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1

Vince, A. "Discrete Lines and Wandering Paths." SIAM Journal on Discrete Mathematics 21, no. 3 (2007): 647–61. http://dx.doi.org/10.1137/050642009.

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2

Braun, Volker. "Discrete Wilson Lines in F-Theory." Advances in High Energy Physics 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/404691.

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F-theory models are constructed where the7-brane has a nontrivial fundamental group. The base manifolds used are a toric Fano variety and a smooth toric threefold coming from a reflexive polyhedron. The discriminant locus of the elliptically fibered Calabi-Yau fourfold can be chosen such that one irreducible component is not simply connected (namely, an Enriques surface) and supports a non-Abelian gauge theory.
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3

Suri, Rajan, and Bor-Ruey Fu. "On using continuous flow lines to model discrete production lines." Discrete Event Dynamic Systems: Theory and Applications 4, no. 2 (1994): 129–69. http://dx.doi.org/10.1007/bf01441209.

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4

ARRIBAS, E., C. GALLARDO, M. MOLINA, and V. SANJOSÉ. "Electric Field Lines." International Journal of Modern Physics C 02, no. 01 (1991): 216–19. http://dx.doi.org/10.1142/s0129183191000196.

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We present the computer program called LINES which is able to calculate and visualize the electric field lines due to seven different discrete configurations of electric point charges. Also we show two examples of the graphic screens generated by LINES.
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5

MOHAUPT, THOMAS. "ORBIFOLD COMPACTIFICATIONS WITH CONTINUOUS WILSON LINES." International Journal of Modern Physics A 09, no. 26 (1994): 4637–68. http://dx.doi.org/10.1142/s0217751x94001850.

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We identify the untwisted moduli of heterotic orbifold compactifications for the case where the gauge twist is realized by a rotation. The Wilson lines are found to have both continuous and discrete parts. For the case of the standard Z3 orbifold we classify all possibilities of breaking the gauge group E(6) ⊗ SU (3) by nine of the eighteen Wilson moduli and by additional discrete Wilson lines.
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6

Basdevant, A.-L., N. Enriquez, L. Gerin, and J.-B. Gouéré. "Discrete Hammersley’s lines with sources and sinksm." Latin American Journal of Probability and Mathematical Statistics 13, no. 1 (2016): 33. http://dx.doi.org/10.30757/alea.v13-02.

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7

Chen, Hui, Lei Li, and Zhichao Zhang. "Similarity Transformation of Discrete Part Production Lines." Journal of Physics: Conference Series 1885, no. 3 (2021): 032024. http://dx.doi.org/10.1088/1742-6596/1885/3/032024.

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8

Kailath, T., A. Bruckstein, and D. Morgan. "Fast matrix factorizations via discrete transmission lines." Linear Algebra and its Applications 75 (March 1986): 1–25. http://dx.doi.org/10.1016/0024-3795(86)90178-3.

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9

Babaei, Vahid, and Roger D. Hersch. "Juxtaposed Color Halftoning Relying on Discrete Lines." IEEE Transactions on Image Processing 22, no. 2 (2013): 679–86. http://dx.doi.org/10.1109/tip.2012.2221727.

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10

Želinský, Tomáš, Jason Wei Jian Ng, and Martina Mysíková. "Estimating subjective poverty lines with discrete information." Economics Letters 196 (November 2020): 109545. http://dx.doi.org/10.1016/j.econlet.2020.109545.

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11

McIlroy, M. D. "A Note on Discrete Representation of Lines." AT&T Technical Journal 64, no. 2 (1985): 481–90. http://dx.doi.org/10.1002/j.1538-7305.1985.tb00359.x.

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12

Xiang, Q. "Difference Families From Lines and Half Lines." European Journal of Combinatorics 19, no. 3 (1998): 395–400. http://dx.doi.org/10.1006/eujc.1997.0193.

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13

Du, L., J. Ben, Y. Li, and R. Wang. "GENERATION ALGORITHM OF DISCRETE LINE IN MULTI-DIMENSIONAL GRIDS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W7 (September 12, 2017): 11–15. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w7-11-2017.

