Relevant bibliographies by topics / Flat functors

Academic literature on the topic 'Flat functors'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Flat functors"

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Crivei, Septimiu. "On Flat Objects of Finitely Accessible Categories." Scientific World Journal 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/451091.

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Flat objects of a finitely accessible additive category are described in terms of some objects of the associated functor category of , called strongly flat functors. We study closure properties of the class of strongly flat functors, and we use them to deduce the known result that every object of a finitely accessible abelian category has a flat cover.
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Hu, Hongde. "Flat functors and free exact categories." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 2 (April 1996): 143–56. http://dx.doi.org/10.1017/s1446788700037575.

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AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.
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Hu, Jiangsheng, Huanhuan Li, Yuxian Geng, and Dongdong Zhang. "Frobenius functors and Gorenstein flat dimensions." Communications in Algebra 48, no. 3 (October 24, 2019): 1257–65. http://dx.doi.org/10.1080/00927872.2019.1677699.

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Crivei, Septimiu. "Flat Weakly FP-Injective and FP-Injective Weakly Flat Functors." Results in Mathematics 71, no. 3-4 (September 1, 2016): 1031–45. http://dx.doi.org/10.1007/s00025-016-0598-8.

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Farjoun, Emmanuel Dror, and Jérôme Scherer. "Conditionally flat functors on spaces and groups." Collectanea Mathematica 66, no. 1 (February 13, 2014): 149–60. http://dx.doi.org/10.1007/s13348-013-0102-7.

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Mao, Lixin. "Strongly FP-injective and strongly flat functors." Rendiconti del Seminario Matematico della Università di Padova 135 (2016): 133–49. http://dx.doi.org/10.4171/rsmup/135-7.

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Nicholson, W. K., and J. F. Watters. "Morita context functors." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (May 1988): 399–408. http://dx.doi.org/10.1017/s0305004100065014.

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AbstractGiven a Morita context (R, V, W, S), there are functors W⊗() and hom (V, ) from R-mod to; S-mod and a natural transformation λ from the first to the second. This has an epi-mono factorization and the intermediate functor we denote by ()° with natural transformations and . The tensor functor is exact if and only if WR is flat, whilst the hom functor is exact if and only if RV is projective. We begin by determining conditions under which ()° is exact; this is Theorem 1.
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Aldrich, Stephen T., Edgar E. Enochs, and Juan A. Lopez Ramos. "Derived Functors of Hom Relative to Flat Covers." Mathematische Nachrichten 242, no. 1 (July 2002): 17–26. http://dx.doi.org/10.1002/1522-2616(200207)242:1<17::aid-mana17>3.0.co;2-f.

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Akatsa, Victor K. "Flat resolvents, minimal injective resolutions and negative torsion functors." Communications in Algebra 20, no. 11 (January 1992): 3105–18. http://dx.doi.org/10.1080/00927879208824508.

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Selvaraj, C., and R. Udhayakumar. "Derived Functors of Hom Relative to n-Flat Covers." Vietnam Journal of Mathematics 43, no. 3 (September 17, 2014): 571–82. http://dx.doi.org/10.1007/s10013-014-0097-8.

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Dissertations / Theses on the topic "Flat functors"

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Mukherjee, Avijit. "Aspects of topological conformal field theory." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360757.

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Jones, Flora. "Disguised Stretch : Changeable knitted textiles with altering functions and visual expressions." Thesis, Högskolan i Borås, Akademin för textil, teknik och ekonomi, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-23504.

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This project places itself in the field of textile design within flat knitting textiles intended as prototypes for interactive textiles with multifunctional purposes and aesthetics. The purpose of the project is to suggest alternative design solutions towards knitted textiles in the field of sportswear that not only acts as a second skin both in terms of appearance and functionality, as well as aesthetic details once the knit interacts with a moving body. The aim of the project, but also offers visual and contrasting functions such as expandability, rigidness and stretch, as well as creating aesthetic details caused by movement of the human body. The design process was conducted in experimental knitting on both industrial and domestic knitting machines, workshops entailing the relation between the knits and the body as well as technically developing the proper bindings to work in unity. Analysis of the knits were made which led to the solely use of these bindings: rib, spacer, links links, ripple and mesh. The outcome of the projects resulted in four knitted textile prototypes, where one of them is designed as a product in the shape of a top, and the others as knitted fabrics each representing two opposing functions. The conclusion drawn in retrospect of this project that by placing opposing bindings parallel, such ripple and links links, it is possible to achieve two opposing functions as well as different visual perception within the same area of a knitted piece.
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Meier, Florian. ""beau platt“ : Contemporary Fashion Practice in the field of concrete and virtual visualizations of flat expressions." Thesis, Högskolan i Borås, Akademin för textil, teknik och ekonomi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-13023.

