The thesis consists of two main results. The first main result is a proof that C^1 rigidity holds for circle maps with a break point for almost all rotation numbers. The second main result is a proof that C^1 robust rigidity holds for circle maps in the fractional linear transformation (FLT) pair family. That is, for this family, C^1 rigidity holds for all irrational rotation numbers. The approach taken here of proving a more general theorem that C^1 rigidity holds for circle maps with a break point satisfying a `derivatives close condition', allows us to obtain both of our main results as corollaries of this more general theorem.

The thesis consists of two main results. The first main result is a proof that C^1 rigidity holds for circle maps with a break point for almost all rotation numbers. The second main result is a proof that C^1 robust rigidity holds for circle maps in the fractional linear transformation (FLT) pair family. That is, for this family, C^1 rigidity holds for all irrational rotation numbers. The approach taken here of proving a more general theorem that C^1 rigidity holds for circle maps with a break point satisfying a `derivatives close condition', allows us to obtain both of our main results as corollaries of this more general theorem.

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According to Kim and Nelson (1999) and McConnell and Perez-Quiros (2000), the timing of the Great Moderation occurred in U.S. at 1984Q1. Summers (2005) found out several reasons and different timings of the Great Moderation in the G-7 countries and Australia. During the past fifty years, there was a significantly sharp decline in the volatility of the real growth rate in Australia. Between 1968 and 1982, the standard deviation of the real growth rate was 1.416%¡Fhowever, between 1983 and 1996, the standard deviation of the real growth rate drastically reduced to 0.917%. Based on this obvious situation described above, we successively build up a Markov-Switching Model and Time-Varying Structural Autoregressive Model to investigate the structural break and the sources of the Great Moderation in Australia. The findings turn out that improved monetary policy and the decreased oil shock can account for the explanation of the moderation with the break date of 1984Q1.

The diploma thesis deals with cost analysis, determination of cost functions, cost evaluation and creation of proper model of solution. It compares theoretical knowledge with reality in society, specifies possibilities of their changes and techniques used to optimize costs. The analyzed company – ABB s.r.o.

The value of remote sensing data is particularly evident where an areal monitoring is needed to provide information on the earth's surface development. The use of temporal high resolution time series data allows for detecting short-term changes. In Kogi State in Nigeria different vegetation types can be found. As the major population in this region is living in rural communities with crop farming the existing vegetation is slowly being altered. The expansion of agricultural land causes loss of natural vegetation, especially in the regions close to the rivers which are suitable for crop production. With regard to these facts, two questions can be dealt with covering different aspects of the development of vegetation in the Kogi state, the determination and evaluation of the general development of the vegetation in the study area (trend estimation) and analyses on a short-term behavior of vegetation conditions, which can provide information about seasonal effects in vegetation development. For this purpose, the GIMMS-NDVI data set, provided by the NOAA, provides information on the normalized difference vegetation index (NDVI) in a geometric resolution of approx. 8 km. The temporal resolution of 15 days allows the already described analyses. For the presented analysis data for the period 1981-2012 (31 years) were used. The implemented work flow mainly applies methods of time series analysis. The results show that in addition to the classical seasonal development, artefacts of different vegetation periods (several NDVI maxima) can be found in the data. The trend component of the time series shows a consistently positive development in the entire study area considering the full investigation period of 31 years. However, the results also show that this development has not been continuous and a simple linear modeling of the NDVI increase is only possible to a limited extent. For this reason, the trend modeling was extended by procedures for detecting structural breaks in the time series.

Quantitative analysis of trends in vegetation cover, especially in Kogi state, Nigeria, where agriculture plays a major role in the region’s economy, is very important for detecting long-term changes in the phenological behavior of vegetation over time. This study employs the use of normalized difference vegetation index (NDVI) [global inventory modeling and mapping studies 3g (GIMMS)] data from 1983 to 2011 with detailed methodological and statistical approach for analyzing trends within the NDVI time series for four selected locations in Kogi state. Based on the results of a comprehensive study of seasonalities in the time series, the original signals are decomposed. Different linear regression models are applied and compared. In order to detect structural changes over time a detailed breakpoint analysis is performed. The quality of linear modeling is evaluated by means of statistical analyses of the residuals. Standard deviations of the regressions are between 0.015 and 0.021 with R2 of 0.22–0.64. Segmented linear regression modeling is performed for improvement and a decreasing standard deviation of 33%–40% (0.01–0.013) and R2 up to 0.82 are obtained. The approach used in this study demonstrates the added value of long-term time series analyses of vegetation cover for the assessment of agricultural and rural development in the Guinea savannah region of Kogi state, Nigeria.