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Journal articles on the topic 'Rank 3'

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Published: 4 June 2021
Last updated: 5 February 2022

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1

BOROVIK, ALEXANDRE, and ADRIEN DELORO. "RANK 3 BINGO." Journal of Symbolic Logic 81, no. 4 (December 2016): 1451–80. http://dx.doi.org/10.1017/jsl.2016.36.

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2

Stellmacher, Bernd, and Franz Georg Timmesfeld. "Rank 3 amalgams." Memoirs of the American Mathematical Society 136, no. 649 (1998): 0. http://dx.doi.org/10.1090/memo/0649.

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3

Lavrauw, Michel, Andrea Pavan, and Corrado Zanella. "On the rank of 3×3×3-tensors." Linear and Multilinear Algebra 61, no. 5 (May 2013): 646–52. http://dx.doi.org/10.1080/03081087.2012.701299.

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4

Benkart, Georgia, and Alicia Labra. "Representations of Rank 3 Algebras." Communications in Algebra 34, no. 8 (August 2006): 2867–77. http://dx.doi.org/10.1080/00927870600637157.

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5

Jaszuńska, Joanna, and Jan Okniński. "Chinese Algebras of Rank 3." Communications in Algebra 34, no. 8 (August 2006): 2745–54. http://dx.doi.org/10.1080/00927870600651760.

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6

Kubat, Łukasz, and Jan Okniński. "Plactic algebra of rank 3." Semigroup Forum 84, no. 2 (September 7, 2011): 241–66. http://dx.doi.org/10.1007/s00233-011-9337-3.

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7

Kalhoff, F. B. "Realization of rank 3 matroids." Applied Mathematics Letters 9, no. 1 (January 1996): 55–58. http://dx.doi.org/10.1016/0893-9659(95)00102-6.

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8

Devillers, Alice, and J. I. Hall. "Rank 3 Latin square designs." Journal of Combinatorial Theory, Series A 113, no. 5 (July 2006): 894–902. http://dx.doi.org/10.1016/j.jcta.2005.06.004.

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9

Albrecht, Ulrich F., and Paul Hill. "Butler groups of infinite rank and axiom 3." Czechoslovak Mathematical Journal 37, no. 2 (1987): 293–309. http://dx.doi.org/10.21136/cmj.1987.102155.

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10

Ilten, Nathan, and Zach Teitler. "Product Ranks of the 3 × 3 Determinant and Permanent." Canadian Mathematical Bulletin 59, no. 2 (June 1, 2016): 311–19. http://dx.doi.org/10.4153/cmb-2015-076-1.

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AbstractWe show that the product rank of the 3 × 3 determinant det3 is 5, and the product rank of the 3 × 3 permanent perm3 is . As a corollary, we obtain that the tensor rank of det3 is 5 and the tensor rank of perm3 is 4. We show moreover that the border product rank of permn is larger than n for any n ≥ 3.
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11

Hsu, Tim, Mark J. Logan, and Shahriar Shahriari. "Methods for nesting rank 3 normalized matching rank-unimodal posets." Discrete Mathematics 309, no. 3 (February 2009): 521–31. http://dx.doi.org/10.1016/j.disc.2008.07.013.

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12

Mir�-Roig, Rosa M. "Stable rank 3 reflexive sheaves on ?3 with extremalc 3." Mathematische Zeitschrift 196, no. 4 (December 1987): 537–46. http://dx.doi.org/10.1007/bf01160895.

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13

Arnez, Maya Fernanda Manfrin, Larissa Soares Nogueira Ribeiro, Gabriel Dessotti Barretto, Patrícia Maria Monteiro, Edilson Ervolino, and Maria Bernadete Sasso Stuani. "RANK/RANKL/OPG Expression in Rapid Maxillary Expansion." Brazilian Dental Journal 28, no. 3 (June 2017): 296–300. http://dx.doi.org/10.1590/0103-6440201601116.

