...i Computational Complexity: A Modern Approach Draft of a book: Dated January 2007 Comments welcome! Sanjeev Arora and Boaz Barak Princeton University complexitybook@gmail.com Not to be reproduced or distributed without the authors’ permission This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us). Please send us bugs, typos, missing references or general comments to complexitybook@gmail.com — Thank You!! DRAFT ii DRAFT About this book Computational complexity theory has developed rapidly in the past three decades. The list of surprising and fundamental results proved since 1990 alone could fill a book: these include new probabilistic definitions of classical complexity classes (IP = PSPACE and the PCP Theorems) and their implications for the field of approximation algorithms; Shor’s algorithm to factor integers using a quantum computer; an understanding of why current approaches to the famous P versus NP will not be successful; a theory of derandomization and pseudorandomness based upon computational hardness; and beautiful constructions of pseudorandom objects such as extractors and expanders. This book aims to describe such recent achievements of complexity theory in the context of the classical results. It is intended to both serve as a textbook as a reference for self-study. This means...
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...1 1 Fundamentals of Semiconductor Electrochemistry and Photoelectrochemistry Krishnan Rajeshwar The University of Texas at Arlington, Arlington, Texas 1.1 1.2 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.4 1.4.1 1.4.2 1.4.3 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.6 1.7 1.7.1 1.7.2 1.7.3 1.7.4 1.7.5 Introduction and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron Energy Levels in Semiconductors and Energy Band Model . The Semiconductor–Electrolyte Interface at Equilibrium . . . . . . . . The Equilibration Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Depletion Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mapping of the Semiconductor Band-edge Positions Relative to Solution Redox Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface States and Other Complications . . . . . . . . . . . . . . . . . . . Charge Transfer Processes in the Dark . . . . . . . . . . . . . . . . . . . . Current-potential Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dark Processes Mediated by Surface States or by Space Charge Layer Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rate-limiting Steps in Charge Transfer Processes in the Dark . . . . . Light Absorption by the Semiconductor Electrode and Carrier Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light Absorption...
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