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Abstract

The article presents the process of functional changes in the area of the Metropolis of Poznań, i.e. 22 communes belonging to the Metropolia Poznań Association. The process was examined on the basis of changes in the employment structure and spatially different tendencies and segregation in the scope of dominant functions.
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Abstract

The research was carried out on species diversity, density and similarity of Gastrotricha living on two species of macrophytes Myriophyllum spicatum L. and Elodea canadensis Michx. in a mesotrophic lake. Gastrotricha occurring on the studied macrophytes were represented by 23 species (21 on M. spicatum L. and 22 on E. canadensis Michx.). Species diversity (expressed by the Shannon index) for the Gastrotricha occurring on the two studied species of macrophytes amounted to 2.70 for M. spicatum L. and 2.81 for E. canadensis Michx., what suggests equal distribution of the gastrotrich species revealed in the studied species of macrophytes. The definite dominants inhabiting the two species of macrophytes were: Heterolepidoderma macrops Kisielewski, 1981, Heterolepidoderma ocellatum (Mečnikow, 1865), Lepidoderma squamata (Dujardin, 1841) and Aspidiophorus squamulosus Roszczak, 1936, and their inclusive percentage participation in the whole gastrotrich fauna for M. spicatum L. and E. canadensis Michx. was 41.8 and 40.3% respectively. The domination structure of the gastrotrich fauna of the two species of macrophytes was similar for each gastrotrich species (G-test, for all p > 0.05). Average density of Gastrotricha inhabiting M. spicatum L. amounted to 588.0 10³ indiv. m-2, and density of Gastrotricha occurring on E. canadensis Michx. amounted to 670.0 10³ indiv. m-2. Statistic analysis based on the Mann-Whitney test showed that differences of the gastrotrich densi-ty on the studied species of macrophytes: M. spicatum L. and E. canadensis Michx. (Z = -1.9282; p = 0.05) are statistically insignificant.
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Abstract

The paper concerns the two-machine non-preemptive flow shop scheduling problem with a total late work criterion and a common due date (F2|dj = d|Y ). The late work performance measure estimates the quality of a solution with regard to the duration of late parts of activities performed in the system, not taking into account the quantity of this delay. In the paper, a few theorems are formulated and proven, describing features of an optimal solution for the problem mentioned, which is NP-hard. These theorems can be used in exact exponential algorithms (as dominance relations reducing the number of solutions enumerated explicitly), as well as in heuristic and metaheuristic methods (supporting the construction of sub-optimal schedules of a good quality).
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