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Relevant bibliographies by topics / Noncommutative derived algebraic geometry

Academic literature on the topic 'Noncommutative derived algebraic geometry'

Author: Grafiati

Published: 4 April 2023

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Journal articles on the topic "Noncommutative derived algebraic geometry"

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Chen, Yiping, and Wei Hu. "Approximations, ghosts and derived equivalences." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (January 26, 2019): 813–40. http://dx.doi.org/10.1017/prm.2018.120.

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AbstractApproximation sequences and derived equivalences occur frequently in the research of mutation of tilting objects in representation theory, algebraic geometry and noncommutative geometry. In this paper, we introduce symmetric approximation sequences in additive categories and weakly n-angulated categories which include (higher) Auslander-Reiten sequences (triangles) and mutation sequences in algebra and geometry, and show that such sequences always give rise to derived equivalences between the quotient rings of endomorphism rings of objects in the sequences modulo some ghost and coghost ideals.

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Cirio, Lucio S., Giovanni Landi, and Richard J. Szabo. "Instantons and vortices on noncommutative toric varieties." Reviews in Mathematical Physics 26, no. 09 (October 2014): 1430008. http://dx.doi.org/10.1142/s0129055x14300088.

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We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit.

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Dolbeault, Pierre. "On a noncommutative algebraic geometry." Banach Center Publications 107 (2015): 119–31. http://dx.doi.org/10.4064/bc107-0-8.

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Nikolaev, Igor V. "Noncommutative geometry of algebraic curves." Proceedings of the American Mathematical Society 137, no. 10 (October 1, 2009): 3283. http://dx.doi.org/10.1090/s0002-9939-09-09917-1.

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Sharygin, G. I. "Geometry of Noncommutative Algebraic Principal Bundles." Journal of Mathematical Sciences 134, no. 2 (April 2006): 1911–82. http://dx.doi.org/10.1007/s10958-006-0092-z.

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Škoda, Zoran. "Some Equivariant Constructions in Noncommutative Algebraic Geometry." gmj 16, no. 1 (March 2009): 183–202. http://dx.doi.org/10.1515/gmj.2009.183.

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Abstract We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which provide affine examples. We introduce a compatibility of monoidal actions and localizations which is a distributive law. There are satisfactory notions of equivariant objects, noncommutative fiber bundles and quotients in this setup.

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Beil, Charlie. "The Bell states in noncommutative algebraic geometry." International Journal of Quantum Information 12, no. 05 (August 2014): 1450033. http://dx.doi.org/10.1142/s0219749914500336.

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We introduce new mathematical aspects of the Bell states using matrix factorizations, non-noetherian singularities, and noncommutative blowups. A matrix factorization of a polynomial p consists of two matrices ϕ1, ϕ2 such that ϕ1ϕ2 = ϕ2ϕ1 = p id. Using this notion, we show how the Bell states emerge from the separable product of two mixtures, by defining pure states over complex matrices rather than just the complex numbers. We then show in an idealized algebraic setting that pure states are supported on non-noetherian singularities. Moreover, we find that the collapse of a Bell state is intimately related to the representation theory of the noncommutative blowup along its singular support. This presents an exchange in geometry: the nonlocal commutative spacetime of the entangled state emerges from an underlying local noncommutative spacetime.

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Reineke, Markus, J. Toby Stafford, Catharina Stroppel, and Michel Van den Bergh. "Interactions between Algebraic Geometry and Noncommutative Algebra." Oberwolfach Reports 11, no. 2 (2014): 1365–402. http://dx.doi.org/10.4171/owr/2014/25.

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Reineke, Markus, J. Toby Stafford, Catharina Stroppel, and Michel Van den Bergh. "Interactions between Algebraic Geometry and Noncommutative Algebra." Oberwolfach Reports 15, no. 2 (April 11, 2019): 1465–515. http://dx.doi.org/10.4171/owr/2018/24.

