Flash column chromatography is a quick and (usually) easy way to separate complex mixtures of compounds. We will be performing relatively large scale separations in 5.301,around 1.0 g of compound. Columns are often smaller in scale than this and some of you will experience these once you move into the research lab. Column chromatography uses the same principles

Introduction Are people unaffected by tax increase if they pay zero in taxes afterwards? No, consumption may have changed in response to the tax increase Bundle consumed is less desirable Excess burden is a loss of welfare above and beyond the tax revenues collected

In this lecture, we consider the problem of a body in which the mass of the body changes during the motion, that is, m is a function of t, i.e. m(t). Although there are many cases for which this particular model is applicable, one of obvious importance to us are rockets. We shall see that a significant fraction of the mass of a rocket is the fuel, which is expelled during flight at a high velocity and thus, provides the propulsive force for the rocket

In this lecture, we will consider how to transfer from one orbit, or trajectory, to another. One of the assumptions that we shall make is that the velocity changes of the spacecraft, due to the propulsive effects, occur instantaneously. Although it obviously takes some time for the spacecraft to accelerate to the velocity of the new orbit, this assumption is reasonable when the burn time of the rocket is much smaller than the period of the orbit. In such cases, the Av required to do the maneuver is simply the difference between the

Ch. 22 Unit root in Vector Time series 1 Multivariate Wiener Processes and multivari- ate FCLT Section 2.1 of Chapter 21 described univariate standard Brownian motion W(r) as a scalar continuous-time process(W: rE0, 1-R). The variable W(r) has a N(O, r)distribution across realization, and for any given realization, w(r) is continuous function of the date r with independent increments. If a set of k such independent processes, denoted

Ch. 20 Processes with Deterministic Trends 1 Traditional Asymptotic Results of OlS Suppose a linear regression model with stochastic regressor given by Y=x!3+e,t=1,2,…,T,;B∈R or in matrix form y=xB+E We are interested in the asymptotic properties such as consistency and limiting

Ch. 15 Forecasting Having considered in Chapter 14 some of the properties of ARMA models, we now show how they may be used to forecast future values of an observed time series. For the present we proceed as if the model were known ecactly Forecasting is an important concept for the studies of time series analysis. In the scope of regression model we usually

This paper is an updated version of a previous working paper, Capital Budgeting in the Presence of Managerial Overconfidence and Optimism, by the same authors. Financial support by the Rodney L. white Center for Financial Research is gratefully acknowledged. The authors would like to thank Andrew Abel, Jonathan Berk, Domenico Cuoco, David Denis, Janice Eberly, Robert Goldstein, Peter Swan, and seminar

Bayesian Learning in Social Networks Douglas Gale(Corresponding Author) Department of Economics. New York University

the standard theory of co.apters 1 and 2 when we covered Modigliani-Miller As we discussed in the Ch apital structure that has been the mainstay of text- books is the trade-off theory This argues that the benefit of debt is the tax shield and the cost is the deadweight costs of bankruptcy. The tradi tional view was that these deadweight