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9 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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Some remarks on fluid flow in hourglasses

Bryll A., Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

29--36

In the paper the authors analyse different shapes of an hourglass for the linearity of their graduation. We also assume that any hourglass (more precisely, each of the two congruent parts) has the shape of a solid of revolution and any cross section at height h of this hourglass depends on the base radius r, i.e. h = ƒ(r).

A certain approach to Kripke semantics for normal modal logics

Bryll G., Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

13-20

In this paper the authors propose a method of verifying formulae in normal modal logics. In order to show that a formula α is a thesis of a normal modal logic, a set of decomposition rules for any formula is given. These decomposition rules are based on the symbols of assertion and rejection of formulae.

Recurrent equations for the arithmetical and geometrical sequences of higher degree

Bryll A., Bryll G., Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

155-162

Recurrent equations concern relationships between some (in general in a neighbourhood) elements of sequences. By these equations one can evaluate an arbitrary element of such sequences. In this paper we consider recurrent equations for the arithmetical and geometrical sequences of higher degree. We also give some properties of these sequences.

On mistakes connected with differentiating

Sochacki R., Bryll G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

399-405

Many students have problems with solving tasks concerning the existence of the derivative of a function at a point. In this paper we discuss some of them.

On Usability of Ordering and Equivalence Relations to Define and to Ground Some Mathematical Notions in Secondary Schools

Bryll G., Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

131--136

Many important mathematical notions can be introduced by means of the notions of supremum, infimum and equivalence class. Our considerations refer to mainly pupils of mathematical sections.