Memorial Volume For Shoucheng Zhang

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Publisher : World Scientific
ISBN 13 : 9811231729
Total Pages : 510 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Memorial Volume For Shoucheng Zhang by : Xiaoliang Qi

Download or read book Memorial Volume For Shoucheng Zhang written by Xiaoliang Qi and published by World Scientific. This book was released on 2021-08-24 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book honors the remarkable science and life of Shoucheng Zhang, a condensed matter theorist known for his work on topological insulators, the quantum Hall effect, spintronics, superconductivity, and other fields. It contains the contributions displayed at the Shoucheng Zhang Memorial Workshop held on May 2-4, 2019 at Stanford University.

Zhang-Gradient Control

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Author :
Publisher : Springer Nature
ISBN 13 : 9811582572
Total Pages : 310 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Zhang-Gradient Control by : Yunong Zhang

Download or read book Zhang-Gradient Control written by Yunong Zhang and published by Springer Nature. This book was released on 2020-11-24 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to using the simple but effective Zhang-gradient (ZG) method to solve tracking-control problems concerning various nonlinear systems, while also highlighting the applications of the ZG method to tracking control for practical systems, e.g. an inverted-pendulum-on-a-cart (IPC) system and a two-wheeled mobile robot (showing its potential applications). In addition to detailed theoretical analyses of ZG controllers, the book presents a wealth of computer simulations to demonstrate the feasibility and efficacy of the controllers discussed (as well as the method itself). More importantly, the superiority of ZG controllers in overcoming the division-by-zero (DBZ) problem is also illustrated. Given its scope and format, the book is well suited for undergraduate and graduate students, as well as academic and industrial researchers in the fields of neural dynamics/neural networks, nonlinear control, computer mathematics, time-varying problem solving, modeling and simulation, analog hardware, and robotics.

Memorial Volume On Abdus Salam's 90th Birthday

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Publisher : World Scientific
ISBN 13 : 9813144882
Total Pages : 544 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Memorial Volume On Abdus Salam's 90th Birthday by : Brink Lars

Download or read book Memorial Volume On Abdus Salam's 90th Birthday written by Brink Lars and published by World Scientific. This book was released on 2017-03-21 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of one of the most prolific and exciting scientists of the second half of the last century, a memorial meeting was organized by the Institute of Advanced Studies at Nanyang Technological University for Professor Abdus Salam's 90th Birthday in January 2016. Salam believed that "scientific thought is the common heritage of all mankind" and that the developing world should play its part, not merely by importing technology but by being the arbiter of its own scientific destiny. That belief saw him rise from humble beginnings in a village in Pakistan to become one of the world's most original and influential particle physicists, culminating in the 1979 Nobel Prize (shared with Glashow and Weinberg) for contributions to electroweak unification, which forms an integral part of the Standard Model. The book collected the papers presented at this memorable event which saw many distinguished scientists participating as speakers to reflect on Prof Salam's great passion for the science and achievements.

Ludwig Faddeev Memorial Volume: A Life In Mathematical Physics

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Publisher : World Scientific
ISBN 13 : 9813233877
Total Pages : 636 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Ludwig Faddeev Memorial Volume: A Life In Mathematical Physics by : Ge Mo-lin

