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Journal articles on the topic 'Length spectrum'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

PONG, WAI YAN. "LENGTH SPECTRA OF NATURAL NUMBERS." International Journal of Number Theory 05, no. 06 (2009): 1089–102. http://dx.doi.org/10.1142/s1793042109002584.

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A natural number n can generally be written as a sum of m consecutive natural numbers for various values of m ≥ 1. The length spectrum of n is the set of these admissible m. Two numbers are spectral equivalent if they have the same length spectrum. We show how to compute the equivalence classes of this relation. Moreover, we show that these classes can only have either 1,2 or infinitely many elements.

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2

Stoyanov, Luchezar. "On the scattering length spectrum." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 325, no. 11 (1997): 1169–74. http://dx.doi.org/10.1016/s0764-4442(97)83548-3.

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3

Biswas, Debabrata. "Length spectrum of chaotic billiards." Physical Review Letters 71, no. 17 (1993): 2714–17. http://dx.doi.org/10.1103/physrevlett.71.2714.

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4

Sormani, Christina. "Convergence and the length spectrum." Advances in Mathematics 213, no. 1 (2007): 405–39. http://dx.doi.org/10.1016/j.aim.2007.01.001.

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5

Khanevsky, Michael. "Hofer's length spectrum of symplectic surfaces." Journal of Modern Dynamics 9, no. 01 (2015): 219–35. http://dx.doi.org/10.3934/jmd.2015.9.219.

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6

Schenck, Emmanuel. "Exponential gaps in the length spectrum." Journal of Modern Dynamics 16 (2020): 207–23. http://dx.doi.org/10.3934/jmd.2020007.

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7

Canary, Richard D., and Christopher J. Leininger. "Kleinian groups with discrete length spectrum." Bulletin of the London Mathematical Society 39, no. 2 (2007): 189–93. http://dx.doi.org/10.1112/blms/bdl005.

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8

Nozari, K., and P. Pedram. "Minimal length and bouncing-particle spectrum." EPL (Europhysics Letters) 92, no. 5 (2010): 50013. http://dx.doi.org/10.1209/0295-5075/92/50013.

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9

Popov, Georgi S. "Length spectrum invariants of Riemannian manifolds." Mathematische Zeitschrift 213, no. 1 (1993): 311–51. http://dx.doi.org/10.1007/bf03025724.

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10

Stoyanov, L. "Rigidity of the scattering length spectrum." Mathematische Annalen 324, no. 4 (2002): 743–71. http://dx.doi.org/10.1007/s00208-002-0358-9.

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11

BERLINKOV, ARTEMI, and BORIS SOLOMYAK. "Singular substitutions of constant length." Ergodic Theory and Dynamical Systems 39, no. 9 (2018): 2384–402. http://dx.doi.org/10.1017/etds.2017.133.

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We consider primitive aperiodic substitutions of constant length $q$ and prove that, in order to have a Lebesgue component in the spectrum of the associated dynamical system, it is necessary that one of the eigenvalues of the substitution matrix equals $\sqrt{q}$ in absolute value. The proof is based on results of Queffélec combined with estimates of the local dimension of the spectral measure at zero.

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12

Guillarmou and Lefeuvre. "The marked length spectrum of Anosov manifolds." Annals of Mathematics 190, no. 1 (2019): 321. http://dx.doi.org/10.4007/annals.2019.190.1.6.

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13

Dolgopyat, Dmitry, and Dmitry Jakobson. "On small gaps in the length spectrum." Journal of Modern Dynamics 10, no. 02 (2016): 339–52. http://dx.doi.org/10.3934/jmd.2016.10.339.

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14

Turner, M. S., and M. E. Cates. "The relaxation spectrum of polymer length distributions." Journal de Physique 51, no. 4 (1990): 307–16. http://dx.doi.org/10.1051/jphys:01990005104030700.

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15

Bendjoudi, Ahmida, and Noureddine Mebarki. "The quantum tetrahedron and the length spectrum." International Journal of Modern Physics D 26, no. 06 (2016): 1750044. http://dx.doi.org/10.1142/s0218271817500444.

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A new independent approach to the granularity of space is derived. The Bohr–Sommerfeld length spectrum is computed and discussed. Some values of the spectrum are given and compared with those found canonically elsewhere.

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16

Šarić, Dragomir. "Earthquakes in the length-spectrum Teichmüller spaces." Proceedings of the American Mathematical Society 143, no. 4 (2014): 1531–43. http://dx.doi.org/10.1090/s0002-9939-2014-12242-8.

