Wei Zhang

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.

Bei dieser Arbeit handelt es sich um einen Vergleich zwischen deutschen und chinesischen Kontaktanzeigen, definiert als Varianten derselben Textgattung. Deutsche Inserate haben aussenstrukturell gesehen eine langere Gattungsgeschichte und wirken stilistisch persoenlicher sowie umgangssprachlicher als ihre chinesischen Pendants. Inhaltlich werden der "Spassfaktor" und offene Charaktereigenschaften mehr in Deutschland, traditionelle und statusbezogene Attribute mehr in China akzentuiert. Von 1985 bis 2001 haben sich die deutschen Inserate nicht wesentlich verandert. In den chinesischen Daten spiegelt sich der gesellschaftliche Modernisierungsprozess wider. Eine Geschlechtsspezifik der Anzeigen sticht in Deutschland als der moderneren Gesellschaft weniger hervor als in China.

Originally published in 1987, two years before the Tiananmen Square protests, Zhang Wei's award-winning novel is the story of three generations of the Sui, Zhao, and Li families living in the fictional northern town of Wali during China's troubled postliberation years. Spanning four decades following the creation of the People's Republic in 1949, The Ancient Ship is a bold examination of a society in turmoil, the struggle of oppressed people to control their own fate, and the clash between tradition and modernization. In the course of the narrative, the townspeople of Wali face the moments that have defined China's history during the latter part of the twentieth century: the land reform programs, the famine of 1959-1961, the Great Leap Forward, the Anti-Rightist Campaign, and the Cultural Revolution. Translated into English for the very first time, The Ancient Ship is a revolutionary work of Chinese fiction that speaks to people across the globe.

Microarray technology provides researchers in the life sciences with a revolutionary tool for measuring gene expression. However, this highly developed process involves multiple steps, from sample selection to data analysis, each susceptible to potentially costly errors. Without sound quality control, experimental microarrays may produce useless or, even worse, misleading results. Microarray Quality Control provides a comprehensive resource for ensuring quality control in every step of this complex process. From experimental design to data processing, analysis, and interpretation, the emphasis in this text remains on practical advice for each stage of planning and running a microarray study. Chapters cover: *Quality of biological samples *Quality of DNA *Hybridization protocols Scanning *Data acquisition *Image analysis *Data analysis Written for the broad group of workers–biologists, mathematicians, statisticians, engineers, physicians, and computational scientists–involved in microarray studies, Microarray Quality Control features a straightforward style easily accessed by various disciplines. Useful checklists and tips help ensure the integrity of results, and each chapter contains a thorough review of pertinent literature. The only complete, systematic treatment of the topic available, Microarray Quality Control offers students and practitioners an invaluable resource for improving experimental quality and efficiency.

Written for a broad range of researchers and clinicians including oncologists, neurologists, pathologists, neuroscientists, residents, postdoctoral fellows, and others in related fields, this comprehensive reference documents cutting-edge advances in genomic and molecular techniques for brain tumor research and clinical practice and describes their medical and therapeutic implications.