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Books on the topic 'Flat functors'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Bieberbach groups and flat manifolds. New York: Springer-Verlag, 1986.

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2

A, Fialkow Lawrence, ed. Flat extensions of positive moment matrices: Recursively generated relations. Providence, R.I: American Mathematical Society, 1998.

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3

Tuhfatullin, Boris. Nonlinear problems of structural mechanics. Methods of optimal design of structures. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1201340.

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The textbook discusses methods of optimal design of structures, including methods for minimizing the functions of one and several variables; methods for solving linear and nonlinear programming problems; examples of optimal design of flat steel frames with elements made of rolled and composite I-beams. It is intended for students studying in the specialty 08.05.01 "Construction of unique buildings and structures", undergraduates studying in the training program 08.04.01.24 "Modern technologies of design and construction of buildings and structures", studying the discipline "Nonlinear problems of structural mechanics", as well as for postgraduates of the direction 08.06.01 " Engineering and construction technologies. Construction of buildings and structures", studying the discipline "Construction Mechanics".

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4

Wu, K. Chauncey. Free vibration of hexagonal panels simply supported at discrete points. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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5

Gross, Bernard. Least squares best fit method for the three parameter Weibull distribution: Analysis of tensile and bend specimens with volume or surface flaw failure. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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6

1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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7

Caramello, Olivia. Flat functors and classifying toposes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0007.

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This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes induced by embeddings of categories and on geometric morphisms to the classifying topos of a geometric theory induced by a small category of set-based models of the latter. A number of general results of independent interest are established on the way, including developments on colimits of internal diagrams in toposes and a way of representing flat functors by using a suitable internalized version of the Yoneda lemma. These general results will be instrumental for establishing in Chapter 6 the main theorem characterizing the class of geometric theories classified by a presheaf topos and for applying it.

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8

Caramello, Olivia. Topos-theoretic background. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0003.

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This chapter provides the topos-theoretic background necessary for understanding the contents of the book; the presentation is self-contained and only assumes a basic familiarity with the language of category theory. The chapter begins by reviewing the basic theory of Grothendieck toposes, including the fundamental equivalence between geometric morphisms and flat functors. Then it presents the notion of first-order theory and the various deductive systems for fragments of first-order logic that will be considered in the course of the book, notably including that of geometric logic. Further, it discusses categorical semantics, i.e. the interpretation of first-order theories in categories possessing ‘enough’ structure. Lastly, the key concept of syntactic category of a first-order theory is reviewed; this notion will be used in Chapter 2 for constructing classifying toposes of geometric theories.

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9

Caramello, Olivia. Theories of presheaf type: general criteria. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0008.

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This chapter carries out a systematic investigation of the class of geometric theories of presheaf type (i.e. classified by a presheaf topos), by using in particular the results on flat functors established in Chapter 5. First, it establishes a number of general results on theories of presheaf type, notably including a definability theorem and a characterization of the finitely presentable models of such a theory in terms of formulas satisfying a key property of irreducibility. Then it presents a fully constructive characterization theorem providing necessary and sufficient conditions for a theory to be of presheaf type expressed in terms of the models of the theory in arbitrary Grothendieck toposes. This theorem is shown to admit a number of simpler corollaries which can be effectively applied in practice for testing whether a given theory is of presheaf type as well as for generating new examples of such theories.

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10

Caramello, Olivia. Theories, Sites, Toposes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.001.0001.

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This book is devoted to a general study of geometric theories from a topos-theoretic perspective. After recalling the necessary topos-theoretic preliminaries, it presents the main methodology it uses to extract ‘concrete’ information on theories from properties of their classifying toposes—the ‘bridge’ technique. As a first implementation of this methodology, a duality is established between the subtoposes of the classifying topos of a geometric theory and the geometric theory extensions (also called ‘quotients’) of the theory. Many concepts of elementary topos theory which apply to the lattice of subtoposes of a given topos are then transferred via this duality into the context of geometric theories. A second very general implementation of the ‘bridge’ technique is the investigation of the class of theories of presheaf type (i.e. classified by a presheaf topos). After establishing a number of preliminary results on flat functors in relation to classifying toposes, the book carries out a systematic investigation of this class resulting in a number of general results and a characterization theorem allowing one to test whether a given theory is of presheaf type by considering its models in arbitrary Grothendieck toposes. Expansions of geometric theories and faithful interpretations of theories of presheaf type are also investigated. As geometric theories can always be written (in many ways) as quotients of presheaf type theories, the study of quotients of a given theory of presheaf type is undertaken. Lastly, the book presents a number of applications in different fields of mathematics of the theory it develops.

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11

Charlap, Leonard S. Bieberbach Groups and Flat Manifolds. Springer, 2012.

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12

Hughes, Jim. Image receptors. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780198813170.003.0003.

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The receptor head is the system that converts the X-ray beam into a visible image and allows it to be displayed. Modern systems accomplish this by using either an image intensifier (II) or a flat-panel detector (FPD). Both allow real-time fluoroscopy, as well as last-image hold, image storage and retrieval, and other features to assist in procedures or reduce radiation dose. This chapter covers the design and functions of image receptor heads used on C-arm systems that produce images from the incident X-ray beam. This includes the process of intensification and amplification of the image within an II system, as well as the function and the use of newer FPD systems.

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13

Free vibration of hexagonal panels simply supported at discrete points. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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14

Least squares best fit method for the three parameter Weibull distribution: Analysis of tensile and bend specimens with volume or surface flaw failure. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.

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15

Optimization of Objective Functions: Analytics. Numerical Methods. Design of Experiments. Moscow, Russia: Fizmatlit Publisher, 2009.

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16

Buttenwieser, Ann L. The Floating Pool Lady. Cornell University Press, 2021. http://dx.doi.org/10.7591/cornell/9781501716010.001.0001.

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Why on earth would anyone want to float a pool up the Atlantic coastline to bring it to rest at a pier on the New York City waterfront? This book recounts the author's triumphant adventure that started in the bayous of Louisiana and ended with a self-sustaining, floating swimming pool moored in New York Harbor. When the author decided something needed to be done to help revitalize the New York City waterfront, she reached into the city's nineteenth-century past for inspiration. The author wanted New Yorkers to reestablish their connection to their riverine surroundings and she was energized by the prospect of city youth returning to the Hudson and East rivers. What she didn't suspect was that outfitting and donating a swimming facility for free enjoyment by the public would turn into an almost-Sisyphean task. As the book describes, the author battled for years with politicians and struggled with bureaucrats to bring her “crazy” scheme to fruition. The book retells the improbable process that led to a pool named The Floating Pool Lady tying up to a pier at Barretto Point Park in the Bronx, ready for summer swimmers. Throughout, the book raises consciousness about persistent environmental issues and the challenges of developing a constituency for projects to make cities livable in the twenty-first century. The story functions as both warning and inspiration to those who dare to dream of realizing innovative public projects in the modern urban landscape.

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