subject:(Dirac operators)

1. Beheshti Vadeqan, Babak. Geometry of Dirac Operators .

Degree: Mathematics and Statistics, 2016, Queens University

URL: http://hdl.handle.net/1974/14633

► Let M be a compact, oriented, even dimensional Riemannian manifold and let S be a Clifford bundle over M with Dirac operator D. Then [… (more)

Subjects/Keywords: Atiyah-Singer Index Theorem ; Dirac Operators ; Elliptic Geometry

…this thesis to show that elliptic operators and specifically Dirac operators contain certain… …Dirac operators. We shall also see that the study of Dirac operators reveals some… …a more general type of elliptic differential operators which are said to be Dirac type… …operators called Dirac operators. In this thesis we are planning to study this type of operators… …Dirac operators on manifolds. We will start by introducing Clifford algebras and their…

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APA (6^th Edition):

Beheshti Vadeqan, B. (2016). Geometry of Dirac Operators . (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/14633

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Beheshti Vadeqan, Babak. “Geometry of Dirac Operators .” 2016. Thesis, Queens University. Accessed March 04, 2021. http://hdl.handle.net/1974/14633.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Beheshti Vadeqan, Babak. “Geometry of Dirac Operators .” 2016. Web. 04 Mar 2021.

Vancouver:

Beheshti Vadeqan B. Geometry of Dirac Operators . [Internet] [Thesis]. Queens University; 2016. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/1974/14633.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Beheshti Vadeqan B. Geometry of Dirac Operators . [Thesis]. Queens University; 2016. Available from: http://hdl.handle.net/1974/14633

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

ETH Zürich

2. Farinelli, S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.

Degree: 1998, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/143641

Subjects/Keywords: DIRAC-OPERATOREN (FUNKTIONALANALYSIS); RIEMANNSCHE MANNIGFALTIGKEITEN (TOPOLOGIE); DIRAC OPERATORS (FUNCTIONAL ANALYSIS); RIEMANNIAN MANIFOLDS (TOPOLOGY); info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; Mathematics; Mathematics; Mathematics

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APA (6^th Edition):

Farinelli, S. (1998). Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/143641

Chicago Manual of Style (16^th Edition):

Farinelli, S. “Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.” 1998. Doctoral Dissertation, ETH Zürich. Accessed March 04, 2021. http://hdl.handle.net/20.500.11850/143641.

MLA Handbook (7^th Edition):

Farinelli, S. “Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.” 1998. Web. 04 Mar 2021.

Vancouver:

Farinelli S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. [Internet] [Doctoral dissertation]. ETH Zürich; 1998. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/20.500.11850/143641.

Council of Science Editors:

Farinelli S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. [Doctoral Dissertation]. ETH Zürich; 1998. Available from: http://hdl.handle.net/20.500.11850/143641

3. Klaasse, R.L. Seiberg-Witten theory for symplectic manifolds.

Degree: 2013, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/282753

► In this thesis we give an introduction to Seiberg-Witten gauge theory used to study compact oriented four-dimensional manifolds X. Seiberg-Witten theory uses a Spin c… (more)

Subjects/Keywords: Seiberg-Witten theory; four-manifolds; symplectic manifolds; Spin c structures; Dirac operators

…forms, so that we are done. 2.4 Elliptic operators In this section we discuss the notion of… …analogous notion for operators between sections of vector bundles. Definition 2.4.2. An operator D… …of Fredholm operators is that their index is invariant under perturbations. In other words… …if one were to take a family of Fredholm operators parameterized by some connected… …Fredholmness of operators and calculating their index. A key concept is that of ellipticity. Let π…

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APA (6^th Edition):

Klaasse, R. L. (2013). Seiberg-Witten theory for symplectic manifolds. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/282753

Chicago Manual of Style (16^th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Masters Thesis, Universiteit Utrecht. Accessed March 04, 2021. http://dspace.library.uu.nl:8080/handle/1874/282753.

MLA Handbook (7^th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Web. 04 Mar 2021.

Vancouver:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Internet] [Masters thesis]. Universiteit Utrecht; 2013. [cited 2021 Mar 04]. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753.

Council of Science Editors:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Masters Thesis]. Universiteit Utrecht; 2013. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753

University of Michigan

4. Korpas, Levente. Quantization of symplectic cobordisms.

Degree: PhD, Pure Sciences, 1999, University of Michigan

URL: http://hdl.handle.net/2027.42/131922

► In this work we construct a unitary operator acting between Spin^c quantizations of compact integral symplectic manifolds which are symplectically cobordant. The construction is… (more)

Subjects/Keywords: Cobordisms; Dirac Operators; Quantization; Symplectic Manifolds

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APA (6^th Edition):

Korpas, L. (1999). Quantization of symplectic cobordisms. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/131922

Chicago Manual of Style (16^th Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Doctoral Dissertation, University of Michigan. Accessed March 04, 2021. http://hdl.handle.net/2027.42/131922.

