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Author: Andrew Witt
Publisher: MIT Press
ISBN: 0262543001
Category : Architecture
Languages : en
Pages : 385
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Book Description
An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.
Author: Andrew Witt
Publisher: MIT Press
ISBN: 0262543001
Category : Architecture
Languages : en
Pages : 385
Get Book Here
Book Description
An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.
Author: Stephen M. Rowland
Publisher: John Wiley & Sons
ISBN: 111953545X
Category : Science
Languages : en
Pages : 290
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Book Description
STRUCTURAL ANALYSIS & SYNTHESIS STRUCTURAL ANALYSIS & SYNTHESIS A LABORATORY COURSE IN STRUCTURAL GEOLOGY Structural Analysis and Synthesis is the best-selling laboratory manual of its kind. Specifically designed to support the laboratory work of undergraduates in structural geology courses, the book helps students analyze the various aspects of geological structures, and to combine their analyses into an overarching synthesis. This book is intended for use in the laboratory portion of a first course in structural geology. As is explicit in the book’s title, it is concerned with both the analysis and synthesis of structural features. In this fourth edition, the has been broadened to include a range of new content and features, including: Video content that demonstrates how to perform some of the more challenging structural geology techniques An acknowledgment of the increasing importance of environmental applications of structural geology – vital to students who may go on to pursue careers in the environmental sphere An increased emphasis on quantitative techniques, complete with descriptions of computer program applications Contingent with this quantitative emphasis, the book also outlines the limitations of such techniques, helping students to appropriately apply the techniques and evaluate their trustworthiness Structural Analysis and Synthesis is a renowned and widely recognized aid to students in grasping and mastering the techniques required in structural geology, and will find a home wherever the principles and practices of structural geology are taught.
Author: Christina Birkenhake
Publisher: Springer Science & Business Media
ISBN: 9783540204886
Category : Mathematics
Languages : en
Pages : 658
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Book Description
This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.
Author: Mark J. Ablowitz
Publisher: World Scientific
ISBN: 9789812704467
Category : Business & Economics
Languages : en
Pages : 442
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Book Description
Pt. I. Analytical methods. On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons / M.J. Ablowitz, B. Prinari, A.D. Trubatch -- Soliton solutions of coupled nonlinear Klein-Gordon equations / T. Alagesan -- Characteristic initial value problems for integrable hyperbolic reductions of Einstein's equations / G.A. Alekseev -- Discrete sine-Gordon equation / M. Boiti [und weitere] -- Integrable and non-integrable equations with peakons / A. Degasperis, D.D. Holm, A.N.W. Hone -- Solution of a free boundary problem for a nonlinear diffusion-convection equation / S. De Lillo, M.C. Salvatori, G. Sanchini -- Iterative construction of solutions for a nonisospectral problem in 2 + 1 dimensions / P.G. Estevez -- Discrete breathers close to the anticontinuum limit: existence and wave scattering / S. Flach [und weitere] -- Complex Toda chain - an integrable universal model for adiabatic N-soliton interactions! / V.S. Gerdjikov -- On the reductions and scattering data for the generalized Zakharov-Shabat systems / G.G. Grahovski -- Bilinear representation for the modified nonlinear Schrödinger equations and their quantum potential deformations / J.H. Lee, O.K. Pashaev -- Noncommutative Burgers' equations / L. Martina, O.K. Pashaev -- On the quasi-classical [sumbol]-dressing method / B. Konopelchenko, A. Moro -- New solvable matrix integrals - U(n) case / A. Yu. Orlov -- Integrable hydrodynamic chains / M.V. Pavlov -- KPII: new results and open problems / A.K. Pogrebkov -- A workmate for KdV / P.C. Sabatier -- Space-time lattice for operator Schrödinger equation / A. Spire, V.V. Konotop, L. Vazquez -- On isomonodromy deformations for the ZS-AKNS flows / D. Wu -- pt. II. Symmetry properties, Hamiltonian methods and group theoretical methods. New symmetry reductions for a lubrication model / M.S. Bruzón [und weitere] -- Quantum solitons for quantum information and quantum computing / R.K. Bullough, M. Wadati -- Solving renormalization group equations by recursion relations / A. Cafarella, C. Corianò, M. Guzzi -- A tri-Hamiltonian route to spectral curves / L. Degiovanni, G. Magnano -- Construction of real forms of complexified Hamiltonian dynamical systems / V.S. Gerdjikov [und weitere] -- Integrable and super-integrable systems in classical and quantum mechanics / M. Giordano [und weitere] -- Non-commuting coordinates in vortex dynamics and in the Hall effect, related to "exotic" Galilean symmetry / P.A. Horváthy -- Structure of multi-meron knot action / L.S. Isaev, A.P. Protogenov -- Compatible nonlocal Poisson brackets of hydrodynamic type and integrable reductions of the Lamé equations / O.I. Mokhov -- Pseudoanti-Hermiticity in QQM, time-reversal and Kramers degeneracy / G. Scolarici -- On the integrability of supersymmetric equations / P. Tempesta, R.A. Leo, G. Soliani
Author: Vladimir V. Tkachuk
Publisher: Springer
ISBN: 3319243853
Category : Mathematics
Languages : en
Pages : 740
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Book Description
This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.
