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Journal articles on the topic 'Spectral Sequences (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Liu, Youming, and Yuesheng Xu. "Piecewise linear spectral sequences." Proceedings of the American Mathematical Society 133, no. 8 (March 21, 2005): 2297–308. http://dx.doi.org/10.1090/s0002-9939-05-08067-6.

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2

Culver, Dominic Leon, Hana Jia Kong, and J. D. Quigley. "Algebraic slice spectral sequences." Documenta Mathematica 26 (2021): 1085–119. http://dx.doi.org/10.4171/dm/836.

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3

Romero, A., J. Rubio, and F. Sergeraert. "Computing spectral sequences." Journal of Symbolic Computation 41, no. 10 (October 2006): 1059–79. http://dx.doi.org/10.1016/j.jsc.2006.06.002.

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4

Turner, James M. "Operations and Spectral Sequences. I." Transactions of the American Mathematical Society 350, no. 9 (1998): 3815–35. http://dx.doi.org/10.1090/s0002-9947-98-02254-5.

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5

CORNEA, O., K. A. DE REZENDE, and M. R. DA SILVEIRA. "Spectral sequences in Conley’s theory." Ergodic Theory and Dynamical Systems 30, no. 4 (October 13, 2009): 1009–54. http://dx.doi.org/10.1017/s0143385709000479.

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AbstractIn this paper, we analyse the dynamics encoded in the spectral sequence (Er,dr) associated with certain Conley theory connection maps in the presence of an ‘action’ type filtration. More specifically, we present an algorithm for finding a chain complex C and its differential; the method uses a connection matrix Δ to provide a system that spans Er in terms of the original basis of C and to identify all of the differentials drp:Erp→Erp−r. In exploring the dynamical implications of a non-zero differential, we prove the existence of a path that joins the singularities generating E0p and E0p−r in the case where a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow, and proves to be important in some applications.

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6

Kapranov, Mikhail, and Evangelos Routis. "Complete complexes and spectral sequences." Pure and Applied Mathematics Quarterly 13, no. 2 (2017): 215–46. http://dx.doi.org/10.4310/pamq.2017.v13.n2.a2.

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7

Coons, Michael, James Evans, and Neil Mañibo. "Spectral theory of regular sequences." Documenta Mathematica 27 (2022): 629–53. http://dx.doi.org/10.4171/dm/880.

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8

Fujisawa, Taro. "Degeneration of weight spectral sequences." manuscripta mathematica 108, no. 1 (May 1, 2002): 91–121. http://dx.doi.org/10.1007/s002290200256.

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9

Bousfield, A. K. "Homotopy spectral sequences and obstructions." Israel Journal of Mathematics 66, no. 1-3 (December 1989): 54–104. http://dx.doi.org/10.1007/bf02765886.

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10

Livernet, Muriel, and Sarah Whitehouse. "Homotopy theory of spectral sequences." Homology, Homotopy and Applications 26, no. 1 (2024): 69–86. http://dx.doi.org/10.4310/hha.2024.v26.n1.a5.

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11

Lisica, Ju T. "Theory of spectral sequences. II." Journal of Mathematical Sciences 146, no. 1 (October 2007): 5530–51. http://dx.doi.org/10.1007/s10958-007-0367-z.

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12

HURTUBISE, DAVID E. "MULTICOMPLEXES AND SPECTRAL SEQUENCES." Journal of Algebra and Its Applications 09, no. 04 (August 2010): 519–30. http://dx.doi.org/10.1142/s0219498810004087.

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In this note, we present some algebraic examples of multicomplexes whose differentials differ from those in the spectral sequences associated to the multicomplexes. The motivation for constructing examples showing the algebraic distinction between a multicomplex and its associated spectral sequence comes from the author's work on Morse–Bott homology with A. Banyaga [A. Banyaga and D. E. Hurtubise, Morse–Bott homology, Trans. Amer. Math. Soc. (to appear), arXiv:math/0612316v2].

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13

Baas, Nils A. "Book Review: Cobordisms and spectral sequences." Bulletin of the American Mathematical Society 33, no. 01 (January 1, 1996): 111–14. http://dx.doi.org/10.1090/s0273-0979-96-00622-2.

