scholarly journals Easy Identification of Generalized Common and Conserved Nested Intervals

2014 ◽  
Vol 21 (7) ◽  
pp. 520-533
Author(s):  
Fabien de Montgolfier ◽  
Mathieu Raffinot ◽  
Irena Rusu
Keyword(s):  
Nested Intervals

The Nested Intervals Theorem

2017 ◽  
pp. 131-148
Author(s):  
Titu Andreescu ◽  
Cristinel Mortici ◽  
Marian Tetiva
Keyword(s):  
Nested Intervals

scholarly journals Prediction of astrometric microlensing events from Gaia DR2 proper motions

2018 ◽  
Vol 620 ◽  
pp. A175 ◽  
Author(s):  
J. Klüter ◽  
U. Bastian ◽  
M. Demleitner ◽  
J. Wambsganss
Keyword(s):  
Proper Motion ◽  
Proper Motions ◽  
Stellar Objects ◽  
Gravitational Microlensing ◽  
Data Release ◽  
The Future ◽  
Nested Intervals ◽  
Excellent Tool ◽  
Gaia Dr2

Context. Astrometric gravitational microlensing is an excellent tool to determine the mass of stellar objects. Using precise astrometric measurements of the lensed position of a background source in combination with accurate predictions of the positions of the lens and the unlensed source it is possible to determine the mass of the lens with an accuracy of a few percent. Aims. Making use of the recently published Gaia Data Release 2 (DR2) catalogue, we want to predict astrometric microlensing events caused by foreground stars with high proper motion passing a background source in the coming decades. Results. We selected roughly 148 000 high-proper-motion stars from Gaia DR2 with μtot > 150 mas yr−1 as potential lenses. We then searched for background sources close to their paths. Using the astrometric parameters of Gaia DR2, we calculated the future positions of source and lens. With a nested-intervals algorithm we determined the date and separation of the closest approach. Using Gaia DR2 photometry we determined an approximate mass of the lens, which we used to calculate the expected microlensing effects. Conclusions. We predict 3914 microlensing events caused by 2875 different lenses between 2010 and 2065, with expected shifts larger than 0.1 mas between the lensed and unlensed positions of the source. Of those, 513 events are expected to happen between 2014.5 and 2026.5 and might be measured by Gaia. For 127 events we also expect a magnification between 1 mmag and 3 mag.

Nested intervals tree encoding in SQL

2005 ◽  
Vol 34 (2) ◽  
pp. 47-52 ◽  
Author(s):  
Vadim Tropashko
Keyword(s):  
Nested Intervals

scholarly journals Unstable Limit Cycles and Singular Attractors in a Two-Dimensional Memristor-Based Dynamic System

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 415 ◽  
Author(s):  
Hui Chang ◽  
Qinghai Song ◽  
Yuxia Li ◽  
Zhen Wang ◽  
Guanrong Chen
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic System ◽  
Numerical Simulations ◽  
Limit Cycles ◽  
Two Dimensional ◽  
Local Activity ◽  
Period 2 ◽  
Subcritical Hopf Bifurcation ◽  
Dimensional Dynamical System ◽  
Nested Intervals

This paper reports the finding of unstable limit cycles and singular attractors in a two-dimensional dynamical system consisting of an inductor and a bistable bi-local active memristor. Inspired by the idea of nested intervals theorem, a new programmable scheme for finding unstable limit cycles is proposed, and its feasibility is verified by numerical simulations. The unstable limit cycles and their evolution laws in the memristor-based dynamic system are found from two subcritical Hopf bifurcation domains, which are subdomains of twin local activity domains of the memristor. Coexisting singular attractors are discovered in the twin local activity domains, apart from the two corresponding subcritical Hopf bifurcation domains. Of particular interest is the coexistence of a singular attractor and a period-2 or period-3 attractor, observed in numerical simulations.

scholarly journals Cousin’s Lemma

2016 ◽  
Vol 24 (2) ◽  
pp. 107-119 ◽  
Author(s):  
Roland Coghetto
Keyword(s):  
Metric Space ◽  
Complete Metric Space ◽  
Closed Contour ◽  
Riemann Integral ◽  
Euclidean Metric ◽  
Zero Radius ◽  
Connected Area ◽  
Cantor’S Theorem ◽  
Nested Intervals

Summary We formalize, in two different ways, that “the n-dimensional Euclidean metric space is a complete metric space” (version 1. with the results obtained in [13], [26], [25] and version 2., the results obtained in [13], [14], (registrations) [24]). With the Cantor’s theorem - in complete metric space (proof by Karol Pąk in [22]), we formalize “The Nested Intervals Theorem in 1-dimensional Euclidean metric space”. Pierre Cousin’s proof in 1892 [18] the lemma, published in 1895 [9] states that: “Soit, sur le plan YOX, une aire connexe S limitée par un contour fermé simple ou complexe; on suppose qu’à chaque point de S ou de son périmètre correspond un cercle, de rayon non nul, ayant ce point pour centre : il est alors toujours possible de subdiviser S en régions, en nombre fini et assez petites pour que chacune d’elles soit complétement intérieure au cercle correspondant à un point convenablement choisi dans S ou sur son périmètre.” (In the plane YOX let S be a connected area bounded by a closed contour, simple or complex; one supposes that at each point of S or its perimeter there is a circle, of non-zero radius, having this point as its centre; it is then always possible to subdivide S into regions, finite in number and sufficiently small for each one of them to be entirely inside a circle corresponding to a suitably chosen point in S or on its perimeter) [23]. Cousin’s Lemma, used in Henstock and Kurzweil integral [29] (generalized Riemann integral), state that: “for any gauge δ, there exists at least one δ-fine tagged partition”. In the last section, we formalize this theorem. We use the suggestions given to the Cousin’s Theorem p.11 in [5] and with notations: [4], [29], [19], [28] and [12].

The Interval Structure of Optimal Disclosure

Econometrica ◽  
2019 ◽  
Vol 87 (2) ◽  
pp. 653-675 ◽  
Author(s):  
Yingni Guo ◽  
Eran Shmaya
Keyword(s):  
Private Information ◽  
Simple Algorithm ◽  
Optimal Mechanism ◽  
Nested Intervals

A sender persuades a receiver to accept a project by disclosing information about a payoff‐relevant quality. The receiver has private information about the quality, referred to as his type. We show that the sender‐optimal mechanism takes the form of nested intervals: each type accepts on an interval of qualities and a more optimistic type's interval contains a less optimistic type's interval. This nested‐interval structure offers a simple algorithm to solve for the optimal disclosure and connects our problem to the monopoly screening problem. The mechanism is optimal even if the sender conditions the disclosure mechanism on the receiver's reported type.

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