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Toën, Bertrand. "Derived algebraic geometry." EMS Surveys in Mathematical Sciences 1, no. 2 (2014): 153–245. http://dx.doi.org/10.4171/emss/4.

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Dissertations / Theses on the topic "Noncommutative derived algebraic geometry"

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Rennie, Adam Charles. "Noncommutative spin geometry." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phr4163.pdf.

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Lurie, Jacob 1977. "Derived algebraic geometry." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30144.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 191-193).
The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types.
by Jacob Lurie.
Ph.D.

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Toledo, Castro Angel Israel. "Espaces de produits tensoriels sur la catégorie dérivée d'une variété." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4001.

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Dans cette thèse on est intéressé à l'étude des catégories dérivées d'une variété lisse et projective sur un corps. En particulier on étude l'information géométrique et catégorielle d'une variété et sa catégorie dérivée pour mieux comprendre l'ensemble de structures monoïdales qu'on peut munir à la catégorie dérivée. La motivation de ce projet s'inspire en deux théorèmes. L'un c'est le théorème de reconstruction de Bondal-Orlov qu'établisse que la catégorie dérivée d'une variété avec diviseur (anti-)canonique ample est assez pour récupérer la variété. D'un autre côté, on a la construction du spectrum de Balmer qu'utilise le produit tensoriel dérivé pour récupérer un nombre plus grand de variétés à partir de sa catégorie dérivée de complexes parfaits comme une catégorie monoïdale. L'existence de différentes structures monoïdales est par contre garanti par l'existence des variétés avec des catégories dérivées équivalentes. On a pour but alors comprendre quel est le rôle de les produits tensoriels dans l'existence (ou non existence) de ces types de variétés. Les résultats principaux qu'on a obtenu sont : Si X est une variété avec diviseur (anti-)canonique ample, et ⊠ est une structure de catégorie tensoriel triangulée sur Db(X) tel que le spectrum de Balmer Spc(Db(X),⊠) est isomorphe à X, alors pour tous F,G∈Db(X), on a F⊠G≃F⊗G où ⊗ c'est le produit tensoriel dérivée. On utilise le théorème de Morita pour les dg-catégories de Toën pour donner une caractérisation d'une structure tronquée en termes de bimodules sur un produit des dg-algèbres, qu'induisent une structure de catégorie tensoriel triangulée sur la catégorie homotopique. On a étudié la théorie de déformation de ces structures dans le sens de la cohomologie de Davydov-Yetter. On montre qu'il existe une correspondance entre un des groupes de cohomologie et l'ensemble de associateurs dont le produit tensoriel peut s'en déformer. On utilise des techniques à un niveau des catégories triangulées et aussi des perspectives de la théorie des catégories supérieurs comme des dg-catégories et quasi-catégories
In this thesis we are interested in studying derived categories of smooth projective varieties over a field. Concretely, we study the geometric and categorical information from the variety and from it's derived category in order to understand the set of monoidal structures one can equip the derived category with. The motivation for this project comes from two theorems. The first is Bondal-Orlov reconstruction theorem which says that the derived category of a variety with ample (anti-)canonical bundle is enough to recover the variety. On the other hand, we have Balmer's spectrum construction which uses the derived tensor product to recover a much larger number of varieties from it's derived category of perfect complexes as a monoidal category. The existence of different monoidal structure is in turn guaranteed by the existence of varieties with equivalent derived categories. We have as a goal then to understand the role of the tensor products in the existence (or not ) of these sort of varieties. The main results we obtained are If X is a variety with ample (anti-)canonical bundle, and ⊠ is a tensor triangulated category on Db(X) such that the Balmer spectrum Spc(Db(X),⊠) is isomorphic to X, then for any F,G∈Db(X) we have F⊠G≃F⊗G where ⊗ is the derived tensor product. We have used Toën's Morita theorem for dg-categories to give a characterization of a truncated structure in terms of bimodules over a product of dg-algebras, which induces a tensor triangulated category at the level of homotopy categories. We studied the deformation theory of these structures in the sense of Davydov-Yetter cohomology, concretely showing that there is a relationship between one of these cohomology groups and the set of associators that the tensor product can deform into. We utilise techniques at the level of triangulated categories and also perspectives from higher category theory like dg-categories and quasi-categories

