The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.
In biotechnology and bioengineering, small molecules can be used to increase the efficiency reduce the cost and damage to the environment of certain bioprocesses. This book introduces readers to the important field of chemically promoted biotechnology and bioengineering and presents the theory behind the biotechnology of enzymatic reactions and how they can be chemically enhanced. The book covers chemical modulators for enzymatic reactions, chemically promoted biotechnology in plant cell cultures, chemically promoted biotechnology for plant protection and future prospects for the field. Knowledge gained allows both chemists to make use of biotechnology to solve chemical problems in an environmentally-friendly way, and biologists to make use of chemistry to increase biotechnological efficiency. This book is useful for scientists in a broad range of disciplines, including agricultural chemistry, pesticide science, medicinal chemistry, biochemistry, bio-organic chemistry, cell and molecular biology. Students and researchers in both academia and industry will find it a useful handbook.
This book explores various approaches to reconstruct the spatial and temporal distribution of historical farmland in China. The book contains background information about political regimes, economic and social development, population changes and land resource utilization in the past 300 years in China. A literature review focuses on the assumptions, methodologies and models of reconstructing historical land-use datasets while addresses accuracy evaluation issues. Historical population size, its growth rate, and the evolution of spatial-temporal patterns of farmland in China have also been discussed. Almost all available historical data about farmland such as historical documents, archives, taxation records, statistics and research outcomes have been collected to reconstruct the amount of historical farmland. With a few principles and assumptions, a delicate Cellular Automaton (CA) and Multi-Agents (MAS) model based on bottom-up management scheme has been applied to derive the spatial-temporal distribution of farmland with the 1km*1km grid resolution for the period between 1661 and 1980 in China. Suggestions for future studies related to reconstructing historical land-use changes are then provided.
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