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This work traces the visual potential of 2Dimensional space inthree dimensional garments and questions aesthetic standardsin the field of menswear. The aim is to discuss the visualconsensus of flat and spatial construction. Construction has been chosen as the key aspect for digital and analoginvestigations. It builds the main emphasis of this project and leads toa deeper visual understanding of how we perceive garments with clearborders between three - and two dimensional sections. The design process has a dual structure. 1st stage - ‚virtual investigation‘ This is where the experiments start. By using Simulation andrendering software such as ‚CLO3D‘, ‚Marvellous Designer‘ and ‚Keyshot‘the aim is to develop and unlock multiple constructionprinciples that deal with similar visual aspects. These results suggest anetwork of variations (garment types/parts, e.g. sleeve construction,trousers etc..) that need to be translated into real prototypes. 2nd stage - ‚Analog translation‘ Based on the preferred results of the 1st stage, the aim is to filter oneconstruction principle for further studies.The choice of working with the flat sleeve construction is the keyaspect and builds the fundamental for ellaborating the design process.This phase is mainly characterised by material and shape experimentsand relates to a lasting construction principle. The result suggest a spread of examples that deal with the sameconstruction principle. The examplified versions include differentmaterial qualities and differ in terms of their complexity in detailsolutions and production.The final choice works as a unit and offers different ways ofapproaching and developing the construction principle further.Especially the layering aspect in example 8 and 9 became dominantand very important for increasing the visual expression.That indication offers an imidiate and direct approach and showsthe potential within the field of 2D expressions.Nevertheless my next step would lead me back to the digital studiesto understand more about the diversity of layers in two dimensionalgarments. Eventually it would suggest both a wearable as well as aconceptual outcome.
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Gans, Christine. "Investigations of the Crust and Upper Mantle of Modern and Ancient Subduction Zones, using Pn Tomography and Seismic Receiver Functions." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145719.

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Advances in seismology allow us to obtain "high-resolution" images of the Earth's subsurface. This dissertation summarizes the results of three seismic studies on three different continents, with the aim of better understanding the crust and upper mantle structure of seemingly disparate yet ultimately related regions. The seismic techniques of Pn tomography and P-wave receiver function (RF) analysis are applied to central Turkey (Pn tomography), western Argentina and southwestern Wyoming, USA (RF analysis). These studies look at both a present-day convergent margin (Andean subduction zone, Argentina) and two ancient ones (Bitlis-Zagros collision zone of Arabia-Africa with Eurasia, Turkey; Farallon subduction zone, Wyoming).Using Pn tomography, we were able to detect the limit of the slab rupture edge along the Central Anatolian Fault Zone, Turkey. Slab break-off is an important process that modifies the mantle in tectonically active regions, and the limit of the oceanic Arabian slab break-off along the Bitlis-Zagros Suture Zone, thought to have begun at 11 Ma, was previously undetermined.Using RF analysis, we obtained high-resolution images of the subducting slab beneath the Sierras Pampeanas, Argentina. Continental Moho contours roughly follow terrane boundaries, suggesting that ancient terranes continue to exert control over present-day continental deformation. Overthickened oceanic crust is often cited as a cause of flat slab subduction; our RF results indicate that the crust is moderately overthickened, around 11-16 km. Further, we image offsets in the RF arrivals that indicate the subducted slab is broken or offset in along trench-subparallel fractures.The crustal structure beneath southwestern Wyoming, the location of ancient Farallon flat slab subduction, was studied using RF analysis. Looking at regional crustal structure, results include a new depth to Moho map. Coherency of the seismic signal across the dense LaBarge array (55 stations, ~250 m spacing) was investigated, with results showing that complicated shallow structure can greatly impact the resulting RF signal. Modeling of RFs using synthetics helped to separate the complex signal containing multiple primary conversions and their reverberations, which interact constructively and destructively. The dense spacing of the LaBarge array allowed unique opportunities to investigate coherency of waveforms across very short distances.
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Nagel, Daniel Matthias. "Analysis of adhesive and repulsive functions of FLRT proteins in central nervous system development." Diss., Ludwig-Maximilians-Universität München, 2015. http://nbn-resolving.de/urn:nbn:de:bvb:19-178954.

