scholarly journals On the Hofer girth of the sphere of great circles

2021 ◽  
pp. 1-21
Author(s):  
Itamar Rosenfeld Rauch
Keyword(s):  
Upper Bound ◽  
Great Circle ◽  
Equal Area ◽  
Natural Embedding ◽  
Hamiltonian Diffeomorphism

An oriented equator of [Formula: see text] is the image of an oriented embedding [Formula: see text] such that it divides [Formula: see text] into two equal area halves. Following Chekanov, we define the Hofer distance between two oriented equators as the infimal Hofer norm of a Hamiltonian diffeomorphism taking one to another. Consider [Formula: see text] the space of oriented equators. We define the Hofer girth of an embedding [Formula: see text] as the infimum of the Hofer diameter of [Formula: see text], where [Formula: see text] is homotopic to [Formula: see text]. There is a natural embedding [Formula: see text], sending a point on the sphere to the positively oriented great circle perpendicular to it. In this paper, we provide an upper bound on the Hofer girth of [Formula: see text].

Three Dimensional Upper Bound Modelling for Extrusion of Round-to-Octagon Section Using Linearly Converging Die

2009 ◽  
Vol 424 ◽  
pp. 189-196
Author(s):  
Kali Pada Maity ◽  
Akshaya Kumar Rout
Keyword(s):  
Cross Section ◽  
Upper Bound ◽  
Regular Polygon ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Upper Bound Method ◽  
Equal Area ◽  
Admissible Velocity ◽  
Round Billet ◽  
Die Geometry

The extrusion of section from round billet poses a great challenge for theoretical modeling of the process using upper bound method. The greatest difficulty in three-dimensional upper bound method is to determine kinematically admissible velocity field. The SERR (Spatial Elementary Rigid Region) technique is fairly applicable for analyzing extrusion of sections having re-entrant corners. A modified version of SERR technique has been used for extrusion of octagon sections from round billet through a linearly converging die. The circular cross section of the round billet is approximated by a regular polygon of equal area. The extrusion pressure has been computed for different boundary condition at the die billet interface. The optimum die geometry has been determined.

Charts for Great Circle Sailing

1885 ◽  
Vol 20 (501supp) ◽  
pp. 7991-7991
Author(s):  
Richard A. Proctor
Keyword(s):  
Great Circle

Transient Stability Ranking Technique based on System Parameter Estimation and Extended Equal-Area Criterion

2008 ◽  
Vol 128 (1) ◽  
pp. 101-109 ◽  
Author(s):  
Akira Takeuchi ◽  
Takashi Sato ◽  
Kouya Takafuji ◽  
Hideaki Nishiiri ◽  
Kotaro Takasaki ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
System Parameter ◽  
Transient Stability ◽  
Equal Area ◽  
Stability Ranking ◽  
Ranking Technique

From Littoral to Ozone: On Mike Pearson’s Contributions to Indian Ocean History

2019 ◽  
Vol 2 (1) ◽  
pp. 12-24
Author(s):  
Edward A. Alpers
Keyword(s):  
New York ◽  
Indian Ocean ◽  
Great Circle ◽  
Historical Scholarship ◽  
The Indian Ocean ◽  
Seminal Article

In this article I examine two of Michael Pearson’s most important contributions to our understanding of Indian Ocean history: the concept of the littoral, which he first articulated in his seminal article on “Littoral society: the case for the coast” in The Great Circle 7, no. 1 (1985): 1-8, and his comment in The Indian Ocean (London and New York: Routledge, 2003, p. 9) that “I want it to have a whiff of ozone.” Accordingly, I review Pearson’s publications to see how he has written about these two notions and how they have influenced historical scholarship about the Indian Ocean.

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