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Tang, Xin. "Applications of noncommutative algebraic geometry to representation theory /." Search for this dissertation online, 2006. http://wwwlib.umi.com/cr/ksu/main.

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Goetz, Peter D. "The noncommutative algebraic geometry of quantum projective spaces /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102165.

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Thesis (Ph. D.)--University of Oregon, 2003.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 106-108). Also available for download via the World Wide Web; free to University of Oregon users.

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Schelp, Richard Charles. "The standard model and beyond in noncommutative geometry /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Solanki, Vinesh. "Zariski structures in noncommutative algebraic geometry and representation theory." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45.

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A suitable subcategory of aﬃne Azumaya algebras is deﬁned and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is deﬁned and a ﬁrst-order theory is associated to each object. For those theories satisfying a certain technical condition, uncountable categoricity and quantiﬁer elimination results are established. Models are shown to be Zariski structures and a functor from the category of equivariant algebras to Zariski structures is constructed. The two functors obtained in the thesis are shown to agree on a nontrivial class of algebras.

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Francis, John (John Nathan Kirkpatrick). "Derived algebraic geometry over En̳-rings." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43792.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
In title on t.p., double underscored "n" appears as subscript.
Includes bibliographical references (p. 55-56).
We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, these theories converge to the derived algebraic geometry of Tobn-Vezzosi and Lurie. The class of spaces obtained by gluing En-rings form a geometric counterpart to En-categories, which are higher topological variants of braided monoidal categories. These spaces further provide a geometric language for the deformation theory of general E, structures. A version of the cotangent complex governs such deformation theories, and we relate its values to E&-Hochschild cohomology. In the affine case, this establishes a claim made by Kontsevich. Other applications include a geometric description of higher Drinfeld centers of SE-categories, explored in work with Ben-Zvi and Nadler.
by John Francis.
Ph.D.

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Di, Natale Carmelo. "Grassmannians and period mappings in derived algebraic geometry." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709191.

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Melani, Valerio. "Poisson and coisotropic structures in derived algebraic geometry." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC299/document.

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Dans cette thèse, on définit et on étudie les notions de structure de Poisson et coïsotrope sur un champ dérivé, dans le contexte de la géométrie algébrique dérivée. On considère deux présentations différentes de structure de Poisson : la première est purement algébrique, alors que la deuxième est plus géométrique. On montre que les deux approches sont en fait équivalentes. On introduit aussi la notion de structure coïsotrope sur un morphisme de champs dérivés, encore une fois en présentant deux définitions équivalentes : la première est basée sur une généralisation appropriée de l'opérade Swiss-Cheese de Voronov, tandis que la deuxième est formulée en termes de champs de multivecteurs rélatifs. En particulier, on montre que le morphisme identité admet une unique structure coïsotrope ; cela produit une application d'oubli des structures de Poisson n-décalées aux structures de Poisson (n-1)-décalées. On montre aussi que l'intersection de deux morphismes coïsotropes dans un champ de Poisson n-décalée est naturellement equipée d'une structure de Poisson (n-1)-décalée canonique. En outre, on fournit une équivalence entre l'espace de structures coïsotropes non-dégénérées et l'espace des structures Lagrangiennes en géométrie dérivée, introduites dans les travaux de Pantev-Toën-Vaquié-Vezzosi
In this thesis, we define and study Poisson and coisotropic structures on derived stacks in the framework of derived algebraic geometry. We consider two possible presentations of Poisson structures of different flavour: the first one is purely algebraic, while the second is more geometric. We show that the two approaches are in fact equivalent. We also introduce the notion of coisotropic structure on a morphism between derived stacks, once again presenting two equivalent definitions: one of them involves an appropriate generalization of the Swiss Cheese operad of Voronov, while the other is expressed in terms of relative polyvector fields. In particular, we show that the identity morphism carries a unique coisotropic structure; in turn, this gives rise to a non-trivial forgetful map from n-shifted Poisson structures to (n-1)-shifted Poisson structures. We also prove that the intersection of two coisotropic morphisms inside a n-shifted Poisson stack is naturally equipped with a canonical (n-1)-shifted Poisson structure. Moreover, we provide an equivalence between the space of non-degenerate coisotropic structures and the space of Lagrangian structures in derived geometry, as introduced in the work of Pantev-Toën-Vaquié-Vezzosi