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Fibronectin-leucine-rich-repeat-transmembrane proteins (FLRTs) are a family of three single pass transmembrane proteins with extracellular leucine rich repeats and a short intracellular domain of largely unknown function. They are broadly expressed in the developing and adult nervous system as well as in other tissues. FLRTs have been implicated in a variety of different developmental processes mainly via two functions: as homophilic cell adhesion molecules, and as repulsive ligands for Unc5-positive cells. Furthermore, they can regulate cell adhesion via control of surface expression of C Cadherin and are involved in FGF signaling. Previously we found that all FLRTs are localized to synapses in the mouse brain and thus investigated a potential involvement of FLRTs in synapse formation. However, using different in vitro and in vivo approaches ranging from HEK293 cell-neuron coculture assays to ultrastructural analysis of synapse density in FLRT3 knock-out mouse brains, I did not find any evidence for an involvement of FLRTs in synapse development. This is in contrast to published results but can be explained by differences in the experimental approaches and timing of the experiments. In collaboration with structural biologists we solved the crystal structure of the FLRT and Unc5 extracellular domains and a complex of both, to gain insight into the structural basis of the adhesive and repulsive functions of FLRTs. We found that homophilic FLRT FLRT and heterophilic FLRT-Unc5 interactions both occur via the FLRT LRR domain but at distinct structural surfaces. Thus, the interactions can be uncoupled. Based on the structural results we developed FLRT and Unc5 glycosylation mutants that specifically inhibit FLRT-FLRT or FLRT-Unc5 interaction and validated them in vitro. I then used these mutants in in utero electroporation experiments to prove that the repulsive effect of Unc5D overexpression in radially migrating neurons that was discovered previously is indeed, at least partially, mediated by FLRT2. Furthermore I found that overexpression of FLRTs inhibits radial migration of cortical pyramidal neurons and this effect is dependent on FLRT-FLRT homophilic interaction and the FLRT intracellular domain but independent of FLRT-Unc5 binding. In summary, the work presented here provides new insights into adhesive and repulsive functions of the FLRT family of proteins in the regulation of cell migration during cortical development.
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Soong, Shiao-Bin 1967. "Measurement of fLT and fLT' response functions in the quasi-elastic ²H(e̳,e'p) reaction at 200 (MeV/c) missing momentum." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50502.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1998.
Double-underscored letter in title has right-hand arrow above letter.
Includes bibliographical references (p. 208-213).
We report in this thesis the simultaneous measurement of the logitudinal- transverse response functions, fLT and fLT', and the transverse-transverse response function fTT of the deuteron. The quasi-elastic ²H(e̳, e'p) experiment reported here was conducted at the MIT/Bates Linear Accelerator Center in February, 1997. The experiment was carried out with a 40% polarized, 800 MeV electron beam. The measurement took place in the Bates South Hall using the One Hundred Inch Proton Spectrometer(OHIPS) as the electron spectrometer. It was placed at an angle of 37.270 and the energy transfer, w, was set for quasi-elastic kinematics with the square of the four-momentum transfer, Q2, equal to -0.22 (GeV/c) 2 . Three out-of-plane proton spectrometers (OOPS) were positioned at ... . This allowed the simultaneous measurement of fLT, fTT and fLT' at a central missing momentum of - 200 (MeV/c). The measured asymmetries, cross sections and response functions are compared with different theoretical models.
by Shiao-Bin Soong.
Ph.D.
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Nagel, Daniel Matthias [Verfasser], and Rüdiger [Akademischer Betreuer] Klein. "Analysis of adhesive and repulsive functions of FLRT proteins in central nervous system development / Daniel Matthias Nagel. Betreuer: Rüdiger Klein." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2015. http://d-nb.info/1067399801/34.

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Nguyen, Huu Thin. "Polyfunkční dům." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2015. http://www.nusl.cz/ntk/nusl-227694.

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Master thesis is composed from project documentation of Multi-functional building. The object has one basement floor and four floor. The building has flat roof and come up to height 16,65m. The structural system is designed from reinforced concrete skeleton. The building has two main parts. The first is commercial space, which is located on first floor and basement. The second part is used for living. The building has 12 apartments.
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Rotella, Yann. "Mathématiques discrètes appliquées à la cryptographie symétrique." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS092/document.

