...Permutations Definition: A permutation of a set X is a rearrangement of its elements. Example: Let X = {1, 2, 3}. Then there are 6 permutations: 123, 132, 213, 231, 312, 321. Definition : A permutation of a set X is a one-one correspondence (a bijection) from X to itself. Notation: Let X = {1, 2, . . . , n} and α : X → X be a permutation. It is convenient to describe this function in the following way: α= 1 2 ... n α(1) α(2) . . . α(n) . Example: 1 2 2 1 1 2 3 1 2 3 1 2 3 2 3 1 1 2 3 4 1 4 3 2 1 2 3 4 5 3 5 4 1 2 Definition: Let X = {1, 2, . . . , n} and α : X → X be a permutation. Let i1 , i2 , . . . , ir be distinct numbers from {1, 2, . . . , n}. If α(i1 ) = i2 , α(i2 ) = i3 , . . . , α(ir−1 ) = ir , α(ir ) = i1 , and α(iν ) = iν for other numbers from {1, 2, . . . , n}, then α is called an r-cycle. Notation: An r-cycle is denoted by (i1 i2 . . . ir ). Example: 1 2 3 4 5 2 5 3 4 1 1 2 3 4 5 2 5 4 3 1 = (125) 3 − cycle is not a cycle 1 Remark: We can use different notations for the same cycles. For example, 1 2 3 1 2 3 = (1) = (2) = (3), 1 2 3 2 3 1 = (123) = (231) = (312). Warning: Do not confuse notations of a permutation and a cycle. For example, (123) = 123. Instead, (123) = 231 and 123 = (1). Composition (Product) Of Permutations Let α= Then α◦β = β◦α= 1 2 ... n α(β(1)) α(β(2)) . . . α(β(n)) 1 2 ... n β(α(1)) β(α(2)) . . . β(α(n)) , . 1 2 ... n α(1) α(2) . . . α(n) and β = 1 2 ... n β(1) β(2) . . . β(n) . Example: Let α = 1 2 3 4 5 5 1 2 4 3 α◦β...
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...The Wheatley House I realized as I was watching this that there are a lot of people that need help from others. It may not be there fault. Specifically in this film it shows the woman coming from other countries trying to make a better life for their families. As they did this they are not stuck her in the United States without a job and they also did not have anywhere to stay. The thing that stood out to me the most was that no one was helping these woman and they were actually mad that they were immigrating into the states. The thing I learned about this movie is that there is always someone in need of some help. It does not have to be people immigrating from another country and not being able to find a job but there are people who cannot afford things such as food and shelter for their children and they need help. Most of them do not ask for help I have come to realize. In the film I kept thinking about that. They did not ask for help because they felt like no one was going to help them or they just felt ashamed. Some things I have insights about in this case is that people should try to help others if they see that they need help because those people are not going to ask for help. They feel to ashamed. I can apply this by trying my hardest in my everyday life to help others. It does not have to be in a very large scale right now because I don’t have a big voice to be heard right now because I am just a college student. I can make a difference in someone’s life though. I...
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...In Praise oJ Shadows [::s] meditation on the Japanese house bas broadened to uncouer tbe most sensitiue connections betueen interiority, space, culture, etbnicity, body, eroticism, shadou, and human personality. In Praise of Shadows JUNICHIRO TANIZAKI lunicbiro Tanizaki (155G196, is one of tbe giants of modern Japanese 'Vestfi.ction. Born and raised in Tokyo, be fell early under tbe influence of 'Vilde and tried to ern "decadent" writers sach as Baudelaire, Poe, and reconcile bis young man's taste for tbe macabre and modern uitb an nttraction to lapanese tradition, ubicb deepened as be greu oldet. In 1923, ubile in his mid-tbirties, be moued witb his family to Osaka, thus distancing bimself from tbe capital and his past as a "son of Tokyo." Taniwki's work bas a delightful spiq quality and is filled witb brio, b* mor, and robust spirits-especially compared to bis great, dour contempol J I I rary, Yasanari Kautabata. Tbere is frequently also a toucb of tbe peruerse and a fascination witb ctuelty in Tanizaki, thougb somebou (as in tbe work of tbe flmmaker Luis Bufruel) tbe results manage to be liberating and pleasurable. His najor works include Naomi, Some Prefer Nettles, Seven Tales, I The Key, Diary of a Mad Old Man, and uhat is arguably tbe greatest passionate Japanese noael of tbe tuentietb century, The Makioka Sisters. A Tanizaki also adapted the great eleuentb-century classic The antiquarian, Tale of Genji into modern lapanese-a labor of loae...
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...Gene Recognition A project report submitted to M S Ramaiah Institute of Technology An Autonomous Institute, Affiliated to Visvesvaraya Technological University, Belgaum in partial fulfillment for the award of the degree of Bachelor of Engineering in Computer Science & Engineering Submitted by Mudra Hegde 1MS07CS052 Nakul G V 1MS07CS053 Under the guidance of Veena G S Assistant Professor Computer Science and Engineering M S Ramaiah Institute of Technology [pic] DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING M.S.RAMAIAH INSTITUTE OF TECHNOLOGY (Autonomous Institute, Affiliated to VTU) BANGALORE-560054 www.msrit.edu May 2011 Gene Recognition A project report submitted to M. S. Ramaiah Institute of Technology An Autonomous Institute, Affiliated to Visvesvaraya Technological University, Belgaum in partial fulfillment for the award of the degree of Bachelor of Engineering in Computer Science & Engineering Submitted by Mudra Hegde 1MS07CS052 Nakul G V 1MS07CS053 Under the guidance of Veena G S Assistant Professor Computer Science and Engineering M S Ramaiah Institute of Technology [pic] DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING M. S. RAMAIAH INSTITUTE OF TECHNOLOGY (Autonomous Institute, Affiliated to VTU) BANGALORE-560054 www.msrit.edu May 2011 Department of Computer Science...
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...Acknowledgments ix Acknowledgments This book owes a great deal to the mental energy of several generations of scholars. As an undergraduate at the University of Cape Town, Francis Wilson made me aware of the importance of migrant labour and Robin Hallett inspired me, and a generation of students, to study the African past. At the School of Oriental and African Studies in London I was fortunate enough to have David Birmingham as a thesis supervisor. I hope that some of his knowledge and understanding of Lusophone Africa has found its way into this book. I owe an equal debt to Shula Marks who, over the years, has provided me with criticism and inspiration. In the United States I learnt a great deal from ]eanne Penvenne, Marcia Wright and, especially, Leroy Vail. In Switzerland I benefitted from the friendship and assistance of Laurent Monier of the IUED in Geneva, Francois Iecquier of the University of Lausanne and Mariette Ouwerhand of the dépurtement évangélrlyue (the former Swiss Mission). In South Africa, Patricia Davison of the South African Museum introduced me to material culture and made me aware of the richness of difference; the late Monica Wilson taught me the fundamentals of anthropology and Andrew Spiegel and Robert Thornton struggled to keep me abreast of changes in the discipline; Sue Newton-King and Nigel Penn brought shafts of light from the eighteenthcentury to bear on early industrialism. Charles van Onselen laid a major part of the intellectual foundations on...
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