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Books on the topic "Noncommutative derived algebraic geometry"

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Connes, Alain. Noncommutative geometry. San Diego: Academic Press, 1994.

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France) États de la recherche (2017 Toulouse. Derived algebraic geometry. Paris, France: Société mathématique de France, 2021.

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Topics in noncommutative geometry. Princeton, N.J: Princeton University Press, 1991.

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1952-, Várilly Joseph C., and Figueroa Héctor 1957-, eds. Elements of noncommutative geometry. Boston: Birkhäuser, 2001.

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Melles, Caroline Grant, Jean-Paul Brasselet, Gary Kennedy, Kristin Lauter, and Lee McEwan, eds. Topics in Algebraic and Noncommutative Geometry. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/conm/324.

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Kawamata, Yujiro, ed. Derived Categories in Algebraic Geometry. Zuerich, Switzerland: European Mathematical Society Publishing House, 2013. http://dx.doi.org/10.4171/115.

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An introduction to noncommutative differential geometry and its physical applications. 2nd ed. Cambridge [England]: Cambridge University Press, 1999.

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An introduction to noncommutative differential geometry and its physical applications. Cambridge: Cambridge University Press, 1995.

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Rosenberg, Alex. Noncommutative algebraic geometry and representations of quantized algebras. Dordrecht: Kluwer Academic Publishers, 1995.

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Rosenberg, Alexander L. Noncommutative Algebraic Geometry and Representations of Quantized Algebras. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2.

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Book chapters on the topic "Noncommutative derived algebraic geometry"

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Rosenberg, Alexander L. "Noncommutative Affine Schemes." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 1–47. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_1.

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Rosenberg, Alexander L. "Noncommutative Local Algebra." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 110–41. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_3.

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Rosenberg, Alexander L. "Noncommutative Projective Spectrum." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 276–305. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_7.

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Moerdijk, Ieke, and Bertrand Toën. "Derived stacks and derived algebraic stacks." In Simplicial Methods for Operads and Algebraic Geometry, 167–77. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-0052-5_13.

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Toën, Bertrand, and Gabriele Vezzosi. "Chern Character, Loop Spaces and Derived Algebraic Geometry." In Algebraic Topology, 331–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01200-6_11.

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Schmüdgen, Konrad. "Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas." In Emerging Applications of Algebraic Geometry, 325–50. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-09686-5_9.

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Moerdijk, Ieke, and Bertrand Toën. "Examples of derived algebraic stacks." In Simplicial Methods for Operads and Algebraic Geometry, 179–84. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-0052-5_14.

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Natsume, Toshikazu. "C*-Algebraic Deformation and Index Theory." In Noncommutative Differential Geometry and Its Applications to Physics, 155–67. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0704-7_10.

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Rosenberg, Alexander L. "The Left Spectrum and Irreducible Representations of ‘Small’ Quantized and Classical Rings." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 48–109. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_2.

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Rosenberg, Alexander L. "Noncommutative Local Algebra and Representations of certain rings of mathematical physics." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 142–87. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_4.

