13. Symmetric groups 13.1 13.2 13.3 Cycles‚ disjoint cycle decompositions Adjacent transpositions Worked examples 1. Cycles‚ disjoint cycle decompositions The symmetric group Sn is the group of bijections of {1‚ . . . ‚ n} to itself‚ also called permutations of n things. A standard notation for the permutation that sends i −→ i is 1 2 3 1 2 3 ... ... n n Under composition of mappings‚ the permutations of {1‚ . . . ‚ n} is a group. The fixed points of a permutation
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GSB 9001 Lecture 1: What is communication? ‘Communication is the act of exchanging thoughts‚ messages‚ or information’ (de Janasz et al.‚ 2012‚ p.127) 1. It involves rich channels (face-to-face‚ telephone) 2. It involves lean channels (emails‚ texting‚ memos) Think through the implications of this difference in how we communicate‚ formally and informally. What is Listening? Listening is the process of taking in what we hear and mentally organising it; it involves: Sensing: hearing
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A Day in life of Alex Sander: Diyora Hitesh V Regd No. PA1110 Abstract Alex Sander is a new product manager at Landan care products inc. which has been acquired by a European Beauty company. Alex Sander is very talented and has rebranded two national products in one year. She knows very well when to launch product and she is smart enough to do things correctly. Sander is getting her
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Anger‚ Fear‚ Pain‚ these are all compelling sensations. As human beings‚ these are feelings we can’t abstain from‚ but‚ what if something as simple as breathing could help during these stressful times? I believe breathing is a powerful tool the body needs in order to combat these stresses. The most common stress that I think everyone can relate to‚ is anger. Whether it’s a petty squable over whose turn it is to take out the trash‚ or a heated debate on beliefs that make us who we are at our very
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Fish: Fish Niche - Fishes ecological niches that work in with their respiratory systems and gas exchange posess live in water eg. sea‚ rivers‚ streams and ponds. Fish such as cod live near the sea floor with competitors such as red cod‚ spotty and kahawai challenge them. There are predators such as dolphins‚ sharks and also people. Their gas exchange system has to be efficient for them to be able to compete with those fish and escape from predators. Fish live in an acquatic environment. Water
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Change in respiratory rate during exercise Aim: To record and investigate how the breathing rate varies for the duration of light and heavy exercise. Introduction: When an individual exercises‚ the muscles being used needs extra energy from oxygen. The lungs pump oxygen to the heart‚ and then the heart pumps the oxygenated blood through the blood to the particular muscle that is working. The human body has a series of organs working together‚ which is named the respiration system. The organs involved
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Alex Rider: Stormbreaker 1) I liked this book. It was filled with action and suspense. But I didn’t like how it was far-fetched. A 14 year old that knew all different types of karate‚ languages‚ moves‚ and almost taught like a spy from birth. But other than that‚ I really liked the book. I like how everything was detailed. 2) A. The main characters are Alex Rider‚ Ian Rider (dead‚ but an important name)‚ Yassen Gregorovich‚ and Herold Sayle. B. The setting of this book is Present day in London
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Portfolio Management Case 1: Alex Sharpe’s Portfolio Executive Summary As Alex Sharpe’s consultant‚ we recommend a portfolio of 78% S&P 500 and 22% of R.J Reynolds. This portfolio will generate an annual expected return of 8.86% (significantly higher than the index return 6.29%)‚ while the risk increases by only less than 10%. In Qualitative Analysis‚ we find that tobacco industry tends to move with the market less than the toy industry‚ which indicates that R.J Reynolds can diversity the
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the world suddenly seem more real and cruel? In Claire Anderson-Wheeler’s short story‚ “Vernissage”‚ we hear about Alex who is suddenly faced with all these questions he cannot answer. In the story we meet Alex who lives with his parents‚ who have been married probably for a lot of years‚ and it is starting to show in the way they talk to each other. Through the story we follow Alex and only see and experience what he does. The story is written with a 3rd person narrator but an omniscient one‚ because
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tie in with Part One” worksheets‚ the wording and/ or sub questions have been changed. These similar ones can also be used in the same class as additional practice to make sure students answer exactly the question that is given. 62 Written by Alex Case for UsingEnglish.com © 2008 IELTS Speaking Part Two topic cards about Sports‚ hobbies and free time A-Z A Activity- see also “Favourite” and “Future” Describe an activity you like doing. You should say: - Where you do it - Who you do
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