Journal articles on the topic 'Hodge decomposition'

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1

Kozłowski, Wojciech. "Hodge type decomposition." Annales Polonici Mathematici 90, no. 2 (2007): 99–104. http://dx.doi.org/10.4064/ap90-2-1.

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2

Katzarkov, L., T. Pantev, and B. Toën. "Schematic homotopy types and non-abelian Hodge theory." Compositio Mathematica 144, no. 3 (May 2008): 582–632. http://dx.doi.org/10.1112/s0010437x07003351.

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AbstractWe use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the schematization functor$X \mapsto (X\otimes \mathbb {C})^{\mathrm {sch}}$, introduced by the third author as a substitute for the rationalization functor in homotopy theory in the case of non-simply connected spaces. Our main result is the construction of a Hodge decomposition on $(X\otimes \mathbb {C})^{\mathrm {sch}}$. This Hodge decomposition is encoded in an action of the discrete group $\mathbb {C}^{\times \delta }$ on the object $(X\otimes \mathbb {C})^{\mathrm {sch}}$ and is shown to recover the usual Hodge decomposition on cohomology, the Hodge filtration on the pro-algebraic fundamental group, and, in the simply connected case, the Hodge decomposition on the complexified homotopy groups. We show that our Hodge decomposition satisfies a purity property with respect to a weight filtration, generalizing the fact that the higher homotopy groups of a simply connected projective manifold have natural mixed Hodge structures. As applications we construct new examples of homotopy types which are not realizable as complex projective manifolds and we prove a formality theorem for the schematization of a complex projective manifold.
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3

Petronetto, F., A. Paiva, M. Lage, G. Tavares, H. Lopes, and T. Lewiner. "Meshless Helmholtz-Hodge Decomposition." IEEE Transactions on Visualization and Computer Graphics 16, no. 2 (March 2010): 338–49. http://dx.doi.org/10.1109/tvcg.2009.61.

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4

Frediani, Paola, Alessandro Ghigi, and Gian Pietro Pirola. "FUJITA DECOMPOSITION AND HODGE LOCI." Journal of the Institute of Mathematics of Jussieu 19, no. 4 (November 12, 2018): 1389–408. http://dx.doi.org/10.1017/s1474748018000452.

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This paper contains two results on Hodge loci in $\mathsf{M}_{g}$. The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibers and the fibration is non-trivial, an appropriate exterior power of the cohomology of the fiber admits a Hodge substructure. In the case of curves it follows that the moduli image of the fiber is contained in a proper Hodge locus. The second result deals with divisors in $\mathsf{M}_{g}$. It is proved that the image under the period map of a divisor in $\mathsf{M}_{g}$ is not contained in a proper totally geodesic subvariety of $\mathsf{A}_{g}$. It follows that a Hodge locus in $\mathsf{M}_{g}$ has codimension at least 2.
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5

Sanders, Jan A., and Jing Ping Wang. "Hodge decomposition and conservation laws." Mathematics and Computers in Simulation 44, no. 5 (December 1997): 483–93. http://dx.doi.org/10.1016/s0378-4754(97)00077-3.

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6

Libgober, Anatoly. "Hodge decomposition of Alexander invariants." manuscripta mathematica 107, no. 2 (February 1, 2002): 251–69. http://dx.doi.org/10.1007/s002290100243.

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7

Chukanov, S. N. "Signal processing of simplicial complexes." Journal of Physics: Conference Series 2182, no. 1 (March 1, 2022): 012017. http://dx.doi.org/10.1088/1742-6596/2182/1/012017.

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Abstract The paper considered the signal processing of simplicial complexes. Hodge decomposition formula for discrete fields is given, which is similar to the Hodge decomposition formula for smooth vector fields. The construction and the estimation of the gradient, divergence and curl operators and Laplace matrices for discrete vector fields are considered.
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8

Troyanov, M. "On the Hodge Decomposition in Rn." Moscow Mathematical Journal 9, no. 4 (2009): 899–926. http://dx.doi.org/10.17323/1609-4514-2009-9-4-899-926.

