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One tool used to study this problem is a linear map that decreases the weight of nonzero vectors by a constant. We characterize such maps. Using the tools we develop, we give a new elementary proof of the MacWilliams Extension Theorem (which characterizes weight-preserving linear maps).

The real option literature on investment provides insights into firms' decisions to enter and exit markets. This literature emphasizes the role of fixed costs of entry, the salvage value of exit, and uncertainty. A major implication of this literature is that it is often optimal to wait. Nonetheless, since the overwhelming majority of this literature uses models with uncertainty, students are often unclear as to the role of each of these components in determining the value of the option to wait. In this paper, I explain the role of uncertainty and costs/salvage value by considering the question: 'When is it optimal to stop telling the Bob Sacamano story?' In doing so, I provide a simple and entertaining example to illustrate the importance of uncertainty in the real options literature.

Who are we? What are we made of? Answers to these questions and more...

This book is a must read. Joshua D. Johnson gives a glimpseof his life as a chosen vessel. He shares his most intimate confessions in an effort to bring healing and encouragementthrough vulnerability, transparency, and highlighting biblicaltruths. This book will make you laugh, cry, and it will challenge you to dig deep within to share your confessions with God, that you would be healed, delivered and set free.