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14

Wagemann, Friedrich. "Spectral sequences for commutative Lie algebras." Communications in Mathematics 28, no. 2 (September 1, 2020): 123–37. http://dx.doi.org/10.2478/cm-2020-0015.

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AbstractWe construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2. In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley--Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.

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15

Welschinger, Jean-Yves. "Spectral sequences of a Morse shelling." Homology, Homotopy and Applications 24, no. 2 (2022): 241–54. http://dx.doi.org/10.4310/hha.2022.v24.n2.a11.

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16

Kalai, Gil, and Roy Meshulam. "RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES." Mathematika 67, no. 3 (June 26, 2021): 730–37. http://dx.doi.org/10.1112/mtk.12103.

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17

Cirici, Joana, Daniela Egas Santander, Muriel Livernet, and Sarah Whitehouse. "Model category structures and spectral sequences." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (August 1, 2019): 2815–48. http://dx.doi.org/10.1017/prm.2019.45.

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AbstractLet R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage.

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18

Millionshchikov, D. V. "Spectral sequences in analytic homotopy theory." Mathematical Notes of the Academy of Sciences of the USSR 47, no. 5 (May 1990): 458–64. http://dx.doi.org/10.1007/bf01158088.

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19

Oda, Nobuyuki, and Yoshimi Shitanda. "On the unstable homotopy spectral sequences." Manuscripta Mathematica 56, no. 1 (March 1986): 19–35. http://dx.doi.org/10.1007/bf01171031.

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20

Baues, Hans-Joachim, David Blanc, and Boris Chorny. "Truncated derived functors and spectral sequences." Homology, Homotopy and Applications 23, no. 1 (2021): 159–89. http://dx.doi.org/10.4310/hha.2021.v23.n1.a10.

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21

Àlvarez Montaner, Josep, Alberto F. Boix, and Santiago Zarzuela. "On Some Local Cohomology Spectral Sequences." International Mathematics Research Notices 2020, no. 19 (August 24, 2018): 6197–293. http://dx.doi.org/10.1093/imrn/rny186.

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Abstract We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by applying a family of functors to a single module. For the 2nd type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their 2nd page. As a consequence we obtain some decomposition theorems that greatly generalize the well-known decomposition formula for local cohomology modules of Stanley–Reisner rings given by Hochster.

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22

Künzer, Matthias. "Comparison of spectral sequences involving bifunctors." Documenta Mathematica 13 (2008): 677–737. http://dx.doi.org/10.4171/dm/257.

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23

Kozak, P. S., M. M. Luz, and M. P. Moklyachuk. "Minimax prediction of sequences with periodically stationary increments." Carpathian Mathematical Publications 13, no. 2 (August 18, 2021): 352–76. http://dx.doi.org/10.15330/cmp.13.2.352-376.

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The problem of optimal estimation of linear functionals constructed from unobserved values of a stochastic sequence with periodically stationary increments based on its observations at points $ k<0$ is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favourable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

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24

Massey, W. S. "Book Review: User's guide to spectral sequences." Bulletin of the American Mathematical Society 16, no. 1 (January 1, 1987): 135–44. http://dx.doi.org/10.1090/s0273-0979-1987-15489-9.

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25

Bartłomiejczyk, Piotr. "Spectral sequences and detailed connection matrices." Topological Methods in Nonlinear Analysis 36, no. 1 (September 1, 2009): 187. http://dx.doi.org/10.12775/tmna.2009.037.

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26

Luz, M. M., and M. P. Moklyachuk. "Robust interpolation of sequences with periodically stationary multiplicative seasonal increments." Carpathian Mathematical Publications 14, no. 1 (June 13, 2022): 105–26. http://dx.doi.org/10.15330/cmp.14.1.105-126.

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We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the interpolation problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal interpolation of the functionals. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear interpolation of the functionals are proposed in the case where spectral densities of the sequences are not exactly known while some sets of admissible spectral densities are given.

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27

Farsi, Carla, Frédéric Latrémolière, and Judith Packer. "Convergence of inductive sequences of spectral triples for the spectral propinquity." Advances in Mathematics 437 (February 2024): 109442. http://dx.doi.org/10.1016/j.aim.2023.109442.