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Dans cette thèse, nous étudions la sécurité de primitives cryptographiques. Ces systèmes sont fondés sur des transformations utilisant des objets mathématiques représentés de multiples manières. Nous utilisons alors certaines structures inhérentes à leurs composantes, et jusqu'alors non prises en compte, pour mettre en évidence de nouvelles vulnérabilités. Par l'exploitation de diverses représentations, nous avons ainsi cryptanalysé des chiffrements authentifiés de la compétition CAESAR, des chiffrements à flot spécifiques et des constructions génériques. Nous avons donné des critères de conception en vue de la standardisation par le NIST de chiffrements à bas coût. Dans le cas des chiffrements à flot, nous avons défini de nouveaux critères cryptographiques plus pertinents que les critères usuels. Plus précisément, nous analysons la sécurité des chiffrements par bloc légers au regard des récentes attaques par invariant, et nous montrons comment les éviter par un choix approprié de la couche linéaire de diffusion et des constantes de tour. Nous proposons une nouvelle cryptanalyse des registres filtrés, grâce à la décomposition des éléments dans les sous-groupes multiplicatifs du corps fini à 2^n éléments. L'analyse du chiffrement FLIP, mais aussi du générateur pseudo-aléatoire de Goldreich a mis en évidence des faiblesses exploitables dans des attaques de type ``supposer et déterminer'', qui nécessitent la prise en compte de nouveaux critères sur les fonctions booléennes utilisées dans ce contexte. Enfin, nous cryptanalysons une version simplifiée du chiffrement authentifié Ketje en utilisant plusieurs techniques, permettant ainsi d'affiner l'évaluation de sa sécurité
In this thesis, we study the security of symmetric cryptographic primitives. These systems are based on transformations relying on mathematical objects that can be represented in multiple ways. We then exploit different induced structures to highlight new vulnerabilities. By exploiting various representations, we cryptanalyzed some schemes submitted to the CAESAR competition, and also some dedicated and generic stream ciphers. We exhibited design criteria for lightweight block ciphers in view of the NIST standardization process and in the case of stream ciphers we defined new cryptographic criteria more relevant than the usual ones. More precisely, we study the security of lightweight block ciphers with respect to the recent invariant attacks, and we show how to avoid them with an appropriate choice of the linear layer and the round constants. We propose a new cryptanalysis of the filtered registers, by decomposing elements in the multiplicative subgroups of the finite field with 2^n elements. The analysis of the FLIP cipher, but also of the Goldreich pseudo-random generator, revealed weaknesses that are exploitable in ``guess and determine'' attacks. This leads to new criteria on the Boolean functions used in this context. Finally, we cryptanalyze a weaker version of the authenticated encryption scheme Ketje using several techniques, in order to refine the security evaluation of this cipher
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Parriaux, Jérémy. "Contrôle, synchronisation et chiffrement." Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0129/document.

