Title | On the "triangular" inequality in the theory of two-phase random media |
Publication Type | Journal Article |
Year of Publication | 1997 |
Authors | Markov K |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 89 |
Issue | Livre 1 - Mathématiques et Mecanique |
Pagination | 159-166 |
ISSN | 0205-0808 |
Keywords | correlation functions, random materials, two-phase media |
Abstract | A necessary condition on the two-point correlation function of binary random media, noticed by Matheron [1] and called by him "triangular" inequality, is studied in this note. An appropriate result, due to Achiezer and Glazman [2], is first recalled. Simple consequences of this inequality are given, as well as a necessary condition for its validity in a statistically isotropic medium. It is shown that it represents a requirement, independent of that of the familiar positive definiteness, that should be additionally imposed on the two-point correlation function of any realistic binary medium. |
1991/95 MSC | 60G60, 73B35 |
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89-159-166.pdf | 752.31 KB |