Author: Juan-Pablo Ortega
Publisher: Springer Science & Business Media
ISBN: 1475738110
Category : Mathematics
Languages : en
Pages : 526
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Book Description
* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
Author: Cam Nguyen
Publisher: John Wiley & Sons
ISBN: 0471463841
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
A one-stop reference to the major techniques for analyzing microwave planar transmission line structures The last two decades have seen important progress in the development of methods for the analysis of microwave and millimeter-wave passive structures, which contributed greatly to microwave integrated circuit design while also stimulating the development of new planar transmission lines. This timely and authoritative work introduces microwave engineers to the most commonly used techniques for analyzing microwave planar transmission line structures. Designed to be easily accessible to readers with only a fundamental background in electromagnetic theory, the book provides clear explanations of the theory and applications of Green's function, the conformal-mapping method, spectral domain methods, variational methods, and the mode-matching methods. Coverage for each method is self-contained and supplemented with problems and solutions as well as useful figures. In addition to providing detailed formulations of the methods under discussion, this highly practical book also demonstrates how to apply the principles of electromagnetic theory to the analysis of microwave boundary value problems, customize methods for specific needs, and develop new techniques. Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures is an excellent working resource for anyone involved in the design and engineering of RF, microwave, and millimeter-wave integrated circuits.
Author: Christophe Golé
Publisher: World Scientific
ISBN: 9812810765
Category : Mathematics
Languages : en
Pages : 325
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Book Description
0. Introduction. 1. Fall from paradise. 2. Billiards and broken geodesies. 3. An ancestor of symplectic topology -- 1. Twist maps of the annulus. 4. Monotone twist maps of the annulus. 5. Generating functions and variational setting. 6. Examples. 7. The Poincare-Birkhoff theorem -- 2. The Aubry-Mather theorem. 8. Introduction. 9. Cyclically ordered sequences and orbits. 10. Minimizing orbits. 11. CO orbits of all rotation numbers. 12. Aubry-Mather sets -- 3. Ghost circles. 14. Gradient flow of the action. 15. The gradient flow and the Aubry-Mather theorem. 16. Ghost circles. 17. Construction of ghost circles. 18. Construction of disjoint ghost circles. 19. Proof of lemma 18.5. 20. Proof of theorem 18.1. 21. Remarks and applications. 22. Proofs of monotonicity and of the Sturmian lemma -- 4. Symplectic twist maps. 23. Symplectic twist maps of T[symbol] x IR[symbol]. 24. Examples. 25. More on generating functions. 2.6. Symplectic twist maps on general cotangent bundles of compact manifolds -- 5. Periodic orbits for symplectic twist maps of T[symbol] x IR[symbol]. 27. Presentation of the results. 28. Finite dimensional variational setting. 29. Second variation and nondegenerate periodic orbits. 30. The coercive case. 31. Asymptotically linear systems. 32. Ghost tori. 33. Hyperbolicity Vs. action minimizers -- 6. Invariant manifolds. 34. The theory of Kolmogorov-Arnold-Moser. 35. Properties of invariant tori. 36. (Un)stable manifolds and heteroclinic orbits. 37. Instability, transport and diffusion -- 7. Hamiltonian systems vs. twist maps. 38. Case study: The geodesic flow. 39. Decomposition of Hamiltonian maps into twist maps. 40. Return maps in Hamiltonian systems. 41. Suspension of symplectic twist maps by Hamiltonian flows -- 8. Periodic orbits for Hamiltonian systems. 42. Periodic orbits in the cotangent of the n-torus. 43. Periodic orbits in general cotangent spaces. 44. Linking of spheres -- 9. Generalizations of the Aubry-Mather theorem. 45. Theory for functions on lattices and PDE's. 46. Monotone recurrence relationst. 47. Anti-integrable limit. 48. Mather's theory of minimal measures. 49. The case of hyperbolic manifolds. 50. Concluding remarks -- 10. Generating phases and symplectic topology. 51. Chaperon's method and the theorem Of Conley-Zehnder. 52. Generating phases and symplectic geometry.
Author: Sergey Novikov
Publisher: American Mathematical Soc.
ISBN: 1470455919
Category : Education
Languages : en
Pages : 542
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Book Description
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Author: Michel Marie Deza
Publisher: Springer Science & Business Media
ISBN: 3642309585
Category : Mathematics
Languages : en
Pages : 644
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Book Description
This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a developing field now regarded as an essential tool in many areas of pure and applied mathematics. Its publication coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval. The content focuses on providing academics with an invaluable comprehensive listing of the main available distances. As well as standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries, and includes a wealth of fascinating curiosities that enable non-specialists to deploy research tools previously viewed as arcane. Its value-added context is certain to open novel avenues of research.
