Lieven 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
Premium
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
Premium Mathematics Real number Integer
Worksheet #3 Chapter Five: Public Opinion 9th Edition page numbering are highlighted‚ 10th ed. are not. Struggle Chapter Five 1) Define opinion poll/sample survey. What makes a poll random? What are some problems with polls and surveys? An Opinion Poll is an assessment of public opinion obtained by questioning a representative sample. All polls are based on the idea of a random sample. Two methods are used to get the sample. One is called Random Digital Dialing in which the pollster carefully
Premium Voter turnout Election Voting
PROBLEM SET 1 Name: ______________________________________________ Problem Set 1 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 2. 1. Based on the information provided for the market for video games‚ answer the following questions. PRICE Q DEMANDED Q SUPPLIED $50 5 9 $45 7 7 $40 9 5 $35 11 3 $30 13 1 a.) Draw and properly label the demand and supply graphs (this means you must label the axes and any lines you include on the graph). b.) What is the equilibrium
Premium Supply and demand
This file of BUS 640 Week 4 Market Structures and Pricing Decisions Applied Problems comprises: Market Structures and Pricing Decisions Applied Problems. Please‚ complete the following 2 applied problems in a Word or Excel document. Show all your calculations and explain your results. Submit your assignment in the drop box by using the Assignment Submission button. 1. What is the profit-maximizing price and output level? Solve this algebraically for equilibrium P and Q and also plot
Premium Supply and demand English-language films Economics
usually impulsive and unpredictable. 3. A person should consume more of something when its marginal: a) benefit exceeds its marginal cost.** b) cost exceeds its marginal benefit. c) cost equals its marginal benefit. d) benefit is still positive. 4. Microeconomics is concerned with: a) the aggregate or total levels of income‚ employment‚ and output. b) a detailed examination of specific economic units that make up the economic system.** c) positive economics‚ but not normative economics. d)
Premium Supply and demand Consumer theory Economics
management. Economics is the science that deals with the production‚ distribution‚ and consumption of wealth‚ and with the various related problems of labor‚ finance‚ taxation‚ etc. (Webster’s New World) Economics is the study of choice and decision-making in a world with limited resources. Right and prudent administration of assets‚ Public wealth‚ set of services and economic interests. The study of the choices people make to cope with scarcity. Economics is the study of how to use
Premium Economics Inflation Unemployment
Norway. C. Mexico and Brazil. D. Cuba and North Korea. 4. Of the following countries‚ which one best exhibits the characteristics of a market economy? A. Canada. B. Cuba. C. North Korea. D. China. 5. The French term "laissez-faire" means: A. "there is no free lunch." B. "let it be." C. "circular flow." D. "public ownership." 6. An economic system: A. requires a grouping of private markets linked to one another. B. is a particular set of institutional arrangements and a coordinating mechanism
Premium Economics Capitalism Planned economy
online community‚ like elance.com. There people from any country can bid for the right to provide a service. It means that I can often find people to do a job relatively cheaply because labour costs are relatively lower in the Indian sub-continent. 4. Growth of multinational companies with a global presence in many different economies. 5. Growth global trading blocs which have reduced national barriers (e.g. European Union‚ NAFTA‚ ASEAN). 6. Reduced tariff barriers encouraging global trade. Often
Premium International trade Economics Globalization
Expert Systems Ajith Abraham Oklahoma State University‚ Stillwater‚ OK‚ USA 1 Problem Solving Using Heuristics 2 What are Rule-based Systems? 3 Inference Engine in Rule-based Systems 4 Expert System Development 5 Fuzzy Expert Systems 6 Modeling Fuzzy Expert Systems 7 Illustration of Fuzzy Expert System Design 8 Adaptation of Fuzzy Inference Systems 9 Summary References 909 910 911 911 912 914 914 918 918 919 1 PROBLEM SOLVING USING HEURISTICS A general introduction to artificial intelligence methods
Premium Fuzzy logic Expert system