http://hdl.handle.net/11716/13646 2026-04-09T02:13:22Z 2026-04-09T02:13:22Z Dziok, Jacek http://hdl.handle.net/11716/13655 2025-03-26T11:44:06Z 2012-01-01T00:00:00Z

Classes of multivalent analytic functions with Montel's normalization Dziok, Jacek In this paper we define classes of functions with Montel's normalization. We investigate the coeffcients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral means inequalities for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.

2012-01-01T00:00:00Z Domańska, Katarzyna http://hdl.handle.net/11716/13654 2025-03-26T11:36:27Z 2012-01-01T00:00:00Z

An analytic description of the class of rational associative functions Domańska, Katarzyna We dael with the following problem: which rational functions of two variables are associative? We provide a complete answer to that question.

2012-01-01T00:00:00Z Pokora, Piotr Skrzyński, Marcin http://hdl.handle.net/11716/13653 2025-03-26T11:18:43Z 2012-01-01T00:00:00Z

Rank function equations Pokora, Piotr; Skrzyński, Marcin The purpose of this paper is to introduce the notion of rank function equation, and to present some results on such equations. In particular, we find all sequences $(A_{1}, ..., A_{k}, B)$ of nonzero nilpotent $n \times n$ matrices satisfying condition $$ \forall\, m \in \{1, ..., n\} :\, \sum_{i=1}^{k} r_{A_{i}}(m) = r_{B}(m),$$ and give a characterization of all sequences $(A_{1}, ..., A_{k}, B)$ of nilpotent $n \times n$ matrices such that $$ \forall\, m \in \{1, ..., n\} :\, \sum_{i = 1}^k f (r_{A_{i}} (m)) = r_{B} (m),$$ where $f : \mathbb{R} \supset [0, \infty) \longrightarrow \mathbb{R}$ is a function with certain natural properties. We also provide a geometric characterization of some solutions to rank function equations.

2012-01-01T00:00:00Z Górowski, Jan Łomnicki, Adam http://hdl.handle.net/11716/13652 2025-03-26T11:08:59Z 2012-01-01T00:00:00Z

Congruences characterizing twin primes Górowski, Jan; Łomnicki, Adam Inspired by P.A. Clement’s results in [2], we give new necessary and sufficient conditions for two prime numbers to be twin primes.

2012-01-01T00:00:00Z