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Orlicz type category theorems for functional and differential equations

Józef Myjak — 1983

CONTENTSIntroduction.....................................................................................................................................5 1. General results.........................................................................................................................7 1.1. Residual sets.........................................................................................................................7 1.2. Generic properties of abstract functional equations..............................................................8II....

Boundary value problem for functional differential equations

Józef Myjak — 1976

Annales Polonici Mathematici

A remark on Scorza-Dragoni theorem for differential inclusions

Józef Myjak — 1989

Časopis pro pěstování matematiky

Reinforced walk on graphs and neural networks

Józef Myjak; Ryszard Rudnicki — 2008

Studia Mathematica

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.

Some generic properties of concentration dimension of measure

Józef Myjak; Tomasz Szarek — 2003

Bollettino dell'Unione Matematica Italiana

Let $K$ be a compact quasi self-similar set in a complete metric space $X$ and let $M_{1} (K)$ denote the space of all probability measures on $K$ , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in $M_{1} (K)$ the lower concentration dimension is equal to $0$ , while the upper concentration dimension is equal to the Hausdorff dimension of $K$ .

On the Information Dimensions

Józef Myjak; Ryszard Rudnicki — 2007

Bollettino dell'Unione Matematica Italiana

A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.

Szpilrajn type theorem for concentration dimension

Jozef Myjak; Tomasz Szarek — 2002

Fundamenta Mathematicae

Let X be a locally compact, separable metric space. We prove that $d i m_{T} X = i n f d i m_{L} X^{'} : X^{'} i s h o m e o m o r p h i c t o X$ , where $d i m_{L} X$ and $d i m_{T} X$ stand for the concentration dimension and the topological dimension of X, respectively.

Estimates of capacity of self-similar measures

Jozef Myjak; Tomasz Szarek — 2002

Annales Polonici Mathematici

We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems $(S_{i}, p_{i}) : i = 1, . . ., N$ where $S_{i}$ are bi-lipschitzean transformations.

Two density properties of ordinary differential equations

Francesco S. De Blasi; Jozef Myjak — 1976

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Si dimostra che arbitrariamente vicino ad ogni equazione differenziale in $c_{0}$ (§ 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 $l_{p}$ (§2) ne esiste almeno una per cui le successive approssimazioni (3), relative al problema di Cauchy (2), non convergono.

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