W ostatnich dekadach coraz większą popularność wśród metod oceny ekonomicznej i analizy ryzyka projektów inwestycyjnych zdobywa analiza opcji rzeczowych. Metoda ta umożliwia wycenę tzw. elastyczności decyzyjnej mieszczącej w sobie możliwości odkładania inwestycji w czasie oraz modyfikację przyjętych pierwotnie strategii operacyjnych, dzięki czemu w wyniku analizy otrzymuje się wartości przedsięwzięć wyższe niż uzyskiwane w klasycznych metodach dyskontowych - bardziej zbliżone do wartości rynkowych. W zależności od typów, układu opcji, kolejności ich występowania wartość elastyczności może mieć bardziej lub mniej istotne znaczenie. Popularne metody wyceny opcji rzeczowych wykorzystują stanowiące aproksymację ciągłego procesu stochastycznego schematy kratownicowe, w tym najbardziej znane - podejście dwumianowe. Na podejściu tym bazuje metodyka wyceny stosująca tzw. założenie MAD. Artykuł przedstawia sposób wyceny górniczego przedsięwzięcia inwestycyjnego obejmującego trzy, występujące równolegle, opcje rzeczowe: opcję rozszerzenia skali projektu, zmniejszenia zakresu prowadzonych operacji i likwidacji przedsięwzięcia.

The positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and numerical examples.

Introduction of polymers into the cement composites improves same of the properties of concretes and mortars. Therefore, the polymer-cement composites are successfully used in construction. The model of microstructure formation in cement composites modified with thermoplastic polymer (pre-mix modifiers) has already been developed and successfully implemented. However, the formation of microstructure in the case of epoxy-cement composites (containing post-mix modifier) demonstrates same peculiarities which should be taken into account when modelling the process. The microstructure of epoxy-cement composites and its formation is discussed in the paper. The model is offered, formulated on the basis of the microscopic observations and results of testing.

The paper aims at determining the provenance of Roman coins in an early medieval hoard found at Obrzycko in Wielkopolska in the 19th century. It is unlikely, taking into account the occurrence of late Roman silver coins in the territory of Poland and adjacent countries, that a fragment of a siliqua or miliarense with the name of Theodosius (I or II) would come from local finds made in the Early Medieval epoch.

The purpose of the present article is to show the link between apology and the Christian testimony of faith. The author points to those moments of testimony which are characterised by justification, substantiation and thus apology of faith. He does not, therefore, talk about the apology of testimony as something additional, supposed to authenicate the testimony as it were beside it, but about a reality essentially connected with the testimony and pertaining to its nature. The subject in question is presented in three points: the apologetic dimension of the testimony of Jesus of Nazareth, the apologetic character of the permanent testimony of the Church, and the recognition and motivational effectiveness of the Christian testimony of faith.

Paul Valéry (1871-1945) was considered in the 1930s one of the greatest French poet and essayist. He was the author of the famous poems: La Jeune Parque (The Young Fate) and Le Cimetiere marin (The Graveyard by the Sea). Many times in different situations he spoke very highly of Poland and Poles. Wednesday, October 28th 1936, Valéry arrived in Warsaw. He delivered two lectures during his brief stay. They met with great interest, they were in the papers, they have been mentioned by Polish writers: Wacław Grubiński, Zofia Nałkowska, Tadeusz Breza. Also, Czesław Miłosz and Ludwik Hieronim Morstin have written about meetings with Paul Valéry. Poet`s visit, although very short, was a significant event in Polish cultural life.