Готові списки джерел за темами / Equivariant index

Добірка наукової літератури з теми "Equivariant index"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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Статті в журналах з теми "Equivariant index"

Wang, Yong. "The Noncommutative Infinitesimal Equivariant Index Formula." Journal of K-Theory 14, no. 1 (July 3, 2014): 73–102. http://dx.doi.org/10.1017/is014006002jkt268.

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AbstractIn this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regularity and give an explicit formula for them. We also establish an infinitesimal equivariant family index formula and introduce the infinitesimal equivariant eta forms as well as compare them with the equivariant eta forms.

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Garza, Gabriel López, and Slawomir Rybicki. "Equivariant bifurcation index." Nonlinear Analysis: Theory, Methods & Applications 73, no. 9 (November 2010): 2779–91. http://dx.doi.org/10.1016/j.na.2010.06.001.

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Gołębiewska, Anna, and Sławomir Rybicki. "Equivariant Conley index versus degree for equivariant gradient maps." Discrete and Continuous Dynamical Systems - Series S 6, no. 4 (December 2012): 985–97. http://dx.doi.org/10.3934/dcdss.2013.6.985.

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Wruck, Philipp. "Genericity in equivariant dynamical systems and equivariant Fuller index theory." Dynamical Systems 29, no. 3 (April 14, 2014): 399–423. http://dx.doi.org/10.1080/14689367.2014.903588.

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MARZANTOWICZ, WACLAW, and CARLOS PRIETO. "THE UNSTABLE EQUIVARIANT FIXED POINT INDEX AND THE EQUIVARIANT DEGREE." Journal of the London Mathematical Society 69, no. 01 (January 28, 2004): 214–30. http://dx.doi.org/10.1112/s0024610703004721.

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Ono, Kaoru. "Equivariant index of Dirac operators." Tohoku Mathematical Journal 42, no. 3 (1990): 319–32. http://dx.doi.org/10.2748/tmj/1178227613.

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Vergne, Michele. "Equivariant index formulas for orbifolds." Duke Mathematical Journal 82, no. 3 (March 1996): 637–52. http://dx.doi.org/10.1215/s0012-7094-96-08226-5.

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Wang, Yong. "Volterra calculus, local equivariant family index theorem and equivariant eta forms." Asian Journal of Mathematics 20, no. 4 (2016): 759–84. http://dx.doi.org/10.4310/ajm.2016.v20.n4.a8.

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Troitskiĭ, E. V. "THE EQUIVARIANT INDEX OFC*-ELLIPTIC OPERATORS." Mathematics of the USSR-Izvestiya 29, no. 1 (February 28, 1987): 207–24. http://dx.doi.org/10.1070/im1987v029n01abeh000967.

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Dzedzej, Zdzisław. "Fixed orbit index for equivariant maps." Nonlinear Analysis: Theory, Methods & Applications 47, no. 4 (August 2001): 2835–40. http://dx.doi.org/10.1016/s0362-546x(01)00402-3.

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Більше джерел

Дисертації з теми "Equivariant index"

Nguyen, Hans. "Supersymmetric Quantum Mechanics, Index Theorems and Equivariant Cohomology." Thesis, Uppsala universitet, Teoretisk fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-350077.

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In this thesis, we investigate supersymmetric quantum mechanics (SUSYQM) and its relation to index theorems and equivariant cohomology. We define some basic constructions on super vector spaces in order to set the language for the rest of the thesis. The path integral in quantum mechanics is reviewed together with some related calculational methods and we give a path integral expression for the Witten index. Thereafter, we discuss the structure of SUSYQM in general. One shows that the Witten index can be taken to be the difference in dimension of the bosonic and fermionic zero energy eigenspaces. In the subsequent section, we derive index theorems. The models investigated are the supersymmetric non-linear sigma models with one or two supercharges. The former produces the index theorem for the spin-complex and the latter the Chern-Gauss-Bonnet Theorem. We then generalise to the case when a group action (by a compact connected Lie group) is included and want to consider the orbit space as the underlying space, in which case equivariant cohomology is introduced. In particular, the Weil and Cartan models are investigated and SUSYQM Lagrangians are derived using the obtained differentials. The goal was to relate this to gauge quantum mechanics, which was unfortunately not successful. However, what was shown was that the Euler characteristics of a closed oriented manifold and its homotopy quotient by U(1)n coincide.

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Gonzales, Vilcarromero Richard Paul. "Poincaré duality in equivariant intersection theory." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/94996.

