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Content available remote L'equation de translation sur un n-groupe
100%
PL
W artykule rozważane jest ogólne równanie translacji na dowolnej n-grupie, tzn. równanie postaci varphi(varphi(varphi(... varphi(varphi(α, x1), x2), ...), xn-1), xn) = varphi(α, [x1, x2, ..., xn]), gdzie Γ jest zbiorem, (G, [...]) jest dowolną n-grupą zaś varphi: Γ x G → Γ. Przedstawione zostały dowody dwóch twierdzeń, dające charakteryzację rozwiązań wymienionego równania przez rozwiązania klasycznego równania translacji na grupie, tzn. przez rozwiązania równania F(F(a, x), y) = F(α, x · y). Na zakończenie artykułu sformułowane zostały dwa problemy otwarte.
EN
In this paper the general translation equation on an arbitrary n-group is considered, namely the equation of the form varphi(varphi(varphi(... varphi(varphi(α, x1), x2), ...), xn-1), xn = varphi(α, [x1, x2, ..., xn]), where Γ is a set, (G, [...]) is an n-group and varphi: Γ x G → Γ. There are proved two theorems giving a characterization of the solutions of the above-mentioned equation by the solutions of the classical translation equation on a group, this means by the solutions of the equation F(F(a, x), y) = F(α, x · y). At the ending of the paper there are formulated two open problems.
2
Content available remote Symulacja pracy linii produkcyjnej na przykładzie praktycznym
63%
EN
The article focuses on the problems concerning production line capacity. The example of a certain problem concerning a line, on which the axles for grass mower are producing, is analyzed in the paper. To solve the problem authors used lean tools such as value stream mapping and ProModel program for simulation of the production line working. After gathering information about production line and processes realizing on the line, the current state of the value stream map was drawn. On the base of the map analysis and talks with employees and management the improvements, which could improve production line working and its capacity, were proposed. Improvements were discussed and chosen of them were indicated to check in simulations. Then a first version of future state of value stream map with the indicated improvements was prepared. To do simulations a plan was developed. As variables are taken: frequency of delivery, effective working time, number of simultaneously assembled products, number of lathes in the line and number of products in batch. Next a model of the production line in ProModel program was build. With the use of the model, in the range of the analysis, 144 simulations were done. Obtained data are analyzed and proposals for line developing are presented. To increase production line capacity an additional lathe has to be introduced into the line. Authors also indicate that morning break should be cut down to 5 min. Another solution, which has to be introduced, is changing a frequency of delivery. The frequency should equal 8 hours and it is enough. More often deliveries are not cost effective, although they could give even better capacity. It was impossible to double capacity by introducing only other improvements avoiding costs concerning with necessity of buying a new lathe. The proposals are shown in the second version of future state of value stream map. Authors also indicate the further possible development and analysis.
PL
Referat omawia charakterystykę pracy nowo budowanej instalacji osuszania gazu przy Tłoczni Maćkowice. Przedstawiono problemy wynikające z dużej rozpiętości parametrów pracy instalacji oraz omówiono nowatorskie rozwiązania technologiczne z tego wynikające.
EN
The newly built gas drying installment at Maćkowice Gas Pumping Station is characterized in the paper. Problems related to the great diversity of work parameters of such an installment are discussed and the resulting novel technological solutions proposed.
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