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17

Kapovich, Ilya. "Random length-spectrum rigidity for free groups." Proceedings of the American Mathematical Society 140, no. 5 (2012): 1549–60. http://dx.doi.org/10.1090/s0002-9939-2011-11030-x.

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18

Grácio, Clara, and J. Sousa Ramos. "Geodesic length spectrum on compact Riemann surfaces." Journal of Geometry and Physics 60, no. 11 (2010): 1643–55. http://dx.doi.org/10.1016/j.geomphys.2010.06.006.

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19

Hu, Jun, and Francisco G. Jimenez-Lopez. "Length spectrum characterization of asymptotic Teichmüller space." Monatshefte für Mathematik 186, no. 1 (2018): 73–91. http://dx.doi.org/10.1007/s00605-018-1176-9.

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20

Schaller, Paul Schmutz. "The modular torus has maximal length spectrum." Geometric and Functional Analysis 6, no. 6 (1996): 1057–73. http://dx.doi.org/10.1007/bf02246996.

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21

Bonahon, Francis. "Surfaces with the same marked length spectrum." Topology and its Applications 50, no. 1 (1993): 55–62. http://dx.doi.org/10.1016/0166-8641(93)90072-l.

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22

Gornet, Ruth, and Maura B. Mast. "Length minimizing geodesics and the length spectrum of Riemannian two-step nilmanifolds." Journal of Geometric Analysis 13, no. 1 (2003): 107–43. http://dx.doi.org/10.1007/bf02931000.

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23

Popov, Georgi. "Invariants of the length spectrum and spectral invariants of planar convex domains." Communications in Mathematical Physics 161, no. 2 (1994): 335–64. http://dx.doi.org/10.1007/bf02099782.

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24

Jwo, Dah-Jing, I.-Hua Wu, and Yi Chang. "Windowing Design and Performance Assessment for Mitigation of Spectrum Leakage." E3S Web of Conferences 94 (2019): 03001. http://dx.doi.org/10.1051/e3sconf/20199403001.

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This paper investigates the windowing design and performance assessment for mitigation of spectral leakage. A pretreatment method to reduce the spectral leakage is developed. In addition to selecting appropriate window functions, the Welch method is introduced. Windowing is implemented by multiplying the input signal with a windowing function. The periodogram technique based on Welch method is capable of providing good resolution if data length samples are selected optimally. Windowing amplitude modulates the input signal so that the spectral leakage is evened out. Thus, windowing reduces the

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25

Buffett, G. G., C. A. Hurich, E. A. Vsemirnova, et al. "Stochastic heterogeneity mapping around a Mediterranean salt lens." Ocean Science Discussions 7, no. 1 (2010): 1–15. http://dx.doi.org/10.5194/osd-7-1-2010.

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Abstract. We present the first application of stochastic heterogeneity mapping based on the band-limited von Kármán function to a seismic reflection stack of a Mediterranean water eddy (meddy), a large salt lens of Mediterranean water. This process extracts two stochastic parameters directly from the reflectivity field of the seismic data: the Hurst number, which ranges from 0 to 1, and the correlation length (scale length). Lower Hurst numbers represent a richer range of scale lengths and correspond to a broader range of reflection events. The Hurst number estimate for the top of the meddy (0

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26

Taylor, Michael. "Scattering Length and the Spectrum of –Δ + V". Canadian Mathematical Bulletin 49, № 1 (2006): 144–51. http://dx.doi.org/10.4153/cmb-2006-015-5.

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AbstractGiven a non-negative, locally integrable functionV on ℝn, we give a necessary and sufficient condition that –Δ + V have purely discrete spectrum, in terms of the scattering length ofV restricted to boxes.

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27

Gušić, Dž. "On generalized length spectrum in quotients of SL4." Journal of Physics: Conference Series 1564 (June 2020): 012023. http://dx.doi.org/10.1088/1742-6596/1564/1/012023.

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28

Akhoury, R., and Y. P. Yao. "Minimal length uncertainty relation and the hydrogen spectrum." Physics Letters B 572, no. 1-2 (2003): 37–42. http://dx.doi.org/10.1016/j.physletb.2003.07.084.

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29

Abramson, Arthur S., and Nianqi Reo. "Distinctive vowel length: duration vs. spectrum in Thai." Journal of Phonetics 18, no. 2 (1990): 79–92. http://dx.doi.org/10.1016/s0095-4470(19)30395-x.