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Discrete Global Grids System (DGGS) is a kind of digital multi-resolution earth reference model, in terms of structure, it is conducive to the geographical spatial big data integration and mining. Vector is one of the important types of spatial data, only by discretization, can it be applied in grids system to make process and analysis. Based on the some constraint conditions, this paper put forward a strict definition of discrete lines, building a mathematic model of the discrete lines by base vectors combination method. Transforming mesh discrete lines issue in n-dimensional grids into the i
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14

Csajbók, Bence, Peter Sziklai, and Zsuzsa Weiner. "Renitent lines." European Journal of Combinatorics 114 (December 2023): 103792. http://dx.doi.org/10.1016/j.ejc.2023.103792.

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15

Khoshnoudirad, Daniel. "Farey lines defining Farey diagrams and application to some discrete structures." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 73–84. http://dx.doi.org/10.2298/aadm150219008k.

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The aim of the paper is to study some of the analytical properties of Farey diagrams of order (m,n), which are associated to the (m,n)-cubes, that is the pieces of discrete planes, occurring in discrete mathematics. We give a closed formula for the number of Farey lines defining Farey diagrams. This number asymptotically behaves as mn(m+n)=?(3). Then we establish the relation with some discrete structures in the field of discrete geometry in particular.
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16

Abdoulkary, Saïdou, Alidou Mohamadou, and Tibi Beda. "Exact traveling discrete kink-soliton solutions for the discrete nonlinear electrical transmission lines." Communications in Nonlinear Science and Numerical Simulation 16, no. 9 (2011): 3525–32. http://dx.doi.org/10.1016/j.cnsns.2010.12.029.

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17

Atkin, I. L., and E. Abraham. "Control of chaos in discrete Josephson transmission lines." IEEE Transactions on Appiled Superconductivity 7, no. 2 (1997): 2894–96. http://dx.doi.org/10.1109/77.621898.

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18

Love, A., W. A. Sabra, and S. Thomas. "Background symmetries in orbifolds with discrete Wilson lines." Nuclear Physics B 427, no. 1-2 (1994): 181–202. http://dx.doi.org/10.1016/0550-3213(94)90274-7.

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19

Jinook Song and In-Cheol Park. "Pipelined Discrete Wavelet Transform Architecture Scanning Dual Lines." IEEE Transactions on Circuits and Systems II: Express Briefs 56, no. 12 (2009): 916–20. http://dx.doi.org/10.1109/tcsii.2009.2035257.

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20

Karabati, Selcuk, Panagiotis Kouvelis, and Gang Yu. "The Discrete Resource Allocation Problem in Flow Lines." Management Science 41, no. 9 (1995): 1417–30. http://dx.doi.org/10.1287/mnsc.41.9.1417.

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21

Fovell, Robert G., Gretchen L. Mullendore, and Seung-Hee Kim. "Discrete Propagation in Numerically Simulated Nocturnal Squall Lines." Monthly Weather Review 134, no. 12 (2006): 3735–52. http://dx.doi.org/10.1175/mwr3268.1.

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Abstract Simulations of a typical midlatitude squall line were used to investigate a mechanism for discrete propagation, defined as convective initiation ahead of an existing squall line leading to a faster propagation speed for the storm complex. Radar imagery often shows new cells appearing in advance of squall lines, suggesting a causal relationship and prompting the search for an “action-at-a-distance” mechanism to explain the phenomenon. In the simulations presented, the identified mechanism involves gravity waves of both low and high frequency generated in response to the latent heating,
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22

Feng, Xianqun, and Jiafu Wan. "Digital Twins for Discrete Manufacturing Lines: A Review." Big Data and Cognitive Computing 8, no. 5 (2024): 45. http://dx.doi.org/10.3390/bdcc8050045.

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Along with the development of new-generation information technology, digital twins (DTs) have become the most promising enabling technology for smart manufacturing. This article presents a statistical analysis of the literature related to the applications of DTs for discrete manufacturing lines, researches their development status in the areas of the design and improvement of manufacturing lines, the scheduling and control of manufacturing line, and predicting faults in critical equipment. The deployment frameworks of DTs in different applications are summarized. In addition, this article disc
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23

Kara, M., A. Seçgin, and T. Baygün. "Discrete Singular Convolution Method for Acoustic Transmission Lines." Acoustics Australia 48, no. 2 (2020): 271–85. http://dx.doi.org/10.1007/s40857-020-00185-3.