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We study the Poincaré duality map from equivariant Chow cohomology to equivariant Chow groups in the case of torus actions on complete, possibly singular, varieties with isolated fixed points. Our main results yield criteria for the Poincaré duality map to become an isomorphism in this setting. The methods rely on the localization theorem for equivariant Chow cohomology and the notion of algebraic rational cell. We apply our results to complete spherical varieties and their generalizations.
En este artículo estudiamos el homomorfismo de dualidad de Poincaré, el cual relaciona cohomología de Chow equivariante y grupos de Chow equivariante en aquellos casos donde un toro algebraico actúa sobre una variedad singular compacta y con puntos fijos aislados. Nuestros resultados proporcionan criterios bajo los cuales el homomorfismo de dualidadde Poincaré es un isomorfismo. Para ello, usamos el teorema de localización en cohomología de Chow equivariante y la noción de célula algebraica racional. Aplicamos nuestros resultados a las variedades esféricas compactas y sus generalizaciones.

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Takata, Doman. "A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds." Kyoto University, 2018. http://hdl.handle.net/2433/232217.

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Neyra, Norbil Leodan Cordova. "Teorida de G-índice e grau de aplicações G-equivariantes." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-22062010-091958/.

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Antes da publicação do trabalho An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems\"de Fadell e Husseini [20], haviam sido apenas considerados índices numéricos de G-espaços, nos casos G =\'Z IND. 2\' e G um grupo finito. No entanto, tais índices numéricos são obviamente insuficientes no caso de grupos mais complexos, como por exemplo a 1-esfera \'S POT. 1\'. Neste contexto, Fadell e Husseini introduziram o chamado Indice cohomológico de valor ideal: a cada G-espaço X paracompacto, eles associaram um ideal \'Ind POT. G\' (X;K) do anel de cohomología H*(BG;K), onde a cohomologia de Cech H* é considerada com coeficientes em um corpo K e BG é o espaço classificante do grupo G. Além disso, Fadell e Husseini associaram a este ideal o Índice cohomológico de valor numérico, o qual é definido como sendo a dimensão do K-espaço vetorial obtido do quociente entre o anel H*(BG;K) e o ideal \'Ind POT. G\' (X;K). O objetivo principal deste trabalho é apresentar um estudo detalhado deste índice e utilizá-lo no estudo dos resultados sobre grau de aplicações G-equivariantes provados por Hara em \"The degree of equivariant maps\"[24]
Before the appearance of the paper An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems\"of Fadell and Husseini [20], had been considered numerical indices of G-spaces, when G = \'Z IND. 2\' and when G is a finite group. However, such numerical indices are obviously insufficient in the case of groups more complexes, for example, G =\'S POT 1\'. In this context Fadell andHusseini, introduced the called valued-ideal cohomological index: to every paracompact G-space X they associated an ideal \'Ind POT. G\' (X,K) of the cohomology ring H*(BG;K), where the Cech cohomology H* is considered with coefficients in a field K and BG is the classifying space of the group G. Moreover, they associated to this ideal the numerical valued cohomological index, that is, the dimension of K-vector space obtained by the quotient between the ring H*(BG;K) and the ideal \'Ind POT. G\' (X,K). The main objective of this work is to present a detailed study of this index and use such index on the study of results on degree of equivariant maps proved by Hara in his paper The degree of equivariant maps\"[24]

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Chen, Xudong. "Multi-Agent Systems with Reciprocal Interaction Laws." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11424.

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In this thesis, we investigate a special class of multi-agent systems, which we call reciprocal multi-agent (RMA) systems. The evolution of agents in a RMA system is governed by interactions between pairs of agents. Each interaction is reciprocal, and the magnitude of attraction/repulsion depends only on distances between agents. We investigate the class of RMA systems from four perspectives, these are two basic properties of the dynamical system, one formula for computing the Morse indices/co-indices of critical formations, and one formation control model as a variation of the class of RMA systems. An important aspect about RMA systems is that there is an equivariant potential function associated with each RMA system so that the equations of motion of agents are actually a gradient flow. The two basic properties about this class of gradient systems we will investigate are about the convergence of the gradient flow, and about the question whether the associated potential function is generically an equivariant Morse function. We develop systematic approaches for studying these two problems, and establish important results. A RMA system often has multiple critical formations and in general, these are hard to locate. So in this thesis, we consider a special class of RMA systems whereby there is a geometric characterization for each critical formation. A formula associated with the characterization is developed for computing the Morse index/co-index of each critical formation. This formula has a potential impact on the design and control of RMA systems. In this thesis, we also consider a formation control model whereby the control of formation is achieved by varying interactions between selected pairs of agents. This model can be interpreted in different ways in terms of patterns of information flow, and we establish results about the controllability of this control system for both centralized and decentralized problems.
Engineering and Applied Sciences

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Baldare, Alexandre. "Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques." Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS005/document.

