http://hdl.handle.net/11716/57 2026-04-08T22:29:35Z http://hdl.handle.net/11716/13660 Approximation by some combinations of the Poisson integrals for Hermite and Laguerre expansions Krech, Grażyna; Wachnicki, Eugeniusz The aim of this paper is the study of a rate of convergence of some combinations of the Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over the Poisson integrals. We prove also the Voronovskaya type theorem for these new operators. 2013-01-01T00:00:00Z http://hdl.handle.net/11716/13652 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 http://hdl.handle.net/11716/13651 On stability of some functional equations and topology of their target spaces Moszner, Zenon Some remarks about the coherence of the stability of several functional equations with topology of their target spaces are given. The equations in question are: homogeneity (first of all) and quadratic ones, as well as those of Drygas, Jensen and Schröder. Moreover, we prove, by method different than those used in earlier papers, the superstability of the following equations: Dhombres’, Lobachevski’s and Mikusiński’s ones and those of cosine, sine and of homomorphisms. 2012-01-01T00:00:00Z http://hdl.handle.net/11716/13220 Kształcenie przyszłych nauczycieli matematyki - wyzwanie edukacyjne Żeromska, Anna K. The purpose of this paper is to draw attention to the still current (as compared to the reform of higher education) issue: how should we train mathematics teachers in order to attain the desired outcomes? The article presents an extensive range of thought-provoking questions about what knowledge of well-educated mathematics teachers should be. References to the already existing didactic literature are included. Reflections on this question, containing some arguments as to the direction of the desired changes are presented. In support of these statements, two studies were carried out among students acting as teachers. Both studies point to the specificity of the necessary mathematical knowledge of teachers, and especially their need to have some flexibility in the transition from higher mathematics to school mathematics and vice versa. 2012-01-01T00:00:00Z