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Journal articles on the topic 'Large sets'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Halmos, Paul R. "Large Intersections of Large Sets." American Mathematical Monthly 99, no. 4 (April 1992): 307. http://dx.doi.org/10.2307/2324896.

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2

Halmos, Paul R. "Large Intersections of Large Sets." American Mathematical Monthly 99, no. 4 (April 1992): 307–12. http://dx.doi.org/10.1080/00029890.1992.11995853.

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3

Komjáth, Péter. "Large small sets." Colloquium Mathematicum 56, no. 2 (1988): 231–33. http://dx.doi.org/10.4064/cm-56-2-231-233.

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4

Jervell, Herman Ruge. "Large Finite Sets." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 31, no. 35-36 (1985): 545–49. http://dx.doi.org/10.1002/malq.19850313502.

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5

Jasinski. "LARGE SETS CONTAINING COPIES OF SMALL SETS." Real Analysis Exchange 21, no. 2 (1995): 758. http://dx.doi.org/10.2307/44152689.

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6

Etzion, Tuvi, and Junling Zhou. "Large sets with multiplicity." Designs, Codes and Cryptography 89, no. 7 (May 20, 2021): 1661–90. http://dx.doi.org/10.1007/s10623-021-00878-4.

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7

Fraser, Robert, and Malabika Pramanik. "Large sets avoiding patterns." Analysis & PDE 11, no. 5 (April 11, 2018): 1083–111. http://dx.doi.org/10.2140/apde.2018.11.1083.

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8

Miller, DR, and DJ Quammen. "Exploiting large register sets." Microprocessors and Microsystems 14, no. 6 (July 1990): 333–40. http://dx.doi.org/10.1016/0141-9331(90)90105-5.

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9

Teirlinck, Luc. "Large sets with holes." Journal of Combinatorial Designs 1, no. 1 (1993): 69–94. http://dx.doi.org/10.1002/jcd.3180010108.

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10

Etzion, Tuvi. "Large sets of coverings." Journal of Combinatorial Designs 2, no. 5 (1994): 359–74. http://dx.doi.org/10.1002/jcd.3180020509.

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11

QingDe, KANG, and YUAN LanDang. "Large sets and overlarge sets of triple systems." SCIENTIA SINICA Mathematica 47, no. 11 (March 29, 2017): 1409–22. http://dx.doi.org/10.1360/n012016-00144.

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12

Tian, Zi-hong, and Qing-de Kang. "Large Sets and Overlarge Sets of Triangle-Decomposition." Acta Mathematicae Applicatae Sinica, English Series 23, no. 1 (January 2007): 123–32. http://dx.doi.org/10.1007/s10255-006-0356-x.

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13

Shkredov, I. D., and Sergey Yekhanin. "Sets with large additive energy and symmetric sets." Journal of Combinatorial Theory, Series A 118, no. 3 (April 2011): 1086–93. http://dx.doi.org/10.1016/j.jcta.2010.11.001.

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14

Alsallakh, Bilal, Wolfgang Aigner, Silvia Miksch, and Helwig Hauser. "Radial Sets: Interactive Visual Analysis of Large Overlapping Sets." IEEE Transactions on Visualization and Computer Graphics 19, no. 12 (December 2013): 2496–505. http://dx.doi.org/10.1109/tvcg.2013.184.

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15

Magyar, Ákos. "On distance sets of large sets of integer points." Israel Journal of Mathematics 164, no. 1 (March 2008): 251–63. http://dx.doi.org/10.1007/s11856-008-0028-z.

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16

Shelah, Saharon. "Borel sets with large squares." Fundamenta Mathematicae 159, no. 1 (1999): 1–50. http://dx.doi.org/10.4064/fm-159-1-1-50.

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17

Falconer, K. J. "Sets with Large Intersection Properties." Journal of the London Mathematical Society 49, no. 2 (April 1994): 267–80. http://dx.doi.org/10.1112/jlms/49.2.267.

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18

Pandiani, John A., and Steven M. Banks. "Large Data Sets Are Powerful." Psychiatric Services 54, no. 5 (May 2003): 745. http://dx.doi.org/10.1176/appi.ps.54.5.745.

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19

Segal, Steven P. "Large Data Sets Are Powerful." Psychiatric Services 54, no. 5 (May 2003): 745—a—746. http://dx.doi.org/10.1176/appi.ps.54.5.745-a.

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20

Drake, Robert E., and Gregory J. McHugo. "Large Data Sets Are Powerful." Psychiatric Services 54, no. 5 (May 2003): 746. http://dx.doi.org/10.1176/appi.ps.54.5.746.

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21

Landwehr, James M. "Clustering of Large Data Sets." Technometrics 29, no. 4 (November 1987): 497–98. http://dx.doi.org/10.1080/00401706.1987.10488298.

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22

Lauri, Josef. "Large sets of pseudosimilar vertices." Discrete Mathematics 155, no. 1-3 (August 1996): 157–60. http://dx.doi.org/10.1016/0012-365x(95)00379-b.