MLA Handbook (7^th Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Web. 04 Mar 2021.

Vancouver:

Korpas L. Quantization of symplectic cobordisms. [Internet] [Doctoral dissertation]. University of Michigan; 1999. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/2027.42/131922.

Council of Science Editors:

Korpas L. Quantization of symplectic cobordisms. [Doctoral Dissertation]. University of Michigan; 1999. Available from: http://hdl.handle.net/2027.42/131922

5. Lal, Nishu. Spectral Zeta Functions of Laplacians on Self-Similar Fractals.

Degree: Mathematics, 2012, University of California – Riverside

URL: http://www.escholarship.org/uc/item/888903d2

► This thesis investigates the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar… (more)

Subjects/Keywords: Mathematics; Analysis on fractals; decimation method; Dirac delta hyperfunction; fractal Sturm-Liouville operators; multivariable complex dynamics; spectral zeta functions

…the spectral zeta function of fractal differential operators such as the Laplacian on the… …the spectral zeta function of such an operator, expressed in terms of the Dirac delta… …variables associated with fractal Sturm–Liouville operators. Moreover, as a corollary, in the very… …Adjoint Operators and Quadratic Forms . . . . . . 2.5 Introduction To Hyperfunctions… …3.3.1 Main Lemma Regarding the Dirac Delta Hyperfunction . . . . . 3.4 A Representation of the…

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APA (6^th Edition):

Lal, N. (2012). Spectral Zeta Functions of Laplacians on Self-Similar Fractals. (Thesis). University of California – Riverside. Retrieved from http://www.escholarship.org/uc/item/888903d2

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Thesis, University of California – Riverside. Accessed March 04, 2021. http://www.escholarship.org/uc/item/888903d2.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Web. 04 Mar 2021.

Vancouver:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Internet] [Thesis]. University of California – Riverside; 2012. [cited 2021 Mar 04]. Available from: http://www.escholarship.org/uc/item/888903d2.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Thesis]. University of California – Riverside; 2012. Available from: http://www.escholarship.org/uc/item/888903d2

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Michigan State University

6. Maridakis, Manousos. The concentration principle for Dirac operators.

Degree: 2014, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:2604

►

Thesis Ph. D. Michigan State University. Mathematics 2014.

The symbol map σ of an elliptic operator carries essential topological and geometrical information about the underlying… (more)

Subjects/Keywords: Dirac equation; Manifolds (Mathematics); Differential operators; Theoretical mathematics

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APA (6^th Edition):

Maridakis, M. (2014). The concentration principle for Dirac operators. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:2604

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Maridakis, Manousos. “The concentration principle for Dirac operators.” 2014. Thesis, Michigan State University. Accessed March 04, 2021. http://etd.lib.msu.edu/islandora/object/etd:2604.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Maridakis, Manousos. “The concentration principle for Dirac operators.” 2014. Web. 04 Mar 2021.

Vancouver:

Maridakis M. The concentration principle for Dirac operators. [Internet] [Thesis]. Michigan State University; 2014. [cited 2021 Mar 04]. Available from: http://etd.lib.msu.edu/islandora/object/etd:2604.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Maridakis M. The concentration principle for Dirac operators. [Thesis]. Michigan State University; 2014. Available from: http://etd.lib.msu.edu/islandora/object/etd:2604

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Australian National University

7. Morris, Andrew Jordan. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .

Degree: 2010, Australian National University

URL: http://hdl.handle.net/1885/8864

► The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to… (more)

▼ The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood – Paley – Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge – Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincaré inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.

Subjects/Keywords: holomorphic functional calculi; quadratic estimates; sectorial operators; local Hardy spaces; Riemannian manifolds; differential forms; Hodge – Dirac operators; local Riesz transforms; off-diagonal estimates; Davies – Gaffney estimates; Kato square-root problems; submanifolds; divergence form operators; first-order differential operators

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APA (6^th Edition):

Morris, A. J. (2010). Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/8864

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Morris, Andrew Jordan. “Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .” 2010. Thesis, Australian National University. Accessed March 04, 2021. http://hdl.handle.net/1885/8864.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Morris, Andrew Jordan. “Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .” 2010. Web. 04 Mar 2021.

