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Journal articles on the topic 'Density theorem'

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Published: 28 September 2022

Last updated: 28 October 2022

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1

Plewik. "UNIFORM DENSITY THEOREM." Real Analysis Exchange 25, no. 1 (1999): 65. http://dx.doi.org/10.2307/44153034.

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2

Gritsenko, S. A. "On a density theorem." Mathematical Notes 51, no. 6 (June 1992): 553–58. http://dx.doi.org/10.1007/bf01263297.

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3

Narins, Lothar, and Tuan Tran. "A Density Turán Theorem." Journal of Graph Theory 85, no. 2 (September 20, 2016): 496–524. http://dx.doi.org/10.1002/jgt.22075.

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4

Shin, Sug Woo. "Automorphic Plancherel density theorem." Israel Journal of Mathematics 192, no. 1 (February 28, 2012): 83–120. http://dx.doi.org/10.1007/s11856-012-0018-z.

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5

Avraamova, O. D. "On the density theorem." Russian Mathematical Surveys 44, no. 1 (February 28, 1989): 229–30. http://dx.doi.org/10.1070/rm1989v044n01abeh002019.

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6

Reiher, Christian. "The clique density theorem." Annals of Mathematics 184, no. 3 (November 1, 2016): 683–707. http://dx.doi.org/10.4007/annals.2016.184.3.1.

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7

Morgan, Frank. "Myers' theorem with density." Kodai Mathematical Journal 29, no. 3 (October 2006): 455–61. http://dx.doi.org/10.2996/kmj/1162478772.

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8

Stevenhagen, P., and H. W. Lenstra. "Chebotarëv and his density theorem." Mathematical Intelligencer 18, no. 2 (March 1996): 26–37. http://dx.doi.org/10.1007/bf03027290.

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9

Allen, Peter, Julia Böttcher, Jan Hladký, and Diana Piguet. "A density Corrádi-Hajnal theorem." Electronic Notes in Discrete Mathematics 38 (December 2011): 31–36. http://dx.doi.org/10.1016/j.endm.2011.09.006.

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10

Nagy, Á. "Density scaling and virial theorem." Molecular Physics 113, no. 13-14 (March 5, 2015): 1839–42. http://dx.doi.org/10.1080/00268976.2015.1017017.

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11

Allen, Peter, Julia Böttcher, Jan Hladký, and Diana Piguet. "A Density Corrádi–Hajnal Theorem." Canadian Journal of Mathematics 67, no. 4 (August 1, 2015): 721–58. http://dx.doi.org/10.4153/cjm-2014-030-6.

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AbstractWe find, for all sufficiently largenand eachk, the maximum number of edges in ann-vertex graph that does not containk+ 1 vertex-disjoint triangles.This extends a result of Moon [Canad. J.Math. 20 (1968), 96–102], which is in turn an extension of Mantel's Theorem. Our result can also be viewed as a density version of the Corrádi–Hajnal Theorem.

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12

Bienvenu, Laurent, Rupert Hölzl, Joseph S. Miller, and André Nies. "Denjoy, Demuth and density." Journal of Mathematical Logic 14, no. 01 (June 2014): 1450004. http://dx.doi.org/10.1142/s0219061314500044.

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We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy–Young–Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class 𝒞 ⊆ [0, 1] containing z has positive density at z. Under the stronger assumption that z is not LR-hard, we show that every such class has density one at z. These results have since been applied to solve two open problems on the interaction between the Turing degrees of Martin-Löf random reals and K-trivial sets: the noncupping and covering problems. We say that f : [0, 1] → ℝ satisfies the Denjoy alternative at z ∈ [0, 1] if either the derivative f′(z) exists, or the upper and lower derivatives at z are +∞ and -∞, respectively. The Denjoy–Young–Saks theorem states that every function f : [0, 1] → ℝ satisfies the Denjoy alternative at almost every z ∈ [0, 1]. We answer a question posed by Kučera in 2004 by showing that a real z is computably random if and only if every computable function f satisfies the Denjoy alternative at z. For Markov computable functions, which are only defined on computable reals, we can formulate the Denjoy alternative using pseudo-derivatives. Call a real zDA-random if every Markov computable function satisfies the Denjoy alternative at z. We considerably strengthen a result of Demuth (Comment. Math. Univ. Carolin.24(3) (1983) 391–406) by showing that every Turing incomplete Martin-Löf random real is DA-random. The proof involves the notion of nonporosity, a variant of density, which is the bridge between the two themes of this paper. We finish by showing that DA-randomness is incomparable with Martin-Löf randomness.