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28

Huebschmann, Johannes. "Change of rings and characteristic classes." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (July 1989): 29–56. http://dx.doi.org/10.1017/s0305004100067967.

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AbstractWe construct characteristic classes for the change of rings spectral sequences. These have their values in appropriate Ext groups and provide descriptions of the first non-zero differentials in the spectral sequences. We use these classes to do some calculations in the cohomology spectral sequence of an extension of a finite cyclic group by a finite cyclic group.

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29

JORDAN, JONATHAN. "COMB GRAPHS AND SPECTRAL DECIMATION." Glasgow Mathematical Journal 51, no. 1 (January 2009): 71–81. http://dx.doi.org/10.1017/s0017089508004540.

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AbstractWe investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics,Math. Phys. Anal. Geometry6(2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.

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30

Nakayama, Chikara. "Degeneration of l -adic weight spectral sequences." American Journal of Mathematics 122, no. 4 (2000): 721–33. http://dx.doi.org/10.1353/ajm.2000.0030.

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31

Saito, Takeshi. "WEIGHT SPECTRAL SEQUENCES AND INDEPENDENCE OF $\ell$." Journal of the Institute of Mathematics of Jussieu 2, no. 4 (October 2003): 583–634. http://dx.doi.org/10.1017/s1474748003000173.

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32

Popovici, Dan. "Degeneration at E2 of certain spectral sequences." International Journal of Mathematics 27, no. 14 (December 2016): 1650111. http://dx.doi.org/10.1142/s0129167x16501111.

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We propose a Hodge theory for the spaces [Formula: see text] featuring at the second step either in the Frölicher spectral sequence of an arbitrary compact complex manifold [Formula: see text] or in the spectral sequence associated with a pair [Formula: see text] of complementary regular holomorphic foliations on such a manifold. The main idea is to introduce a Laplace-type operator associated with a given Hermitian metric on [Formula: see text] whose kernel in every bidegree [Formula: see text] is isomorphic to [Formula: see text] in either of the two situations discussed. The surprising aspect is that this operator is not a differential operator since it involves a harmonic projection, although it depends on certain differential operators. We then use this Hodge isomorphism for [Formula: see text] to give sufficient conditions for the degeneration at [Formula: see text] of the spectral sequence considered in each of the two cases in terms of the existence of certain metrics on [Formula: see text]. For example, in the Frölicher case, we prove degeneration at [Formula: see text] if there exists an SKT metric [Formula: see text] (i.e. such that [Formula: see text]) whose torsion is small compared to the spectral gap of the elliptic operator [Formula: see text] defined by [Formula: see text]. In the foliated case, we obtain degeneration at [Formula: see text] under a hypothesis involving the Laplacians [Formula: see text] and [Formula: see text] associated with the splitting [Formula: see text] induced by the foliated structure.

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33

Vinogradov, A. M., and J. Moreno. "Domains in infinite jet spaces: -spectral sequences." Doklady Mathematics 75, no. 2 (April 2007): 204–7. http://dx.doi.org/10.1134/s1064562407020081.

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34

Fernández, Marisa, Raúl Ibáñez, and Manuel de León. "The canonical spectral sequences for poisson manifolds." Israel Journal of Mathematics 106, no. 1 (December 1998): 133–55. http://dx.doi.org/10.1007/bf02773464.

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35

Dwyer, William, Haynes Miller, and Joseph Neisendorfer. "Fibrewise completion and unstable Adams spectral sequences." Israel Journal of Mathematics 66, no. 1-3 (December 1989): 160–78. http://dx.doi.org/10.1007/bf02765891.

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36

Gérard, Patrick, and Sandrine Grellier. "Inverse spectral problems for compact Hankel operators." Journal of the Institute of Mathematics of Jussieu 13, no. 2 (April 18, 2013): 273–301. http://dx.doi.org/10.1017/s1474748013000121.

