scholarly journals A positive-definite form of bounce-averaged quasilinear velocity diffusion for the parallel inhomogeneity in a tokamak

2017 ◽  
Vol 60 (2) ◽  
pp. 025007
Author(s):  
Jungpyo Lee ◽  
David Smithe ◽  
John Wright ◽  
Paul Bonoli
Keyword(s):  
Positive Definite ◽  
Definite Form ◽  
Velocity Diffusion

scholarly journals New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Global Asymptotic Stability ◽  
Positive Definite ◽  
Time Varying ◽  
Numerical Example ◽  
Definite Form ◽  
Takagi Sugeno

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods.

scholarly journals Geometry on the variety of subspaces with positive definite form: geometry of the Grassmann spaces over generalized hyperbolic spaces

2021 ◽  
Vol 112 (2) ◽  
Author(s):  
K. Prażmowski
Keyword(s):  
Projective Space ◽  
Vector Space ◽  
Hyperbolic Space ◽  
Bilinear Form ◽  
Positive Definite ◽  
Real Vector Space ◽  
Hyperbolic Spaces ◽  
Real Vector ◽  
Definite Form ◽  
The Family

AbstractWe consider Grassmann structures defined on the family consisting of subspaces on which a given nondegenerate bilinear form defined on a real vector space is positive definite. One may call such structures Grassmann spaces over generalized hyperbolic spaces. We show that the underlying (generalized) hyperbolic space can be recovered in terms of its Grassmannian, and the underlying projective space (equipped with respective associated polarity) can be recovered in terms of the generalized hyperbolic space defined over it.

Sign in / Sign up

Export Citation Format

Share Document