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This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry,...

This book presents our experience in the operative treatment of bone and soft-tissue tumors arising in and around the pelvis, from 1970 to 1999 in the Department of Orthopedic Surgery at the Niigata University Medical Hospital. Histological diagnoses included both benign and malignant tumors. Surgical plan ning was difficult to perform in our early experience in operative treatment, when only angiography and barium enemas were in use. In the meantime, computed tomog raphy scanning and magnetic resonance imaging became available. Subsequent improvement in the quality of these images made...