Vancouver:

Morris AJ. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . [Internet] [Thesis]. Australian National University; 2010. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/1885/8864.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Morris AJ. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . [Thesis]. Australian National University; 2010. Available from: http://hdl.handle.net/1885/8864

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

8. Rahaman, Md Aminoor. Search On A Hypercubic Lattice Using Quantum Random Walk.

Degree: MSc Engg, Faculty of Engineering, 2010, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/972

► Random walks describe diffusion processes, where movement at every time step is restricted only to neighbouring locations. Classical random walks are constructed using the non-relativistic… (more)

Subjects/Keywords: Lattice Theory - Data Processing; Quantum Random Walk; Grover's Algorithm; Dirac Operators; Quantum Computation; Dimensional Hypercubic Lattices; Random Walk Algorithm; Spatial Search; Quantum Physics

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APA (6^th Edition):

Rahaman, M. A. (2010). Search On A Hypercubic Lattice Using Quantum Random Walk. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/972

Chicago Manual of Style (16^th Edition):

Rahaman, Md Aminoor. “Search On A Hypercubic Lattice Using Quantum Random Walk.” 2010. Masters Thesis, Indian Institute of Science. Accessed March 04, 2021. http://etd.iisc.ac.in/handle/2005/972.

MLA Handbook (7^th Edition):

Rahaman, Md Aminoor. “Search On A Hypercubic Lattice Using Quantum Random Walk.” 2010. Web. 04 Mar 2021.

Vancouver:

Rahaman MA. Search On A Hypercubic Lattice Using Quantum Random Walk. [Internet] [Masters thesis]. Indian Institute of Science; 2010. [cited 2021 Mar 04]. Available from: http://etd.iisc.ac.in/handle/2005/972.

Council of Science Editors:

Rahaman MA. Search On A Hypercubic Lattice Using Quantum Random Walk. [Masters Thesis]. Indian Institute of Science; 2010. Available from: http://etd.iisc.ac.in/handle/2005/972

University of Michigan

9. Sandoval, Mary Ruth. Wave-trace asymptotics for operators of Dirac type.

Degree: PhD, Pure Sciences, 1997, University of Michigan

URL: http://hdl.handle.net/2027.42/130578

► Spectral geometry seeks to understand the relationship between the spectra of differential operators and the underlying geometry of a manifold, especially to understand which geometric… (more)

Subjects/Keywords: Asymptotics; Dirac; Operators; Spectral Geometry; Trace; Type; Wave

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APA (6^th Edition):

Sandoval, M. R. (1997). Wave-trace asymptotics for operators of Dirac type. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/130578

Chicago Manual of Style (16^th Edition):

Sandoval, Mary Ruth. “Wave-trace asymptotics for operators of Dirac type.” 1997. Doctoral Dissertation, University of Michigan. Accessed March 04, 2021. http://hdl.handle.net/2027.42/130578.

MLA Handbook (7^th Edition):

Sandoval, Mary Ruth. “Wave-trace asymptotics for operators of Dirac type.” 1997. Web. 04 Mar 2021.

Vancouver:

Sandoval MR. Wave-trace asymptotics for operators of Dirac type. [Internet] [Doctoral dissertation]. University of Michigan; 1997. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/2027.42/130578.

Council of Science Editors:

Sandoval MR. Wave-trace asymptotics for operators of Dirac type. [Doctoral Dissertation]. University of Michigan; 1997. Available from: http://hdl.handle.net/2027.42/130578

University of Waterloo

10. Suan, Caleb. Differential Operators on Manifolds with G2-Structure.

Degree: 2020, University of Waterloo

URL: http://hdl.handle.net/10012/16565

► In this thesis, we study differential operators on manifolds with torsion-free G2-structure. In particular, we use an identification of the spinor bundle S of such… (more)

Subjects/Keywords: differential geometry; G2-structures; twisted Dirac operator; differential operators

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APA (6^th Edition):

Suan, C. (2020). Differential Operators on Manifolds with G2-Structure. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/16565

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Suan, Caleb. “Differential Operators on Manifolds with G2-Structure.” 2020. Thesis, University of Waterloo. Accessed March 04, 2021. http://hdl.handle.net/10012/16565.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Suan, Caleb. “Differential Operators on Manifolds with G2-Structure.” 2020. Web. 04 Mar 2021.

Vancouver:

Suan C. Differential Operators on Manifolds with G2-Structure. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/10012/16565.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Suan C. Differential Operators on Manifolds with G2-Structure. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/16565

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

11. Takata, Doman. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .

Degree: 2018, Kyoto University

URL: http://hdl.handle.net/2433/232217

Subjects/Keywords: infinite-dimensional manifolds; loop groups; Dirac operators; assembly maps; KK-theory; index theory

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APA (6^th Edition):

Takata, D. (2018). A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/232217

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Thesis, Kyoto University. Accessed March 04, 2021. http://hdl.handle.net/2433/232217.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Web. 04 Mar 2021.

Vancouver:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Internet] [Thesis]. Kyoto University; 2018. [cited 2021 Mar 04]. Available from: http://hdl.handle.net/2433/232217.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Thesis]. Kyoto University; 2018. Available from: http://hdl.handle.net/2433/232217

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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