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1
Content available remote

Basic Space-Time Transformations Expressed by Means of Two-Component Number Systems

100%
Majerník V.
Acta Physica Polonica A
|
1994
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vol. 86
|
issue 3
291-295
EN
We slow that the Lorentz and Galilei transformations can be expressed in the algebraic structures called the rings of two-component binary and dual number systems.
2
Content available remote

Galilean Transformation Expressed by the Dual Four-Component Numbers

100%
Majerník V.
Acta Physica Polonica A
|
1995
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vol. 87
|
issue 6
919-923
EN
We express the special Galilean transformation in the algebraic ring of the dual four-component numbers.
3
Content available remote

Multicomponent Number Systems

100%
Majerník V.
Acta Physica Polonica A
|
1996
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vol. 90
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issue 3
491-498
EN
We introduce three types of the four-component number systems which are constructed by joining the complex, binary and dual two-component numbers. We study their algebraic properties and rewrite the Euler and Moivre formulas for them. The most general multicomponent number system joining the complex, binary dual numbers is the eight-component number system, for which we determine the algebraic properties and the generalized Euler and Moivre formulas. Some applications of the multicomponent number systems in differential and integral calculus, which are of physical relevance, are also presented.
4
Content available remote

Uncertainty relations expressed by Shannon-like entropies

51%
Majerník V., Majerníková E., Shpyrko S.
Open Physics
|
2003
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vol. 1
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issue 3
393-420
EN
Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.
5
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Thermal Expansion of Free-Volume in Hexadecane Confined in the Silica Gel Nanopores

45%
Šauša O., Majerník V., Illeková E., Macová E., Berek D.
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vol. 125
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issue 3
798-800
EN
Temperature dependence of the free-volume of voids in hexadecane (HXD) confined in the 3 nm silica gel pores (Develosil-30) was measured by positron annihilation lifetime spectroscopy. Different amount of HXD was filled into the pores of matrix. The anomalous thermal expansion was observed in the partially filled pores with extremely low filling. The thermal expansion coefficient of free-volume voids in this solidified HXD layer has a negative sign at temperatures below 180 K compared to high- or full-filled pores of silica gel. At these temperatures, the positron annihilation lifetime spectroscopy measurements demonstrate the appearance of a new type of the free volume within HXD which has been interpreted as the cracks in the HXD layer on the inner walls of matrix cavities. The differential scanning calorimetry method confirmed that the processes were enacted within pores and not on the outer surfaces of silica gel grains. In the sample with the extremely low filling, only the one HXD solidification/melting effect connected with confined states is manifested.
6
Content available remote

Nanopores in Silica Aerogels

39%
Šauša O., Iskrová M., Majerník V., Krištiak J., Jesenák K., Vargová M.
Acta Physica Polonica A
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2008
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vol. 113
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issue 5
1517-1522
EN
The size of nanopores in thermally treated samples of silica aerogels was determined by ortho-positronium lifetime measurements at room temperature. The annealing of samples in the temperature region of 300-800°C does not make substantial changes in pore size felt by positronium. The annealing at higher temperatures from an interval of 800-1050°C causes shrinkage of the samples reducing the pore size to 1-15 nm. The macropores vanish at temperature treatment at 1000°C and the positron annihilation is not affected by oxygen from air.
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