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13

Moser, Philippe. "Generic density and small span theorem." Information and Computation 206, no. 1 (January 2008): 1–14. http://dx.doi.org/10.1016/j.ic.2007.10.001.

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14

Bergelson, Vitaly. "A density statement generalizing Schur's theorem." Journal of Combinatorial Theory, Series A 43, no. 2 (November 1986): 338–43. http://dx.doi.org/10.1016/0097-3165(86)90074-9.

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15

Furche, Filipp, and Troy Van Voorhis. "Fluctuation-dissipation theorem density-functional theory." Journal of Chemical Physics 122, no. 16 (April 22, 2005): 164106. http://dx.doi.org/10.1063/1.1884112.

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16

Qin, HouRong, and QiQing Shen. "A density theorem and its application." Science China Mathematics 58, no. 8 (April 30, 2015): 1621–26. http://dx.doi.org/10.1007/s11425-015-4999-z.

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17

Wong, Peng-Jie. "Supercharacters and the Chebotarev density theorem." Acta Arithmetica 185, no. 3 (2018): 281–95. http://dx.doi.org/10.4064/aa180320-22-6.

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18

Byszewski, Jakub, and Jakub Konieczny. "A density version of Cobham’s theorem." Acta Arithmetica 192, no. 3 (2020): 235–47. http://dx.doi.org/10.4064/aa180626-13-1.

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19

Bihani, Prerna, and Renling Jin. "Kneser’s theorem for upper Banach density." Journal de Théorie des Nombres de Bordeaux 18, no. 2 (2006): 323–43. http://dx.doi.org/10.5802/jtnb.547.

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20

Żelazko, W. "A density theorem for F-spaces." Studia Mathematica 96, no. 2 (1990): 159–66. http://dx.doi.org/10.4064/sm-96-2-159-166.

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21

Friedland, Shmuel, Jingtong Ge, and Lihong Zhi. "Quantum Strassen’s theorem." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 03 (September 2020): 2050020. http://dx.doi.org/10.1142/s0219025720500204.

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Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen’s theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional.

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22

Kravvaritis, Dimitrie, and Gavriil Păltineanu. "A density theorem for locally convex lattices." Abstract and Applied Analysis 2004, no. 5 (2004): 387–93. http://dx.doi.org/10.1155/s1085337504303088.

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LetEbe a real, locally convex, locally solid vector lattice of (AM)-type. First, we prove an approximation theorem of Bishop's type for a vector subspace of such a lattice. Second, using this theorem, we obtain a generalization of Nachbin's density theorem for weightedspaces.

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23

Geelen, Jim, and Peter Nelson. "A density Hales–Jewett theorem for matroids." Journal of Combinatorial Theory, Series B 112 (May 2015): 70–77. http://dx.doi.org/10.1016/j.jctb.2014.11.008.

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24

Ferenczi, Sébastien, Jan Kwiatkowski, and Christian Mauduit. "A density theorem for (multiplicity, rank) pairs." Journal d'Analyse Mathématique 65, no. 1 (December 1995): 45–75. http://dx.doi.org/10.1007/bf02788765.

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25

Boya, Luis J., and Javier Casahorrán. "Theorem of Levinson via the Spectral Density." International Journal of Theoretical Physics 46, no. 8 (February 24, 2007): 1998–2012. http://dx.doi.org/10.1007/s10773-006-9321-y.

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26

Lieb, Elliott H., Michael Loss, and Robert J. McCann. "Uniform density theorem for the Hubbard model." Journal of Mathematical Physics 34, no. 3 (March 1993): 891–98. http://dx.doi.org/10.1063/1.530199.

