We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra g by another hom-Lie algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie algebras, i.e., we show that in order to have an extendible hom-Lie algebra, there should exist a trivial member of the third cohomology., Abdoreza R. Armakan, Mohammed Reza Farhangdoost., and Seznam literatury
The procedure for identification of the long-term trends in the individual water quality determinands in surface water is described in the study. The methodology is based on requirements of the Directive 2000/60/EC and the existing water quality data in the database of the Slovak Hydrometeorological Institute. The methodology gives guidance for estimation of following issues: - influence of the length of the series on trends of development; - methods for calculation of the statistical characteristics; - methods for identification of the increasing and decreasing trends, as well as of the trend reversal point; - selection of the decision criteria for assessment of the trend significance. The methodology was applied for the trend analysis of the selected pollutants in the middle part of Hron River at Salkova near Banska Bystrica city. The results show that the rapid increase of pollution in 1970`s is followed by gradual improvement of the surface water quality in next period. and V predloženej štúdii je opísaný postup pri identifikácii dlhodobých trendov jednotlivých ukazovateľov kvality vody v povrchových tokoch. Pri vypracovaní metodiky sa vychádzalo z požiadaviek smernice 2000/60/EC a z existujúcich údajov o kvalite vody v databáze Slovenského hydrometeorologického ústavu. Vypracovaná metodika navrhuje konkrétne postupy na určovanie, napr. - vplyvu dĺžky obdobia na vývojové trendy; - spôsobov výpočtu štatistických ukazovateľov; - spôsobov identifikácie trendov rastu a poklesu, ako i bodov obratu trendu; - kritérií na rozhodovanie o významnosti jednotlivých trendov. Navrhnutá metodika bola aplikovaná pri analýze vybraných ukazovateľov kvality vody v mieste odberu Hron-Šalková , situovanom pri Banskej Bystrici. Z výsledkov vyplýva, že po prudkom náraste znečistenia stredného Hrona v sedemdesiatych rokoch dvadsiateho storočia dochádza k postupnému zlepšovaniu kvality povrchových vôd v tomto úseku.
The photosynthetic responses to salt stress were examined in a wheat (Triticum aestivum L. cv. Asakaze)-barley (Hordeum vulgare L. cv. Manas) 7H addition line having elevated salt tolerance and compared to the parental wheat genotype. For this purpose, increasing NaCl concentrations up to 300 mM were applied and followed by a 7-day recovery period. Up to moderate salt stress (200 mM NaCl), forcible stomatal closure, parallel with a reduction in the net assimilation rate (PN), was only observed in wheat, but not in the 7H addition line or barley. Since the photosynthetic electron transport processes of wheat were not affected by NaCl, the impairment in PN could largely be accounted for the salt-induced decline in stomatal conductance (gs), accompanied by depressed intercellular CO2 concentration and carboxylation efficiency. Both, PN and nonstomatal limitation factors (Lns) were practically unaffected by moderate salt stress in barley and in the 7H addition line due to the sustained gs, which might be an efficient strategy to maintain the efficient photosynthetic activity and biomass production. At 300 mM NaCl, both PN and gs decreased significantly in all the genotypes, but the changes in PN and Lns in the 7H addition line were more favourable similar to those in wheat. The downregulation of photosynthetic electron transport processes around PSII, accompanied by increases in the quantum yield of regulated energy dissipation and of the donor side limitation of PSI without damage to PSII, was observed in the addition line and barley during severe stress. Incomplete recovery of PN was observed in the 7H addition line as a result of declined PSII activity probably caused by enhanced cyclic electron flow around PSI. These results suggest that the better photosynthetic tolerance to moderate salt stress of barley can be manifested in the 7H addition line which may be a suitable candidate for improving salt tolerance of wheat., D. Szopkó, É. Darkó, I. Molnár, K. Kruppa, B. Háló, A. Vojtkó,
M. Molnár-Láng, S. Dulai., and Obsahuje bibliografii