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Cette thèse traite de la synchronisation des systèmes dynamiques.La synchronisation est étudiée pour une configuration de type maître-esclave, c'est-à-dire pour des systèmes couplés de façon unidirectionnelle. Ce type de configuration s'avère d'un intérêt tout particulier car elle correspond à des architectures de communications chiffrées un-vers-un ou un-vers-plusieurs. Une attention spécifique est portée sur l'autosynchronisation, comportement qui caractérise la synchronisation par le simple couplage maître-esclave et donc en l'absence de tout contrôle extérieur. Elle joue un rôle majeur dans les communications impliquant des chiffreurs par flot autosynchronisants. L'étude de l'autosynchronisation dans le contexte cryptographique s'appuie sur la théorie du contrôle. Un lien original entre l'autosynchronisation et le principe de chiffrement/déchiffrement en cryptographie est mis en évidence. Il fait appel à la propriété de platitude des systèmes dynamiques, un concept emprunté à l'automatique. On montre que les systèmes dynamiques plats définissent complètement l'ensemble des systèmes autosynchronisants et permettent d'élargir les structures existantes des chiffreurs autosynchronisants. La platitude est tout d'abord étudiée pour deux types de systèmes non linéaires~: les systèmes linéaires commutés et à paramètres variants (LPV). La caractérisation des sorties plates s'appuie sur le concept de semigroupes nilpotents et un algorithme performant est proposé. Une approche constructive pour réaliser des structures maître-esclave autosynchronisantes est proposée sur la base de systèmes plats et les notions d'inversibilité à gauche et à droite empruntées à la théorie du contrôle. Par la suite, l'autosynchronisation est étudiée dans le contexte booléen, privilégié en cryptographie.Elle est caractérisée en premier lieu au travers la notion d'influence. Ensuite, différentes représentations matricielles associées aux fonctions booléennes sont proposées. Ces représentations s'avèrent particulièrement intéressantes pour l'analyse des propriétés liées à la sécurité. Un lien entre l'autosynchronisation et les structures propres des représentations matricielles est établi. Une approche orientée graphes est finalement élaborée pour la caractérisation. De nouvelles constructions de structures autosynchronisantes en sont déduites et des éléments de sécurité sont discutés. Enfin, une plateforme de test à base de FPGA qui a été réalisée est décrite
This thesis deals with the synchronization of dynamical systems. The synchronization considered is called master-slave, that is, the dynamical systems are connected in a unidirectional way. This configuration is of interest because it corresponds to an architecture encountered in secured communications of type one-to-one or one-to-many. A special attention is paid to self-synchronization. A behaviour that characterizes synchronization achieved with a simple master-slave coupling and so, without any external control. It is a central feature of self-synchronizing stream ciphers. The study of self-synchronization in the cryptographic context relies on control theory. An original connection between self-synchronization and encryption/decryption is provided. It is based on the flatness property of dynamical systems, a property borrowed from automatic control. It is shown that flat dynamical systems completly define the set of all self-synchronizing systems and thus, enlarge the existing structures of self-synchronizing stream ciphers. Flatness is first of all studied for the case of two nonlinear systems: switched linear systems and linear parameter-varying (LPV) systems. Flatness caracterization is based on the concept of nilpotent semigroups and an efficient algorithm is provided. A constructive approach for self-synchronizing master-slave structures is proposed. It relies on the construction of flat systems as well as on left and right invertibility also borrowed from control theory. Then, self-synchronization is studied in the Boolean context which is preferred in cryptography. Self-synchronization is caracterized through the notion of influence. Several matrix representations of Boolean functions are proposed. These representations are especially interesting for security analysis. A connection between self-synchronization and the eigenstructures of these matrices is established. Then, a graph oriented approach is provided. New self-synchronizing constructions are deduced and security elements are discussed. Eventually, the description of a realized FPGA based test plateform is provided
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Books on the topic "Flat functors"

1

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

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

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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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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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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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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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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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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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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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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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Book chapters on the topic "Flat functors"

1

Conrad, Brian. "The Flat Deformation Functor." In Modular Forms and Fermat’s Last Theorem, 373–420. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1974-3_13.

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Qarooni, Jalal. "Properties and Functions of Sourdough and Noncereal Ingredients in Flat Bread Production." In Flat Bread Technology, 37–66. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1175-1_3.

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Bruns, Winfried, Aldo Conca, Claudiu Raicu, and Matteo Varbaro. "Grassmannians, Flag Varieties, Schur Functors and Cohomology." In Springer Monographs in Mathematics, 325–77. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-05480-8_9.

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Bartolo, L., and A. Bader. "Flat Membrane Bioreactor for the Replacement of Liver Functions." In Stem Cell Transplantation and Tissue Engineering, 89–104. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04816-0_7.

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Polo, Guilherme, and Neucimar J. Leite. "From Extrema Relationships to Image Simplification Using Non-flat Structuring Functions." In Lecture Notes in Computer Science, 377–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38294-9_32.

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Guha, Partha. "Witten’s Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions." In Quantum Field Theory, 95–116. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8736-5_6.

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Braverman, Alexander. "Instanton counting via affine Lie algebras. I. Equivariant 𝐽-functions of (affine) flag manifolds and Whittaker vectors." In CRM Proceedings and Lecture Notes, 113–32. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/crmp/038/04.

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Ortéga, Nathalie, and Jean Plouët. "Determination of the Functions Mediated by each of the Two VEGF Receptors KDR/FLK-1 and FLT-1." In Vascular Endothelium, 272. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-0133-0_34.

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"Flat functors and Cauchy completeness." In Handbook of Categorical Algebra, 250–80. Cambridge University Press, 1994. http://dx.doi.org/10.1017/cbo9780511525858.008.

