scholarly journals New metric properties for prox-regular sets

2020 ◽  
Author(s):  
S. Adly ◽  
F. Nacry ◽  
L. Thibault
Keyword(s):  
Metric Properties ◽  
Regular Sets

scholarly journals Prox-regular sets and Legendre-Fenchel transform related to separation properties

Optimization ◽  
2020 ◽  
pp. 1-33
Author(s):  
Samir Adly ◽  
Florent Nacry ◽  
Lionel Thibault
Keyword(s):  
Fenchel Transform ◽  
Regular Sets

scholarly journals Plenty of big projections imply big pieces of Lipschitz graphs

2021 ◽  
Author(s):  
Tuomas Orponen
Keyword(s):  
Lipschitz Graphs ◽  
Regular Sets ◽  
Big Pieces

AbstractI prove that closed n-regular sets $$E \subset {\mathbb {R}}^{d}$$ E ⊂ R d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.

scholarly journals Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh
Keyword(s):  
Risk Management ◽  
Invariant Measure ◽  
Invariant Measures ◽  
Interval Exchange ◽  
Management Model ◽  
Closing Lemma ◽  
Symbolic Model ◽  
Metric Properties ◽  
Ergodic Measures ◽  
Maximal Invariant

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

scholarly journals The Walking Index for Spinal Cord Injury (WISCI/WISCI II): nature, metric properties, use and misuse

Spinal Cord ◽  
2013 ◽  
Vol 51 (5) ◽  
pp. 346-355 ◽  
Author(s):  
J F Ditunno ◽  
P L Ditunno ◽  
G Scivoletto ◽  
M Patrick ◽  
M Dijkers ◽  
...  
Keyword(s):  
Spinal Cord ◽  
Spinal Cord Injury ◽  
Metric Properties ◽  
Cord Injury

Topological and metric properties of sets of real numbers with conditions on their expansions in Ostrogradskii series

2007 ◽  
Vol 59 (9) ◽  
pp. 1281-1299
Author(s):  
O. M. Baranovs’kyi ◽  
M. V. Prats’ovytyi ◽  
H. M. Torbin
Keyword(s):  
Real Numbers ◽  
Metric Properties

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

The metric properties of a novel non-motor symptoms scale for Parkinson's disease: Results from an international pilot study

2007 ◽  
Vol 22 (13) ◽  
pp. 1901-1911 ◽  
Author(s):  
Kallol Ray Chaudhuri ◽  
Pablo Martinez-Martin ◽  
Richard G. Brown ◽  
Kapil Sethi ◽  
Fabrizio Stocchi ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Pilot Study ◽  
Motor Symptoms ◽  
Metric Properties ◽  
Non Motor Symptoms

Equational axioms for regular sets

1993 ◽  
Vol 3 (1) ◽  
pp. 1-24 ◽  
Author(s):  
S. L. Bloom ◽  
Z. Ésik
Keyword(s):  
Star Operation ◽  
Regular Sets

We show that, aside from the semiring equations, three equations and two equation schemes characterize the semiring of regular sets with the Kleene star operation.

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