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23

Judah, Haim, and Otmar Spinas. "Large cardinals and projective sets." Archive for Mathematical Logic 36, no. 2 (February 1, 1997): 137–55. http://dx.doi.org/10.1007/s001530050059.

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24

Sadek, Mohammad, and Nermine El-Sissi. "On large F-Diophantine sets." Monatshefte für Mathematik 186, no. 4 (October 9, 2017): 703–10. http://dx.doi.org/10.1007/s00605-017-1106-2.

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25

Alvarado, José D., Simone Dantas, and Dieter Rautenbach. "Dominating sets inducing large components." Discrete Mathematics 339, no. 11 (November 2016): 2715–20. http://dx.doi.org/10.1016/j.disc.2016.05.016.

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26

STONE, A. H. "Covering Dimension from Large Sets." Annals of the New York Academy of Sciences 806, no. 1 Papers on Gen (December 1996): 438–43. http://dx.doi.org/10.1111/j.1749-6632.1996.tb49186.x.

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27

Koutsofios, E. E., S. C. North, and D. A. Keim. "Visualizing large telecommunication data sets." IEEE Computer Graphics and Applications 19, no. 3 (1999): 16–19. http://dx.doi.org/10.1109/38.761543.

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28

Ajoodani-Namini, S. "Extending Large Sets oft-Designs." Journal of Combinatorial Theory, Series A 76, no. 1 (October 1996): 139–44. http://dx.doi.org/10.1006/jcta.1996.0093.

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29

Braun, Michael, Michael Kiermaier, Axel Kohnert, and Reinhard Laue. "Large sets of subspace designs." Journal of Combinatorial Theory, Series A 147 (April 2017): 155–85. http://dx.doi.org/10.1016/j.jcta.2016.11.004.

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30

Graefe, John F., and Ronald W. Wood. "Dealing with large data sets." Neurotoxicology and Teratology 12, no. 5 (September 1990): 449–54. http://dx.doi.org/10.1016/0892-0362(90)90006-x.

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31

Toth, Gabor. "Convex Sets with Large Distortion." Journal of Geometry 92, no. 1-2 (February 17, 2009): 174–92. http://dx.doi.org/10.1007/s00022-009-1901-6.

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32

Laue, Reinhard, Spyros S. Magliveras, and Alfred Wassermann. "New large sets oft-designs." Journal of Combinatorial Designs 9, no. 1 (2001): 40–59. http://dx.doi.org/10.1002/1520-6610(2001)9:1<40::aid-jcd4>3.0.co;2-0.

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33

Zhang, Yanfang. "On large sets ofPk-decompositions." Journal of Combinatorial Designs 13, no. 6 (2005): 462–65. http://dx.doi.org/10.1002/jcd.20056.

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34

Khosrovshahi, G. B., and B. Tayfeh-Rezaie. "Large sets of t-designs through partitionable sets: A survey." Discrete Mathematics 306, no. 23 (December 2006): 2993–3004. http://dx.doi.org/10.1016/j.disc.2004.07.043.

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35

Goldring, Noa. "Measures: Back and Forth Between Point sets and Large sets." Bulletin of Symbolic Logic 1, no. 2 (June 1995): 170–88. http://dx.doi.org/10.2307/421039.

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It was questions about points on the real line that initiated the study of set theory. Points paved the way to point sets and these to ever more abstract sets. And there was more: Reflection on structural properties of point sets not only initiated the study of ordinary sets; it also supplied blueprints for defining extra-ordinary, “large” sets, transcending those provided by standard set theory. In return, the existence of such large sets turned out critical to settling open conjectures about point sets.How to explain such action at a distance between the very large and the rather small? Rather than having an air of magic, could these results rest on deep structural similarities between the two superficially distant species of sets?In this essay I dissect one group of such two-way results. Their linchpin is the notion of measure.§1. Vitali's impossibility result. Our starting point is a problem in measure theory regarding the notion of “Lebesgue measure.” Before presenting the problem, I would like to review the notion of Lebesgue measure. Rather than listing its main properties, I would like to show how Lebesgue measure is born out of an attempt to generalize the notion of the length of an interval to arbitrary sets of reals. One tries to approximate arbitrary sets of reals by intervals, in the hope that the lengths of the intervals will induce a measure on these sets.

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36

Lauer, Joseph, and Nicholas Wormald. "Large independent sets in regular graphs of large girth." Journal of Combinatorial Theory, Series B 97, no. 6 (November 2007): 999–1009. http://dx.doi.org/10.1016/j.jctb.2007.02.006.

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37

Alves, Thiago R., and Daniel Carando. "Holomorphic functions with large cluster sets." Mathematische Nachrichten 294, no. 7 (May 3, 2021): 1250–61. http://dx.doi.org/10.1002/mana.201900238.

