Where Are W e Doing in This Chapter? After modeling consumers' choice set and his preference (represented by utility functions), we now put them together and model how he/she makes optimal choice. In mathematical terms, this is constrained maximization problem; In economics, this is rational choice problem

Counting III Today we'll briefly review some facts you dervied in recitation on Friday and then turn to some applications of counting. 1 The Bookkeeper Rule In recitation you learned that the number of ways to rearrange the letters in the wore BOOKKEEPER is:

An explorer is trying to reach the Holy Grail, which she believes is located in a desert shrine d days walk from the nearest oasis. In the desert heat, the explorer must drink continuously. She can carry at most 1 gallon of water, which is enough for 1 day. However, she is free to create water caches out in the desert. For example, if the shrine were 2/3 of day's walk into the desert, then she could recover

Images removed due to copyright considerations. See the following: Figure 1 and Table 1 in Reed SI. 2003. Ratchets and clocks: The cell cycle nover ubiquitylation and protein turnover. Nat Rev. Mol. Cell Biol. 4: 855-864. Figure 1 in Bartek J, Lukas J. Mammalian G1-and S-phase checkpoints in response to DNA damage. Curr Opin Cell

7-1: The IS Relation in the open Economy 7-2: Equilibrium Output and the Trade Balance 7-3. Increases in Demand, Domestic or Foreign 7-4: Depreciation, the Trade Balance,and output 7-5: Looking at Dynamics: The J-Curve 7-6: Saving, Investment, and Trade Deficits

The students will learn strong forms and weak forms in English. Objectives: Students will be able to: 1. Define - in their own words a definition for strong forms and weak forms in a sentence. It is a revision and therefore, easy for most of the students;

Space Systems Laboratory Massachusetts Institute of Technology Optimization of Separated Spacecraft Interferometer Trajectories in the Absence of A Gravity-Well Optimization of Separated Spacecraft Optimization of Separated Spacecraft Interferometer Trajectories in the Interferometer Trajectories in the Absence of A Gravity Absence of A Gravity-Well Edmund M. Edmund M. Kong Prof David W. Miller David W. Miller

Subject: English Pronunciation for Communication Purpose: The students will learn stressed syllables & unstressed syllables in English. Objectives: Students will be able to: 1. Define - in their own words a definition for stressed syllables & unstressed syllables. It is a revision and therefore, easy for most of the students; 2. Compare – based on the understanding of the basic concept, compare stressed and unstressed syllables in words and sentences;

Date: Sept.16-20 Class: Classes 1, 2 & 3, Grade 2002 Subject: English Pronunciation for Communication Purpose: The students will learn some basic concepts in English pronunciation. We are going to learn something about syllables, stress and rhythm in English. At the same time, they will learn to say greetings and farewell with appropriate pronunciation and intonation in English

In addition to the 'pure vowels' (ones where the tongue positioning is fairly static) shown above there is also the set of vowel diphthongs. These are effectively long vowels during which the tongue moves to produce a definite change of quality during the sound. In phonetic transcription we usually use a pair of linked symbols for each diphthong - one indicating the quality of the sound at the start of the vowel, and the other indicating its quality as it ends. Examples of diphthongs are found in words like 'boy', 'hear', 'may', 'my