Download or read book Ludwig Faddeev Memorial Volume: A Life In Mathematical Physics written by Ge Mo-lin and published by World Scientific. This book was released on 2018-05-18 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ludwig Faddeev is widely recognized as one of the titans of 20th century mathematical physics. His fundamental contributions to scattering theory, quantum gauge theories, and the theory of classical and quantum completely integrable systems played a key role in shaping modern mathematical physics. Ludwig Faddeev's major achievements include the solution of the three-body problem in quantum mechanics, the mathematical formulation of quantum gauge theories and corresponding Feynman rules, Hamiltonian and algebraic methods in mathematical physics, with applications to gauge theories with anomalies, quantum systems with constraints and solitons, the discovery of the algebraic structure of classical and quantum integrable systems and quantum groups, and solitons with the topology of knots. Faddeev's name is imprinted in many areas of mathematics and theoretical physics, including "Faddeev's equations" and "Faddeev's Green function" in scattering theory, "Faddeev-Popov ghosts" and "Faddeev-Popov determinant" in gauge theories, "Gardner-Faddeev-Zakharov bracket" for the KdV equation, "Faddeev-Zamolodchikov algebra" in quantum integrable systems, "Faddeev-Reshetikhin-Takhtajan construction" in the theory of quantum groups, knotted solitons in the "Skyrme-Faddeev model" and many others. Ludwig Faddeev founded the St. Petersburg school of modern mathematical physics and distinguished himself by serving the mathematics community for over three decades including his leadership of the International Mathematical Union in the period of 1986-1990. He was conferred numerous prizes and memberships of prestigious institutions in recognition of the importance of his work. These include the Dannie Heineman Prize for Mathematical Physics, the Dirac Medal, the Max Planck Medal, the Shaw Prize and the Lomonosov Gold Medal among others. A gathering of contributions from some of the biggest names in mathematics and physics, this volume serves as a tribute to this legendary figure. Volume contributors include: Fields medalist Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Vladimir Korepin, Nikita Nekrasov, André Neveu, Alexander M Polyakov, Samson Shatashvili, Fedor Smirnov as well as Nobel laureates Frank Wilczek and C N Yang. "Ludwig and I had been good friends since the early 1970s. We had overlapping interests in several areas of physics. He was very powerful mathematically. I had written in several places that he should have shared the 1999 Nobel Prize in Physics with 't Hooft and Veltman" C N Yang, Nobel Laureate in Physics 1997 in Seoul. Faddeev with Baxter and Yang. 2005 in Tsinghua University. Left to right: Faddeev, Yang, Niemi and Ge.

Journey to the West

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Publisher : Asiapac Books Pte Ltd
ISBN 13 : 9812298894
Total Pages : 176 pages
Book Rating : 4.8/5 (122 download)

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Book Synopsis Journey to the West by : Wu Cheng'en

Download or read book Journey to the West written by Wu Cheng'en and published by Asiapac Books Pte Ltd. This book was released on 2018-08-14 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The bestselling Journey to the West comic book by artist Chang Boon Kiat is now back in a brand new fully coloured edition. Journey to the West is one of the greatest classics in Chinese literature. It tells the epic tale of the monk Xuanzang who journeys to the West in search of the Buddhist sutras with his disciples, Sun Wukong, Sandy and Pigsy. Along the way, Xuanzang's life was threatened by the diabolical White Bone Spirit, the menacing Red Child and his fearsome parents and, a host of evil spirits who sought to devour Xuanzang's flesh to attain immortality. Bear witness to the formidable Sun Wukong's (Monkey God) prowess as he takes them on, using his Fiery Eyes, Golden Cudgel, Somersault Cloud, and quick wits! Be prepared for a galloping read that will leave you breathless!

Festschrift In Honor Of The C N Yang Centenary, A: Scientific Papers

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Publisher : World Scientific
ISBN 13 : 9811264163
Total Pages : 638 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Festschrift In Honor Of The C N Yang Centenary, A: Scientific Papers by : Fong-ching Chen

Download or read book Festschrift In Honor Of The C N Yang Centenary, A: Scientific Papers written by Fong-ching Chen and published by World Scientific. This book was released on 2022-08-03 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: C N Yang is a towering figure of science who has significantly extended human understanding of nature, headed one of the foremost research institutes in physics for three decades, and made great contributions to the advances of Chinese physics. This Festschrift in honor of Professor Yang on his centenary birthday consists of two volumes: Volume A consists of general essays concerning Professor Yang the person, as well as the authors' impressions and reminiscences of him, which are mainly (but not exclusively) in Chinese. This volume, that is Volume B, consists of over thirty scientific papers in English on subjects broadly related to his work and contributed by two different groups: Professor Yang's colleagues, friends, and former students; and graduates from the Tsinghua University Physics Department or Institute for Advanced Study, who have come under the influence of Professor Yang and are now established in their own careers; review papers presented at a Symposium held in his honor in 2021 are also included. It is hoped that this Festschrift can serve as a fit tribute to Professor Yang's lifelong achievements, and also increase public awareness of the many different sides of this giant — his life, his personality, his work, his influence, as well as what he strives for.

Mirror Symmetry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821829556
Total Pages : 954 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry by : Kentaro Hori

Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.

