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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The consequences of the lack of water By J. C. Cardona 884 million people lack access to safe water supplies; approximately one in eight people. UNICEF/WHO 2008. Progress on Drinking Water and Sanitation: Special Focus on Sanitation. 3.575 million People die each year from water-related disease.World Health Organization. 2008. Safer Water‚ Better Health: Costs‚ benefits‚ and sustainability of interventions to protect and promote health. The water and sanitation crisis claims more lives through
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Electricity Essay – Its Shortage and Suggestions for overcoming it AATISH PALEKAR ARTICLES As a result of the drought in 1979‚ the Indian economy received a severe jolt. All of a sudden it was reported that there was acute power-famine. There was a wide gap between demand for electricity and its supply. Power cuts were imposed for long periods. To conserve electricity‚ market timings were changed from 8 A.M. to 7 P.M. Electricity was not supplied to consumers for several hours every day. Power-cuts
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Q-1 A surgeon wish to predict the live or death (status) of a CABG patient through their pulse rate‚ systolic blood pressure‚ sugar level‚ hemoglobin etc. He got the data from last 1600 surgeries held in a local hospital and applied an analysis. He got the following result Identification: It is binary logistic regression (LOIGT) Coding 0 = Death 1 = Alive The two post-operative status of the patients are death and alive coded by 0 and 1 respectively to use in binary logistic regression. Hosmer and
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Abstract: This thesis examines Deepa Mehta’s trilogy—Water‚ Earth‚ Fire—and the trilogy’s exploration and contestation of colonial‚ anti-colonial nationalist‚ and religious ideologies as intersecting with patriarchal norms to enact symbolic and actual violence on the bodies of women. I argue that Mehta’s trilogy foregrounds the ways in which patriarchal nationalism legitimizes violence against women’s bodies and sexualities through different social and cultural practices and discourses which are
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Hello Mauritius… Tata Nano. 2010 Table of Contents Page No Executive Summary 1.0 Introduction 2 1.1 Company Background 3 1.2 Target Market 5 1.4 PEST Analysis
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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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determine how an excess amount of liquid‚ which was water‚ Gatorade and wine in this case‚ along with an excess amount of solute‚ which was the 7g NaCl pill‚ would affect the kidneys and the osmolarity of urine. Measurements of urine volume‚ specific gravity and chloride concentrations were recorded in order to investigate this. Our hypothesis stated that the volume of urine would increase for all groups other than the group drinking 80 ml of water along with taking a 7g. This portion of the hypothesis
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Water is a chemical compound with the chemical formula H 2O. A water molecule contains one oxygen and two hydrogen atoms that are connected by covalent bonds. Water is a liquid at standard ambient temperature and pressure‚ but it often co-exists on Earth with its solid state‚ ice‚ and gaseous state‚ steam (water vapor). Water covers 71% of the Earth’s surface.[1] It is vital for all known forms of life. On Earth‚ 96.5% of the planet’s water is found in seas and oceans‚ 1.7% in groundwater‚ 1
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bottled water Industry established in the early 1980s as a result of a number of factors containing convenience‚ taste and fear about public drinking water. Along today’s importance on healthy living. Bottled water is seen as a natural and healthy beverage. However‚ the bottled water industry and the denationalization of water is linked to a number of social‚ economical and environmental durability issues. Bottled water can be an alternate source of clean‚ safe drinking water. Bottled water is actually
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