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Conference papers on the topic "Noncommutative derived algebraic geometry"

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Sharygin, G. I. "A new construction of characteristic classes for noncommutative algebraic principal bundles." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-15.

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Zhang, Hongbo, Hongchun Wu, and Liangzhi Cao. "Acceleration Technique Using Krylov Subspace Methods for 2D Arbitrary Geometry Characteristics Solver." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29420.

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The Generalized Minimal RESidual (GMRES) method, which is a widely-used version of Krylov subspace methods for solving large sparse non-symmetric linear systems, is adopted to accelerate the 2D arbitrary geometry characteristics solver AutoMOC. In this technique, a formulism of linear algebraic equation system for angular flux moments and boundary fluxes is derived as an alternative to traditional characteristics sweep (i.e. inner iteration) formalism, and then the GMRES method is implemented as an efficient linear system solver. Several numerical results demonstrate that the acceleration technique based on Krylov subspace methods can be applied to arbitrary geometry MOC solver successfully, and may obtain higher efficiency than the original characteristics solver does because of its spectacular effect on reducing both the number of outer iterations and the total computing time. Moreover, the results could be improved by Lyusternik-Wagner extrapolation technique in some cases.

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Ghaderi, P., and M. Bankehsaz. "Effects of Material Properties Estimations on the Thermo-Elastic Analysis for Functionally Graded Thick Spheres and Cylinders." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41475.

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In this paper effects of material properties estimations, used for particulate reinforced composites, on the thermo-mechanical response of functionally graded sphere and cylinder are presented. A numerical solution for an arbitrary material gradation is obtained for each geometry independently. With this assumption, the governing partial differential equations are reduced to an ordinary differential equation in each geometry. The thermo-elastic solution for hollow sphere is derived using spherical symmetry. However, plane strain and axial symmetry are assumed for solving hollow cylinder. In the numerical method, radial domain is divided into some finite sub-domains and material properties are assumed to be constant in each sub-domain. With this assumption, the governing thermal and mechanical equations in each sub-domain are an ODE with constant coefficients. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the thermo-elastic responses for the thick-walled FG sphere and cylinder are obtained. Three methods of gradation are used for comparing the effects of different material properties estimations on the results; Rule of Mixtures as a conventional method, Mori-Tanaka estimation and self-consistent scheme. The results show that estimations for material properties could be influential to the thermo-elastic response for some profiles of volume fractions of constituents. However, the effect on elastic response is negligible.

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Yan, Hong-Sen, and Wen-Hsiang Hsieh. "On the Coupler Curve of RCPCR Linkages." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5900.

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Abstract The purpose of this paper is to investigate the properties of the coupler curves generated by all RCPCR linkages. First, the 3 × 3 matrix with dual elements is used to establish the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCPCR and RRCPC linkages are used as examples for illustrations. Moreover, the results on the application of dimensional synthesis are discussed.

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Kong, Xianwen. "Kinematic Analysis of Conventional and Multi-Mode Spatial Mechanisms Using Dual Quaternions." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59194.

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Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots (or mechanisms and robots with multiple operation modes) require re-examining this fundamental issue. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the kinematic analysis of not only conventional mechanisms and robots but also reconfigurable mechanisms and robots. This paper first presents a method for setting up a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of a spatial mechanism is composed of six equations. The effectiveness of the proposed kinematic loop equations is then demonstrated by deriving the explicit input-output equations of a line symmetric 1-DOF (degree-of-freedom) 7R single-loop spatial mechanism, the re-configuration analysis of a novel multi-mode 1-DOF 7R spatial mechanism. In the former case, an explicit input-output equation of degree 8 is derived. In the latter case, it is found that the 7R multi-mode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Unlike the 7R multi-mode mechanisms in the literature, the 7R multi-mode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

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Daneshkhah, Kasra, and Wahid Ghaly. "Redesign of a Highly Loaded Transonic Turbine Nozzle Blade Using a New Viscous Inverse Design Method." In ASME Turbo Expo 2007: Power for Land, Sea, and Air. ASMEDC, 2007. http://dx.doi.org/10.1115/gt2007-27430.