Fractional Quantum Hall Effects: New Developments

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Publisher : World Scientific
ISBN 13 : 9811217505
Total Pages : 551 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Fractional Quantum Hall Effects: New Developments by : Bertrand I Halperin

Download or read book Fractional Quantum Hall Effects: New Developments written by Bertrand I Halperin and published by World Scientific. This book was released on 2020-06-09 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect has been one of the most active areas of research in quantum condensed matter physics for nearly four decades, serving as a paradigm for unexpected and exotic emergent behavior arising from interactions. This book, featuring a collection of articles written by experts and a Foreword by Klaus von Klitzing, the discoverer of quantum Hall effect and winner of 1985 Nobel Prize in physics, aims to provide a coherent account of the exciting new developments and the current status of the field.

Chinese History in Economic Perspective

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Publisher : Univ of California Press
ISBN 13 : 0520414047
Total Pages : 382 pages
Book Rating : 4.5/5 (24 download)

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Book Synopsis Chinese History in Economic Perspective by : Thomas G. Rawski

Download or read book Chinese History in Economic Perspective written by Thomas G. Rawski and published by Univ of California Press. This book was released on 2024-07-26 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume marks a turning point in the study of Chinese economic history. It arose from a realization that the economic history of China—as opposed to the history of the Chinese economy—had yet to be written. Most histories of the Chinese economy, whether by Western or Chinese scholars, tend to view the economy in institutional or social terms. In contrast, the studies in this volume break new ground by systematically applying economic theory and methods to the study of China. While demonstrating to historians the advantages of an economic perspective, the contributors, comprising both historians and economists, offer important new insights concerning issues of long-standing interest to both disciplines. Part One, on price behavior, presents for the first time preliminary analyses of the incomparably rich and important grain price data from the imperial archives in Beijing and Taibei during the Qing Dynasty (1644–1911). These studies reveal long-term trends in the Chinese economy since the seventeenth century and contain surprising discoveries about market integration, the agricultural economy, and demographic behavior in different regions of China. The essays in Part Two, on market response, deal with different aspects of the economy of Republican China (1912–49), showing that markets for land, labor, and capital sometimes functioned as predicted by models of economic "rationality" but at other times behaved in ways that can be explained only by combining economic analysis with knowledge of political, regional, class, and gender differences. Based on new types of data, they suggest novel interpretations of the Chinese economic experience. The resulting collection is interdisciplinary scholarship of a high order, which weaves together the analytic framework provided by economic theory and the rich texture of social phenomena gathered by accomplished historians. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992.

The Role of Topology in Materials

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Publisher : Springer
ISBN 13 : 3319765965
Total Pages : 297 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Role of Topology in Materials by : Sanju Gupta

Download or read book The Role of Topology in Materials written by Sanju Gupta and published by Springer. This book was released on 2018-04-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure–property–function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

Japan and China

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Publisher : Routledge
ISBN 13 : 1136821090
Total Pages : 310 pages
Book Rating : 4.1/5 (368 download)

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Book Synopsis Japan and China by : Matsuda Wataru

Download or read book Japan and China written by Matsuda Wataru and published by Routledge. This book was released on 2013-09-13 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume ties together the histories of Japan and China for the modern period prior to the 20th century. The chapters look at Chinese and Japanese works which were written in response to events in the other country. None of these works has received any sustained attention in the west. As a result we get a view of how Chinese and Japanese saw each other at a time when there were few personal contacts allowed. Many of these texts were built on fanciful embellishments of stories that migrated from one land to the other. But the unique qualities of the Sino-Japanese cultural bond seem to have conditioned the interaction so that these texts all reveal a fascinatingly well-defined area.

Quantum Theory of Condensed Matter

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Publisher : World Scientific
ISBN 13 : 9814304468
Total Pages : 261 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Quantum Theory of Condensed Matter by : Bertrand I. Halperin

Download or read book Quantum Theory of Condensed Matter written by Bertrand I. Halperin and published by World Scientific. This book was released on 2010 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since 1911, the Solvay Conferences have shaped modern physics. The 24th edition chaired by Bertrand Halperin did not break the tradition. Held in October 2008, it gathered in Brussels most of the leading figures working on the ?quantum theory of condensed matter?, addressing some of the most profound open problems in the field. The proceedings contain the ?rapporteur talks? giving a broad overview with unique insights by distinguished renowned scientists. These lectures cover the five sessions treating: mesoscopic and disordered systems; exotic phases and quantum phase transitions in model systems; experimentally realized correlated-electron materials; quantum Hall systems, and one-dimensional systems; systems of ultra-cold atoms, and advanced computational methods. In the Solvay tradition, the proceedings include also the prepared comments to the rapporteur talks. The discussions among the participants ? some of which are quite lively and involving dramatically divergent points of view ? have been carefully edited and reproduced in full.