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9

Bhatia, H., G. Norgard, V. Pascucci, and Peer-Timo Bremer. "The Helmholtz-Hodge Decomposition—A Survey." IEEE Transactions on Visualization and Computer Graphics 19, no. 8 (August 2013): 1386–404. http://dx.doi.org/10.1109/tvcg.2012.316.

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10

Henkin, Gennadi M., and Peter L. Polyakov. "Explicit Hodge decomposition on Riemann surfaces." Mathematische Zeitschrift 289, no. 1-2 (October 28, 2017): 711–28. http://dx.doi.org/10.1007/s00209-017-1972-2.

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11

ITOH, Mitsuhiro. "SASAKIAN MANIFOLDS, HODGE DECOMPOSITION AND MILNOR ALGEBRAS." Kyushu Journal of Mathematics 58, no. 1 (2004): 121–40. http://dx.doi.org/10.2206/kyushujm.58.121.

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12

Bhatia, Harsh, Gregory Norgard, Valerio Pascucci, and Peer-Timo Bremer. "Comments on the "Meshless Helmholtz-Hodge Decomposition"." IEEE Transactions on Visualization and Computer Graphics 19, no. 3 (March 2013): 527–28. http://dx.doi.org/10.1109/tvcg.2012.62.

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13

Robbin, Joel W., Robert C. Rogers, and Blake Temple. "On weak continuity and the Hodge decomposition." Transactions of the American Mathematical Society 303, no. 2 (February 1, 1987): 609. http://dx.doi.org/10.1090/s0002-9947-1987-0902788-8.

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14

Bahl, Monika, and P. Senthilkumaran. "Helmholtz Hodge decomposition of scalar optical fields." Journal of the Optical Society of America A 29, no. 11 (October 22, 2012): 2421. http://dx.doi.org/10.1364/josaa.29.002421.

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15

Guo, Qinghong, Mrinal K. Mandal, and Micheal Y. Li. "Efficient Hodge–Helmholtz decomposition of motion fields." Pattern Recognition Letters 26, no. 4 (March 2005): 493–501. http://dx.doi.org/10.1016/j.patrec.2004.08.008.

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16

PIRASHVILI, T. "Hodge decomposition for higher order Hochschild homology." Annales Scientifiques de l’École Normale Supérieure 33, no. 2 (March 2000): 151–79. http://dx.doi.org/10.1016/s0012-9593(00)00107-5.

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17

Miura, Keiji, and Takaaki Aoki. "Hodge–Kodaira decomposition of evolving neural networks." Neural Networks 62 (February 2015): 20–24. http://dx.doi.org/10.1016/j.neunet.2014.05.021.

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18

Arai, Asao, and Itaru Mitoma. "De Rham-Hodge-Kodaire decomposition in ?-dimensions." Mathematische Annalen 291, no. 1 (March 1991): 51–73. http://dx.doi.org/10.1007/bf01445190.

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19

Haufe, Daniel, Johannes Gürtler, Anita Schulz, Friedrich Bake, Lars Enghardt, and Jürgen Czarske. "Aeroacoustic analysis using natural Helmholtz–Hodge decomposition." Journal of Sensors and Sensor Systems 7, no. 1 (March 1, 2018): 113–22. http://dx.doi.org/10.5194/jsss-7-113-2018.

