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Grbner Bases in Ring Theory
This monograph strives to introduce a solid foundation on the usage of Grbner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grbner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grbner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand?Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation...
Grobner Bases in Ring Theory
1. Preliminaries. 1.1. Presenting algebras by relations. 1.2. S-graded algebras and modules. 1.3. [symbol]-filtered algebras and modules -- 2. The [symbol]-leading homogeneous algebra A[symbol]. 2.1. Recognizing A via G[symbol](A): part 1. 2.2. Recognizing A via G[symbol](A): part 2. 2.3. The [symbol-graded isomorphism A[symbol](A). 2.4. Recognizing A via A[symbol] -- 3. Grobner bases: conception and construction. 3.1. Monomial ordering and admissible system. 3.2. Division algorithm and Grobner basis. 3.3. Grobner bases and normal elements. 3.4. Grobner bases w.r.t. skew multiplicative K-bases. 3.5. Grobner bases in K[symbol] and KQ. 3.6. (De)homogenized Grobner bases. 3.7. dh-closed homogen...
Battling Climate Change and Transforming Agri-Food Systems
The Asian Development Bank hosted the Asia-Pacific Rural Development and Food Security Forum 2022 to prompt governments to provide leadership to rethink the future of agriculture amid complex and evolving challenges; explore new research, innovations, and technologies to build nature-positive food systems; and forge partnerships and collaboration to mobilize financing for innovation, research, and business for food and nutrition security. This publication provides the forum’s key highlights and takeaways on sustainable, resilient, and inclusive food systems, financing for sustainable agriculture and natural capital, nutrition security, and the rural–urban divide, and offers recommendations for moving forward.
Economics of the Environment
Economics of the Environment, Seventh Edition is a compendium of the best, most timely articles by a dream team of environmental economists, together with an original introductory chapter by the editor. Now in its seventh edition, Economics of the Environment serves as a valuable supplement to environmental economics text books and as a stand-alone reference book of key, up-to-date readings from the field. Edited by Robert N. Stavins, the book covers the core areas of environmental economics courses as taught around the world; and the included authors are the top scholars in the field. Overall, more than half of the chapters are new to this edition while the rest have remained seminal works.
The Student Supercomputer Challenge Guide
This guide provides a comprehensive overview of High Performance Computing (HPC) to equip students with a full skill set including cluster setup, network selection, and a background of supercomputing competitions. It covers the system, architecture, evaluating approaches, and other practical supercomputing techniques. As the world’s largest supercomputing hackathon, the ASC Student Supercomputer Challenge has attracted a growing number of new talent to supercomputing and has greatly promoted communications in the global HPC community. Enclosed in this book, readers will also find how to analyze and optimize supercomputing systems and applications in real science and engineering cases.
Supporting Post-COVID-19 Economic Recovery in Southeast Asia
This report identifies well-established sectors needing transformation or improvement (tourism, agro-processing, and garments), along with evolving sectors with high potential for growth (electronics and digital trade) as Southeast Asian countries hammer out policies to boost post-COVID-19 recovery and secure a greener future. The first in a four-part series, the report looks at the pandemic’s impact on these five sectors across Cambodia, Indonesia, Myanmar, the Philippines and Thailand. It identifies reforms and strategies to help core industries recover and grow over the medium term. This report underscores how deepening regional cooperation can help policy makers boost their countries’ COVID-19 recovery and build more resilient economies and societies.
