Results 11 to 20 of about 53,985 (263)

General Chen Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Mathematics, 2022
Chen’s first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature was obtained by B.-Y. Chen et al. Other particular cases of Chen inequalities in a statistical setting were given by different authors.
Ion Mihai, Radu-Ioan Mihai
doaj   +3 more sources

Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature

Mathematics, 2020
In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant ...
Simona Decu, Stefan Haesen, Leopold Verstraelen   +2 more
doaj   +3 more sources

Sasakian statistical manifolds

Journal of Geometry and Physics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Furuhata, Hitoshi, Hasegawa, Izumi, Okuyama, Yukihiko, Sato, Kimitake, Shahid, Mohammad Hasan   +4 more
openaire   +4 more sources

Conformal Control Tools for Statistical Manifolds and for γ-Manifolds

Mathematics, 2022
The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the γ-manifolds are introduced. New conformal invariant tools are defined.
Iulia-Elena Hirica, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae, Vasile Preda   +3 more
doaj   +2 more sources

Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions

Entropy, 2015
In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending ...
Alina-Daniela Vîlcu, Gabriel-Eduard Vîlcu   +1 more
doaj   +3 more sources

Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Mathematics, 2018
We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.
Adela Mihai, Ion Mihai
doaj   +3 more sources

Jacobi Fields on Statistical Manifolds of Negative Curvature

Physica D: Nonlinear Phenomena, 2007
Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved.
Amari, Amari, Arnold, Arwini, C. Cafaro, Campbell, Casetti, Caticha, Caticha, Caticha, Caticha, Caticha, Caves, Chentsov (Cencov), Chicone, De Felice, Eckmann, Efron, Fisher, Jaynes, Kawabe, Misner, Rao, Rodriguez, S.A. Ali, Zurek   +25 more
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Lifts of a Semi-Symmetric Metric Connection from Sasakian Statistical Manifolds to Tangent Bundle

Mathematics
The lifts of Sasakian statistical manifolds associated with a semi-symmetric metric connection in the tangent bundle are characterized in the current research.
Rajesh Kumar, Sameh Shenawy, Nasser Bin Turki, Lalnunenga Colney, Uday Chand De   +4 more
doaj   +3 more sources

Learning on dynamic statistical manifolds. [PDF]

Proc Math Phys Eng Sci, 2020
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge.
Boso F, Tartakovsky DM.
europepmc   +6 more sources

Quantum statistical manifolds: the linear growth case

Reports on Mathematical Physics, 2019
A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear.
Naudts, Jan
core   +4 more sources