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@article{1305857, author = {Beránek, Jaroslav and Chvalina, Jan}, article_location = {Nitra}, article_number = {1}, keywords = {mono-unary algebra; orbital decomposition; cascade}, language = {eng}, issn = {2453-6091}, journal = {Acta Mathematica Nitriensia}, title = {Extensions of Cascades Created by Certain Function Systems}, volume = {1}, year = {2015} }
TY - JOUR ID - 1305857 AU - Beránek, Jaroslav - Chvalina, Jan PY - 2015 TI - Extensions of Cascades Created by Certain Function Systems JF - Acta Mathematica Nitriensia VL - 1 IS - 1 SP - 50-56 EP - 50-56 PB - Fakulta prírodných vied UKF v Nitre SN - 24536091 KW - mono-unary algebra KW - orbital decomposition KW - cascade N2 - The article was created on the basis of scientific research in the area of interdisciplinary relations between algebra and mathematical analysis with the aim to find deeper connections between these two branches.Considering three simple function systems which consists of power functions with odd exponents and two linear functions of one real variable, we are constructing actions of the additive group of all integers on the set of all real numbers, i. e. cascades. Using certain extensions based on prolongations of flows we obtain the system of cascades which are mutually isomorphic. One from consequences of the result is that all solution sets of corresponding functional equations formed with the use of given functions are non-empty, moreover all solution sets consisting of permutations of the set of all reals are non-empty, as well. ER -
BERÁNEK, Jaroslav a Jan CHVALINA. Extensions of Cascades Created by Certain Function Systems. \textit{Acta Mathematica Nitriensia}. Nitra: Fakulta prírodných vied UKF v Nitre, 2015, roč.~1, č.~1, s.~50-56. ISSN~2453-6091.
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