scholarly journals The behaviour of the total twist and self-linking number of a closed space curve under inversions.

1975 ◽  
Vol 36 ◽  
pp. 254 ◽  
Author(s):  
Thomas F. Banchoff ◽  
James H. White
Keyword(s):  
Space Curve ◽  
Closed Space ◽  
Linking Number

scholarly journals Geometry of Călugăreanu's theorem

2005 ◽  
Vol 461 (2062) ◽  
pp. 3245-3254 ◽  
Author(s):  
M.R Dennis ◽  
J.H Hannay
Keyword(s):  
Crossing Number ◽  
Space Curve ◽  
Closed Space ◽  
Linking Number ◽  
Space Geometry ◽  
The Common ◽  
Central Result

A central result in the space geometry of closed twisted ribbons is Călugăreanu's theorem (also known as White's formula, or the Călugăreanu–White–Fuller theorem). This enables the integer linking number of the two edges of the ribbon to be written as the sum of the ribbon twist (the rate of rotation of the ribbon about its axis) and its writhe. We show that twice the twist is the average, over all projection directions, of the number of places where the ribbon appears edge-on (signed appropriately)—the ‘local’ crossing number of the ribbon edges. This complements the common interpretation of writhe as the average number of signed self-crossings of the ribbon axis curve. Using the formalism we develop, we also construct a geometrically natural ribbon on any closed space curve—the ‘writhe framing’ ribbon. By definition, the twist of this ribbon compensates its writhe, so its linking number is always zero.

Closed polylines inscribed in a closed space curve

2011 ◽  
Vol 175 (5) ◽  
pp. 556-558
Author(s):  
V. V. Makeev
Keyword(s):  
Space Curve ◽  
Closed Space

COMPUTING THE WRITHE OF A KNOT

2001 ◽  
Vol 10 (03) ◽  
pp. 387-395 ◽  
Author(s):  
DAVID CIMASONI
Keyword(s):  
Space Curve ◽  
Closed Formula ◽  
Closed Space ◽  
Polygonal Curves

We study the variation of the Tait number of a closed space curve according to its different projections. The results are used to compute the writhe of a knot, leading to a closed formula in case of polygonal curves.

An index formula for the self-linking number of a space curve

2008 ◽  
Vol 134 (1) ◽  
pp. 197-202 ◽  
Author(s):  
Peter Røgen
Keyword(s):  
Space Curve ◽  
The Self ◽  
Index Formula ◽  
Linking Number

Framed curves and knotted DNA

2013 ◽  
Vol 41 (2) ◽  
pp. 635-638 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Space Curve ◽  
Closed Space ◽  
Global Geometry

The present mini-review covers the local and global geometry of framed curves and the computation of twist and writhe in knotted DNA circles. Classical inequalities relating the total amount of bending of a closed space curve and associated knot parameters are also explained.

scholarly journals Chords and arclength of a closed space curve

1992 ◽  
Vol 42 (3) ◽  
pp. 471-474
Author(s):  
Pavel Pech
Keyword(s):  
Space Curve ◽  
Closed Space

scholarly journals Use of masks in public places in Poland during SARS-Cov-2 epidemic: a covert observational study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Maria Ganczak ◽  
Oskar Pasek ◽  
Łukasz Duda – Duma ◽  
Dawid Świstara ◽  
Marcin Korzeń
Keyword(s):  
Health Promotion ◽  
Observational Study ◽  
Control Measure ◽  
Communication Channels ◽  
Public Spaces ◽  
Personal Health ◽  
Closed Space ◽  
Public Places ◽  
Health Control ◽  
Over Time

Abstract Background Face masks have been employed in the COVID-19 pandemic plans as a public and personal health control measure against the spread of SARS-CoV-2. In Poland, obligatory wearing of masks in public spaces was introduced on April 10th, 2020; a relaxation of previous universal measures was announced on May 29th, 2020, limiting use to indoor public places. Objective To assess use of masks or other protective devices in public spaces in Poland during the SARS-Cov-2 epidemic. Methods A non-participatory covert observational study was conducted on three dates, (10.05/18.05/25.05.2020) at public spaces in 13 regions with different risks. Ten consecutive individuals were observed by each of 82 medical students (n = 2460 observations), using a structured checklist. Results Among 2353 observed persons, the female/male ratios were 1.0, 1.1, and 1.0 on the three dates. Almost three quarters - 73.6% (n = 552/750) were using masks on date 1, 66.5% (544/818) on date 2; and 65.7% (516/785) on date 3. Cloth masks predominated on all dates (64.7–62.3%-62.6%), followed by medical (23.4–28.5%-26.9%). Being female (OR = 1.77–1.47-1.53 respectively) and location in a closed space (OR = 2.60–2.59-2.32) were each associated with higher usage. Participants in sports were about two times less likely to use masks (OR = 0.64–0.53-0.53) as compared to other activities. The proportion using masks correctly decreased gradually over time (364/552; 65.9%; 339/544; 62.3% and 304/516; 58.9%). More females wore masks correctly (date 1: 205/294; 69.7% vs 159/258; 61.6%, and date 3: 186/284; 65.5% vs 118/232; 50.9%; p = 0.045; p = 0.0008 respectively). Uncovered noses (47.3–52.7%) and masks around the neck (39.2–42.6%) were the most frequent incorrect practices. Conclusions Practices were not in line with official recommendations, especially among males, and deteriorated over time. Cloth masks were predominantly used in public spaces. Health promotion, through utilizing all available communication channels, would be helpful to increase compliance.

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