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Abstract The aim of this study was to evaluate osteoclastogenesis signaling in midpalatal suture after rapid maxillary expansion (RME) in rats. Thirty male Wistar rats were randomly assigned to two groups with 15 animals each: control (C) and RME group. RME was performed by inserting a 1.5-mm-thick circular metal ring between the maxillary incisors. The animals were euthanized at 3, 7 and 10 days after RME. qRT-PCR was used to evaluate expression of Tnfsf11 (RANKL), Tnfrsf11a (RANK) and Tnfrsf11b (OPG). Data were submitted to statistical analysis using two-way ANOVA followed by Tukey test (a=0.05). There was an upregulation of RANK and RANKL genes at 7 and 10 days and an upregulation of the OPG gene at 3 and 7 days of healing. Interestingly, an increased in expression of all genes was observed over time in both RME and C groups. The RANKL/OPG ratio showed an increased signaling favoring bone resorption on RME compared to C at 3 and 7 days. Signaling against bone resorption was observed, as well as an upregulation of OPG gene expression in RME group, compared to C group at 10 days. The results of this study concluded that the RANK, RANK-L and OPG system participates in bone remodeling after RME.
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14

Ostrik, V. "Pre-Modular Categories of Rank 3." Moscow Mathematical Journal 8, no. 1 (2008): 111–18. http://dx.doi.org/10.17323/1609-4514-2008-8-1-111-118.

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15

Ostrik, Victor. "Pivotal Fusion Categories of Rank 3." Moscow Mathematical Journal 15, no. 2 (2015): 373–96. http://dx.doi.org/10.17323/1609-4514-2015-15-2-373-396.

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16

Wang, Yi, Bo-Jun Yuan, Shuang-Dong Li, and Chong-Jun Wang. "Mixed graphs with H -rank 3." Linear Algebra and its Applications 524 (July 2017): 22–34. http://dx.doi.org/10.1016/j.laa.2017.02.037.

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17

Li, Tao. "Rank and genus of 3-manifolds." Journal of the American Mathematical Society 26, no. 3 (February 27, 2013): 777–829. http://dx.doi.org/10.1090/s0894-0347-2013-00767-5.

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18

Devillers, Alice, Michael Giudici, Cai Heng Li, Geoffrey Pearce, and Cheryl E. Praeger. "On imprimitive rank 3 permutation groups." Journal of the London Mathematical Society 84, no. 3 (September 11, 2011): 649–69. http://dx.doi.org/10.1112/jlms/jdr009.

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19

Devillers, Alice, Michael Giudici, Cai Heng Li, Geoffrey Pearce, and Cheryl E. Praeger. "On imprimitive rank 3 permutation groups." Journal of the London Mathematical Society 85, no. 2 (April 2012): 592. http://dx.doi.org/10.1112/jlms/jdr074.

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20

Böhmer, Andreas. "Rank 3 Amalgams with Diagram •—•—ˆ." Communications in Algebra 18, no. 12 (January 1, 1990): 4255–305. http://dx.doi.org/10.1080/00927872.1990.12098260.

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21

Costa, R. "On train algebras of rank 3." Linear Algebra and its Applications 148 (April 1991): 1–12. http://dx.doi.org/10.1016/0024-3795(91)90081-7.

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22

Chen, Shih-Tse, Lin Kang, Chau-Zen Wang, Peng-Ju Huang, Hsuan-Ti Huang, Sung-Yen Lin, Shih-Hsiang Chou, et al. "(−)-Epigallocatechin-3-Gallate Decreases Osteoclastogenesis via Modulation of RANKL and Osteoprotegrin." Molecules 24, no. 1 (January 3, 2019): 156. http://dx.doi.org/10.3390/molecules24010156.