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24

Schilli, Bruno, Günther Mechler, Alexander Fay, Peter Bort, and Rainer Drath. "EFFICIENT ENGINEERING OF FLEXIBLE ASSEMBLY LINES IN DISCRETE MANUFACTURING." IFAC Proceedings Volumes 39, no. 3 (2006): 479–84. http://dx.doi.org/10.3182/20060517-3-fr-2903.00251.

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25

Sato, M., S. Yasui, M. Kimura, T. Hikihara, and A. J. Sievers. "Management of localized energy in discrete nonlinear transmission lines." Europhysics Letters (EPL) 80, no. 3 (2007): 30002. http://dx.doi.org/10.1209/0295-5075/80/30002.

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26

Wang, Wenjie, Zhao Li, Liwen Jing, Qingfeng Zhang, and Ross D. Murch. "Super-Resolution of Discrete Point Faults in Transmission Lines." IEEE Transactions on Antennas and Propagation 68, no. 4 (2020): 3111–23. http://dx.doi.org/10.1109/tap.2019.2957088.

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27

Dulcic, A., R. H. Crepeau та J. H. Freed. "Discrete microwave absorption lines in YBa2Cu3O7−δ single crystals". Physica C: Superconductivity 160, № 3-4 (1989): 223–26. http://dx.doi.org/10.1016/0921-4534(89)90053-1.

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28

Chattopadhyay, S., and P. P. Das. "A new method of analysis for discrete straight lines." Pattern Recognition Letters 12, no. 12 (1991): 747–55. http://dx.doi.org/10.1016/0167-8655(91)90072-t.

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29

Mehrez, Abraham, and B. Eddy Patuwo. "Discrete unreliable transfer lines with exogenous random unit demand." Computers & Industrial Engineering 26, no. 2 (1994): 307–20. http://dx.doi.org/10.1016/0360-8352(94)90064-7.

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30

Gu, Xi, Seungchul Lee, Xinran Liang, Mark Garcellano, Mark Diederichs, and Jun Ni. "Hidden maintenance opportunities in discrete and complex production lines." Expert Systems with Applications 40, no. 11 (2013): 4353–61. http://dx.doi.org/10.1016/j.eswa.2013.01.016.

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31

Rörig, Thilo, and Gudrun Szewieczek. "The Ribaucour families of discrete R-congruences." Geometriae Dedicata 214, no. 1 (2021): 251–75. http://dx.doi.org/10.1007/s10711-021-00614-1.

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AbstractWhile a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete enveloping surfaces. The main purpose of this paper is to gain geometric insights into this ambiguity. In particular, discrete R-congruences that are enveloped by discrete channel surfaces and discrete Legendre maps with one family of spherical curvature lines are discussed.
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32

Nguyen, Duc Manh, and Sunghwan Kim. "The fog on: Generalized teleportation by means of discrete-time quantum walks on N-lines and N-cycles." Modern Physics Letters B 33, no. 23 (2019): 1950270. http://dx.doi.org/10.1142/s0217984919502701.

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The recent paper entitled “Generalized teleportation by means of discrete-time quantum walks on [Formula: see text]-lines and [Formula: see text]-cycles” by Yang et al. [Mod. Phys. Lett. B 33(6) (2019) 1950069] proposed the quantum teleportation by means of discrete-time quantum walks on [Formula: see text]-lines and [Formula: see text]-cycles. However, further investigation shows that the quantum walk over the one-dimensional infinite line can be based over the [Formula: see text]-cycles and cannot be based on [Formula: see text]-lines. The proofs of our claims on quantum walks based on finit
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33

ERLER, JENS, and MICHAŁ SPALIŃSKI. "MODULAR GROUPS FOR TWISTED NARAIN MODELS." International Journal of Modern Physics A 09, no. 25 (1994): 4407–29. http://dx.doi.org/10.1142/s0217751x94001758.

