Formalization Of Complex Analysis And Matrix Theory

Author : Zhiping Shi,Yong Guan,Ximeng Li
Publisher : Springer Nature
Page : 172 pages
File Size : 53,6 Mb
Release : 2020-08-10
Category : Mathematics
ISBN : 9789811572616

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Formalization of Complex Analysis and Matrix Theory by Zhiping Shi,Yong Guan,Ximeng Li Pdf

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 : Frédéric Lang,Francesco Flammini
Publisher : Springer
Page : 213 pages
File Size : 44,7 Mb
Release : 2014-09-01
Category : Computers
ISBN : 9783319107028

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Formal Methods for Industrial Critical Systems by Frédéric Lang,Francesco Flammini Pdf

This book constitutes the proceedings of the 19th International Conference on Formal Methods for Industrial Critical Systems, FMICS 2014, held in Florence, Italy, in September 2014. The 13 papers presented in this volume were carefully reviewed and selected from 26 submissions. They are organized in topical sections named: cyber-physical systems; computer networks; railway control systems; verification methods; and hardware and software testing.

Author : Daniel Breaz,Michael Th. Rassias
Publisher : Springer Nature
Page : 538 pages
File Size : 47,6 Mb
Release : 2020-05-12
Category : Mathematics
ISBN : 9783030401207

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Advancements in Complex Analysis by Daniel Breaz,Michael Th. Rassias Pdf

The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.

Author : Joe Hurd
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 53,9 Mb
Release : 2005-08-08
Category : Computers
ISBN : 9783540283720

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Theorem Proving in Higher Order Logics by Joe Hurd Pdf

This book constitutes the refereed proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, held in Oxford, UK, in August 2005. The 20 revised full papers presented together with 2 invited papers and 4 proof pearls (concise and elegant presentations of interesting examples) were carefully reviewed and selected from 49 submissions. All current issues in HOL theorem proving and formal verification of software and hardware systems are addressed. Among the topics of this volume are theorem proving, verification, recursion and induction, mechanized proofs, mathematical logic, proof theory, type systems, program verification, and proving systems like HOL, Coq, ACL2, Isabelle/HOL and Isabelle/HOLCF.

Author : John Chi-Kin Lee,Kerry J. Kennedy
Publisher : Taylor & Francis
Page : 326 pages
File Size : 50,6 Mb
Release : 2017-03-27
Category : Education
ISBN : 9781317616559

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Theorizing Teaching and Learning in Asia and Europe by John Chi-Kin Lee,Kerry J. Kennedy Pdf

There has been much debate in recent times between the Anglo American tradition of curriculum studies and the Continental and North European tradition of didactics (Didaktik). As important as such debate has been, this book seeks to add new voices to the debate representing ideas and traditions from a different part of the world. The focus is on Chinese curriculum thinking that has passed through a number of stages and currently represents a blend of some aspects of the American tradition and Chinese cultural traditions. How does Chinese thinking about curriculum, teaching and learning resonate with European didactic traditions and what are the implications for theorizing an expanded field of curriculum studies? This book deliberately transcends borders and cultures to explore new territory, to provide a platform for open dialogue and to open up new areas of investigation Chapters include, Curriculum Reform and Research in China: A Social-Historical Perspective What Mathematics Did Teachers Learn? Comparison of the School and the Pre-Service Teacher Mathematics Curricula in Germany and Taiwan Living in Parallel Worlds: A Transatlantic Dialogue between General Didactics and Instructional Design

Author : Zhong Li
Publisher : International Press of Boston
Page : 288 pages
File Size : 51,9 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015038138957

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Proceedings of the Conference on Complex Analysis by Zhong Li Pdf

This volume documents the talks of the International Conference on Complex Analysis, 1992. Sessions focused on the areas of complex dynamical systems, the theory of value distribution, the quasi-conformal mappings, and the geometric theory of functions.

Author : Percy Deift,Dimitri Gioev
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 55,7 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 0821847376

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Random Matrix Theory by Percy Deift,Dimitri Gioev Pdf

This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles--orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derived. The book is based in part on a graduate course given by the first author at the Courant Institute in fall 2005. Subsequently, the second author gave a modified version of this course at the University of Rochester in spring 2007. Anyone with some background in complex analysis, probability theory, and linear algebra and an interest in the mathematical foundations of random matrix theory will benefit from studying this valuable reference.

