This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen-Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Bio-Instructive Scaffolds for Musculoskeletal Tissue Engineering and Regenerative Medicine explores musculoskeletal tissue growth and development across populations, ranging from elite athletes to the elderly. The regeneration and reparation of musculoskeletal tissues present the unique challenges of requiring both the need to withstand distinct forces applied to the body and ability to support cell populations. The book is separated into sections based on tissue type, including bone, cartilage, ligament and tendon, muscle, and musculoskeletal tissue interfaces. Within each tissue type, the chapters are subcategorized into strategies focused on cells, hydrogels, polymers, and other materials (i.e. ceramics and metals) utilized in musculoskeletal tissue engineering applications. In each chapter, the relationships that exist amongst the strategy, stem cell differentiation and somatic cell specialization at the intracellular level are emphasized. Examples include intracellular signaling through growth factor delivery, geometry sensing of the surrounding network, and cell signaling that stems from altered population dynamics.

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen-Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Google is the most popular search engine ever created, but Google's search capabilities are so powerful, they sometimes discover content that no one ever intended to be publicly available on the Web, including social security numbers, credit card numbers, trade secrets, and federally classified documents. Google Hacking for Penetration Testers, Third Edition, shows you how security professionals and system administratord manipulate Google to find this sensitive information and "self-police" their own organizations. You will learn how Google Maps and Google Earth provide pinpoint military accuracy, see how bad guys can manipulate Google to create super worms, and see how they can "mash up" Google with Facebook, LinkedIn, and more for passive reconnaissance. This third edition includes completely updated content throughout and all new hacks such as Google scripting and using Google hacking with other search engines and APIs. Noted author Johnny Long, founder of Hackers for Charity, gives you all the tools you need to conduct the ultimate open source reconnaissance and penetration testing.

The man who went around the United Kingdom on a G-String sets off to cross the United States on a golfing odyssey. His goal is to play golf with whoever happens to feature on the front page of the newspaper in each town he visitsthose, that is, who havent been shot or arrested.Along the way he encounters an alligator-hunting New York deli owner, a clown wedding, a blind baseball commentator, a 91-year-old beach queen, a 200-year-old cactus, the runner-up in a New Orleans waiter race, and a Stevie Wonder impersonatorbut would any of them play golf?

Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is a detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of Grassmann varieties, flag varieties, and their Schubert subvarieties. Because of their connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. In this second edition, two recent results on Schubert varieties in the Grassmannian have been added, and some errors in the first edition corrected.