http://hdl.handle.net/11089/18154 2026-04-04T02:41:47Z http://hdl.handle.net/11089/18160 Some Non-Measurable Sets Kierus, Alicja This paper contains constructions of some non-measurable sets, based on classical Vitali’s and Bernstein’s constructions (see for example [6]). This constructions probably belong to mathematical folklore, but as far as we know they are rather hard to be found in literature. It seems that the constructed sets can be used as examples in some interesting situations. 2010-01-01T00:00:00Z http://hdl.handle.net/11089/18157 On Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1 Akkouchi, Mohamed F. Galaz-Fontes (Proc. AMS., 1998) has established a criterion for a subset of the space of compact linear operators from a reflexive and separable space X into a Banach space Y to be compact. F. Mayoral (Proc. AMS., 2000) has extended this criterion to the case of Banach spaces not containing a copy of l^1 . The purpose of this note is to give a new proof of the result of F. Mayoral. In our proof, we use l^∞ -spaces, a well known result of H. P. Rosenthal and L.E. Dor which characterizes the spaces without a copy of l^1 and a recent result obtained by G. Nagy in 2007 concerining compact sets in normed spaces. We point out that another proof of Mayoral’s result was given by E. Serrano, C. Pineiro and J.M. Delgado (Proc. AMS., 2006) by using a different method. 2010-01-01T00:00:00Z http://hdl.handle.net/11089/18156 On a Generalized Sturm-Liouville Problem Andrzejczak, Grzegorz; Poreda, Tadeusz Basic results of our paper are devoted to a generalized Sturm-Liouville problem. 2010-01-01T00:00:00Z http://hdl.handle.net/11089/18155 A Classical Approach to Dynamics of Parabolic Competitive Systems Pietruk, Małgorzata; Przeradzki, Bogdan We study the reaction-diffusion system, its stationary solutions, the behavior of the system near them and discuss similarities and differences for different boundary conditions. 2010-01-01T00:00:00Z