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Critical Analysis and Discussion of The Biological, Social and Environmental Determinants of Health
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Continued Fraction Factorisation Algorithm
Get PDFIn mathematics, especially number theory, continued fractions allow us to represent a real number by successive divisions of integers. Applications of continued fractions include constructing rational approximations to irrational numbers and helping to solve the Diophantine and Pell’s equations. In particular, the continued fraction algorithm (CFRAC) is a powerful integer factorisation algorithm. It was described by D. H. Lehmer and R. E. Powers in 1931, whose theoretical basis will be explored today. It has been described as a general-purpose algorithm, meaning that it is suitable for factoring any integer , independent of the number’s properties. The CFRAC, in its operation, also helps us find congruences of the form . I will introduce some statements about continued fractions to motivate the purpose of this report. This will be followed with an introduction of -th complete quotients and how they produce the integers needed for the CFRAC. The CFRAC can be carried out via two methods which I will call the “A method” and “P method”, whose strengths and weaknesses will be discussed. Lastly, a faster algorithm, described by Michael A. Morrison and John Brillhart, which computerised the A method, will also be examined
The Brandenburg Gate: Mirror of German History: A historical investigation of the meaning and role of the Brandenburg Gate throughout German history
No full textThis paper investigates the meaning and symbolism behind the Brandenburg Gate, one of the most well-known monuments in Germany. Two key historical periods and the presence of the gate in these periods; Napoleons occupation of Prussia in 1806 and his defeat in 1814 as well as the period between 1961 and 2000, are examined through their ability to reflect their respective views of German unity and national identity
The effects of Phoracantha-induced dieback on photosynthesis, respiration and estimated leaf nitrogen in Eucalyptus pauciflora: Photosynthesis, respiration and nitrogen in dieback-affected snow gums
No full textEucalyptus pauciflora stands in Kosciuszko National Park are experiencing severe dieback events induced by Phoracantha beetles, threatening the habitat complexity of subalpine ecosystems. This study investigated the effects of Phoracantha-induced dieback on the maximum photosynthetic rate (Amax), average dark respiration (rdark) and nitrogen (N) concentration in E. pauciflora leaves, and the relations between Amax, rdark and estimated leaf N concentration. We collected leaf samples from a healthy stand in Charlotte Pass and a dieback-affected stand in Perisher and measured their rates of photosynthesis and dark respiration using a LI-COR 6400, and estimated leaf nitrogen using a SPAD. We found no difference in Amax and rdark between leaf categories, but epicormic leaves had significantly higher N content than healthy canopy leaves. In contrast to the literature, we found no correlation between Amax and N. Our findings suggest that E. pauciflora may exhibit a plastic response in photosynthetic rate to drought or dieback stress, but that dieback may damage vascular tissue, limiting dark respiration. The high nitrogen content in epicormic leaves does not have a corresponding increase in photosynthetic rate. These results suggest the effects of Phoracantha attack on the vascular system and source-sink flows within a tree