Jan Ligęza (1998)
Mathematica Bohemica
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In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in , where denotes the Colombeau algebra.
Josef Král, Beloslav Riečan (1962)
Matematicko-fyzikálny časopis
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Štefan Schwabik (2000)
Mathematica Bohemica
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This paper is a continuation of []. In [] results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) were presented. The Kurzweil type Stieltjes integration in the setting of [] for Banach space valued functions was used. Here we consider operator valued solutions of the homogeneous problem (t) = I +dt [A(s)](s) as well as the variation-of-constants formula for the former equation.
Jiří Klaška (1997)
Mathematica Bohemica
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In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary -element set up to .