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Hafien, Chedhli, Adnen Bourehla, and Mounir Bouzaiane. "Boundary Layer Theory: New Analytical Approximations with Error and Lambert Functions for Flat Plate without/with Suction." In Aerodynamics. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.88637.

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In this work, we investigated the problem of the boundary layer suction on a flat plate with null incidence and without pressure gradient. There is an analytical resolution using the Bianchini approximate integral method. This approximation has been achieved by Lambert or Error functions for boundary layer profiles with uniform suction, even in the case without suction. Based on these new laws, we brought out analytical expressions of several boundary layer features. This gives a necessary data to suction effect modeling for boundary layer control. To recommend our theoretical results, we numerically studied the boundary layer suction on a porous flat plate equipped with trailing edge flap deflected to 40°. We showed that this flap moves the stagnation point on the upper surface, resulting to avoid the formation of the laminar bulb of separation. Good agreement was obtained between the new analytical laws, the numerical results (CFD Fluent), and the literature results.
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Conference papers on the topic "Flat functors"

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ten Thije Boonkkamp, J. H. M., L. B. Romijn, M. J. H. Anthonissen, and W. L. IJzerman. "Mathematical framework for freeform design." In Flat Optics: Components to Systems. Washington, D.C.: Optica Publishing Group, 2021. http://dx.doi.org/10.1364/flatoptics.2021.jth3a.2.

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Leder, Judith. "Cubic forms generated by functions on projectively flat spaces." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0017.

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Lucko, Gunnar, and Angel A. Pena Orozco. "Calculating float in linear schedules with singularity functions." In 2008 Winter Simulation Conference (WSC). IEEE, 2008. http://dx.doi.org/10.1109/wsc.2008.4736361.

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Flores, M. E., and M. B. Milam. "Trajectory generation for differentially flat systems via NURBS basis functions with obstacle avoidance." In 2006 American Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/acc.2006.1657645.

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Eckman, David J., Matthew Plumlee, and Barry L. Nelson. "Flat Chance! Using Stochastic Gradient Estimators to Assess Plausible Optimality for Convex Functions." In 2021 Winter Simulation Conference (WSC). IEEE, 2021. http://dx.doi.org/10.1109/wsc52266.2021.9715288.

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Ai, Chiayu, and James C. Wyant. "Absolute testing of flats decomposed to even and odd functions." In San Diego '92, edited by Katherine Creath and John E. Greivenkamp. SPIE, 1992. http://dx.doi.org/10.1117/12.139247.

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Saavedra, Jorge, Venkat Athmanathan, Guillermo Paniagua, Terrence Meyer, Doug Straub, James Black, and Sridharan Ramesh. "Scalable Heat Transfer Characterization on Film Cooled Geometries Based on Discrete Green’s Functions." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-16304.

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Abstract The aerothermal characterization of film cooled geometries is traditionally performed at reduced temperature conditions, which then requires a debatable procedure to scale the convective heat transfer performance to engine conditions. This paper describes an alternative engine-scalable approach, based on Discrete Green’s Functions (DGF) to evaluate the convective heat flux along film cooled geometries. The DGF method relies on the determination of a sensitivity matrix that accounts for the convective heat transfer propagation across the different elements in the domain. To characterize a given test article, the surface is discretized in multiple elements that are independently exposed to perturbations in heat flux to retrieve the sensitivity of adjacent elements, exploiting the linearized superposition. The local heat transfer augmentation on each segment of the domain is normalized by the exposed thermal conditions and the given heat input. The resulting DGF matrix becomes independent from the thermal boundary conditions, and the heat flux measurements can be scaled to any conditions given that Reynolds number, Mach number, and temperature ratios are maintained. The procedure is applied to two different geometries, a cantilever flat plate and a film cooled flat plate with a 30 degree 0.125” cylindrical injection orifice with length-to-diameter ratio of 6. First, a numerical procedure is applied based on conjugate 3D Unsteady Reynolds Averaged Navier Stokes simulations to assess the applicability and accuracy of this approach. Finally, experiments performed on a flat plate geometry are described to validate the method and its applicability. Wall-mounted thermocouples are used to monitor the surface temperature evolution, while a 10 kHz burst-mode laser is used to generate heat flux addition on each of the discretized elements of the DGF sensitivity matrix.
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Lee, Shong-Leih, and Chao-Fu Yang. "Detachment Criterion for Static Axisymmetric Bubbles on Horizontal Flat Surfaces." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78081.

