scholarly journals Purely infinite totally disconnected topological graph algebras

2016 ◽  
Vol 60 (3-4) ◽  
pp. 739-750 ◽  
Author(s):  
Hui Li
Keyword(s):  
Graph Algebras ◽  
Topological Graph ◽  
Totally Disconnected

scholarly journals Traces on topological-graph algebras

2017 ◽  
Vol 38 (5) ◽  
pp. 1923-1953
Author(s):  
CHRISTOPHER SCHAFHAUSER
Keyword(s):  
Probability Measures ◽  
Graph Algebras ◽  
Topological Graph ◽  
Gauge Invariant ◽  
Gauge Action ◽  
Tracial State ◽  
Suitable Sense ◽  
Affine Homeomorphism ◽  
Totally Disconnected ◽  
Tracial States

Given a topological graph $E$, we give a complete description of tracial states on the $\text{C}^{\ast }$-algebra $\text{C}^{\ast }(E)$ which are invariant under the gauge action; there is an affine homeomorphism between the space of gauge invariant tracial states on $\text{C}^{\ast }(E)$ and Radon probability measures on the vertex space $E^{0}$ which are, in a suitable sense, invariant under the action of the edge space $E^{1}$. It is shown that if $E$ has no cycles, then every tracial state on $\text{C}^{\ast }(E)$ is gauge invariant. When $E^{0}$ is totally disconnected, the gauge invariant tracial states on $\text{C}^{\ast }(E)$ are in bijection with the states on $\text{K}_{0}(\text{C}^{\ast }(E))$.

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.

scholarly journals Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Fuwei Lu ◽  
Rongjiang Cui ◽  
Chuanyu Wu
Keyword(s):  
Degree Of Freedom ◽  
Adjacent Vertex ◽  
Topological Graph ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Effectiveness And Efficiency ◽  
Definition Of ◽  
Specific Definition

AbstractIsomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

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