Author : Guillaume Brat,Neha Rungta,Arnaud Venet
Publisher : Springer
Page : 504 pages
File Size : 47,5 Mb
Release : 2013-05-09
Category : Computers
ISBN : 9783642380884

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NASA Formal Methods by Guillaume Brat,Neha Rungta,Arnaud Venet Pdf

This book constitutes the refereed proceedings of the 5th International Symposium on NASA Formal Methods, NFM 2013, held in Moffett Field, CA, USA, in May 2013. The 28 revised regular papers presented together with 9 short papers talks were carefully reviewed and selected from 99 submissions. The topics are organized in topical sections on model checking; applications of formal methods; complex systems; static analysis; symbolic execution; requirements and specifications; probabilistic and statistical analysis; and theorem proving.

Author : London Mathematical Society
Publisher : Unknown
Page : 600 pages
File Size : 42,8 Mb
Release : 1980
Category : Mathematics
ISBN : UCAL:B4406606

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Aspects of Contemporary Complex Analysis by London Mathematical Society Pdf

Author : Rubi Rodriguez,Irwin Kra,Jane P. Gilman
Publisher : Springer
Page : 306 pages
File Size : 52,5 Mb
Release : 2012-11-20
Category : Mathematics
ISBN : 1441973249

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Complex Analysis by Rubi Rodriguez,Irwin Kra,Jane P. Gilman Pdf

The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.

Author : Anthony Joseph,Fulbert Mignot,Francois Murat,Bernard Prum,Rudolf Rentschler
Publisher : Nelson Thornes
Page : 614 pages
File Size : 42,8 Mb
Release : 1994-08
Category : Mathematics
ISBN : 3764328002

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First European Congress of Mathematics by Anthony Joseph,Fulbert Mignot,Francois Murat,Bernard Prum,Rudolf Rentschler Pdf

The book contains the round table reports of the first European Congress of Mathematics, a new feature of this Congress devoted to furthering the contribution of mathematics to society and reporting on its interaction with the exact and social sciences. Topics: • Mathematics and the general public • Women and mathematics • Mathematics and educational policy • Let's cultivate mathematics! • Mathematical Europe: Myth or historical reality? • Philosophie des mathématiques : pourquoi ? comment ? • Mathématiques et sciences sociales • Mathe- matics and industry • Degree harmonization and student exchange programmes • The Pythagoras programme • Collaboration with devel- oping countries • Mathematical libraries in Europe • Mathematics and economics • Mathématiques et Chimie • Mathematics in medicine and biology. This book is also available in hardcover as Volume 121 of the series Progress in Mathematics, where it forms part of the three-volume set First European Congress of Mathematics. Volumes I (Invited Lectures Part 1) and II (Invited Lectures Part 2) of this set are also available separately as Volumes 119 and 120, respectively, of Progress in Mathematics.

Author : Gerwin Klein,Ruben Gamboa
Publisher : Springer
Page : 555 pages
File Size : 54,8 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9783319089706

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Interactive Theorem Proving by Gerwin Klein,Ruben Gamboa Pdf

This book constitutes the proceedings of the 5th International Conference on Interactive Theorem Proving, ITP 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 35 papers presented in this volume were carefully reviewed and selected from 59 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.

Author : Zhenhua Duan,Luke Ong
Publisher : Springer
Page : 498 pages
File Size : 42,5 Mb
Release : 2017-10-13
Category : Computers
ISBN : 9783319686905

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Formal Methods and Software Engineering by Zhenhua Duan,Luke Ong Pdf

This book constitutes the refereed proceedings of the 19th International Conference on Formal Engineering Methods, ICFEM 2017, held in Xi'an, China, in November 2017. The 28 revised full papers presented together with one invited talk and two abstracts of invited talks were carefully reviewed and selected from 80 submissions. The conference focuses on all areas related to formal engineering methods, such as verification and validation, software engineering, formal specification and modeling, software security, and software reliability.

Author : University of Utah. Graduate School
Publisher : Unknown
Page : 198 pages
File Size : 47,5 Mb
Release : 1964
Category : Electronic
ISBN : UIUC:30112114113423

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The Graduate School by University of Utah. Graduate School Pdf

Author : Jing Sun,Meng Sun
Publisher : Springer
Page : 474 pages
File Size : 41,6 Mb
Release : 2018-11-05
Category : Computers
ISBN : 9783030024505

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Formal Methods and Software Engineering by Jing Sun,Meng Sun Pdf

This book constitutes the refereed proceedings of the 20th International Conference on Formal Engineering Methods, ICFEM 2018, held in Gold Coast, QLD, Australia, in November 2018. The 22 revised full papers presented together with 14 short papers were carefully reviewed and selected from 66 submissions. The conference focuses on all areas related to formal engineering methods, such as verification; network systems; type theory; theorem proving; logic and semantics; refinement and transition systems; and emerging applications of formal methods.