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The static Young-Laplace equation is solved with the geometry method to yield the bubble shape on a horizontal flat surface under various contact angles. Multi-solution modes are found. Among the many possible equilibrium shapes of the bubble, however, only the fundamental solution mode could occur naturally. The value of VAR (volume to contact area ratio) could be a good measure for stability of equilibrium bubbles. The bubble becomes less stable when VAR increases. The numerical result reveals that in the course of bubble growth (i.e. volume increases) the VAR of the bubble increases linearly until the maximum contact area is reached. After that, VAR has a sharp increase due to a decreasing contact area. Beyond the maximum volume, equilibrium bubble does not seem possible. Based on the finding, it is postulated that bubble detachment occurs somewhere between the maximum contact area and the maximum volume according to perturbations from environment. However, the postulation seems to underestimate the stability of the bubble significantly for contact angles of larger than 160 degrees. A correction is proposed in the paper. Numerical result of bubble detachment criterion is fitted with polynomial functions of the contact angle.
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Katsuyama, Jinya, Yuhei Miyamoto, Kai Lu, Akihiro Mano, and Yinsheng Li. "Improved Bayesian Update Method on Flaw Distributions Reflecting Non-Destructive Inspection Result." In ASME 2020 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/pvp2020-21430.

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Abstract We have developed a probabilistic fracture mechanics (PFM) analysis code named PASCAL4 for evaluating the failure frequency of reactor pressure vessels (RPVs) through consideration of neutron irradiation embrittlement and transients such as pressurized thermal shock events. It is well-known that flaw distributions, including flaw size and density, have an important role in the failure frequency calculations of a PFM analysis. NUREG-2163 report provides a methodology to obtain much more realistic flaw distributions based on a Bayesian updating approach by reflecting the non-destructive inspection (NDI) results, which is applicable for case when there are flaw indications through NDI. There may, however, be no flaw indications resulting after inspection of some RPVs. Therefore, we proposed likelihood functions applicable for both cases when flaws are detected and when there is no flaw indication as the NDI results. In the Bayesian updating method, the likelihood functions were applied to independently acquire the posterior distributions of flaw depth and density using the same NDI results. In this study, we further improve the likelihood functions to enable them to update flaw depth and density simultaneously. Based on this improved likelihood function, several application examples are presented where the flaw distributions are estimated by reflecting the NDI results through Bayesian update. In addition, PFM analyses are also performed considering those estimated flaw distributions. All the results indicate that the improved likelihood functions are useful for estimating flaw distributions.
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A. Scarth, Douglas, Joanna Wu, Ted Smith, and Dennis M. Kawa. "Development of Weight Functions for Modelling Delayed Hydride Cracking Initiation at a Blunt Flaw." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2302.

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Delayed Hydride Cracking (DHC) in Zr-2.5 Nb alloy material is of interest to the CANDU (Canada Deuterium Uranium) industry in the context of the potential to initiate DHC at a blunt flaw in a CANDU reactor pressure tube. The material is susceptible to DHC when there is diffusion of hydrogen atoms to the flaw, precipitation of hydride platelets, and development of a hydrided region at the flaw tip. The hydrided region can then fracture to the extent that a crack forms, and is able to grow by the DHC crack growth mechanism. An engineering process-zone model for evaluation of DHC initiation at a blunt flaw that takes into account flaw geometry has been developed. The model is based on representing the stress relaxation due to hydride formation, and crack initiation, by an infinitesimally thin process zone. Application of the engineering process-zone model requires calculation of the stress intensity factor, and the crack-mouth opening displacement, for a fictitious crack at the tip of a blunt flaw. In the current model, calculation of these quantities is based on a cubic polynomial fit to represent the stress distribution ahead of the blunt flaw tip, where the stress distribution is generally calculated by finite element analysis. However, the cubic polynomial is not always an optimum fit to the stress distribution for very small root radius flaws, due to the large stress gradients near the flaw tip. Application of the weight function method will enable a more accurate representation of the flaw-tip stress distribution for the calculation of the stress intensity factor and the crack-mouth opening displacement. Weight functions for a crack at the tip of a blunt flaw in a thin wall cylinder have been developed for implementation into the engineering process-zone model. These weight functions are applicable to a wide range of blunt flaw depths and root radii, as well as a wide range of flaw-tip crack depths. The development and verification of the weight functions is described in this paper. The verification calculations are in reasonable agreement with alternate solutions, and have confirmed that the weight functions have reasonable accuracy for engineering applications of the process-zone methodology.
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Reports on the topic "Flat functors"

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Schach von Wittenau, A. E. Edge-Spread Functions Expected for Several Changes in a Commercial Flat-Panel System. Office of Scientific and Technical Information (OSTI), February 2002. http://dx.doi.org/10.2172/15002230.

