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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Did Colonialism Change or “Transform” Africa “Forever”? From 1440 until 1833 the Atlantic slave trade was the principle reason for “normal” relationships between Europeans and Africans. This trade‚ along with other forms of commerce‚ allowed for a healthy‚ friendly and somewhat fair relationship between Africans and Europeans. After 1833—and the end of the slave trade—the relationship between Africans and Europeans took such a significant turn that it would change the African continent significantly
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COT3103 10/21/2014 Exercises Section 2.5 2. Determine whether each of these sets is finite‚ countably infinite‚ or uncountable. For those that are countably infinite‚ exhibit a one-to-one correspondence between the set of positive integers and that set. a. The integers greater than 10. This is countably infinite. Starting from the first integer greater than 10‚ which is 11‚ one can infinitely count upwards since there is no boundary on the right side of the number line for this instance. The equation
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Haas and Hahn’s TED Talk‚ “How Painting Can Transform Communities” describes the effort and planning that is needed to create such astounding works of art. This duo’s first piece of artwork on buildings came from Vila Cruzeiro; this is a poor and dilapidated town in Brazil with buildings clustered together while each seems to scream with agony from the claustrophobic space. To begin with‚ the community was not very well-behaved and did not set an example for others; not many people ventured out of
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The opinion can be either discrete or continuous depending on the available resources/methods or simply a contractor’s preference. Figure 1.1(B) shows an example the contractor can choose one of the three (A‚ B or C) methods to complete the activity. Each method has its associated time and cost. This type of time cost relation in literature is referred to as Discrete Time Cost Trade-off Problem. Figure 1.1(B): Discrete TCT relation The classification used is
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Christianity Transformed the Roman Empire Christianity started with Jesus. Jesus had many followers that spread the good news about Christianity not only in Rome but to its surrounding countries. New ideas can change people and places rapidly. These ideas had an impact on the family life of Romans‚ the Pax Romana‚ the Roman Tolerance for other religions‚ and the Rebirth of Roman State Religion. The family life of Romans was changed. Paterfamilias is where the male is the head of the household and
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6. To perform sampling and explain the concept of aliasing using MATLAB. To perform convolution between two continuous time signals using MATLAB. To perform correlation and autocorrelation using programming in MATLAB. To perform Fourier Series Analysis and Find Fourier coefficients from a complex signal in MATLAB. To plot frequency response of LPF‚ HPF‚ BPF filters in MATLAB. *To design and realize on a breadboard MOD 10 UP/DOWN Counter. 7. *To design and realize on a breadboard a 7-segment code
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advancesindifferenceequations.com/content/2013/1/57 RESEARCH Open Access Global dynamics in a class of discrete-time epidemic models with disease courses Lei Wang‚ Qianqian Cui and Zhidong Teng* * Correspondence: zhidong@xju.edu.cn College of Mathematics and System Sciences‚ Xinjiang University‚ Urumqi‚ Xinjiang 830046‚ P.R. China Abstract In this paper‚ a class of discrete SIRS epidemic models with disease courses is studied. The basic reproduction number R0 is computed. The main
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From tattoos to piercings‚ tanning salons and botox booths‚ people have always been fascinating with modifying their body. Since early colonial travel‚ different ideals of beauty have been of interest. Seventeenth century physician and natural philosopher John Bulwer demonstrated the fascinating observations of early English colonialists’ in his book Anthropometamorphosis: Man Transform’d‚ or The Artificial Changeling. The book‚ released in 1653‚ describes how different cultures modify the body for
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During his time as prime minister Gough Whitlam‚ and his government were able to transform the rights of indigenous Australians through reformed policies. • Additionally Gough Whitlam introduced the policies‚ which changed the rights of women and challenged the social norms of the current time. Gough Whitlam transformed women’s rights
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