scholarly journals Hyperconvexity and tight-span theory for diversities

2012 ◽  
Vol 231 (6) ◽  
pp. 3172-3198 ◽  
Author(s):  
David Bryant ◽  
Paul F. Tupper
Keyword(s):  
Tight Span

scholarly journals Trimming of metric spaces and the tight span

2018 ◽  
Vol 341 (10) ◽  
pp. 2925-2937
Author(s):  
Vladimir Turaev
Keyword(s):  
Metric Spaces ◽  
Tight Span

Microslip friction in flat belt drives

2005 ◽  
Vol 219 (10) ◽  
pp. 1097-1106 ◽  
Author(s):  
L Kong ◽  
R G Parker
Keyword(s):  
Static Friction ◽  
Relative Displacement ◽  
Operating Conditions ◽  
Creep Model ◽  
Shear Model ◽  
Inertia Effects ◽  
Tight Span ◽  
Entry Points ◽  
Creep Models ◽  
Axially Moving

The microslip shear model of belt mechanics is extended to fully incorporate belt inertia effects and used to analyse the steady state of a two-pulley drive. The belt is modelled as an axially moving string consisting of a tension-bearing member and a pliable elastomer envelope. Relative displacement between the tension-bearing member and the pulley surfaces shears the elastomer envelope, transferring the friction from the pulley surface to the tension-bearing member. The belt-pulley contact arcs consist of adhesion and sliding zones. Static friction exists in the adhesion zones, whereas kinetic friction exists in the sliding zones. An iteration method involving one outer and two inner loops is proposed to find the steady mechanics, including the sliding and adhesion zones, belt-pulley friction, and belt tension distribution. The outer loop iterates on the tight span tension similar to that used in published creep models. Two inner loops iterate on the tight span and driven pulley speeds respectively, necessitated by the speed differences between the tension-bearing member and the pulley at the entry points in the shear theory. Comparisons between the shear and creep models are conducted. Dramatic differences in belt-pulley mechanics between these two models are highlighted. Nevertheless, the key system performance measures such as the belt tight/slack span tensions, the maximum transmissible moment, and efficiency differ only modestly for the most normal operating conditions. Correspondingly, the adoption of the creep model for flat belts in industry is well justified because it is well developed and simple, although the shear model seems more relevant for modern belts with grid layers.

scholarly journals Characterizing Cell-Decomposable Metrics

10.37236/882 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Katharina T. Huber ◽  
Jacobus Koolen ◽  
Vincent Moulton ◽  
Andreas Spillner
Keyword(s):  
Phylogenetic Analysis ◽  
Convex Hull ◽  
Metric Space ◽  
Molecular Data ◽  
Multicommodity Flow ◽  
Flow Problems ◽  
Canonical Metric ◽  
Tight Span ◽  
Finite Metric Space ◽  
A Cell

To a finite metric space $(X,d)$ one can associate the so called tight-span $T(d)$ of $d$, that is, a canonical metric space $(T(d),d_\infty)$ into which $(X,d)$ isometrically embeds and which may be thought of as the abstract convex hull of $(X,d)$. Amongst other applications, the tight-span of a finite metric space has been used to decompose and classify finite metrics, to solve instances of the server and multicommodity flow problems, and to perform evolutionary analyses of molecular data. To better understand the structure of $(T(d),d_\infty)$ the concept of a cell-decomposable metric was recently introduced, a metric whose associated tight-span can be decomposed into simpler tight-spans. Here we show that cell-decomposable metrics and totally split-decomposable metrics — a class of metrics commonly applied within phylogenetic analysis — are one and the same thing, and also provide some additional characterizations of such metrics.

scholarly journals The polytopal structure of the tight-span of a totally split-decomposable metric

2019 ◽  
Vol 342 (3) ◽  
pp. 868-878
Author(s):  
K.T. Huber ◽  
J. Koolen ◽  
V. Moulton
Keyword(s):  
Tight Span

From metrics to networks: The tight span

2012 ◽  
pp. 75-103
Author(s):  
Andreas Dress ◽  
Katharina T. Huber ◽  
Jacobus Koolen ◽  
Vincent Moulton ◽  
Andreas Spillner
Keyword(s):  
Tight Span

scholarly journals An algorithm for the construction of the tight span of finite subsets of the Manhattan plane

2021 ◽  
Vol 95 ◽  
pp. 101741
Author(s):  
Mehmet Kılıç ◽  
Şahin Koçak ◽  
Yunus Özdemir
Keyword(s):  
Tight Span

scholarly journals Block realizations of finite metrics and the tight-span construction I: The embedding theorem

2008 ◽  
Vol 21 (12) ◽  
pp. 1306-1309 ◽  
Author(s):  
Andreas W.M. Dress ◽  
Katharina T. Huber ◽  
Jacobus Koolen ◽  
Vincent Moulton
Keyword(s):  
Embedding Theorem ◽  
Tight Span

scholarly journals On the structure of the tight-span of a totally split-decomposable metric

2006 ◽  
Vol 27 (3) ◽  
pp. 461-479 ◽  
Author(s):  
K.T. Huber ◽  
J.H. Koolen ◽  
V. Moulton
Keyword(s):  
Tight Span

scholarly journals On the Topological and Uniform Structure of Diversities

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Andrew Poelstra
Keyword(s):  
Uniform Convergence ◽  
Natural Transformation ◽  
Uniform Continuity ◽  
Uniform Structure ◽  
Natural Analogue ◽  
Uniform Spaces ◽  
Tight Span ◽  
Cauchy Sequences ◽  
Analytical Properties ◽  
Uniformly Continuous

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note, we consider the analytical properties of diversities, in particular the generalizations of uniform continuity, uniform convergence, Cauchy sequences, and completeness to diversities. We develop conformities, a diversity analogue of uniform spaces, which abstract these concepts in the metric case. We show that much of the theory of uniform spaces admits a natural analogue in this new structure; for example, conformities can be defined either axiomatically or in terms of uniformly continuous pseudodiversities. Just as diversities can be restricted to metrics, conformities can be restricted to uniformities. We find that these two notions of restriction, which are functors in the appropriate categories, are related by a natural transformation.

scholarly journals Tight span of subsets of the plane with the maximum metric

2016 ◽  
Vol 301 ◽  
pp. 693-710 ◽  
Author(s):  
Mehmet Kılıç ◽  
Şahin Koçak
Keyword(s):  
Tight Span
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