Canonical coordinates and natural equations for minimal time-like surfaces in $\mathbf{R}^4_2$

2020 ◽  
Vol 43 (3) ◽  
pp. 524-572
Author(s):  
Georgi Ganchev ◽  
Krasimir Kanchev
Keyword(s):  
Canonical Coordinates ◽  
Minimal Time

scholarly journals Forecasting Hamiltonian dynamics without canonical coordinates

2021 ◽  
Author(s):  
Anshul Choudhary ◽  
John F. Lindner ◽  
Elliott G. Holliday ◽  
Scott T. Miller ◽  
Sudeshna Sinha ◽  
...  
Keyword(s):  
Hamiltonian Dynamics ◽  
Canonical Coordinates

scholarly journals Construction of canonical coordinates for exponential Lie groups

2009 ◽  
Vol 361 (12) ◽  
pp. 6283-6348 ◽  
Author(s):  
Didier Arnal ◽  
Bradley Currey ◽  
Bechir Dali
Keyword(s):  
Lie Groups ◽  
Canonical Coordinates ◽  
Exponential Lie Groups

A compass without a map: tortuosity and orientation of eastern painted turtles (Chrysemys picta picta) released in unfamiliar territory

2006 ◽  
Vol 84 (8) ◽  
pp. 1129-1137 ◽  
Author(s):  
I.R. Caldwell ◽  
V.O. Nams
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Spatial Scales ◽  
Chrysemys Picta ◽  
Reference Stimulus ◽  
Correlated Random Walk ◽  
Specific Mechanism ◽  
Minimal Time ◽  
Painted Turtles

Orientation mechanisms allow animals to spend minimal time in hostile areas while reaching needed resources. Identification of the specific mechanism used by an animal can be difficult, but examining an animal's path in familiar and unfamiliar areas can provide clues to the type of mechanism in use. Semiaquatic turtles are known to use a homing mechanism in familiar territory to locate their home lake while on land, but little is known about their ability to locate habitat in unfamiliar territory. We tested the tortuosity and orientation of 60 eastern painted turtles ( Chrysemys picta picta (Schneider, 1783)). We released turtles at 20 release points located at five distances and in two directions from two unfamiliar lakes. Turtle trails were quite straight (fractal dimension between 1.1 and 1.025) but were not oriented towards water from any distance (V-test; u < 0.72; P > 0.1). Turtles maintained their initially chosen direction but either could not detect water or were not motivated to reach it. Furthermore, paths were straighter at larger spatial scales than at smaller spatial scales, which could not have occurred if the turtles had been using a correlated random walk. Turtles must therefore be using a reference stimulus for navigation even in unfamiliar areas.

Anthropometric comparison of muscular and obese men

1961 ◽  
Vol 16 (6) ◽  
pp. 955-959 ◽  
Author(s):  
W. Leonard Taylor ◽  
Albert R. Behnke
Keyword(s):  
Body Weight ◽  
Anthropometric Data ◽  
Reference Base ◽  
Minimal Time ◽  
Tape Measure ◽  
Large Numbers ◽  
Special Apparatus ◽  
Physiologic Parameters ◽  
D Values

Body weight is frequently too gross as a reference base for physiologic parameters. Adequate techniques are available to measure such components as water and fat, but these procedures are time consuming and require special apparatus. The high correlation, however, between anthropometric circumferences, stature, and body weight makes possible a partition of weight into components, W( A) and W( B). In obese men it can be shown that the “trunk” W( A) component greatly exceeds the weight of W( B) referable chiefly to the extremities. In athletes, W( B) exceeds W( A). The average of W( A) and W( B) closely approximates body weight. From the anthropometric perimeters it is possible to calculate d values which can be used to construct a somatogram to provide quantitative representation of bodily configuration. The technique for procurement of the anthropometric data can be carried out on large numbers of individuals in minimal time and requires only a tape measure. Submitted on April 28, 1961

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