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27

Grenié, Loïc, and Giuseppe Molteni. "An explicit Chebotarev density theorem under GRH." Journal of Number Theory 200 (July 2019): 441–85. http://dx.doi.org/10.1016/j.jnt.2018.12.005.

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28

Sury, B. "Frobenius and his Density theorem for primes." Resonance 8, no. 12 (December 2003): 33–41. http://dx.doi.org/10.1007/bf02839049.

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29

Hadwin, Don. "Subnormal operators and the Kaplansky density theorem." Mathematische Annalen 316, no. 2 (February 1, 2000): 201–13. http://dx.doi.org/10.1007/s002080050010.

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30

Nagy, Á., and Robert G. Parr. "Local virial theorem in density-functional theory." Physical Review A 42, no. 1 (July 1, 1990): 201–3. http://dx.doi.org/10.1103/physreva.42.201.

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31

Kowalski, Kenneth L. "Goldstone theorem at finite temperature and density." Physical Review D 35, no. 12 (June 15, 1987): 3940–43. http://dx.doi.org/10.1103/physrevd.35.3940.

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32

Woolley, R. G. "The density functional theorem and Hückel theories." Philosophical Magazine B 69, no. 5 (May 1994): 745–53. http://dx.doi.org/10.1080/01418639408240143.

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33

Dmitrašinović, V. "Extension of the chiral low-density theorem." Physical Review C 59, no. 5 (May 1, 1999): 2801–6. http://dx.doi.org/10.1103/physrevc.59.2801.

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34

Jacquet, Herve. "A theorem of density for Kloosterman integrals." Asian Journal of Mathematics 2, no. 4 (1998): 759–78. http://dx.doi.org/10.4310/ajm.1998.v2.n4.a7.

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35

Tsuneda, Takao, Jong-Won Song, Satoshi Suzuki, and Kimihiko Hirao. "On Koopmans’ theorem in density functional theory." Journal of Chemical Physics 133, no. 17 (November 7, 2010): 174101. http://dx.doi.org/10.1063/1.3491272.

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36

Chousionis, Vasilis, and Jeremy T. Tyson. "Marstrand's density theorem in the Heisenberg group." Bulletin of the London Mathematical Society 47, no. 5 (September 18, 2015): 771–88. http://dx.doi.org/10.1112/blms/bdv056.

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37

Faure, Claude-Alain. "A Short Proof of Lebesgue's Density Theorem." American Mathematical Monthly 109, no. 2 (February 2002): 194–96. http://dx.doi.org/10.1080/00029890.2002.11919854.

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38

Nagy, A. "Regional virial theorem in density-functional theory." Physical Review A 46, no. 9 (November 1, 1992): 5417–19. http://dx.doi.org/10.1103/physreva.46.5417.

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39

Cruz, Federico G., Kin-Chung Lam, and Kieron Burke. "Exchange−Correlation Energy Density from Virial Theorem." Journal of Physical Chemistry A 102, no. 25 (June 1998): 4911–17. http://dx.doi.org/10.1021/jp980950v.

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40

TALBI, Mohamed Elamine. "The density theorem for hermitian K-theory." TURKISH JOURNAL OF MATHEMATICS 42, no. 5 (September 9, 2018): 2380–88. http://dx.doi.org/10.3906/mat-1610-40.

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41

Saito, Hiroshi. "Global density theorem for a Federer measure." Tohoku Mathematical Journal 44, no. 4 (1992): 581–95. http://dx.doi.org/10.2748/tmj/1178227252.

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42

Thorner, Jesse, and Asif Zaman. "A unified and improved Chebotarev density theorem." Algebra & Number Theory 13, no. 5 (July 12, 2019): 1039–68. http://dx.doi.org/10.2140/ant.2019.13.1039.

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43

Groszek, Marcia J., Michael E. Mytilinaios, and Theodore A. Slaman. "The Sacks density theorem and Σ2-bounding." Journal of Symbolic Logic 61, no. 2 (June 1996): 450–67. http://dx.doi.org/10.2307/2275670.