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38

MURAI, Tetsuya. "Large Rough Sets and Modal Logics." Journal of Japan Society for Fuzzy Theory and Systems 13, no. 6 (2001): 571–80. http://dx.doi.org/10.3156/jfuzzy.13.6_571.

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39

ÇETİNKAYA, Zeynep, and Fahrettin HORASAN. "Decision Trees in Large Data Sets." Uluslararası Muhendislik Arastirma ve Gelistirme Dergisi 13, no. 1 (January 18, 2021): 140–51. http://dx.doi.org/10.29137/umagd.763490.

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40

De Boeck, Maarten, and Geertrui Van de Voorde. "A note on large Kakeya sets." Advances in Geometry 21, no. 3 (July 1, 2021): 401–5. http://dx.doi.org/10.1515/advgeom-2021-0018.

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Abstract A Kakeya set 𝓚 in an affine plane of order q is the point set covered by a set 𝓛 of q + 1 pairwise non-parallel lines. By Dover and Mellinger [6], Kakeya sets with size at least q 2 – 3q + 9 contain a large knot, i.e. a point of 𝓚 lying on many lines of 𝓛. We improve on this result by showing that Kakeya set of size at least ≈ q 2 – q + q contain a large knot, and we obtain a sharp result for planes containing a Baer subplane.

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41

Alon, Noga, and Mario Szegedy. "Large Sets of Nearly Orthogonal Vectors." Graphs and Combinatorics 15, no. 1 (March 1999): 1–4. http://dx.doi.org/10.1007/pl00021187.

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42

Yang, Robert (Xu). "Existence of large independent-like sets." Colloquium Mathematicum 159, no. 1 (2020): 107–18. http://dx.doi.org/10.4064/cm7649-11-2018.

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43

Coen, Frank, Nate Gillman, Tamás Keleti, Dylan King, and Jennifer Zhu. "Large sets with small injective projections." Annales Fennici Mathematici 46, no. 2 (2021): 683–702. http://dx.doi.org/10.5186/aasfm.2021.4622.

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44

Chen, Changhao. "Discretized sum-product for large sets." Moscow Journal of Combinatorics and Number Theory 9, no. 1 (January 8, 2020): 17–27. http://dx.doi.org/10.2140/moscow.2020.9.17.

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45

Park, Hongrak, Hyungtae Hwang, and Byungju Kim. "LS-SVM for large data sets." Journal of the Korean Data and Information Science Society 27, no. 2 (March 31, 2016): 549–57. http://dx.doi.org/10.7465/jkdi.2016.27.2.549.

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46

Hida, Clayton Suguio, and Piotr Koszmider. "Large Irredundant Sets in Operator Algebras." Canadian Journal of Mathematics 72, no. 4 (March 7, 2019): 988–1023. http://dx.doi.org/10.4153/s0008414x19000142.

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AbstractA subset ${\mathcal{X}}$ of a C*-algebra ${\mathcal{A}}$ is called irredundant if no $A\in {\mathcal{X}}$ belongs to the C*-subalgebra of ${\mathcal{A}}$ generated by ${\mathcal{X}}\setminus \{A\}$. Separable C*-algebras cannot have uncountable irredundant sets and all members of many classes of nonseparable C*-algebras, e.g., infinite dimensional von Neumann algebras have irredundant sets of cardinality continuum.There exists a considerable literature showing that the question whether every AF commutative nonseparable C*-algebra has an uncountable irredundant set is sensitive to additional set-theoretic axioms, and we investigate here the noncommutative case.Assuming $\diamondsuit$ (an additional axiom stronger than the continuum hypothesis), we prove that there is an AF C*-subalgebra of ${\mathcal{B}}(\ell _{2})$ of density $2^{\unicode[STIX]{x1D714}}=\unicode[STIX]{x1D714}_{1}$ with no nonseparable commutative C*-subalgebra and with no uncountable irredundant set. On the other hand we also prove that it is consistent that every discrete collection of operators in ${\mathcal{B}}(\ell _{2})$ of cardinality continuum contains an irredundant subcollection of cardinality continuum.Other partial results and more open problems are presented.

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47

Bigorajska, Teresa, and Henryk Kotlarski. "Some combinatorics involving ξ-large sets." Fundamenta Mathematicae 175, no. 2 (2002): 119–25. http://dx.doi.org/10.4064/fm175-2-2.

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48

Falconer, K. J. "Classes of sets with large intersection." Mathematika 32, no. 2 (December 1985): 191–205. http://dx.doi.org/10.1112/s0025579300010986.

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49

Carbery, Anthony. "Large sets with limited tube occupancy." Journal of the London Mathematical Society 79, no. 2 (March 16, 2009): 529–43. http://dx.doi.org/10.1112/jlms/jdn086.

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50

Garnett, John, and Stan Yoshinobu. "Large sets of zero analytic capacity." Proceedings of the American Mathematical Society 129, no. 12 (June 13, 2001): 3543–48. http://dx.doi.org/10.1090/s0002-9939-01-06261-x.

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