Location of polygon vertices on circles and its application in transport studies

Ján Černý; Filip Guldan

Aplikace matematiky (1987)

  • Volume: 32, Issue: 2, page 81-95
  • ISSN: 0862-7940

Abstract

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The paper deals with the problem how to locate a set of polygon vertices on given circles fulfilling some criteria of "regularity" of individual and composed polygons. Specifying the conditions we can obtain a lot of particular versions of this general problem. Some of them are already solved, the others are not. Applications of this theory can be found in scheduling of periodically repeating processes, e.g. in coordination of several urban lines on a common leg, in optimization of the rhythm of a marshalling yard etc.

How to cite

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Černý, Ján, and Guldan, Filip. "Location of polygon vertices on circles and its application in transport studies." Aplikace matematiky 32.2 (1987): 81-95. <http://eudml.org/doc/15482>.

@article{Černý1987,
abstract = {The paper deals with the problem how to locate a set of polygon vertices on given circles fulfilling some criteria of "regularity" of individual and composed polygons. Specifying the conditions we can obtain a lot of particular versions of this general problem. Some of them are already solved, the others are not. Applications of this theory can be found in scheduling of periodically repeating processes, e.g. in coordination of several urban lines on a common leg, in optimization of the rhythm of a marshalling yard etc.},
author = {Černý, Ján, Guldan, Filip},
journal = {Aplikace matematiky},
keywords = {regularity measures; optimal location; coordination; transport; common leg; marshalling yard; polygon vertices; scheduling of periodically repeating processes; regularity measures; optimal location; coordination; transport; common leg; marshalling yard; polygon vertices; scheduling of periodically repeating processes},
language = {eng},
number = {2},
pages = {81-95},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Location of polygon vertices on circles and its application in transport studies},
url = {http://eudml.org/doc/15482},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Černý, Ján
AU - Guldan, Filip
TI - Location of polygon vertices on circles and its application in transport studies
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 2
SP - 81
EP - 95
AB - The paper deals with the problem how to locate a set of polygon vertices on given circles fulfilling some criteria of "regularity" of individual and composed polygons. Specifying the conditions we can obtain a lot of particular versions of this general problem. Some of them are already solved, the others are not. Applications of this theory can be found in scheduling of periodically repeating processes, e.g. in coordination of several urban lines on a common leg, in optimization of the rhythm of a marshalling yard etc.
LA - eng
KW - regularity measures; optimal location; coordination; transport; common leg; marshalling yard; polygon vertices; scheduling of periodically repeating processes; regularity measures; optimal location; coordination; transport; common leg; marshalling yard; polygon vertices; scheduling of periodically repeating processes
UR - http://eudml.org/doc/15482
ER -

References

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  1. J. Černý M. Hejný, Optimization of the rhythm of a net of urban transport with respect to the total waiting time of passengers for a net of type Y, (Slovak) Doprava 6 (1965), 437-443. (1965) 
  2. J. Černý M. Hejný, Mathematical solution of optimization of the rhythm of a net of type У, (Slovak) Sborník prací VŠD a VÚD 5, (1967), 5-15. (1967) 
  3. J. Černý, Problems of systems of regular polygons on a circle and their application in transport, (Slovak) Matematické obzory l, (1972), 51 - 59. (1972) 
  4. J. Černý, Applied mathematics and transport, (Slovak) Pokroky matematiky, fyziky a astronómie 6 (1974), 316-323. (1974) MR0469252
  5. F. Guldan, Mathematical problems of transport schedules design, (Slovak) (Thesis) Comenius University (1975). (1975) 
  6. F. Guldan, Maximization of distances of regular polygons on a circle and a generalization of the problem, (Slovak) (Dissertation) Comenius University (1976). (1976) Zbl0444.90101
  7. F. Guldan, Maximization of distances of regular polygons on a circle, Aplikace matematiky 25 (1980), 182-195. (1980) Zbl0444.90101MR0568524

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