A History of Chinese Science and Technology

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Publisher : Springer
ISBN 13 : 3662441632
Total Pages : 634 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis A History of Chinese Science and Technology by : Yongxiang Lu

Download or read book A History of Chinese Science and Technology written by Yongxiang Lu and published by Springer. This book was released on 2014-10-20 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: A History of Chinese Science and Technology (Voulumes 1, 2 & 3) presents 44 individual lectures, beginning with Ancient Chinese Science and Technology in the Process of Human Civilizations and An Overview of Ancient Chinese Science and Technology, and continuing with in-depth discussions of several issues in the history of science and the Needham Puzzle, interspersed with topics on Astronomy, Arithmetic, Agriculture, and Medicine, The Four Great Inventions, and various technological areas closely related to clothing, food, shelter, and transportation. This book is the most authoritative work on the history of Chinese Science and Technology. It is the Winner of the China Book Award, the Shanghai Book Award (1st prize), and the China Classics International (State Administration of Press, Publication, Radio, Film and Television of The People’s Republic of China) and offers an essential resource for academic researchers and non-experts alike. It originated with a series of 44 lectures presented to top Chinese leaders, which received very positive feedback. Written by top Chinese scholars in their respective fields from the Institute for the History of Nature Sciences, Chinese Academic Sciences and many other respected Chinese organizations, the book is intended for scientists, researchers and postgraduate students working in the history of science, philosophy of science and technology, and related disciplines. Yongxiang Lu is a professor, former president and member of the Chinese Academy of Sciences.

Holographic Entanglement Entropy

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Publisher : Springer
ISBN 13 : 3319525735
Total Pages : 246 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Holographic Entanglement Entropy by : Mukund Rangamani

Download or read book Holographic Entanglement Entropy written by Mukund Rangamani and published by Springer. This book was released on 2017-05-08 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.

Reviving Ancient Chinese Mathematics

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Publisher : Routledge
ISBN 13 : 1134468253
Total Pages : 223 pages
Book Rating : 4.1/5 (344 download)

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Book Synopsis Reviving Ancient Chinese Mathematics by : Jiri Hudecek

Download or read book Reviving Ancient Chinese Mathematics written by Jiri Hudecek and published by Routledge. This book was released on 2014-07-25 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China’s independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China’s most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun’s story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu’s intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.

Information in Contemporary Society

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Publisher : Springer
ISBN 13 : 3030157423
Total Pages : 829 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Information in Contemporary Society by : Natalie Greene Taylor

Download or read book Information in Contemporary Society written by Natalie Greene Taylor and published by Springer. This book was released on 2019-03-12 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Conference on Information in Contemporary Society, iConference 2019, held in Washington, DC, USA, in March/April 2019. The 44 full papers and 33 short papers presented in this volume were carefully reviewed and selected from 133 submitted full papers and 88 submitted short papers. The papers are organized in the following topical sections: Scientific work and data practices; methodological concerns in (big) data research; concerns about “smart” interactions and privacy; identity questions in online communities; measuring and tracking scientific literature; limits and affordances of automation; collecting data about vulnerable populations; supporting communities through public libraries and infrastructure; information behaviors in academic environments; data-driven storytelling and modeling; online activism; digital libraries, curation and preservation; social-media text mining and sentiment analysis; data and information in the public sphere; engaging with multi-media content; understanding online behaviors and experiences; algorithms at work; innovation and professionalization in technology communities; information behaviors on Twitter; data mining and NLP; informing technology design through offline experiences; digital tools for health management; environmental and visual literacy; and addressing social problems in iSchool research.

The Theory of Jacobi Forms

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Publisher : Springer Science & Business Media
ISBN 13 : 1468491628
Total Pages : 150 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis The Theory of Jacobi Forms by : Martin Eichler

Download or read book The Theory of Jacobi Forms written by Martin Eichler and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.