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The redesign of VKI-LS89 turbine vane, which is typical of a highly loaded transonic turbine guide vane is presented. The redesign is accomplished using a new inverse design method where the blade walls move with a virtual velocity distribution derived from the difference between the current and the target pressure distributions on the blade surfaces. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes (RANS) equations that are expressed in an arbitrary Lagrangian-Eulerian (ALE) form to account for mesh movement. A cell-vertex finite volume method is used to discretize the equations in space; time accurate integration is obtained using dual time stepping. An algebraic Baldwin-Lomax model is used for turbulence closure. The flow analysis formulation is first assessed against the LS89 experimental data. The inverse formulation that is implemented in the same code, is also assessed for its robustness and accuracy, by inverse designing the LS89 original geometry through running the inverse method with the original LS89 pressure distributions as target distributions but starting from an arbitrary geometry. The inverse design method is then used to redesign the LS89 using an arbitrary pressure distributions at a subsonic and a transonic outflow condition and the results are interpreted in terms of the blade overall aerodynamic performance.

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Kong, Xianwen, Jingjun Yu, and Duanling Li. "Reconfiguration Analysis of a 2-DOF 3-4R Parallel Manipulator With Planar Base and Platform." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46219.

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This paper deals with a 2-DOF 3-4R parallel manipulator (PM) with planar base and platform — a novel PM with multiple operation mode (or disassembly-free reconfigurable PM) with minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM is derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R parallel manipulator (PM) with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

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Osborne, Alfred R. "Theory of Nonlinear Fourier Analysis: The Construction of Quasiperiodic Fourier Series for Nonlinear Wave Motion." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18850.

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Abstract I give a description of nonlinear water wave dynamics using a recently discovered tool of mathematical physics I call nonlinear Fourier analysis (NLFA). This method is based upon and is an application of a theorem due to Baker [1897, 1907] and Mumford [1984] in the field of algebraic geometry and from additional sources by the author [Osborne, 2010, 2018, 2019]. The theory begins with the Kadomtsev-Petviashvili (KP) equation, a two dimensional generalization of the Korteweg-deVries (KdV) equation: Here the NLFA method is derived from the complete integrability of the equation by finite gap theory or the inverse scattering transform for periodic/quasiperiodic boundary conditions. I first show, for a one-dimensional, plane wave solution, that the KP equation can be rotated to a solution of the KdV equation, where the coefficients of KdV are now functions of the rotation angle. I then show how the rotated KdV equation can be used to compute the spectral solutions of the KP equation itself. Finally, I write the spectral solutions of the KP equation as a finite gap solution in terms of Riemann theta functions. By virtue of the fact that I am able to write a theta function formulation of the KP equation, it is clear that the wave dynamics lie on tori and constitute parallel dynamics on the tori in the integrable cases and non-parallel dynamics on the tori for certain perturbed quasi-integrable cases. Therefore, we are dealing with a Kolmogorov-Arnold-Moser KAM theory for nonlinear partial differential wave equations. The nonlinear Fourier series have particular nonlinear Fourier modes, including: sine waves, Stokes waves and solitons. Indeed the theoretical formulation I have developed is a kind of exact two-dimensional “coherent wave turbulence” or “integrable wave turbulence” for the KP equation, for which the Stokes waves and solitons are the coherent structures. I discuss how NLFA provides a number of new tools that apply to a wide range of problems in offshore engineering and coastal dynamics: This includes nonlinear Fourier space and time series analysis, nonlinear Fourier wave field analysis, a nonlinear random phase approximation, the study of nonlinear coherent functions and nonlinear bi and tri spectral analysis.

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