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AbstractThe Sacks Density Theorem [7] states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of P− + BΣ2. The proof has two components: a lemma that in any model of P− + BΣ2, if B is recursively enumerable and incomplete then IΣ1 holds relative to B and an adaptation of Shore's [9] blocking technique in α-recursion theory to models of arithmetic.

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44

Murty, M. Ram, V. Kumar Murty, and N. Saradha. "Modular Forms and the Chebotarev Density Theorem." American Journal of Mathematics 110, no. 2 (April 1988): 253. http://dx.doi.org/10.2307/2374502.

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45

FUKUDA, Ryoji, and Hiroshi SATO. "Φ-DENSITY THEOREM ON A METRIC SPACE." Kyushu Journal of Mathematics 51, no. 1 (1997): 89–100. http://dx.doi.org/10.2206/kyushujm.51.89.

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46

Faure, Claude-Alain. "A Short Proof of Lebesgue's Density Theorem." American Mathematical Monthly 109, no. 2 (February 2002): 194. http://dx.doi.org/10.2307/2695333.

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47

BINGHAM, N. H., and A. J. OSTASZEWSKI. "Dichotomy and infinite combinatorics: the theorems of Steinhaus and Ostrowski." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 1 (October 8, 2010): 1–22. http://dx.doi.org/10.1017/s0305004110000496.

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AbstractWe define combinatorial principles which unify and extend the classical results of Steinhaus and Piccard on the existence of interior points in the distance set. Thus the measure and category versions are derived from one topological theorem on interior points applied to the usual topology and the density topology on the line. Likewise we unify the subgroup theorem by reference to a Ramsey property. A combinatorial form of Ostrowski's theorem (that a bounded additive function is linear) permits the deduction of both the measure and category automatic continuity theorems for additive functions.

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48

KHAN, MUSHFEQ. "LEBESGUE DENSITY AND CLASSES." Journal of Symbolic Logic 81, no. 1 (March 2016): 80–95. http://dx.doi.org/10.1017/jsl.2015.66.

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AbstractAnalyzing the effective content of the Lebesgue density theorem played a crucial role in some recent developments in algorithmic randomness, namely, the solutions of the ML-covering and ML-cupping problems. Two new classes of reals emerged from this inquiry: thepositive density pointswith respect toeffectively closed(or$\prod _1^0$) sets of reals, and a proper subclass, thedensity-one points. Bienvenu, Hölzl, Miller, and Nies have shown that the Martin-Löf random positive density points are exactly the ones that do not compute the halting problem. Treating this theorem as our starting point, we present several new results that shed light on how density, randomness, and computational strength interact.

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49

Bhardwaj, Vinod K., Shweta Dhawan, and Sandeep Gupta. "Density by Moduli and Statistical Boundedness." Abstract and Applied Analysis 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/2143018.

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We have generalized the notion of statistical boundedness by introducing the concept off-statistical boundedness for scalar sequences wherefis an unbounded modulus. It is shown that bounded sequences are precisely those sequences which aref-statistically bounded for every unbounded modulusf. A decomposition theorem forf-statistical convergence for vector valued sequences and a structure theorem forf-statistical boundedness have also been established.

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50

Yang, Weiguo. "The Asymptotic Equipartition Property for a Nonhomogeneous Markov Information Source." Probability in the Engineering and Informational Sciences 12, no. 4 (October 1998): 509–18. http://dx.doi.org/10.1017/s0269964800005350.

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In this paper, we study the asymptotic equipartition property (AEP) for a nonhomogeneous Markov information source. We first give a limit theorem for the averages of the functions of two variables of this information source by using the convergence theorem for the martingale difference sequence. As corollaries, we get several limit theorems and a limit theorem of the relative entropy density, which hold for any nonhomogeneous Markov information source. Then, we get a class of strong laws of large numbers for nonhomogeneous Markov information sources. Finally, we prove the AEP for a class of nonhomogeneous Markov information sources.

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