ATILIM UNIVERSITY DEPARTMENT OF MATHEMATICS Math 211 - Discrete Mathematics with Applications 2010-2011 Fall Semester Problem Set I Prepared by Mehmet TURAN O−‚ Ω−‚ Θ− Notations 1. Let f and g be real valued functions defined on the same set of nonnegative real numbers. (a) Prove that if g(x) is O(f (x))‚ then f (x) is Ω(g(x)). (b) Prove that if f (x) is O(g(x)) and c is any nonzero ral number‚ then cf (x) is O(cg(x)). (c) Prove that if f (x) is O(h(x)) and g(x) is O(k(x))‚ then f (x) + g(x) is
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During the operation of sand washing machine‚ customers may encounter some problems‚ such as the amount of washed asnd is decreasing‚ the sand is leaking‚ the damage of sand net‚ bolt ollseness‚ vibration of sand making machine‘s fixing frame‚ the sudden raised noise of transmission part‚ gear damage due to its lack of lubrication‚ etc. Here are some tips about sand making machine’s damage and resolution. 1). As to its bearing‚ the usual damage is lubrication shortage and seal ring breakdown
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A COMPARATIVE ANALYSIS BETWEEN EGYPT AND TUNISIA In the truest sense‚ freedom cannot be bestowed; it must be achieved. - Franklin D. Roosevelt It appears that many countries are settling into a form of government that mixes a substantial degree of democracy with a substantial degree of illiberalism (Zakaria: 1997). Just like what Egypt and Tunisia are portraying to us. From authoritarian rule‚ they moved forward to become a democratic country and perceived a concept of democratic
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to be followed‚ and that students are free to express their creativity and that they can embellish this project however they want. In the grading rubric‚ it does not say you need a poster‚ just that you needed hieroglyphics (which I have) and the essay (which is what you’re reading). So overall‚ I think that my project is much more creative and artsy than a poster‚ even though that’s what you were originally supposed to
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eSectoral Survey Pharmaceutical Industry in Egypt November 2010 Sectoral survey: Pharmaceutical Industry Index Page 1. Introduction 2. Definition 3. Regulatory framework 3.1.Regulatory body 3.2.Pricing 3.3.TRIPS 3 4 4 4. Market analysis 4.1.Market structure 4.2.Consumption 4.3.Production 4.4.Key players 7 5. Trade 5.1.Exports 5.2.Imports 5.3.Balance of trade 9 6. SWOT analysis 7. Outlook 8. Recommendations 9. Conclusion Appendix References 11 12 13 13 2
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Evaluate the main problems associated with using plastic bags.Critically assess possible solutions to reduce these problems. The serious pollution caused by plastic bags has become an urgent environmental issue‚ it has attracted more and more concern.Today‚plastic bags are widely used in retail industry‚Kaplan(2010)states that nearly 1 trillion plastic bags are supplied in supermarkets‚ordinary shops and street markets.They are popular with both consumers and retailers mainly owning to their
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When one imagines Ancient Egypt‚ the images of sand‚ mummies‚ and pyramids usually come to mind. Modern times portray cats as a lovable‚ furry household animal. Did the thought of the two intertwining ever occur? By examining the goddess Bast‚ tombs where cat mummies reside‚ and the process of mummifying cats‚ one can better understand the true significance of the gentle creature in the days of the Ancient Egyptian. Ancient Egyptians worshipped gods and goddesses frequently. They seemed to posses
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Mesopotamia and Egypt: Geographical Surroundings and the Shaping of Their Societies Both civilizations of Mesopotamia and Egypt were developed in river valleys and relied on the rivers and the flooding they brought for agriculture. Mesopotamia was between the Tigris and Euphrates river valleys‚ giving them more room for agriculture. But the Mesopotamians had to deal with harsh‚ irregular flooding‚ which would often damage their crops. Flooding was a major issue for the farmers in Mesopotamia‚ and
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September 2014 Mini Comparative Complex Cultures Essay The Neolithic Revolution led to the discovery of agriculture and allowed for the development of sedentary civilizations‚ permanently changing the human way of life. The rise and fall of the Egyptian and Mesopotamian societies occurred around the same time and were both centered on mighty rivers. Although located less than 1000 miles from each other‚ the geographical situations of Mesopotamia and Egypt from 3000 B.C.E. to 600 C.E. were strongly dissimilar
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Mesopotamia VS Egypt In discussing the ancient world‚ many aspects in ancient Mesopotamia and ancient Egypt seem to be different and similar in different ways. Mesopotamia and Egypt differ in the way their kings govern and the social standings of woman. But were the similar in how religion played a big part in their lives. Mesopotamians kingship difference from Egypt in the way they governed. In Mesopotamia kings were the representatives of the gods. Also in Mesopotamia kings followed Hammurabi’s
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