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30

Gallopoulos, A., C. Heegard, and P. H. Siegel. "The power spectrum of run-length-limited codes." IEEE Transactions on Communications 37, no. 9 (1989): 906–17. http://dx.doi.org/10.1109/26.35370.

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31

GORNET, R., and M. MAST. "The length spectrum of Riemannian two-step nilmanifolds1." Annales Scientifiques de l’École Normale Supérieure 33, no. 2 (2000): 181–209. http://dx.doi.org/10.1016/s0012-9593(00)00111-7.

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32

Meyerhoff, G. "The ortho-length spectrum for hyperbolic 3-manifolds." Quarterly Journal of Mathematics 47, no. 187 (1996): 349–59. http://dx.doi.org/10.1093/qjmath/47.187.349.

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33

Sormani, Christina, and Guofang Wei. "The covering spectrum of a compact length space." Journal of Differential Geometry 67, no. 1 (2004): 35–77. http://dx.doi.org/10.4310/jdg/1099587729.

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34

MEYERHOFF, G. ROBERT. "THE ORTHO-LENGTH SPECTRUM FOR HYPERBOLIC 3-MANIFOLDS." Quarterly Journal of Mathematics 47, no. 3 (1996): 349–59. http://dx.doi.org/10.1093/qmath/47.3.349.

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35

Hassani, Hossein, Rahim Mahmoudvand, and Mohammad Zokaei. "Separability and window length in singular spectrum analysis." Comptes Rendus Mathematique 349, no. 17-18 (2011): 987–90. http://dx.doi.org/10.1016/j.crma.2011.07.012.

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36

Wang, Rui, Hong-Guang Ma, Guo-Qing Liu, and Dong-Guang Zuo. "Selection of window length for singular spectrum analysis." Journal of the Franklin Institute 352, no. 4 (2015): 1541–60. http://dx.doi.org/10.1016/j.jfranklin.2015.01.011.

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37

Sharp, Richard. "Degeneracy in the length spectrum for metric graphs." Geometriae Dedicata 149, no. 1 (2010): 177–88. http://dx.doi.org/10.1007/s10711-010-9475-x.

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38

Maungchang, Rasimate. "The Sunada construction and the simple length spectrum." Geometriae Dedicata 163, no. 1 (2012): 349–60. http://dx.doi.org/10.1007/s10711-012-9753-x.

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39

Biswas, Debabrata. "Universality in the length spectrum of integrable systems." Pramana 42, no. 6 (1994): 447–53. http://dx.doi.org/10.1007/bf02847126.

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40

Gornet, Ruth. "The marked length spectrum vs. the Laplace spectrum on forms on Riemannian nilmanifolds." Commentarii Mathematici Helvetici 71, no. 1 (1996): 297–329. http://dx.doi.org/10.1007/bf02566421.

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41

Liu, Shen, Fu Ping Wang, and Xiu Cheng Liu. "UM2000 Spectrum Estimation Using Multiple Signal Classification Method." Advanced Materials Research 734-737 (August 2013): 2622–29. http://dx.doi.org/10.4028/www.scientific.net/amr.734-737.2622.

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This paper focused on UM2000 signal spectrum estimation using MUSIC algorithm. Because of the limitation of data window length, traditional frequency discrimination methods fail to meet the requirement of high frequency resolution. In this paper, the influence of SNR on MUSIC spectrum estimation is analyzed and MDL (minimum description length) principle is used to determine the dimension of the signal. Simulation results based on several other modern spectral estimation methods are also presented and compared with that of MUSIC method, from which the superiority of MUSIC method is verified.

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42

Kume, Kenji, and Naoko Nose-Togawa. "Additive Decomposition of Power Spectrum Density in Singular Spectrum Analysis." Advances in Data Science and Adaptive Analysis 08, no. 01 (2016): 1650003. http://dx.doi.org/10.1142/s2424922x16500030.

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Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging lead to a time-series decomposition. In this paper, we propose an novel algorithm for the additive decomposition of the power spectrum density of a time series based on the filtering interpretation of SSA. This can be used to examine the spectral overlap or the admixture of the SSA decomposition. We can obtain insights into the spectral structure of the SSA decomposition which helps us for the proper

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43

Su, Bo Ni, Hong Xie, and Xi Yao Hua. "The Simulation Research of Classic Spectrum Estimation Periodogram Method Based on Matlab." Advanced Materials Research 926-930 (May 2014): 2857–60. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.2857.

