CONTENTSIntroduction.....................................................................................................................................5 1. General results.........................................................................................................................7 1.1. Residual sets.........................................................................................................................7 1.2. Generic properties of abstract functional equations..............................................................8II....
A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.
Let be a compact quasi self-similar set in a complete metric space and let denote the space of all probability measures on , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in the lower concentration dimension is equal to , while the upper concentration dimension is equal to the Hausdorff dimension of .
A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.
Let X be a locally compact, separable metric space. We prove that , where and stand for the concentration dimension and the topological dimension of X, respectively.
We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems where are bi-lipschitzean transformations.
Si dimostra che arbitrariamente vicino ad ogni equazione differenziale in (§ 1) ne esiste almeno una per cui il corrispondente problema di Cauchy (1) è sprovvisto di soluzioni. Similmente, arbitrariamente vicino ad ogni equazione differenziale in (§2) ne esiste almeno una per cui le successive approssimazioni (3), relative al problema di Cauchy (2), non convergono.
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