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Le problème de l'indice est de calculer l'indice d'un opérateur elliptique en termes topologiques. Ce problème fut résolu par M. Atiyah et I. Singer en 1963 dans "The index of elliptic operators on compact manifolds". Quelques années plus tard, ces auteurs ont fourni une nouvelle preuve dans "The index of elliptic operators I" permettant plusieurs généralisations et applications. La première est la prise en compte de l'action d'un groupe compact G, dans ce cadre on obtient une égalité dans l'anneau des représentations de G. Par la suite ils ont généralisé ce résultat au cadre des familles d'opérateurs elliptiques paramétrées par un espace compact dans "The index of elliptic operators IV", ici l'égalité vit dans la K-théorie de l'espace paramétrant la famille.Une autre généralisation importante est celle des opérateurs transversalement elliptiques par rapport à l'action d'un groupe G, c'est-à-dire elliptiques dans le sens transverse aux orbites de l'action d'un groupe sur une variété. Cette classe d'opérateurs a été étudié pour la première fois dans le cadre d'un opérateur P agissant sur une variété M par M. Atiyah (et I. Singer) dans "Elliptic operators and compact groups", en 1974. Dans cet article l'auteur définit une classe indice et montre qu'elle ne dépend que de la classe du symbole en K-théorie. Il montre ensuite qu'elle vérifie différents axiomes : action libre, multiplicativité et excision. Ces différents axiomes permettent alors de ramener le calcul de l'indice à un espace euclidien muni de l'action d'un tore. Par la suite, cette classe d'opérateurs a été étudier du point de vue de la K-théorie bivariante par P. Julg [1982] et plus récemment dans le cadre des actions propres sur une variété non compacte par G. Kasparov [2016].Dans cette thèse, nous nous intéressons aux familles d'opérateurs G-transversalement elliptiques. Nous définissons une classe indice en K-théorie bivariante de Kasparov. Nous vérifions qu'elle ne dépend que de la classe du symbole de la famille en K-théorie. Nous montrons que notre classe indice vérifie les propriétés d'action libre, de multiplicativité et d'excision espérées en K-théorie bivariante. Nous montrons ensuite un théorème d'induction et de compatibilité avec les applications de Gysin. Ces derniers théorèmes permettent de ramener le calcul de l'indice au cas d'une famille triviale pour l'action d'un tore comme dans le cadre d'un seul opérateur sur une variété. Nous démontrons ensuite qu'on peut associer à cette classe indice un caractère de Chern à coefficients distributionnels sur G à valeurs dans la cohomologie de de Rham de l'espace paramétrant lorsque c'est une variété. Pour ce faire, nous utilisons l'homologie locale de M. Puschnigg [2003] et une technique de M. Hilsum et G. Skandalis [1987]. Par la suite, nous nous intéressons aux formules de Berline et Vergne dans ce cadre. Avant de passer aux formules générales pour une famille d'opérateurs G-transversalment elliptiques, on commence par regarder si on obtient les mêmes formules dans le cadre elliptique. On montre alors des égalités similaires à celles obtenues par N. Berline et M. Vergne [1985] dans le cadre d'un opérateur elliptique G-invariant. Dans un dernier chapitre, on montre la formule de Berline-Vergne dans le cadre des familles d'opérateurs G-transversalement elliptiques. On utilise ici la formule de Berline-Vergne pour un opérateur G-transversalement elliptique et les différentes techniques mises en place dans les chapitres précédents
The index problem is to calculate the index of an elliptic operator in topological terms. This problem was solved by M. Atiyah and I. Singer in 1963 in "The index of elliptic operators on compact manifolds". Few years later, these authors have given a new proof in "The index of elliptic operators I" allowing several generalizations and applications. The first is taking into account of the action of a compact group G, in this frame they obtain an equality in the ring of the representations of G. Later they generalized this result to the framework of the families of elliptic operators parameterized by a compact space in "The index of elliptic operators IV", here equality lives in the K-theory of the space of parameter.Another important generalization is the transversely elliptic operators with respect to a group action, that is to say, elliptic in the transverse direction to the orbits of a group action on a manifold. This class of operators has been studied for the first time by M. Atiyah (and I. Singer) in "Elliptic operators and compact groups", in 1974. In this article the author defines an index class and shows that it depends only on the symbol class in K-theory. Then he shows that it verifies different axioms: free action, multiplicativity and excision. These different axioms allows to reduce the calculation of the index to an Euclidean space equipped with an action of a torus. Next, this class of operators has been studied from the point of view of bivariant K-theory by P. Julg [1982] and more recently in the context of proper action on a non-compact manifolds by G. Kasparov [2016].In this thesis, we are interested in families of G-transversely elliptic operators. We define an index class in Kasparov bivariant K-theory. We verify that it depends only on the class of the symbol of the family in K-theory. We show that our index class satisfies the expected free action, multiplicativity and excision properties in bivariant K-theory. We then show a theorem of induction and compatibility with Gysin maps. These last theorems allows to reduce the calculation of the index to the case of a trivial family for the action of a torus as in the framework of a single operator on a manifold. We then prove that we can associate to this index class a Chern character with distributional coefficients on G with values in the de Rham cohomology of the parameter space when it is a manifold. To do this, we use the bivariant local cyclic homology of M. Puschnigg [2003] and a technique of M. Hilsum and G. Skandalis [1987].Before treating the general framework of families of G-transversely elliptic operators, we look at the elliptic case. We show that the expected formulas are true in this context. In the last chapter, we show the Berline-Vergne formula in the context of families of G-transversely elliptic operators. We use here the Berline-Vergne formula for a G-transversely elliptic operator and the different methods used in the previous chapters