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Osteoporosis is the second most common epidemiologic disease in the aging population worldwide. Previous studies have found that frequent tea drinkers have higher bone mineral density and less hip fracture. We previously found that (−)-epigallocatechin gallate (EGCG) (20–100 µmol/L) significantly suppressed receptor activator of nuclear factor-kB ligand (RANKL)-induced osteoclastogenesis and pit formation via inhibiting NF-κB transcriptional activity and nuclear transport of NF-κB in RAW 264.7 cells and murine primary bone marrow macrophage cells. The most important regulation in osteoclastogenesis is the receptor activator of nuclear factor-kB/RANKL/osteoprotegrin (RANK/RANKL/OPG) pathway. In this study, we used the coculture of RAW 264.7 cells and the feeder cells, ST2, to evaluate how EGCG regulated the RANK/RANKL/OPG pathway in RAW 264.7 cells and ST2 cells. We found EGCG decreased the RANKL/OPG ratio in both mRNA expression and secretory protein levels and eventually decreased osteoclastogenesis by TRAP (+) stain osteoclasts and TRAP activity at low concentrations—1 and 10 µmol/L—via the RANK/RANKL/OPG pathway. The effective concentration can be easily achieved in daily tea consumption. Taken together, our results implicate that EGCG could be an important nutrient in modulating bone resorption.
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23

Chan, Song Heng, and Renrong Mao. "The rank and crank of partitions modulo 3." International Journal of Number Theory 12, no. 04 (April 10, 2016): 1027–53. http://dx.doi.org/10.1142/s1793042116500640.

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In this paper, we prove formulas for the generating functions for the rank and crank differences for partitions modulo 3. In 2000, Andrews and Lewis made conjectures on inequalities satisfied by ranks and cranks modulo 3. These conjectures were first proved by Bringmann and Kane, respectively, using the circle method. Working directly on the generating functions, we obtain improvements to these inequalities.
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24

Dougall, William C., and Michelle Chaisson. "The RANK/RANKL/OPG triad in cancer-induced bone diseases." Cancer and Metastasis Reviews 25, no. 4 (December 19, 2006): 541–49. http://dx.doi.org/10.1007/s10555-006-9021-3.

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25

Marsay, David. "Risk rank." New Scientist 199, no. 2674 (September 2008): 19. http://dx.doi.org/10.1016/s0262-4079(08)62362-3.

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26

Miyazaki, Mitsuhiro, Toshio Sumi, and Toshio Sakata. "Typical ranks of certain 3-tensors and absolutely full column rank tensors." Linear and Multilinear Algebra 66, no. 1 (March 2017): 193–205. http://dx.doi.org/10.1080/03081087.2017.1292994.

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27

Labudzynskyi, D. O., І. О. Shymanskyi, O. O. Lisakovska, and М. М. Veliky. "Osteoprotective effects of vitamin D(3) in diabetic mice is VDR-mediated and regulated via RANKL/RANK/OPG axis." Ukrainian Biochemical Journal 90, no. 2 (April 10, 2018): 56–65. http://dx.doi.org/10.15407/ubj90.02.056.

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28

Grasedyck, Lars, and Wolfgang Hackbusch. "An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples." Computational Methods in Applied Mathematics 11, no. 3 (2011): 291–304. http://dx.doi.org/10.2478/cmam-2011-0016.

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Abstract We review two similar concepts of hierarchical rank of tensors (which extend the matrix rank to higher order tensors): the TT-rank and the H-rank (hierarchical or H-Tucker rank). Based on this notion of rank, one can define a data-sparse representation of tensors involving O(dnk + dk^3) data for order d tensors with mode sizes n and rank k. Simple examples underline the differences and similarities between the different formats and ranks. Finally, we derive rank bounds for tensors in one of the formats based on the ranks in the other format.
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29

Stegeman, Alwin, and Shmuel Friedland. "On best rank-2 and rank-(2,2,2) approximations of order-3 tensors." Linear and Multilinear Algebra 65, no. 7 (September 27, 2016): 1289–310. http://dx.doi.org/10.1080/03081087.2016.1234578.

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30

Rasulov, Tulkin Husenovich. "THRESHOLD EIGENVALUES AND RESONANCES OF A FRIEDRICHS MODEL WITH RANK TWO PERTURBATION." Scientific Reports of Bukhara State University 3, no. 3 (March 30, 2019): 31–38. http://dx.doi.org/10.52297/2181-1466/2019/3/3/3.

