Flows in Networks and Hausdorff Measures Associated. Applications to Fractal Sets in Euclidian Space

Quansheng Liu

Publications mathématiques et informatique de Rennes (1994)

  • Issue: 2, page 1-77

How to cite

top

Liu, Quansheng. "Flows in Networks and Hausdorff Measures Associated. Applications to Fractal Sets in Euclidian Space." Publications mathématiques et informatique de Rennes (1994): 1-77. <http://eudml.org/doc/274026>.

@article{Liu1994,
author = {Liu, Quansheng},
journal = {Publications mathématiques et informatique de Rennes},
keywords = {tree process; network; flow; branching process; random fractal; Hausdorff measure},
language = {eng},
number = {2},
pages = {1-77},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Flows in Networks and Hausdorff Measures Associated. Applications to Fractal Sets in Euclidian Space},
url = {http://eudml.org/doc/274026},
year = {1994},
}

TY - JOUR
AU - Liu, Quansheng
TI - Flows in Networks and Hausdorff Measures Associated. Applications to Fractal Sets in Euclidian Space
JO - Publications mathématiques et informatique de Rennes
PY - 1994
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - 2
SP - 1
EP - 77
LA - eng
KW - tree process; network; flow; branching process; random fractal; Hausdorff measure
UR - http://eudml.org/doc/274026
ER -

References

top
  1. [1] K.B. Athereya and P.E. Ney, Branching processes, Springer-Verlag, Berlin and New York, 1972. Zbl0259.60002MR373040
  2. [2] A.S. Besicovitch, On the fundamental geometrical properties of linearly measurable plan sets of points, Mathematische Annalen, 98 (1928) 422-64. Zbl53.0175.04MR1512414JFM53.0175.04
  3. [3] B. Bollobás, Graph theory, an introductory course. Berlin: Springer Verlag. Zbl0411.05032MR536131
  4. [4] K.J. Falconer, The Geometry of Fractal Sets, Cambridge Univ. Press, (1985). Zbl0587.28004MR867284
  5. [5] K.J. Falconer, Random fractals, Math. Proc. Camb. Phil. Soc., 100 (1986) 559-582. Zbl0623.60020MR857731
  6. [6] K.J. Falconer, Cut set sums and tree processes, Proc. Amer. Math. Soc, (2) 101 (1987) 337-346. Zbl0636.90031MR902553
  7. [7] K.J. Falconer, Fractal Geometry, John Wiley & Sons Ltd, 1990. Zbl0689.28003MR3236784
  8. [8] L.R. Ford and D.R. Fulkerson, Flows in networks, Princeton University Press, 1962. Zbl1216.05047MR159700
  9. [9] S. Graf, Statistically self-similar fractals, Probab. Th. & Rel. Fields74 (1987) 357-392. Zbl0591.60005MR873885
  10. [10] S. Graf, R.D. Maudin and S.C. Williams, The exact Hausdorff dimension in random recursive constructions, Mem.Amer.Math.Soc., Vol.71 (1988) no.381. Zbl0641.60003MR920961
  11. [11] G.R. Grimmett, Random flows network flows : and electrical flows through random media, London Math. Soc. Lecture Note Series: 103 (1985) 59-95. (Surveys in combinatorics 1985. Edited by IAN ANDERSON, Cambridge Univ. press.) Zbl0565.90017MR822770
  12. [12] Y. Guivarc'h, Sur une extension de la notion de loi semi-stable, Anal. Inst.Henri Poincaré, 26 (1990) 261-285. Zbl0703.60012MR1063751
  13. [13] J. Hawkes, Trees generated by a simple branching process, J. London Math. Soc. (2) 24 (1981) 373-384. Zbl0468.60081MR631950
  14. [14] J.P.Kahane, J. Peyrière, Sur certaines martingales de B.Mandelbrot, Adv.Math.22 (1976) 131-145. Zbl0349.60051MR431355
  15. [15] Q.S. Liu, The exact Hausdorff dimension of a branching set, Prépublication N° 135, Laboratoire de Probabilités, Univ. Paris VI, 1992. Zbl0842.60084
  16. [16] R.D. Maudin and S.C. Williams, Random constructions, Asympototic geometric and topological properties, Trans. Amer. Math. Soc.295 (1986), 325-346. Zbl0625.54047MR831202
  17. [17] J. Neveu, Arbres et processus de Galton-Watson, Ann. Inst. Henri Poincaré, 22 (1986) no.2, 199-207. Zbl0601.60082MR850756
  18. [18] C.A. Rogers, Hausdoff measures, Cambridge University Press, 1970. Zbl0915.28002MR281862

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.