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Wruck, Philipp [Verfasser]. "Genericity in equivariant dynamical systems and equivariant Fuller Index theory / von Philipp Wruck." 2011. http://d-nb.info/1010440063/34.

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Shan, Lin. "Equivariant index theory and non-positively curved manifolds." Diss., 2007. http://etd.library.vanderbilt.edu/ETD-db/available/etd-04022007-140838/.

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Guo, Hao. "Positive scalar curvature and Callias-type index theorems for proper actions." Thesis, 2018. http://hdl.handle.net/2440/118136.

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This thesis by publication is a study of the equivariant index theory of Dirac operators and Callias-type operators in two distinct settings, namely on cocompact and non-cocompact manifolds with a Lie group action. The first two chapters are a short resumé of Dirac operators and index theory and form a common introduction to the papers in the appendices. Appendix A is joint work with my supervisors, Elder Professor Mathai Varghese and Dr. Hang Wang. For G an almost-connected Lie group acting properly and cocompactly on a manifold M, we study G-index theory of G- invariant Dirac operators. By establishing Poincaré duality for equivariant K-theory and K-homology, we are able to extend the scope of our results to include all elements of equivariant analytic K-homology, which we also show is isomorphic to equivariant geometric K-homology. Our results are applied to prove: a rigidity result for almost-complex manifolds, generalising a vanishing theorem of Hattori; an analogue of Petrie's conjecture; and Lichnerowicz-type obstructions to G-invariant Riemannian metrics on M. Appendix B studies the much more general situation when the quotient M=G is non-compact and G is an arbitrary Lie group. I define G-Callias- type operators and show that they are C*(G)-Fredholm by adapting analysis of Kasparov to new Hilbert C*(G)-module analogues of Sobolev spaces. Questions of adjointability, regularity and essential self-adjointness are addressed in detail. The estimates on G-Callias-type operators are based on the work of Bunke [8] in the non-equivariant context. We construct explicit admissible endomorphisms for G-Callias-type operators from the K-theory of the Higson G-corona of M, a highly non-trivial group. The index theory developed here is applied to prove a general obstruction theorem for G- invariant metrics of positive scalar curvature in the non-cocompact setting.
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2018

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Fitzpatrick, Daniel. "Almost CR Quantization via the Index of Transversally Elliptic Dirac Operators." Thesis, 2009. http://hdl.handle.net/1807/19033.

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Let $M$ be a smooth compact manifold equipped with a co-oriented subbundle $E\subset TM$. We suppose that a compact Lie group $G$ acts on $M$ preserving $E$, such that the $G$-orbits are transverse to $E$. If the fibres of $E$ are equipped with a complex structure then it is possible to construct a $G$-invariant Dirac operator $\dirac$ in terms of the resulting almost CR structure. We show that there is a canonical equivariant differential form with generalized coefficients $\mathcal{J}(E,X)$ defined on $M$ that depends only on the $G$-action and the co-oriented subbundle $E$. Moreover, the group action is such that $\dirac$ is a $G$-transversally elliptic operator in the sense of Atiyah \cite{AT}. Its index is thus defined as a generalized function on $G$. Beginning with the equivariant index formula of Paradan and Vergne \cite{PV3}, we obtain an index formula for $\dirac$ computed as an integral over $M$ that is free of choices and growth conditions. This formula necessarily involves equivariant differential forms with generalized coefficients and we show that the only such form required is the canonical form $\mathcal{J}(E,X)$. In certain cases the index of $\dirac$ can be interpreted in terms of a CR analogue of the space of holomorphic sections, allowing us to view our index formula as a character formula for the $G$-equivariant quantization of the almost CR manifold $(M,E)$. In particular, we obtain the ``almost CR'' quantization of a contact manifold, in a manner directly analogous to the almost complex quantization of a symplectic manifold.

