scholarly journals Topological isomorphism for rank-1 systems

2016 ◽  
Vol 128 (1) ◽  
pp. 1-49 ◽  
Author(s):  
Su Gao ◽  
Aaron Hill
Keyword(s):  
Topological Isomorphism

scholarly journals On the lifting of bounded sets in Fréchet spaces

1993 ◽  
Vol 36 (2) ◽  
pp. 277-281 ◽  
Author(s):  
José Bonet ◽  
Susanne Dierolf
Keyword(s):  
Topological Isomorphism ◽  
Fréchet Spaces ◽  
Bounded Sets

This paper considers the behaviour of a quotient map between Fréchet spaces concerning the lifting of bounded sets. The main result shows that a quotient map between Fréchet spaces that lifts bounded sets with closure (or equivalently such that its strong transpose is a topological isomorphism) must also lift bounded sets without closure.

scholarly journals Multiphase Open Phase Processes Differential Equations

Processes ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 148
Author(s):  
Nikolay Charykov ◽  
Marina Charykova ◽  
Konstantin Semenov ◽  
Victor Keskinov ◽  
Alexey Kurilenko ◽  
...  
Keyword(s):  
Differential Equations ◽  
Phase Diagrams ◽  
Thermodynamic Modeling ◽  
Van Der Waals ◽  
Salt System ◽  
Thermodynamic Approach ◽  
Topological Isomorphism ◽  
Van Der Waals Equation ◽  
Open Phase ◽  
Water Salt

The thermodynamic approach for the description of multiphase open phase processes is developed based on van der Waals equation in the metrics of Gibbs and incomplete Gibbs potentials. Examples of thermodynamic modeling of the multiphase and multicomponent A3B5 systems (In-Ga-As-Sb and In-P-As-Sb) and Na+, K+, Mg2+, Ca2+//Cl−, SO42−-H2O water–salt system are presented. Topological isomorphism of different type phase diagrams is demonstrated.

scholarly journals Doubly stochastic right multipliers

1984 ◽  
Vol 7 (3) ◽  
pp. 477-489
Author(s):  
Choo-Whan Kim
Keyword(s):  
Convex Hull ◽  
Compact Group ◽  
Compact Convex ◽  
Strong Operator Topology ◽  
Left Translation ◽  
Closed Convex Hull ◽  
Topological Isomorphism ◽  
Doubly Stochastic ◽  
Borel Measures ◽  
Translation Operators

LetP(G)be the set of normalized regular Borel measures on a compact groupG. LetDrbe the set of doubly stochastic (d.s.) measuresλonG×Gsuch thatλ(As×Bs)=λ(A×B), wheres∈G, andAandBare Borel subsets ofG. We show that there exists a bijectionμ↔λbetweenP(G)andDrsuch thatϕ−1=m⊗μ, wheremis normalized Haar measure onG, andϕ(x,y)=(x,xy−1)forx,y∈G. Further, we show that there exists a bijection betweenDrandMr, the set of d.s. right multipliers ofL1(G). It follows from these results that the mappingμ→Tμdefined byTμf=μ∗fis a topological isomorphism of the compact convex semigroupsP(G)andMr. It is shown thatMris the closed convex hull of left translation operators in the strong operator topology ofB[L2(G)].

scholarly journals Strong shift equivalence of 2 × 2 matrices of non-negative integers

1983 ◽  
Vol 3 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Kirby A. Baker
Keyword(s):  
Markov Chains ◽  
Sufficient Conditions ◽  
Topological Isomorphism ◽  
Strong Shift ◽  
Shift Equivalence ◽  
Integral Matrices ◽  
Strong Shift Equivalence

AbstractThe concept of strong shift equivalence of square non-negative integral matrices has been used by R. F. Williams to characterize topological isomorphism of the associated topological Markov chains. However, not much has been known about sufficient conditions for strong shift equivalence even for 2×2 matrices (other than those of unit determinant). The main theorem of this paper is: If A and B are positive 2×2 integral matrices of non-negative determinant and are similar over the integers, then A and B are strongly shift equivalent.

scholarly journals Groupoids associated to inverse semigroups

2021 ◽  
Author(s):  
Malcolm Jones
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Topological Isomorphism ◽  
Similar Group ◽  
Self Similar