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Abstract. The analysis of aeroacoustic phenomena is crucial for a deeper understanding of the damping mechanisms of a sound-absorbing bias flow liner (BFL). For this purpose, simultaneous measurements of the sound field and the flow field in a BFL are required. The fluid velocity can serve as the measurand, where both the acoustic particle velocity and the aerodynamic flow velocity contribute and, thus, can be acquired simultaneously. However, there is a need to separate these two quantities to distinguish between them. This is challenging because they generally coincide with each other in the time domain. Due to the interaction of sound and flow in a BFL, both velocities also overlap in the temporal frequency domain, having a coherent oscillation at the acoustic frequency. For this reason, the recently developed natural Helmholtz–Hodge decomposition (NHHD) is applied to separate both quantities from the measured oscillation velocity field in the spatial domain. The evaluation of synthetic vector field data shows that the quality of the decomposition is enhanced when a smaller grid size is chosen. The velocity field in a generic BFL, necessarily recorded within a three-dimensional region of interest at more than 4000 measurement locations, is evaluated using NHHD. As a result, the measured oscillation velocity in the BFL is dominated by the flow that is related to vortices and also by irrotational aerodynamic flow. Moreover, indications for an aeroacoustic source near the facing sheet of the liner are revealed.
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20

Gong, Fu-Zhou, and Feng-Yu Wang. "On Gromov's theorem andL 2-Hodge decomposition." International Journal of Mathematics and Mathematical Sciences 2004, no. 1 (2004): 25–44. http://dx.doi.org/10.1155/s0161171204210365.

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Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the correspondingL 2-harmonic sections. In particular, some known results concerning Gromov's theorem and theL 2-Hodge decomposition are considerably improved.
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21

Speliotopoulos, Achilles D., and Harry L. Morrison. "The Hodge decomposition and the vortex hamiltonian." Physics Letters A 141, no. 5-6 (November 1989): 278–84. http://dx.doi.org/10.1016/0375-9601(89)90485-4.

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22

Sushch, Volodymyr. "2D Discrete Hodge–Dirac Operator on the Torus." Symmetry 14, no. 8 (July 28, 2022): 1556. http://dx.doi.org/10.3390/sym14081556.

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We discuss a discretization of the de Rham–Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge–Dirac and Laplace operators in which key geometric aspects of the continuum counterpart are captured. We provide and prove a discrete version of the Hodge decomposition theorem. The goal of this work is to develop a satisfactory discrete model of the de Rham–Hodge theory on manifolds that are homeomorphic to the torus. Special attention has been paid to discrete models on a combinatorial torus. In this particular case, we also define and calculate the cohomology groups.
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23

MALIK, R. P. "BRST COHOMOLOGY AND HODGE DECOMPOSITION THEOREM IN ABELIAN GAUGE THEORY." International Journal of Modern Physics A 15, no. 11 (April 30, 2000): 1685–705. http://dx.doi.org/10.1142/s0217751x00000756.

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We discuss the Becchi–Rouet–Stora–Tyutin (BRST) cohomology and Hodge decomposition theorem for the two-dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We take a single photon state in the quantum Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem, transversality of photon and establish the topological nature of this theory by exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In fact, the topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. On the two-dimensional compact manifold, we derive two sets of topological invariants with respect to the conserved and nilpotent BRST- and co-BRST charges and express the Lagrangian density of the theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of both Witten- and Schwarz-type of topological field theories.
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24

Gu, Jian Tao, Chun Xia Gao, and Yu Xia Tong. "Local Boundedness for Very Weak Solutions of Leray-Lions Equation." Advanced Materials Research 457-458 (January 2012): 210–13. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.210.

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25

Hajłasz, Piotr. "A counterexample to the $L^{p}$-Hodge decomposition." Banach Center Publications 33, no. 1 (1996): 79–83. http://dx.doi.org/10.4064/-33-1-79-83.

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26

Suda, Tomoharu. "Construction of Lyapunov functions using Helmholtz–Hodge decomposition." Discrete & Continuous Dynamical Systems - A 39, no. 5 (2019): 2437–54. http://dx.doi.org/10.3934/dcds.2019103.

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27

Slupinski, M. J. "A Hodge type decomposition for spinor valued forms." Annales scientifiques de l'École normale supérieure 29, no. 1 (1996): 23–48. http://dx.doi.org/10.24033/asens.1734.

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28

Ferone, A., M. A. Jalal, J. M. Rakotoson, and R. Volpicelli. "Some refinements of the Hodge decomposition and applications." Applied Mathematics Letters 14, no. 1 (January 2001): 75–79. http://dx.doi.org/10.1016/s0893-9659(00)00115-4.