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We demonstrate how to find modular discrete symmetry groups for ZN orbifolds. The Z7 orbifold is treated in detail as a nontrivial example of a (2, 2) orbifold model. We give the generators of the modular group for this case which, surprisingly, does not contain SL (2; Z)3 as had been speculated. The treatment models with discrete Wilson lines are also discussed. We consider examples which demonstrate that discrete Wilson lines affect the modular group in a nontrivial manner. In particular, we show that it is possible for a Wilson line to break SL (2, Z).
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34

Froeschlé, Claude, and Elena Lega. "On the Diffusion Along Resonant Lines in Continuous and Discrete Dynamical Systems." International Journal of Modern Physics B 17, no. 22n24 (2003): 3964–76. http://dx.doi.org/10.1142/s0217979203023033.

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We detect and measure diffusion along resonances in a discrete symplectic map for different values of the coupling parameter. Qualitatively and quantitatively the results are very similar to those obtained for a quasi-integrable Hamiltonian system, i.e. in agreement with Nekhoroshev predictions, although the discrete mapping does not fulfill completely, a priori, the conditions of the Nekhoroshev theorem.
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35

Aronov, Boris, Otfried Cheong, Xavier Goaoc, and Günter Rote. "Lines Pinning Lines." Discrete & Computational Geometry 45, no. 2 (2010): 230–60. http://dx.doi.org/10.1007/s00454-010-9288-6.

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36

Beaudou, Laurent, Adrian Bondy, Xiaomin Chen, et al. "Lines in hypergraphs." Combinatorica 33, no. 6 (2013): 633–54. http://dx.doi.org/10.1007/s00493-013-2910-5.

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37

Deza, M., and V. P. Grishukhin. "Cut Lattices and Equiangular Lines." European Journal of Combinatorics 17, no. 2-3 (1996): 143–56. http://dx.doi.org/10.1006/eujc.1996.0013.

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38

REZAI-RAD, GHOLAMALI, and AHMAD CHELDAVI. "DISCRETE TIME-DOMAIN ANALYSIS OF NONUNIFORM LOSSLESS COUPLED TRANSMISSION LINES." Journal of Circuits, Systems and Computers 14, no. 05 (2005): 973–86. http://dx.doi.org/10.1142/s0218126605002763.

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In this paper, a discrete time-domain method to analyze multiple coupled nonuniform lossless transmission lines has been presented. The solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is decomposed into a large number of coupled steplines with different characteristics. Then, using modal decomposition method, the system of coupled partial differential equations for each step is decomposed to a set of uncoupled ordinary wave equation. Using time-dom
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39

Caputo, P., M. Darula, A. V. Ustinov, and H. Kohlstedt. "Fluxon dynamics in discrete Josephson transmission lines with stacked junctions." Journal of Applied Physics 81, no. 1 (1997): 309–14. http://dx.doi.org/10.1063/1.364110.

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40

Modeste Nguimdo, Romain, Samuel Noubissie, and Paul Woafo. "Waves Amplification in Discrete Nonlinear Electrical Lines: Direct Numerical Simulation." Journal of the Physical Society of Japan 77, no. 12 (2008): 124006. http://dx.doi.org/10.1143/jpsj.77.124006.

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41

Ho, K. P. "Broadcast digital subscriber lines using discrete multitone for broadband access." Microprocessors and Microsystems 22, no. 10 (1999): 605–10. http://dx.doi.org/10.1016/s0141-9331(99)00006-x.

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42

Demongodin, Isabel, and François Prunet. "Production Lines Modeling by Discrete / Continuous Aspect in Petri Nets." IFAC Proceedings Volumes 30, no. 19 (1997): 199–205. http://dx.doi.org/10.1016/s1474-6670(17)42299-3.

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43

Lim, Yun Fong, and Yue Wu. "Cellular Bucket Brigades on U-Lines with Discrete Work Stations." Production and Operations Management 23, no. 7 (2013): 1113–28. http://dx.doi.org/10.1111/poms.12091.

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44

Bauer, Ulrich, Konrad Polthier, and Max Wardetzky. "Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines." Discrete & Computational Geometry 43, no. 4 (2010): 798–823. http://dx.doi.org/10.1007/s00454-009-9237-4.

