COMPLETE LOCAL CHARACTERIZATION OF STRONG 26-SURFACES: CONTINUOUS ANALOGS FOR STRONG 26-SURFACES

Author(s):  
RÉMY MALGOUYRES ◽  
GILLES BERTRAND

In Ref. 6, two similar characterizations of discrete surfaces of ℤ3 are proposed which are called strong 18-surfaces and strong 26-surfaces. The proposed characterizations consist in some natural global properties of surfaces. In this paper, we first give local necessary conditions for an object to be a strong 26-surface. An object satisfying these local properties is called a near strong 26-surface. Then we construct continuous analogs for near strong 26-surfaces and, using the continuous Jordan Theorem, we prove that the necessary local conditions previously introduced in fact give a complete local characterization of strong 26-surfaces: the class of near strong 26-surfaces coincides with the class of strong 26-surfaces.

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.


2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll

Author(s):  
Andrea Lucibello ◽  
Christopher Hardly Joseph ◽  
Emanuela Proietti ◽  
Giovanni Maria Sardi ◽  
Giovanni Capoccia ◽  
...  

10.37236/3414 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Sarah Behrens ◽  
Catherine Erbes ◽  
Michael Ferrara ◽  
Stephen G. Hartke ◽  
Benjamin Reiniger ◽  
...  

A sequence of nonnegative integers is $k$-graphic if it is the degree sequence of a $k$-uniform hypergraph. The only known characterization of $k$-graphic sequences is due to Dewdney in 1975. As this characterization does not yield an efficient algorithm, it is a fundamental open question to determine a more practical characterization. While several necessary conditions appear in the literature, there are few conditions that imply a sequence is $k$-graphic. In light of this, we present sharp sufficient conditions for $k$-graphicality based on a sequence's length and degree sum.Kocay and Li gave a family of edge exchanges (an extension of 2-switches) that could be used to transform one realization of a 3-graphic sequence into any other realization. We extend their result to $k$-graphic sequences for all $k \geq 3$. Finally we give several applications of edge exchanges in hypergraphs, including generalizing a result of Busch et al. on packing graphic sequences.


2021 ◽  
Author(s):  
Choolwe Muzyamba

Abstract Background The onset of the covid19 pandemic has sparked heated debate among scholars on the relevance of lockdowns. There are those in favor of the lockdown and others who are critical of it. However, despite the increased interest in understanding the relevance of lockdowns, there still has not been much focus on its relevance in low income countries like Zambia. Thus with the help of the SRT, we set out to explore and document the local characterization of the lockdown by residents of Lusaka, Zambia.Methods A qualitative study in the form of interviews was conducted in Lusaka, Zambia involving a sample of 68 participants. Due to the lockdown measures that were in place during the study, the interviews were conducted via phone calls and the data collected were later analyzed by use of thematic analysis technique.Results The lockdown was on one hand lauded for slowing down the incidence rates, preventing fatalities, and for protecting the healthcare system from collapse. On the other hand, it was criticized for exacerbating poverty levels, unemployment rates, increasing the rate of mental health problems, aiding gender based violence, and intensifying political repression and corruption. The results speak to the complexity in the characterization of the lockdown as a response to covid19 in Zambia. This observation demonstrates the folly of viewing, applying and characterizing the covid19 lockdown as a ‘one-size-fits-all’ approach in Zambia.Conclusion Thus rather than definitely establishing the lockdown as an incontestable good, as it is depicted by some scholars or as useless by its critics, our findings instead demonstrate the diversity and complexity in how it is locally viewed by Zambians. The study provides grounds for caution on simplistic and binary characterization of lockdowns. It indicates the need for careful dialog between the designers of lockdowns and citizens in order to tailor such interventions to local realities in context-specific ways. It also shows that though the development of such interventions, all the various and complex elements it embodies must be taken into account in order to realize optimum outcomes.


10.37236/1882 ◽  
2006 ◽  
Vol 11 (2) ◽  
Author(s):  
Eric Babson ◽  
Isabella Novik

Certain necessary conditions on the face numbers and Betti numbers of simplicial complexes endowed with a proper action of a prime order cyclic group are established. A notion of colored algebraic shifting is defined and its properties are studied. As an application a new simple proof of the characterization of the flag face numbers of balanced Cohen-Macaulay complexes originally due to Stanley (necessity) and Björner, Frankl, and Stanley (sufficiency) is given. The necessity portion of their result is generalized to certain conditions on the face numbers and Betti numbers of balanced Buchsbaum complexes.


Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 89-97 ◽  
Author(s):  
Martin Shoptrajanov ◽  
Nikita Shekutkovski

We give necessary conditions for a set to be topologically transitive attractor of an analytic plane flow using topological characterization of ?-limit sets and the concept of upper semi-continuity of multi valued maps.


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