Konzistentnost i problemi kompletiranja operatorskih matrica: doktorske disertacije

In this thesis different types of operator matrix completions have been studied, as well as consistency in invertibility and in Fredholmnes. The property consistency has been considered on Banach algebras in the sense of concsistency in invertibility and consistence in Fredholmnes. Result concering completions of operator matrices are linked to certain properties of a linear combination of two arbitrary Hilbert space operators. The properties studied in this thesis are: invertibility, injectivity, left (right) invertibility, closednes of range, consistency in invertibility of a linear combination of two arbitrary Hilbert space operators. Some of these results are applied to the study of the Generalized Bott-Duffin inverse, primarily to represent the Generalized Bott-Duffin inverse of bounded linear operator on a Hilbert space using an operator matrix. The obtained operator matrix representation of the Generalized Bott-Duffin inverse is a generalization of previous results

Konzistentnost i problemi kompletiranja operatorskih matrica: doktorske disertacije

In this thesis different types of operator matrix completions have been studied, as well as consistency in invertibility and in Fredholmnes. The property consistency has been considered on Banach algebras in the sense of concsistency in invertibility and consistence in Fredholmnes. Result concering completions of operator matrices are linked to certain properties of a linear combination of two arbitrary Hilbert space operators. The properties studied in this thesis are: invertibility, injectivity, left (right) invertibility, closednes of range, consistency in invertibility of a linear combination of two arbitrary Hilbert space operators. Some of these results are applied to the study of the Generalized Bott-Duffin inverse, primarily to represent the Generalized Bott-Duffin inverse of bounded linear operator on a Hilbert space using an operator matrix. The obtained operator matrix representation of the Generalized Bott-Duffin inverse is a generalization of previous results

Impact of precipitation and human activities on suspended sediment transport load in the Velika Morava River Basin (Serbia)

Sediment transport time series have shown a severe change in the suspended sediment load transported by the Velika Morava River (Republic of Serbia) during the last few decades. The research objectives of this study were to determine the suspended sediment trends, and to assess the impact of variations in precipitation and human activities on the suspended sediment load. The causes and timing of this severe decrease were analyzed, and the results show that there has been a significant sudden shift downwards for the suspended sediment load (p<0.0001) during the research period. The change points for sediment load were very similar and the transition years all ranged between 1982 and 1984. The combined effects of precipitation and human activities are responsible for the decrease in the suspended sediment load, with human activity being the most active factor in the sediment regime changes. The contribution rate for human activities amounts to 87.7–91.9%, while precipitation explains 8.1–12.3% of the reduction in the suspended sediment load. The processes of deagrarization and depopulation had an influence on the sediment load decrease in the study area. The results of the spatial autocorrelation analysis of rural settlements showed that the reduction in sediment was due to the process of depopulation and the large reduction in the amount of arable land in rural areas and settlements. The changes in sediment regimes were also influenced by soil and water conservation program