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Noble, Chris V., Rhonde Evans, Marti McGulre, Katherine Trott, and Mary David. A Regional Guidebook for Applying the Hydrogeomorphic Approach to Assessing Wetland Functions of Flats Wetlands in the Everglades. Fort Belvoir, VA: Defense Technical Information Center, July 2002. http://dx.doi.org/10.21236/ada405650.

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Lin, Hongwei, Yanjun Gao, Kang Sun, and Faguang Jin. Association between PM2.5 pollution and outpatient visits for respiratory diseases in China: a systematic review and meta-analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, May 2022. http://dx.doi.org/10.37766/inplasy2022.5.0144.

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Review question / Objective: Previous epidemiological studies on the association between PM2.5 pollution and outpatient visits for respiratory diseases in China were mostly limited to one region， and the different papers have no coherent results. Our objective is to perform a systematic review and meta-analysis of the relevant literature in order to summarize the association between PM2.5 pollution and outpatient visits for respiratory diseases in multiple cities in China. Condition being studied: As an important component of air pollutants, particulate matter 2.5 (PM2.5) can float in the atmosphere for a long time with a small aerodynamic size (≤2.5μm) and large specific surface area which is attached to a variety of toxic and harmful substances . PM2.5 can deposite under the trachea of the respiratory tract, reaching deep into the alveolar area, damaging alveolar macrophages and type Ⅱ alveolar epithelial cells, inducing alveolar inflammation, resulting in decreased immunity of the respiratory tract and interfering with normal physiological functions of the lungs.
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Rahmani, Mehran, Xintong Ji, and Sovann Reach Kiet. Damage Detection and Damage Localization in Bridges with Low-Density Instrumentations Using the Wave-Method: Application to a Shake-Table Tested Bridge. Mineta Transportation Institute, September 2022. http://dx.doi.org/10.31979/mti.2022.2033.

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This study presents a major development to the wave method, a methodology used for structural identification and monitoring. The research team tested the method for use in structural damage detection and damage localization in bridges, the latter being a challenging task. The main goal was to assess capability of the improved method by applying it to a shake-table-tested prototype bridge with sparse instrumentation. The bridge was a 4-span reinforced concrete structure comprising two columns at each bent (6 columns total) and a flat slab. It was tested to failure using seven biaxial excitations at its base. Availability of a robust and verified method, which can work with sparse recording stations, can be valuable for detecting damage in bridges soon after an earthquake. The proposed method in this study includes estimating the shear (cS) and the longitudinal (cL) wave velocities by fitting an equivalent uniform Timoshenko beam model in impulse response functions of the recorded acceleration response. The identification algorithm is enhanced by adding the model’s damping ratio to the unknown parameters, as well as performing the identification for a range of initial values to avoid early convergence to a local minimum. Finally, the research team detect damage in the bridge columns by monitoring trends in the identified shear wave velocities from one damaging event to another. A comprehensive comparison between the reductions in shear wave velocities and the actual observed damages in the bridge columns is presented. The results revealed that the reduction of cS is generally consistent with the observed distribution and severity of damage during each biaxial motion. At bents 1 and 3, cS is consistently reduced with the progression of damage. The trends correctly detected the onset of damage at bent 1 during biaxial 3, and damage in bent 3 during biaxial 4. The most significant reduction was caused by the last two biaxial motions in bents 1 and 3, also consistent with the surveyed damage. In bent 2 (middle bent), the reduction trend in cS was relatively minor, correctly showing minor damage at this bent. Based on these findings, the team concluded that the enhanced wave method presented in this study was capable of detecting damage in the bridge and identifying the location of the most severe damage. The proposed methodology is a fast and inexpensive tool for real-time or near real-time damage detection and localization in similar bridges, especially those with sparsely deployed accelerometers.
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