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29

Henkin, Gennadi M., and Peter L. Polyakov. "Explicit Hodge-Type Decomposition on Projective Complete Intersections." Journal of Geometric Analysis 26, no. 1 (October 13, 2015): 672–713. http://dx.doi.org/10.1007/s12220-015-9643-1.

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30

Zhong, Chunping, and Tongde Zhong. "Hodge decomposition theorem on strongly Kähler Finsler manifolds." Science in China Series A: Mathematics 49, no. 11 (November 2006): 1696–714. http://dx.doi.org/10.1007/s11425-006-2055-8.

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31

Varma, Sandeep. "On linear Hodge-Newton decomposition for reductive monoids." Semigroup Forum 85, no. 3 (December 21, 2011): 381–416. http://dx.doi.org/10.1007/s00233-011-9366-y.

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32

Kasuya, Hisashi. "Hodge symmetry and decomposition on non-Kähler solvmanifolds." Journal of Geometry and Physics 76 (February 2014): 61–65. http://dx.doi.org/10.1016/j.geomphys.2013.10.012.

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33

Yuan, Jing, Christoph Schnörr, and Gabriele Steidl. "Convex Hodge Decomposition and Regularization of Image Flows." Journal of Mathematical Imaging and Vision 33, no. 2 (November 26, 2008): 169–77. http://dx.doi.org/10.1007/s10851-008-0122-1.

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34

Kasuya, Hisashi. "Flat Bundles and Hyper-Hodge Decomposition on Solvmanifolds." International Mathematics Research Notices 2015, no. 19 (December 4, 2014): 9638–59. http://dx.doi.org/10.1093/imrn/rnu244.

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35

Guo, Qinghong, Mrinal K. Mandal, Gang Liu, and Katherine M. Kavanagh. "Cardiac video analysis using Hodge–Helmholtz field decomposition." Computers in Biology and Medicine 36, no. 1 (January 2006): 1–20. http://dx.doi.org/10.1016/j.compbiomed.2004.06.011.

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36

Gerstenhaber, Murray, and S. D. Schack. "A hodge-type decomposition for commutative algebra cohomology." Journal of Pure and Applied Algebra 48, no. 1-2 (September 1987): 229–47. http://dx.doi.org/10.1016/0022-4049(87)90112-5.

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37

Xu, Xu Juan, Jian Tao Gu, and Xiao Li Liu. "Uniqueness for Very Weak Solution to a Class of Elliptic Equations." Advanced Materials Research 457-458 (January 2012): 863–66. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.863.

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38

UPADHYAY, SUDHAKER, and BHABANI PRASAD MANDAL. "NONCOMMUTATIVE GAUGE THEORIES: MODEL FOR HODGE THEORY." International Journal of Modern Physics A 28, no. 25 (October 8, 2013): 1350122. http://dx.doi.org/10.1142/s0217751x13501224.

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The nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra, as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.
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39

Kottwitz, Robert, and Eva Viehmann. "Generalized affine Springer fibres." Journal of the Institute of Mathematics of Jussieu 11, no. 3 (January 3, 2012): 569–609. http://dx.doi.org/10.1017/s147474801100020x.

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AbstractThis paper studies two new kinds of affine Springer fibres that are adapted to the root valuation strata of Goresky–Kottwitz–MacPherson. In addition it develops various linear versions of Katz's Hodge–Newton decomposition.
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40

Harikumar, E., R. P. Malik, and M. Sivakumar. "Hodge decomposition theorem for Abelian two-form gauge theory." Journal of Physics A: Mathematical and General 33, no. 40 (September 29, 2000): 7149–63. http://dx.doi.org/10.1088/0305-4470/33/40/312.

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41

Turchin, Victor. "Hodge-type decomposition in the homology of long knots." Journal of Topology 3, no. 3 (2010): 487–534. http://dx.doi.org/10.1112/jtopol/jtq015.