<p>Starting with an arbitrary inverse semigroup with zero, we study two well-known groupoid constructions, yielding groupoids of filters and groupoids of germs. The groupoids are endowed with topologies making them étale. We use the bisections of the étale groupoids to show there is a topological isomorphism between the groupoids. This demonstrates a widely useful equivalence between filters and germs. We use the isomorphism to characterise Exel’s tight groupoid of germs as a groupoid of filters, to find a nice basis for the topology on the groupoid of ultrafilters and to describe the ultrafilters in the inverse semigroup of an arbitrary self-similar group.</p>

Moving tracking with approximate topological isomorphism

2015 ◽  
Vol 75 (23) ◽  
pp. 15553-15570 ◽  
Author(s):  
Weina Fu ◽  
Jiantao Zhou ◽  
Yingdong Ma
Keyword(s):  
Topological Isomorphism

scholarly journals A topological isomorphism invariant for certain AF algebras

2005 ◽  
Vol 2005 (11) ◽  
pp. 1665-1673 ◽  
Author(s):  
Ryan J. Zerr
Keyword(s):  
Topological Space ◽  
Automorphism Groups ◽  
Bratteli Diagram ◽  
Topological Isomorphism ◽  
Dimension Group ◽  
Af Algebras

For certain AF algebras, a topological space is described which provides an isomorphism invariant for the algebras in this class. These AF algebras can be described in graphical terms by virtue of the existence of a certain type of Bratteli diagram, and the order-preserving automorphisms of the corresponding AF algebra's dimension group are then studied by utilizing this graph. This will also provide information about the automorphism groups of the corresponding AF algebras.

scholarly journals Multi-Hypothesis Topological Isomorphism Matching Method for Synthetic Aperture Radar Images with Large Geometric Distortion

2021 ◽  
Vol 13 (22) ◽  
pp. 4637
Author(s):  
Runzhi Jiao ◽  
Qingsong Wang ◽  
Tao Lai ◽  
Haifeng Huang
Keyword(s):  
Synthetic Aperture Radar ◽  
Stable Matching ◽  
Synthetic Aperture ◽  
Topological Isomorphism ◽  
Matching Method ◽  
Sar Images ◽  
Keypoint Detection ◽  
Radar Images ◽  
Geometric Distortions ◽  
Aperture Radar

The dramatic undulations of a mountainous terrain will introduce large geometric distortions in each Synthetic Aperture Radar (SAR) image with different look angles, resulting in a poor registration performance. To this end, this paper proposes a multi-hypothesis topological isomorphism matching method for SAR images with large geometric distortions. The method includes the Ridge-Line Keypoint Detection (RLKD) and Multi-Hypothesis Topological Isomorphism Matching (MHTIM). Firstly, based on the analysis of the ridge structure, a ridge keypoint detection module and a keypoint similarity description method are designed, which aim to quickly produce a small number of stable matching keypoint pairs under large look angle differences and large terrain undulations. The keypoint pairs are further fed into the MHTIM module. Subsequently, the MHTIM method is proposed, which uses the stability and isomorphism of the topological structure of the keypoint set under different perspectives to generate a variety of matching hypotheses, and iteratively achieves the keypoint matching. This method uses both local and global geometric relationships between two keypoints, hence it achieving better performance compared with traditional methods. We tested our approach on both simulated and real mountain SAR images with different look angles and different elevation ranges. The experimental results demonstrate the effectiveness and stable matching performance of our approach.

Topologies Extending Valuations

1978 ◽  
Vol 30 (01) ◽  
pp. 164-169 ◽  
Author(s):  
Thomas Rigo ◽  
Seth Warner
Keyword(s):  
Vector Space ◽  
Cartesian Product ◽  
Field Extension ◽  
Valuation Theory ◽  
Topological Isomorphism ◽  
Product Topology ◽  
Hausdorff Topology ◽  
Absolute Value ◽  
Finite Dimensional ◽  
Multilinear Mapping

Let K be a field complete for a proper valuation (absolute value) v. It is classic that a finite-dimensional K-vector space E admits a unique Hausdorff topology making it a topological K-vector space, and that that topology is the “cartesian product topology” in the sense that for any basis c1 …, cn of E, is a topological isomorphism from K n to E [1, Chap. I, § 2, no. 3; 2, Chap. VI, § 5, no. 2]. It follows readily that any multilinear mapping from E m to a Hausdorff topological K-vector space is continuous. In particular, any multiplication on E making it a K-algebra is continuous in both variables. If for some such multiplication E is a field extension of K, then by valuation theory the unique Hausdorff topology of E is given by a valuation (absolute value) extending v.

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