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45

Schramm, Oded, and Scott Sheffield. "Contour lines of the two-dimensional discrete Gaussian free field." Acta Mathematica 202, no. 1 (2009): 21–137. http://dx.doi.org/10.1007/s11511-009-0034-y.

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46

RABENSTEIN, R., and H. KRAUß. "DISCRETE SIMULATION OF UNIFORM TRANSMISSION LINES BY MULTIDIMENSIONAL DIGITAL FILTERS." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9, no. 4 (1996): 271–94. http://dx.doi.org/10.1002/(sici)1099-1204(199607)9:4<271::aid-jnm239>3.0.co;2-x.

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47

CHANG, FUNG-YUEL, and OMAR WING. "TRANSIENT SIMULATION OF LOSSY COUPLED TRANSMISSION LINES CHARACTERIZED WITH FREQUENCY-DEPENDENT PARAMETERS." International Journal of High Speed Electronics and Systems 02, no. 04 (1991): 319–53. http://dx.doi.org/10.1142/s0129156491000156.

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The method of characteristics is generalized to simulate the transient response of coupled transmission lines, which are characterized with frequency-dependent parameters. The discrete-time transient simulation is carried out from the equivalent decoupled transmission lines with an arbitrary set of characteristic impedances. The method eliminates the time-consuming convolution integration and has been adapted for iterative waveform relaxation simulation using the Fast Fourier Transform (FFT) for reduction of simulation cost. Examples are given to substantiate the accuracy and the efficiency of
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48

Bai, Yuchan, Jinyu Liu, Huihao Wu, Lei Fan, Renqing Li, and Jun Xing. "Sinusoidal Frequency Estimator by Using Interpolation of Four DTFT Spectral Lines." Journal of Physics: Conference Series 2564, no. 1 (2023): 012016. http://dx.doi.org/10.1088/1742-6596/2564/1/012016.

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Abstract This paper proposes a sinusoid frequency estimator by interpolating four Discrete Time Fourier Transform (DTFT) samples. Firstly, Discrete Fourier Transform (DFT) is performed on the received sinusoid. Then we find the positional information of the maximal DFT bin and obtain the coarse estimation results. Next, the proposed method uses four symmetrical DTFT samples on both sides of the maximal DFT bin to interpolate the signal frequency and obtain accurate estimation results. Simulation experiment results illustrate that the proposed method’s accuracy is higher than that of the compet
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49

Ballereau, D., J. Chauville, H. Cao, M. Floquet, A. M. Hubert та J. Zorec. "Discrete Structures in the CS Envelope of the Be star ζ Tau". International Astronomical Union Colloquium 175 (2000): 539–42. http://dx.doi.org/10.1017/s0252921100056451.

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AbstractThe recent cycle of the V/R ratio and RV variations in ζ Tau has been found similar to that reported by Delplace (1970). As a rule, in both cycles, singly-ionized metallic shell lines display discrete components when the descending branch of RV curve of Balmer lines crosses the stellar RV value; a narrow sharp feature is mainly superimposed on a broad and bluer one, both being slowly varying over some months; very weak additional components are suspected on stronger Fe II lines. On another hand, in the ascending branch of RV curve (RV ≥ RVstar), secondary shell components varying in in
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50

BARRERA VARGAS, WALDEMAR DEL JESÚS, ANGEL CANO CORDERO та JUAN PABLO NAVARRETE CARRILLO. "The limit set of discrete subgroups of PSL(3, ℂ)". Mathematical Proceedings of the Cambridge Philosophical Society 150, № 1 (2010): 129–46. http://dx.doi.org/10.1017/s0305004110000423.

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AbstractIf Γ is a discrete subgroup of PSL(3, ℂ), it is determined the equicontinuity region Eq(Γ) of the natural action of Γ on ℙ2ℂ. It is also proved that the action restricted to Eq(Γ) is discontinuous, and Eq(Γ) agrees with the discontinuity set in the sense of Kulkarni whenever the limit set of Γ in the sense of Kulkarni, Λ(Γ), contains at least three complex lines in general position. Under some additional hypothesis, it turns out to be the largest open set on which Γ acts discontinuously. Moreover, if Λ(Γ) contains at least four complex lines and Γ acts on ℙ2ℂ without fixed points nor i
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