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Author: Zhiping Shi
Publisher: Springer Nature
ISBN: 9811572615
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.
Author: Zhiping Shi
Publisher: Springer Nature
ISBN: 9811572615
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.
Author: Semen Grigorʹevich Gindikin
Publisher: American Mathematical Soc.
ISBN: 9780821834725
Category : Geometry, Differential
Languages : en
Pages : 372
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Book Description
The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927-2000). Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as thearticle by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest. The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.
Author: Shojiro Sakata
Publisher: Springer Science & Business Media
ISBN: 9783540541950
Category : Computers
Languages : en
Pages : 410
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Book Description
The AAECC conferences focus on the algebraic aspects of modern computer science, which include the most up-to-date and advanced topics. The topic of error-correcting codes is one where theory and implementation are unified into a subject both of mathematical beauty and of practical importance. Algebraic algorithms are not only interesting theoretically but also important in computer and communication engineering and many other fields. This volume contains the proceedings of the 8th AAECC conference, held in Tokyo in August 1990. Researchers from Europe, America, Japan and other regions of the world presented papers at the conference. The papers present new results of recent theoretical and application-oriented research on applied algebra, algebraic algorithms and error-correcting codes.
Author: Alicia Dickenstein
Publisher: Springer Science & Business Media
ISBN: 3540243267
Category : Computers
Languages : en
Pages : 433
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Book Description
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Author: Carlo Borromeo Giannoni
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111349497
Category : Language Arts & Disciplines
Languages : en
Pages : 160
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Book Description
Author: Huaiyu Wang
Publisher: World Scientific Publishing Company
ISBN: 9813146508
Category : Science
Languages : en
Pages : 751
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Book Description
This book covers the necessary aspects of mathematics for graduate students in physics and engineering. Advanced undergraduate students and researchers who intend to enter the field of theoretical physics can also pick up this book. The first eight chapters include variational method, Hilbert space and operators, ordinary linear differential equations, Bessel functions, Dirac delta function, the Green's function in mathematical physics, norm, integral equations. Beside these traditional contents, the last two chapters introduce some recent achievements of scientific research while presenting their mathematical background. Like the basis of number theory and its application in physics, material science and other scientific fields, the fundamental equations in spaces with arbitrary dimensions, not limited to Euclid space; Pseudo spherical coordinates. Plain terminologies were used to present the concept of metric, as well as new and interesting work on the Klein-Gorden equation and Maxwell equation.
Author: John David White
Publisher: Rowman & Littlefield
ISBN: 081082681X
Category : Musical analysis
Languages : en
Pages : 316
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Book Description
Presents material on Heinrich Schenker and reductive linear analysis and additional material on set theoretical analysis. Replete with musical examples, charts, and diagrams.
Author: Roberto Pasini
Publisher: Springer
ISBN: 3319778870
Category : Political Science
Languages : en
Pages : 240
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Book Description
This book presents: 1) an urban-studies panorama on the emergence of a built/landscape continuum following the anthropic expansion at the geographic scale and the consequent demise of the city/country divide; 2) an in-depth theoretical analysis of disparate landscape constructs, culminating in the proposal of a comprehensive spatial paradigm addressing both manmade and natural contexts; 3) the in-situ transcription of the proposed spatial paradigm into a landscape installation implementing a territorial narrative in the Sierra Madre Oriental of Mexico. Foreword by Peter G. Rowe and afterword by Elisa C. Cattaneo. By virtue of its openness, fluidity, and volatility, fluctuating between heterogeneity and diversity, today’s built/landscape continuum exhibits analogies with distinct notions of landscape. The book determines an open-ended classification of contemporary space-making strategies exceeding the urban and metropolitan ambit, through a comparative anatomy of global case studies ranging from hard to soft: geotechnics or applied geographies, machinic micro-ecologies, aesthetic prostheses for operative metabolism, cybernetic utopias, atmospheric assemblages, psychic spheres, creole horizons, semiotic landscapes, geopolitical landscapes, geophilosophical excavations. The proposed spatial paradigm, accommodating aggregates of artificial and living systems, physical and mental spaces, and machinic and cultural landscapes, intends to reconcile the traditionally opposed ‘scientific-cognitive-metabolist’ and ‘cultural-geophilosophical-territorialist’ visions of the landscape. The resulting model transcends the exhausted myths of urban space, metropolitanism, and their filiations, in favor of a new form of urbanity and its attributes. Parts of the work were developed in the frame of research projects of Universidad de Monterrey and Parque Ecológico Chipinque and the IDAUP of UniFE and Polis. The target audience of the book is researchers, teachers, and advanced students engaged in landscape and urban studies with a prevalent focus on theory. The book can also benefit professional and institutional audiences looking for ethical/methodological orientation.
Author: Israel Kleiner
Publisher: Springer Science & Business Media
ISBN: 0817646841
Category : Mathematics
Languages : en
Pages : 175
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Book Description
This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
Author: Andrea Asperti
Publisher: Springer Science & Business Media
ISBN: 3540230297
Category : Computers
Languages : en
Pages : 402
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Book Description
This book constitutes the refereed proceedings of the Third International Conference on Mathematical Knowledge Management, MKM 2004, held in Bialowieza, Poland, in September 2004. The 27 revised full papers presented were carefully reviewed and selected from 48 submissions. Among the topics addressed are mathematics retrieval, formalizing mathematics, formal mathematics, digital mathematical libraries, semantic Web, knowledge repositories, mathematical knowledge representation, theorem proving systems, OWL, proof verification, formal representation, mathematical formulae processing, and the OpenMath project.
