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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Pacific Oil Company Pacific Oil Company was founded in 1902 as the Sweetwater Oil Company of Oklahoma City‚ Oklahoma. The founder of Sweetwater Oil‚ E.M. Hutchinson‚ pioneered a major oil strike in north central Oklahoma that touched off the Oklahoma "black gold" rush of the early 1900s. It developed extensive oil holdings in North Africa and the Middle East‚ as well as significant coal beds in the western United States. In 1979‚ Pacific Oil established the first major contract with
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Why is the Pacific Ocean unsafe? In 2011‚ Japan suffered a major travesty due to the 9.0 magnitude earthquake‚ and tsunami that followed soon after. However‚ during that earthquake and tsunami‚ a nuclear power plant known as Fukushima Daichii was hit‚ and exposed to the community. Being exposed to a nuclear power plant is extremely harmful because of the symptoms that may occur from it‚ due to radiation. According to the 2013 edition of the Encyclopedia‚ radiation is a‚ “flow of atomic and subatomic
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The Railway that Benefitted All The Canadian Pacific Railway and its benefits to farmers‚ financiers‚ and consumers. Eric Best November 13th‚ 2012 Mr. Moore CHC2Da The Canadian Pacific Railway (CPR) is commonly argued to be the most important transportation route in Canadian history‚ but most do not know the substantial benefits it provided. More specifically‚ it provided benefits to farmers‚ financiers‚ and consumers. The financiers of the railway were the group of people that the railway benefitted
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later‚ in early March‚ 1996. - In February 1998‚ Cebu Pacific Air was grounded by the government‚ but continued its services next month‚ after the re-certification of its aircraft. - In late November‚ 2001‚ Cebu Pacific Air started operating international flights with a twice-daily service to Hong-Kong. - On the 1st of March‚ 2002‚ Cebu Pacific Air introduced thrice-weekly flights to Seoul. - In the following years‚ Cebu Pacific Air continued to introduce new routes and increase flight
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saving the Pacific Salmon English 101 4/26/2011 Saving the Pacific Salmon Salmon are one of the most important fish species in the world‚ and in the Pacific Northwest the fish are a way of life for many species of plants and animals‚ including humans. The major problem that humans are facing is that the population of wild salmon is dangerously low as compared to historic numbers due to over-fishing and human degradation (including dams‚ chemical pollution and land use impacts.). Pacific Salmon
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EFFECT OF BANKING SECTOR REFORMS ON NIGERIAN ECONOMY BY AJAYI‚ L. B. (Ph.D) DEPARTMENT OF BANKING AND FINANCE FACULTY OF MANAGEMENT SCIENCES EKITI STATE UNIVERSITY OF ADO-EKITI‚ NIGERIA E-mail: boblaw2006@yahoo.com AND OPADOTUN B.A DEPARTMENT OF BANKING AND FINANCE FACULTY OF MANAGEMENT SCIENCES EKITI STATE UNIVERSITY OF ADO-EKITI‚ NIGERIA E-mail: bishopobey@yahoo.com ABSTRACT This paper investigates the
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Native animals of Asia Treeshrews : native to the tropical forest of Southeast Asia. Spalacidae : native to eastern Asia‚ the Horn of Africa‚ the Middle East‚ & south-eastern Europe. Civets : native to the tropics of Africa and Asia. Natural Wonders Mt. Everest : On the Nepal-Tiber border looms the world’s highest peak‚ Mt. Everest (29‚028 ft.)‚ along the Himalayan Range. Dead Sea : The world’s lowest land area is
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Graduate Programme – Term IV – AY 20012-13 Business Intelligence And Data Mining Group Assignment on NGO Donations Maximization Abstract The problem is associated to devising a strategy to maximize the profits from a Direct Marketing Campaign to a selected group of customers while minimizing costs . The exercise requires the use of Business Intelligence tools and techniques to build a model ‚ trained and tested on the historical data for the last year’s donation raising campaign
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ECONOMIC LIFE OF ASIA The economy of Asia comprises more than 4 billion people (60% of the world population) living in 46 different states. Six further states lie partly in Asia‚ but are considered to belong to another region economically and politically. As in all world regions‚ the wealth of Asia differs widely between‚ and within‚ states. This is due to its vast size‚ meaning a huge range of differing cultures‚ environments‚ historical ties and government systems. The largest
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