This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and t...(展开全部)

This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and t...(展开全部)

One night in October when he was ten years old, Tyler Dupree stood in his back yard and watched the stars go out. They all flared into brilliance at once, then disappeared, replaced by a flat, empty black barrier. He and his best friends, Jason and Diane Lawton, had seen what became known as the Big Blackout. It would shape their lives. The effect is worldwide. The sun is now a...(展开全部)

One night in October when he was ten years old, Tyler Dupree stood in his back yard and watched the stars go out. They all flared into brilliance at once, then disappeared, replaced by a flat, empty black barrier. He and his best friends, Jason and Diane Lawton, had seen what became known as the Big Blackout. It would shape their lives. The effect is worldwide. The sun is now a...(展开全部)

One night in October when he was ten years old, Tyler Dupree stood in his back yard and watched the stars go out. They all flared into brilliance at once, then disappeared, replaced by a flat, empty black barrier. He and his best friends, Jason and Diane Lawton, had seen what became known as the Big Blackout. It would shape their lives. The effect is worldwide. The sun is now a...(展开全部)

One night in October when he was ten years old, Tyler Dupree stood in his back yard and watched the stars go out. They all flared into brilliance at once, then disappeared, replaced by a flat, empty black barrier. He and his best friends, Jason and Diane Lawton, had seen what became known as the Big Blackout. It would shape their lives. The effect is worldwide. The sun is now a...(展开全部)

What makes success in major sales? How do some salespeople consistently outsell their competition? Why do techniques like closing work in small sales but fail in larger ones? How can salespeople dramatically increase their sales volume from major accounts? Now you can find answers to all these questions with the SPIN strategy.

What makes success in major sales? How do some salespeople consistently outsell their competition? Why do techniques like closing work in small sales but fail in larger ones? How can salespeople dramatically increase their sales volume from major accounts? Now you can find answers to all these questions with the SPIN strategy.

This text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format – the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and p...(展开全部)