Bundles with totally disconnected structure group

1971 ◽  
Vol 46 (1) ◽  
pp. 257-273 ◽  
Author(s):  
John W. Wood
Keyword(s):  
Structure Group ◽  
Disconnected Structure ◽  
Totally Disconnected

FRACTAL TRANSITION: HIERARCHICAL STRUCTURE AND NOISE EFFECT

Fractals ◽  
1999 ◽  
Vol 07 (03) ◽  
pp. 313-326 ◽  
Author(s):  
KAZUTOSHI GOHARA ◽  
ARATA OKUYAMA
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Hierarchical Structure ◽  
Noise Effect ◽  
Hierarchical Tree ◽  
The Difference ◽  
Disconnected Structure ◽  
Dissipative Dynamical Systems ◽  
Totally Disconnected ◽  
Hierarchical Tree Structure

A Sierpinski gasket with continuous trajectories is presented as an example of the fractal transition that characterizes the behavior of dissipative dynamical systems excited by external temporal inputs. Using this example, we investigate the fractal transition from two points of views, i.e. a hierarchical structure and a noise effect. Depending on internal and external parameters, the structure can be geometrically classified as one of three types, i.e. totally disconnected, just-touching, and overlapping. For the totally disconnected structure, continuous trajectories and their starting points can be characterized by a definite hierarchical tree structure. Even for the just-touching and overlapping structure, a similar hierarchy exists. White noise contaminating the external inputs breaks the hierarchy. In particular, small clustered structures are sensitive to the noise. In such a case, the difference between trajectories and starting points is remarkable in the hierarchy.

scholarly journals Complete regularity of Ellis semigroups of -actions

2020 ◽  
pp. 1-17
Author(s):  
MARCY BARGE ◽  
JOHANNES KELLENDONK
Keyword(s):  
Complete Regularity ◽  
Completely Regular ◽  
Ellis Semigroup ◽  
Totally Disconnected

Abstract It is shown that the Ellis semigroup of a $\mathbb Z$ -action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$ - or $\mathbb R$ -action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.

scholarly journals Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 971
Author(s):  
Oded Shor ◽  
Felix Benninger ◽  
Andrei Khrennikov
Keyword(s):  
Experimental Data ◽  
Clustering Algorithms ◽  
Realistic Model ◽  
Minkowski Geometry ◽  
Ultrametric Spaces ◽  
Chsh Inequality ◽  
Classical Quantum ◽  
Basic Features ◽  
Totally Disconnected ◽  
Explicate Order

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical–quantum interrelations lose their sharpness; generally, simple dendrograms are “more quantum” than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.

Totally Disconnected and Locally Compact Heisenberg-Weyl Groups

2010 ◽  
Vol 16 (5) ◽  
pp. 748-767 ◽  
Author(s):  
A. Vourdas
Keyword(s):  
Weyl Groups ◽  
Locally Compact ◽  
Totally Disconnected

The Structure Group of a Generalized Orthomodular Lattice

Studia Logica ◽  
2017 ◽  
Vol 106 (1) ◽  
pp. 85-100 ◽  
Author(s):  
Wolfgang Rump
Keyword(s):  
Orthomodular Lattice ◽  
Structure Group

scholarly journals Yang–Mills connections on compact complex tori

2015 ◽  
Vol 07 (02) ◽  
pp. 293-307
Author(s):  
Indranil Biswas
Keyword(s):  
Algebraic Group ◽  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Structure Group ◽  
Kähler Structure ◽  
Yang Mills ◽  
Complex Torus ◽  
Complex Tori

Let G be a connected reductive complex affine algebraic group and K ⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (EG, θ) a polystable Higgs G-bundle on M. Take any C∞ reduction of structure group EK ⊂ EG to the subgroup K that solves the Yang–Mills equation for (EG, θ). We prove that the principal G-bundle EG is polystable and the above reduction EK solves the Einstein–Hermitian equation for EG. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (EG, θ) on a compact connected Calabi–Yau manifold, the underlying principal G-bundle EG is semistable (respectively, polystable).

Change of Structure Group in Fibre Bundles

1966 ◽  
pp. 70-74
Author(s):  
Dale Husemoller
Keyword(s):  
Structure Group ◽  
Fibre Bundles
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