Our purpose is to prove the existence of solutions of a Nicoletti problem for an integro-differential equation with advanced argument of the form
(1)     x'(t) = ∫₀^h(t)f(t,x(t+s))d_sr(t,s),  t∈ℝ⁺,
(2)     Nx = η.

The behaviour of solutions of the Burgers system (1)-(3) is studied. In earlier papers [4], [5] the problem of the global stability of the constant solution (U,υ) = (P/ν,0) when P/ν ≤ ν was solved. The behaviour of those solutions (U,υ) which do not converge to the constant solution when t tends to infinity is studied here. In part 3 some of its properties are studied, while in parts 2 and 4 several a priori estimates needed in the proof of existence of solutions are presented.

J. Mikusiński presented in the paper [2] the estimation of the operational function e^{-s^αλ}, α∈(0,1), in some unbounded set of ℝ⁺×ℝ⁺. The results obtained by J. Mikusiński were generalized in the paper [3]. The similar estimation of the function
exp[(Σ_ν=1ⁿβ_νs^p_ν)λ]
is made in the above paper, where β_ν∈ℝ and p_ν∈(0.1), ν = 1,...,n.
This paper is devoted to the investigation of the behaviour more general operational functions, when the coefficients β_ν are in ℂ and fulfilling some relations concerning their real and imaginary parts.

The aim of this note is to give a short proof of the Ščepin theorem concerning maps of inverse limits. This theorem was generalized by several authors; see e.g. W. Kulpa [5], A. Archangelskii [1] and M.G. Tkačenko [7], [8].
Our method of the proof gives also the most general version of the Ščepin theorem due to Tkačenko. It can be also applied for obtaining in a very general setting the theorem of H.H. Corson and J.R. Isbell [3], [4] concerning maps from products.

Der Kleinschen Raum ist ein System aus drei Elementen (M,G,f) wo M eine beliebige nichtleere Menge ist, G eine gruppe bedeutet und die Abbildung f: M×G→M eine effektive linksseitige Wirkung von G auf M darstellt. In diesem Raume werden gewisse Untermengen, so genannte ,,affine Pseudogeraden”, definiert, die eine Verallgemeinerung der Geraden im affinen Kleinschen Raume darstellen. In vorliegender Arbeit werden grudlegende Eigenschaften der affinen Pseudogeraden gegeben. Insbesondere wird es gezeigt, dass im allgemeinen viele verschiedene affine Pseudogerade durch zwei verschiedene Punkte druchgehen können. Darum werden einige notwendige und hinreichende Bedingungen für die Eindeutigkeit der affinen Pseudogeraden im Kleinschen Raume bewiesen, die zwei angegebene verschiedene Punkte enthalten. Endlich sind gewisse offene Probleme gestellt.