This book is intended to provide a practical introduction to high-speed, high-efficiency liquid chromatography. It covers modern column technology (which has leapt into prominence only in the last five years) and relates this to the well-established thin-layer techniques. The development of liquid chromatography has proceeded in fits and starts over many years and in alliance with various scientific disciplines. Liquid chromatography has for years fulfilled an effective role in various fields. Ion-exchange chromatography, for example, is particularly associated with the separation of the rare earths, and exclusion chromatography with the fractionation of naturally occurring materials like proteins and of syn thetic polymers. Partition chromatography, especially in the form of paper chromatography, has been an indispensable tool in the study of biochemical systems, while its more recent adsorption counterpart, thin-layer chromatog raphy, developed most rapidly within the pharmacognosic and pharma ceutical fields. Until recently, however, liquid chromatography has not played a prominent role in the field of industrial organic analysis.
A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.
Over the past few years significant progress has been achieved in the field of nonlinear model predictive control (NMPC), also referred to as receding horizon control or moving horizon control. More than 250 papers have been published in 2006 in ISI Journals. With this book we want to bring together the contributions of a diverse group of internationally well recognized researchers and industrial practitioners, to critically assess the current status of the NMPC field and to discuss future directions and needs. The book consists of selected papers presented at the International Workshop on Assessment an Future Directions of Nonlinear Model Predictive Control that took place from September 5 to 9, 2008, in Pavia, Italy.
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.