• Title/Summary/Keyword: spectral sequence

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The Spectral Radii of Graphs with Prescribed Degree Sequence

  • Li, Jianxi;Shiu, Wai Chee
    • Kyungpook Mathematical Journal
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    • v.54 no.3
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    • pp.425-441
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    • 2014
  • In this paper, we first present the properties of the graph which maximize the spectral radius among all graphs with prescribed degree sequence. Using these results, we provide a somewhat simpler method to determine the unicyclic graph with maximum spectral radius among all unicyclic graphs with a given degree sequence. Moreover, we determine the bicyclic graph which has maximum spectral radius among all bicyclic graphs with a given degree sequence.

Impact of the Spectral Linewidth of a Pseudorandom Binary Sequence (PRBS)-Modulated Laser on Stimulated Brillouin Scattering and Beam Quality

  • Aeri Jung;Sanggwon Song;Kwang Hyun Lee;Jung Hwan Lee;Kyunghwan Oh
    • Current Optics and Photonics
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    • v.7 no.6
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    • pp.665-672
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    • 2023
  • This study focuses on investigating the impact of the spectral linewidth of a seed laser in a master-oscillator power amplifier (MOPA) configuration on stimulated Brillouin scattering and the beam quality of the output diffracted by a grating. To conduct the study, a distributed feedback (DFB) laser is modulated in a pseudorandom binary sequence (PRBS) and amplified by a two-stage Yb-doped fiber amplifier to achieve an output power of over 1 kW. The spectral linewidth of the seed laser is systematically varied from 1 to 12 GHz in the frequency domain by varying the PRBS modulation parameters. The experimental results reveal a tradeoff between suppressing stimulated Brillouin scattering and enhancing beam quality with increased spectral linewidth. Therefore, the study provides valuable insights into optimizing spectral beam combining to achieve high beam quality and scalable power upgrade in fiber lasers.

ON THE EXTENSION PROBLEM IN THE ADAMS SPECTRAL SEQUENCE CONVERGING TO $BP_*(\Omega^2S^{2n+1})$

  • Choi, Young-Gi
    • Journal of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.633-644
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    • 2001
  • Revenel computed the Adams spectral sequence converging to BP(Ω$^2$S(sup)2n+1) and got the E(sub)$\infty$-term. Then he gave the conjecture about the extension. Here we prove that there should be non-trivial extension. We also study the BP(sub)*BP comodule structures on the polynomial algebras which are related with BP(sub)*(Ω$^2$S(sup)2n+1).

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NON-TRIVIALITY OF TWO HOMOTOPY ELEMENTS IN π*S

  • Liu Xiugui
    • Journal of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.783-801
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    • 2006
  • Let A be the mod p Steenrod algebra for p an arbitrary odd prime and S the sphere spectrum localized at p. In this paper, some useful propositions about the May spectral sequence are first given, and then, two new nontrivial homotopy elements ${\alpha}_1{\jmath}{\xi}_n\;(p{\geq}5,n\;{\geq}\;3)\;and\;{\gamma}_s{\alpha}_1{\jmath}{\xi}_n\;(p\;{\geq}\;7,\;n\;{\geq}\;4)$ are detected in the stable homotopy groups of spheres, where ${\xi}_n\;{\in}\;{\pi}_{p^nq+pq-2}M$ is obtained in [2]. The new ones are of degree 2(p - 1)($p^n+p+1$) - 4 and 2(p - 1)($p^n+sp^2$ + sp + (s - 1)) - 7 and are represented up to nonzero scalar by $b_0h_0h_n,\;b_0h_0h_n\tilde{\gamma}_s\;{\neq}\;0\;{\in}\;Ext^{*,*}_A^(Z_p,\;Z_p)$ in the Adams spectral sequence respectively, where $3\;{\leq}\;s\;<\;p-2$.

ALGEBRAIC SPECTRAL SUBSPACES OF OPERATORS WITH FINITE ASCENT

  • Han, Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.4
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    • pp.677-686
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    • 2016
  • Algebraic spectral subspaces were introduced by Johnson and Sinclair via a transnite sequence of spaces. Laursen simplified the definition of algebraic spectral subspace. Algebraic spectral subspaces are useful in automatic continuity theory of intertwining linear operators on Banach spaces. In this paper, we characterize algebraic spectral subspaces of operators with finite ascent. From this characterization we show that if T is a generalized scalar operator, then T has finite ascent.