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AbstractGiven two arbitrary sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $ of real numbers satisfying $$\begin{eqnarray*}\displaystyle \vert {\lambda }_{1} \vert \gt \vert {\mu }_{1} \vert \gt \vert {\lambda }_{2} \vert \gt \vert {\mu }_{2} \vert \gt \cdots \gt \vert {\lambda }_{j} \vert \gt \vert {\mu }_{j} \vert \rightarrow 0, &&\displaystyle\end{eqnarray*}$$ we prove that there exists a unique sequence $c= ({c}_{n} )_{n\in { \mathbb{Z} }_{+ } } $, real valued, such that the Hankel operators ${\Gamma }_{c} $ and ${\Gamma }_{\tilde {c} } $ of symbols $c= ({c}_{n} )_{n\geq 0} $ and $\tilde {c} = ({c}_{n+ 1} )_{n\geq 0} $, respectively, are selfadjoint compact operators on ${\ell }^{2} ({ \mathbb{Z} }_{+ } )$ and have the sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $, respectively, as non-zero eigenvalues. Moreover, we give an explicit formula for $c$ and we describe the kernel of ${\Gamma }_{c} $ and of ${\Gamma }_{\tilde {c} } $ in terms of the sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $. More generally, given two arbitrary sequences $({\rho }_{j} )_{j\geq 1} $ and $({\sigma }_{j} )_{j\geq 1} $ of positive numbers satisfying $$\begin{eqnarray*}\displaystyle {\rho }_{1} \gt {\sigma }_{1} \gt {\rho }_{2} \gt {\sigma }_{2} \gt \cdots \gt {\rho }_{j} \gt {\sigma }_{j} \rightarrow 0, &&\displaystyle\end{eqnarray*}$$ we describe the set of sequences $c= ({c}_{n} )_{n\in { \mathbb{Z} }_{+ } } $ of complex numbers such that the Hankel operators ${\Gamma }_{c} $ and ${\Gamma }_{\tilde {c} } $ are compact on ${\ell }^{2} ({ \mathbb{Z} }_{+ } )$ and have sequences $({\rho }_{j} )_{j\geq 1} $ and $({\sigma }_{j} )_{j\geq 1} $, respectively, as non-zero singular values.

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37

Li, Haitao, and Dunyan Yan. "Characterizations of multi-knot piecewise linear spectral sequences." Advances in Computational Mathematics 27, no. 4 (June 15, 2006): 401–22. http://dx.doi.org/10.1007/s10444-005-9006-8.

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38

Gu, Yan, Rui Wang, and Dunyan Yan. "Multidimensional multi-knots piecewise linear spectral sequences." Analysis in Theory and Applications 26, no. 4 (December 2010): 367–82. http://dx.doi.org/10.1007/s10496-010-0367-6.

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39

KILIAS, T. "GENERATION OF PSEUDO-CHAOTIC SEQUENCES." International Journal of Bifurcation and Chaos 04, no. 03 (June 1994): 709–13. http://dx.doi.org/10.1142/s0218127494000502.

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This paper deals with the spectral properties of pseudo-random signals generated in maximum-length shift registers. It is shown that infinitely long registers are comparable in behavior with one-dimensional discrete-time chaotic maps. Therefore the theory, results and tools developed for chaotic systems can be applied to the design of the spectral properties of maximum-length shift register sequences.

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40

Bielińska-Wa̧ż, Dorota. "Four-component spectral representation of DNA sequences." Journal of Mathematical Chemistry 47, no. 1 (February 12, 2009): 41–51. http://dx.doi.org/10.1007/s10910-009-9535-3.

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41

Chen, Dongmei, Zhibing Chen, and Xiao-Dong Zhang. "Spectral radius of uniform hypergraphs and degree sequences." Frontiers of Mathematics in China 12, no. 6 (January 14, 2017): 1279–88. http://dx.doi.org/10.1007/s11464-017-0626-3.

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42

Giraud, L., S. Gratton, and E. Martin. "Incremental spectral preconditioners for sequences of linear systems." Applied Numerical Mathematics 57, no. 11-12 (November 2007): 1164–80. http://dx.doi.org/10.1016/j.apnum.2007.01.005.

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43

Jordan, Jonathan. "The spectra of the Laplacians of fractal graphs not satisfying spectral decimation." Proceedings of the Edinburgh Mathematical Society 53, no. 3 (August 12, 2010): 731–46. http://dx.doi.org/10.1017/s0013091508000898.

