Vandenberghe January 4‚ 2006 Chapter 2 Convex sets Exercises Exercises Definition of convexity 2.1 Let C ⊆ Rn be a convex set‚ with x1 ‚ . . . ‚ xk ∈ C‚ and let θ1 ‚ . . . ‚ θk ∈ R satisfy θi ≥ 0‚ θ1 + · · · + θk = 1. Show that θ1 x1 + · · · + θk xk ∈ C. (The definition of convexity is that this holds for k = 2; you must show it for arbitrary k.) Hint. Use induction on k. Solution. This is readily shown by induction from the definition of convex set. We illustrate the idea for k = 3‚ leaving the
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Hundred Flowers Campaign‚ also termed the Hundred Flowers Movement‚ (simplified Chinese: 百花运动; traditional Chinese: 百花運動; pinyin: Bǎihuā yùndòng) was a period in 1956 in the People’s Republic of China[1] during which the Communist Party of China (CPC) encouraged its citizens to openly express their opinions of the communist regime. Differing views and solutions to national policy were encouraged based on the famous expression by Communist Party Chairman Mao Zedong: "The policy of letting a hundred
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The Hundred Years’ War Have you wondered what were the causes of The Hundred Years’ War? Well‚ the immediate cause of the war was the conflict between Edward II of England and Philip VI of France for the duchy of Gascony. But there was already tension between the two on who was the rightful leader heir to the French throne. Edward declared war and the willing personalities of both rulers contributed to the start of the war. Also‚ because the king of French tried to take the territory claimed by
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Contracts Summary DAMAGES – REMEDIES FOR BREACH OF CONTRACT THE INTERESTS PROTECTED Fuller and Perdue‚ “The Reliance Interest in Contract Damages” There are three principle purposes in awarding contract damages: restitution interest – object is the prevention of unjust enrichment by the defaulting promisor at the expense of the promisee reliance interest – object is to put the plaintiff in a good position as he was before the promise was made expectation interest – object is to put the
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Anderson was one character that stood out to me. He was really shy and quiet and didn’t really fit in at school. He also didn’t embrace life like he really should have. Verse 52 from ¨Song Of Myself ¨ by Walt Whitman and a quote by Thoreau from Walden were great forms of literature that made connections with Todd Anderson. Todd Anderson was very shy but he started to stand up for what he believed in. In Walt Whitman’s poem verse 52 from ¨Song Of Myself¨ it states “Missing me one place‚ search
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CONTRACT AND RELATED OBLIGATION Prof. Hillman I) Theories of Obligation A) CONTRACT: Agreement with Consideration – Bargain Theory of Consideration Definition: A promise that is supported by consideration because the promisor gets something (extracts) from the promissee in exchange for the promise. Ex: I tell Alice I will sell her my piano for 400 dollars and she agrees. I promised my piano in exchange for something (400 dollars) therefore my promise is enforceable. 1) Bargained
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victim to one hundred and seven fatal maladies”. The text is written by an English writer and humorist Jerome K. Jerome‚ best known for the comic travelogue “Three Men in a Boat”. The story is about one young healthy men who thought he became “a victim to one hundred and seven fatal maladies”. The story is written by a humorist‚ that’s why it contains a lot of different funny moments and special stylistic devises. The first one we met already in the name of the story “A victim to one hundred and seven
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JUDGMENT V.N. Khare‚ CJI 1. This appeal which arises out of a judgment and order dated 23-11-2001 passed by the High Court of Kerala at Ernakulam revolves round the question as to whether an arbitration clause in a contract agreement survives despite purported satisfaction thereof. 2. The parties to this appeal entered into an agreement for a project at Kayamkulam. Upon completion of the work the respondent herein submitted final bill which was allegedly not accepted by the appellant‚ where
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Week 1 – Welcome / Introduction to Law I. 1. 2. 3. 4. Introduction to Law Not Not Not Not Divine Law‚ law of religion and faith Natural Law‚ justice‚ fairness and righteousness Moral Law‚ norms of good and right conduct Physical Law‚ order or regularity in nature Sources of Law i) i) Constitution – Fundamental Law of the land ii) ii) Legislations – Passed by Senate and House of Representatives iii) iii) Administrative issuances – Quasi Legislative Functions iv) iv) Jurisprudence – Decisions of the
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Zappos.com: Developing Supply Chain to Deliver WOW Strategic Management of Operations Prof. Saibal Ray By: Jaycie Zhang Xinqi Wang Arturo Cabezudo Maria Campos Juan Carlos Neira Executive Summary Zappos.com is a privately held online retailer with an extensive product category mainly including apparel‚ footwear‚ handbags‚ and watches. Headquartered in Nevada‚ it primarily operates in the US with about 1‚300 employees and revenues mounting to $635M in 2008. Thanks to its strength in
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