This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting: ? A systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering.? The geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces.
This book is an English translation of the authoritative autobiography by the late South Korean President Kim Dae-jung. The 2000 Nobel Peace Prize winner, often called the Asian Nelson Mandela, is best known for his tolerant and innovative “Sunshine Policy” towards North Korea. Written in the five years between the end of his presidency and his death in 2009, this book offers a poignant first-hand account of Korea’s turbulent modern history. It spans the pivotal time span between the Japanese colonial period (1910-1945) and reconciliation in the Korean Peninsula (2000-2009). In between are insightful insider descriptions of everything from wars and dictatorships to the hopeful period of economic recovery, blooming democracy, peace, and reconciliation. Conscience in Action serves as an intimate record of the Korean people’s persistent and heroic struggle for democracy and peace. It is also an inspiring story of an extraordinary individual whose formidable perseverance and selfless dedication to the values he believed in led him to triumph despite more than four decades of extreme persecution.
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