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AbstractWe consider the spectra of the Laplacians of two sequences of fractal graphs in the context of the general theory introduced by Sabot in 2003. For the sequence of graphs associated with the pentagasket, we give a description of the eigenvalues in terms of the iteration of a map from (ℂ2)3 to itself. For the sequence of graphs introduced in a previous paper by the author, we show that the results found therein can be related to Sabot's theory.

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44

Jian, Xiao Er. "Jet Cohomology of Isolated Hypersurface Singularities and Spectral Sequences." Transactions of the American Mathematical Society 349, no. 2 (1997): 547–77. http://dx.doi.org/10.1090/s0002-9947-97-01689-9.

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45

Lapin, S. V. "D -Differentials and A -Structures in Spectral Sequences." Journal of Mathematical Sciences 123, no. 4 (October 2004): 4221–54. http://dx.doi.org/10.1023/b:joth.0000039819.04730.a1.

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46

Ivanov, Sergei O., Roman Mikhailov, and Jie Wu. "Leibniz Rule on Higher Pages of Unstable Spectral Sequences." Proceedings of the Edinburgh Mathematical Society 61, no. 1 (February 2018): 265–82. http://dx.doi.org/10.1017/s0013091517000220.

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A natural composition ⊙ on all pages of the lower central series spectral sequence for spheres is defined. Moreover, it is defined for the p-lower central series spectral sequence of a simplicial group. It is proved that the rth differential satisfies a ‘Leibniz rule with suspension’: dr(a ⊙ σ b) = ±dra ⊙ b + a ⊙ dr σ b, where σ is the suspension homomorphism.

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47

Andler, Martin. "Jean Leray. 7 November 1906 — 10 November 1998." Biographical Memoirs of Fellows of the Royal Society 52 (January 2006): 137–48. http://dx.doi.org/10.1098/rsbm.2006.0011.

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Jean Leray was one of the major mathematicians of the twentieth century. His primary focus in mathematics came from applications; indeed, a majority of his contributions were in the theory of partial differential equations arising in physics, notably his 1934 paper on the Navier–Stokes equation. World War II, during which he was a prisoner–of–war in Austria for five years, induced him to turn to pure mathematics to avoid helping the German war effort. There he worked in topology, developing two radically new ideas: sheaf theory and spectral sequences. After 1950 he came back to partial differential equations and became interested in complex analysis, writing a remarkable series of papers on the Cauchy problem. Leray remained mathematically active until the end of his life; in the course of his career he wrote 132 papers. His influence on present mathematics is tremendous. On the one hand, sheaf theory and spectral sequences became essential tools in contemporary pure mathematics, reaching far beyond their initial scope in topology. On the other hand, Leray can rightly be considered the intellectual guide of the distinguished French school of applied mathematics.

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48

Soltani, A. R., and Z. Shishebor. "Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization." gmj 6, no. 1 (February 1999): 91–98. http://dx.doi.org/10.1515/gmj.1999.91.

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Abstract Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {An } ⊂ be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (Spectral theory of periodically and quasi-periodically stationary SαS sequences, University of North Carolina, Chapel Hill, 1991). In this work we proceed further to characterize {An } by a positive measure μ and a number T of -valued functions a 0, . . . , a T–1; in the spectral form , where and Φ is an -valued Borel set function on [0, 2π) such that (Φ(Δ)x, Φ(Δ′)x′) Y = (x, x′) X μ(Δ ∩ Δ′).

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49

Vati, Kedumetse, and László Székelyhidi. "Moment functions on hypergroup joins." Advances in Pure and Applied Mathematics 10, no. 3 (July 1, 2019): 215–20. http://dx.doi.org/10.1515/apam-2018-0027.

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Abstract Moment functions play a basic role in probability theory. A natural generalization can be defined on hypergroups which leads to the concept of generalized moment function sequences. In a former paper we studied some function classes on hypergroup joins which play a basic role in spectral synthesis. Moment functions are also important basic blocks of spectral synthesis. All these functions can be characterized by well-known functional equations. In this paper we describe generalized moment function sequences on hypergroup joins.

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50

Yagita, Nobuaki. "Applications of Atiyah–Hirzebruch spectral sequences for motivic cobordism." Proceedings of the London Mathematical Society 90, no. 03 (April 22, 2005): 783–816. http://dx.doi.org/10.1112/s0024611504015084.

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