where Φ is a C ∞ -function and {x 1 ,...,x n } is an affine local coordinate system. Let M be a Hessian manifold. We show that if M is homogeneous, the universal covering manifold of M is a convex domain in R n
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Nonlinear Feature Extraction Through Manifold Learning in an Electronic Tongue Classification Task
Sensors, 2020 A nonlinear feature extraction-based approach using manifold learning algorithms is developed in order to improve the classification accuracy in an electronic tongue sensor array.
Jersson X. Leon-Medina +3 more
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Information Geometry on the \(\kappa\)-Thermostatistics
Entropy, 2015 We explore the information geometric structure of the statistical manifold generated by the \(\kappa\)-deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fisher
Tatsuaki Wada, Antonio M. Scarfone
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