By Le Mehaute A.

ISBN-10: 0849377226

ISBN-13: 9780849377228

Fractal geometry, according to recursive mathematical schemas, offers a way for modeling loads of usual phenomena. therefore, it really is of accelerating curiosity to physicists, chemists, biologists, and geographers, between others. an enormous caliber of fractality is that it not just unifies phenomena formerly considered anomalous or disparate in one theoretical framework, however it additionally promotes a go back to graphical remedy, which were virtually thoroughly banished from clinical proposal in want of analysis.This e-book casts a brand new, vigorous mild on clinical territories nonetheless now not absolutely explored. it really is designed for examine staff, engineers, and experimentalists confronted with difficulties of degree and motion in heterogenous fabrics and environments. a number of colour plates illustrate the consequences and results of this thought for many of the questions raised by means of the making an allowance for of time in a fractal area.

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Weak maps (or maps, as they were then called) were first defined in Higgs [66]. A survey can be found in Kung and Nguyen [86]. A more restricted notion of morphisms is the notion of strong maps. e. a(x v y) = a(x) v a(y) for elements x andy in G). Equivalently, a is a strong map if the inverse image of a closed set of points is 48 also a closed set of points in G. Thus, strong maps are analogues for matroids of continuous maps in topology. The foundations of the theory of strong maps were laid in the paper "Strong maps of geometries" by Higgs, the last paper reprinted in this chapter.

30(1978), 238- 249. : A factorization theorem for comaps of geometric lattices, J. Combin. Theory Ser. B 34(1983), 40-47. L. ), Cambridge Univ. Press, Cambridge, 1986. S. L. ), Cambridge Univ. Press, Cambridge, 1986. : Acyclic and totally cyclic orientations of combinatorial geometries, Discrete Math. 20(1977178), 51-61. : On the Tutte polynomial of a morphism of matroids, Combinatorics 79, Part I, Ann. Discrete Math. 8(1980), 7-20. : Matroids as the study of geometrical configurations, Higher Combinatorics (M.

ALT and 0. SCHREIBER), New foundations of projective and affine geometry, Annals of Math. (2) 37(1936), 456-481. The aim of this paper is to find a lattice-theoretic (or "algebraic") formulation of the axioms of affine and projective geometry and using it, to determine the theorems which are true in both affine and projective geometry. 36 Along the way, several elementary theorems (such as upper semimodularity of the rank function) which are also true in matroid theory are derived. 1937 F. KLEIN-BARMEN, Birkhoffsche und harmonische Verbande, Math.

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