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Книги з теми "Equivariant index"

Georgia International Topology Conference (2009 University of Georgia). Low-dimensional and symplectic topology. Edited by Usher Michael 1978-. Providence, R.I: American Mathematical Society, 2011.

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1926-, Fadell Edward R., Bowszyc Cezary, Jaworowski Jan, and NATO Advanced Study Institute, eds. Topics in equivariant topology: Part 3 of the proceedings of the NATO ASI "variational methods in nonlinear problems.". Montréal, Québec, Canada: Presses de l'Université de Montréal, 1989.

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Частини книг з теми "Equivariant index"

Mukherjee, Amiya. "Equivariant K-Theory." In Atiyah-Singer Index Theorem, 178–99. Gurgaon: Hindustan Book Agency, 2013. http://dx.doi.org/10.1007/978-93-86279-60-6_7.

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Berline, Nicole, Ezra Getzler, and Michèle Vergne. "The Equivariant Index Theorem." In Heat Kernels and Dirac Operators, 181–201. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-58088-8_7.

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Gęba, Kazimierz. "Degree for Gradient Equivariant Maps and Equivariant Conley Index." In Topological Nonlinear Analysis II, 247–72. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4126-3_5.

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Nest, Ryszard, and Florin Radulescu. "Index of Γ-Equivariant Toeplitz Operators." In C*-Algebras, 151–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57288-3_8.

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de Monvel, L. Boutet. "Toeplitz Operators and Asymptotic Equivariant Index." In Modern Aspects of the Theory of Partial Differential Equations, 1–16. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0069-3_1.

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Berline, Nicole, Ezra Getzler, and Michèle Vergne. "The Kirillov Formula for the Equivariant Index." In Heat Kernels and Dirac Operators, 243–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-58088-8_9.

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Ulrich, Hanno. "The fixed point index of equivariant vertical maps." In Lecture Notes in Mathematics, 61–136. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079803.

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de Monvel, Louis Boutet, Eric Leichtnam, Xiang Tang, and Alan Weinstein. "Asymptotic equivariant index of Toeplitz operators and relative index of CR structures." In Geometric Aspects of Analysis and Mechanics, 57–79. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8244-6_2.

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Paradan, Paul-`Emile, and Mich`ele Vergne. "Equivariant Index of Twisted Dirac Operators and Semi-classical Limits." In Lie Groups, Geometry, and Representation Theory, 419–58. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02191-7_15.

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Guseǐn-Zade, S. M. "An equivariant analogue of the index of a gradient vector field." In Lecture Notes in Mathematics, 196–210. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075966.

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Тези доповідей конференцій з теми "Equivariant index"

RICHARDSON, KEN. "GENERALIZED EQUIVARIANT INDEX THEORY." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772640_0020.

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Saghafi, Mehdi, and Harry Dankowicz. "Nondegenerate Continuation Problems for the Excitation Response of Nonlinear Beam Structures." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13115.

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Анотація:

This paper investigates the dynamics of a slender beam subjected to transverse periodic excitation. Of particular interest is the formulation of nondegenerate continuation problems that may be analyzed numerically, in order to explore the parameter-dependence of the steady-state excitation response, while accounting for geometric nonlinearities. Several candidate formulations are presented, including finite-difference (FD) and finite-element (FE) discretizations of the governing scalar, integro-partial differential boundary-value problem (BVP), as well as of a corresponding first-order-in-space, mixed formulation. As an example, a periodic BVP — obtained from a Galerkin-type, FE discretization with continuously differentiable, piecewise-polynomial trial and test functions, and an elimination of Lagrange multipliers associated with spatial boundary conditions — is analyzed to determine the beam response via numerical continuation using a MATLAB-based software suite. In the case of an FE discretization of the mixed formulation with continuous, piecewise-polynomial trial and test functions, it is shown that the choice of spatial boundary conditions may render the resultant index-1, differential-algebraic BVP equivariant under a symmetry group of state-space translations. The paper demonstrates several methods for breaking the equivariance in order to obtain a nondegenerate continuation problem, including a projection onto a symmetry-reduced state space or the introduction of an artificial continuation parameter. As is further demonstrated, an orthogonal collocation discretization in time of the BVP gives rise to ghost solutions, corresponding to arbitrary drift in the algebraic variables. This singularity is resolved by using an asymmetric discretization in time.

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