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The spectrum estimation is a main content of modern signal processing, it is very important for random signal detection and analysis. This paper researched the classical spectrum estimation method, simulated the periodogram method, Barlett method, and Welch method of power spectrum estimation, then mainly discussed the spectral resolution about different length of data, also discussed the resolution of the spectral estimation and the performance of variance in the different way.

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44

Tokovyy, Yu V. "Cosserat Spectrum of an Axisymmetric Elasticity Problem for a Finite-Length Solid Cylinder." Journal of Mechanics 35, no. 3 (2018): 343–49. http://dx.doi.org/10.1017/jmech.2018.6.

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ABSTRACTAn algorithm for the computation and analysis of the Cosserat spectrum for an axisymmetric elasticity boundary-value problem in a finite-length solid cylinder with boundary conditions in terms of stresses is proposed. By making use of the cross-wise superposition method, the spectral problem is reduced to systems of linear algebraic equations. A solution method for the mentioned systems is presented and the asymptotic behavior of the Cosserat eigenvalues is established. On this basis, the key features of the Cosserat spectrum for the mentioned problem are analyzed with special attentio

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45

CONSTANTINE, DAVID, and JEAN-FRANÇOIS LAFONT. "Marked length rigidity for Fuchsian buildings." Ergodic Theory and Dynamical Systems 39, no. 12 (2018): 3262–91. http://dx.doi.org/10.1017/etds.2018.12.

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We consider finite $2$-complexes $X$ that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT($-1$) metrics on $X$, which are piecewise hyperbolic and satisfy a natural non-singularity condition at vertices, are marked length spectrum rigid within certain classes of negatively curved, piecewise Riemannian metrics on $X$. As a key step in our proof, we show that the marked length spectrum function for such metrics determines the volume of $X$.

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46

Anantharaman, Nalini, Maxime Ingremeau, Mostafa Sabri, and Brian Winn. "Absolutely Continuous Spectrum for Quantum Trees." Communications in Mathematical Physics 383, no. 1 (2021): 537–94. http://dx.doi.org/10.1007/s00220-021-03994-3.

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AbstractWe study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.

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47

Thomas Barthelmé. "On deformations of the spectrum of a Finsler-Laplacian that preserve the length spectrum." Bulletin de la Société mathématique de France 145, no. 3 (2017): 421–48. http://dx.doi.org/10.24033/bsmf.2743.

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48

Judge, R. H., D. C. Moule, A. Biernacki, M. Benkel, J. M. Ross, and J. Rustenburg. "Laser excitation spectrum and the long path length absorption spectrum of formyl cyanide, CHOCN." Journal of Molecular Spectroscopy 116, no. 2 (1986): 364–70. http://dx.doi.org/10.1016/0022-2852(86)90133-5.

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49

SONG, H., U. C. PAEK, and D. Y. KIM. "WALK-OFF LENGTH LIMITED SPECTRAL BROADENING IN SUPERCONTINUUM GENERATION." Journal of Nonlinear Optical Physics & Materials 18, no. 01 (2009): 99–110. http://dx.doi.org/10.1142/s0218863509004464.

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Detailed spectrum broadening mechanisms in supercontinuum (SC) generation are studied with an all-fiber pulsed laser source and a highly nonlinear dispersion-shifted fiber (HN-DSF). Mode-locked fiber laser pulses are stretched to four different pulse widths, and SC spectra are measured with different propagation distances with these pulses. By observing the development of spectral width with distance, we have observed that self-phase modulation (SPM) rather than soliton fission is the dominant process at the beginning of SC generation in our case. We have also confirmed that four-wave mixing (

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50

Fotiy, O., M. Ostrovskii, and M. Popov. "Isomorphic spectrum and isomorphic length of a Banach space." Carpathian Mathematical Publications 12, no. 1 (2020): 88–93. http://dx.doi.org/10.15330/cmp.12.1.88-93.

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We prove that, given any ordinal $\delta < \omega_2$, there exists a transfinite $\delta$-sequence of separable Banach spaces $(X_\alpha)_{\alpha < \delta}$ such that $X_\alpha$ embeds isomorphically into $X_\beta$ and contains no subspace isomorphic to $X_\beta$ for all $\alpha < \beta < \delta$. All these spaces are subspaces of the Banach space $E_p = \bigl( \bigoplus_{n=1}^\infty \ell_p \bigr)_2$, where $1 \leq p < 2$. Moreover, assuming Martin's axiom, we prove the same for all ordinals $\delta$ of continuum cardinality.

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