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42

Heckenberger, István, and Axel Schüler. "De Rham Cohomology and Hodge Decomposition For Quantum Groups." Proceedings of the London Mathematical Society 83, no. 3 (November 2001): 743–68. http://dx.doi.org/10.1112/plms/83.3.743.

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43

Wu, Jie, Murray Gerstenhaber, and James Stasheff. "On the Hodge decomposition of differential graded bi-algebras." Journal of Pure and Applied Algebra 162, no. 1 (August 2001): 103–25. http://dx.doi.org/10.1016/s0022-4049(00)00166-3.

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44

Alvarez López, Jesús A., and Philippe Tondeur. "Hodge decomposition along the leaves of a Riemannian foliation." Journal of Functional Analysis 99, no. 2 (August 1991): 443–58. http://dx.doi.org/10.1016/0022-1236(91)90048-a.

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45

Hanlon, Phil, and Patricia Hersh. "A Hodge decomposition for the complex of injective words." Pacific Journal of Mathematics 214, no. 1 (March 1, 2004): 109–25. http://dx.doi.org/10.2140/pjm.2004.214.109.

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46

Chuang, Joseph, and Andrey Lazarev. "Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras." Letters in Mathematical Physics 89, no. 1 (March 25, 2009): 33–49. http://dx.doi.org/10.1007/s11005-009-0314-7.

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47

Wang, Chunlin, and Liping Yang. "Newton polygons for L-functions of generalized Kloosterman sums." Forum Mathematicum 34, no. 1 (December 1, 2021): 77–96. http://dx.doi.org/10.1515/forum-2021-0220.

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Abstract In the present paper, we study the Newton polygons for the L-functions of n-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon. In order to determine the Hodge polygon, we explicitly construct a basis of the top-dimensional Dwork cohomology. Using Wan’s decomposition theorem and diagonal local theory, we obtain when the Newton polygon coincides with the Hodge polygon. In particular, we concretely get the slope sequence for the L-function of F ¯ ⁢ ( λ ¯ , x ) := ∑ i = 1 n x i a i + λ ¯ ⁢ ∏ i = 1 n x i - 1 , \bar{F}(\bar{\lambda},x):=\sum_{i=1}^{n}x_{i}^{a_{i}}+\bar{\lambda}\prod_{i=1}% ^{n}x_{i}^{-1}, with a 1 , … , a n {a_{1},\ldots,a_{n}} being pairwise coprime for n ≥ 2 {n\geq 2} .
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48

Bhatia, Harsh, Valerio Pascucci, and Peer-Timo Bremer. "The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis." IEEE Transactions on Visualization and Computer Graphics 20, no. 11 (November 2014): 1566–78. http://dx.doi.org/10.1109/tvcg.2014.2312012.

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49

Poon, Yat Sun, and John Simanyi. "A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds." Complex Manifolds 4, no. 1 (February 23, 2017): 137–54. http://dx.doi.org/10.1515/coma-2017-0009.

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Abstract A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bicomplex where one of the two operators is the classical მ̄-operator, while the other operator is the adjoint action of the Poisson bivector with respect to the Schouten-Nijenhuis bracket. The first page of the associated spectral sequence is the Dolbeault cohomology with coefficients in the sheaf of germs of holomorphic polyvector fields. In this note, the authors investigate the conditions for which this spectral sequence degenerates on the first page when the underlying complex manifolds are nilmanifolds with an abelian complex structure. For a particular class of holomorphic Poisson structures, this result leads to a Hodge-type decomposition of the holomorphic Poisson cohomology. We provide examples when the nilmanifolds are 2-step.
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50

Baratchart, Laurent, Pei Dang, and Tao Qian. "Hardy-Hodge decomposition of vector fields in $\mathbb {R}^n$." Transactions of the American Mathematical Society 370, no. 3 (September 15, 2017): 2005–22. http://dx.doi.org/10.1090/tran/7202.

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