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In this paper in the Hilbert space a bounded self-adjoint Friedrichs model with rank two perturbation is considered. Number and location of the eigenvalues of are studied. An existence conditions of these eigenvalues are found. Under some conditions we prove that the lower (upper) bound of the essential spectrum of is either threshold eigenvalue or virtual level of .
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31

Zhao, Haijun, Oxana P. Lazarenko, and Jin‐Ran Chen. "Hippuric acid and 3‐(3‐hydroxyphenyl) propionic acid inhibit murine osteoclastogenesis through RANKL‐RANK independent pathway." Journal of Cellular Physiology 235, no. 1 (July 4, 2019): 599–610. http://dx.doi.org/10.1002/jcp.28998.

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32

Krishna, Siddharth, and Visu Makam. "On the tensor rank of the 3 x 3 permanent and determinant." Electronic Journal of Linear Algebra 37 (June 10, 2021): 425–33. http://dx.doi.org/10.13001/ela.2021.5107.

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The tensor rank and border rank of the $3 \times 3$ determinant tensor are known to be $5$ if the characteristic is not two. In characteristic two, the existing proofs of both the upper and lower bounds fail. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well.
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33

Ballico, Edoardo. "Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank." Mathematics 6, no. 8 (August 14, 2018): 140. http://dx.doi.org/10.3390/math6080140.

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Let X ⊂ P r be an integral and non-degenerate variety. We study when a finite set S ⊂ X evinces the X-rank of the general point of the linear span of S. We give a criterion when X is the order d Veronese embedding X n , d of P n and | S | ≤ ( n + ⌊ d / 2 ⌋ n ) . For the tensor rank, we describe the cases with | S | ≤ 3 . For X n , d , we raise some questions of the maximum rank for d ≫ 0 (for a fixed n) and for n ≫ 0 (for a fixed d).
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34

WALDHERR, MATTHIAS. "ASYMPTOTICS FOR MOMENTS OF HIGHER RANKS." International Journal of Number Theory 09, no. 03 (April 7, 2013): 675–712. http://dx.doi.org/10.1142/s1793042112501552.

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Bringmann, Mahlburg, and Rhoades have found asymptotic expressions for all moments of the partition statistics rank and crank. In this work we extend their methods to higher ranks. The T-rank, introduced by Garvan, for odd integers T = 3 is a natural generalization of the rank (T = 3) and crank (T = 1).
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35

Lee, Kyungyong, and Ralf Schiffler. "Positivity for Cluster Algebras of Rank 3." Publications of the Research Institute for Mathematical Sciences 49, no. 3 (2013): 601–49. http://dx.doi.org/10.4171/prims/114.

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36

Shaohua, Tao, Qiu Yingyu, and Zhang Zhili. "Phase Synchronization Enhance of Rank 3 Graphs." Open Cybernetics & Systemics Journal 8, no. 1 (January 21, 2015): 93–97. http://dx.doi.org/10.2174/1874110x01408010093.

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37

Nyman, Kathryn L. "Linear Inequalities for Rank 3 Geometric Lattices." Discrete and Computational Geometry 31, no. 2 (February 1, 2004): 229–42. http://dx.doi.org/10.1007/s00454-003-0807-6.

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38

Peretyat'kin, M. G. "Uncountably categorical quasisuccession of Morley rank 3." Algebra and Logic 30, no. 1 (January 1991): 51–61. http://dx.doi.org/10.1007/bf01978416.

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39

Labra, Alicia, and Cristián Reyes. "Representations on train algebras of rank 3." Linear Algebra and its Applications 400 (May 2005): 91–97. http://dx.doi.org/10.1016/j.laa.2004.11.014.

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40

Francisco Giuliani, Osmar, and Luiz Antonio Peresi. "Minimal identities of algebras of rank 3." Communications in Algebra 27, no. 10 (January 1999): 4909–17. http://dx.doi.org/10.1080/00927879908826737.

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41

Kerner, Otto. "Wild cluster tilted algebras of rank 3." Journal of Pure and Applied Algebra 212, no. 1 (January 2008): 222–27. http://dx.doi.org/10.1016/j.jpaa.2007.05.012.

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42

Allcock, Daniel. "The reflective Lorentzian lattices of rank 3." Memoirs of the American Mathematical Society 220, no. 1033 (2012): 0. http://dx.doi.org/10.1090/s0065-9266-2012-00648-4.

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43

Aulicino, David, and Duc-Manh Nguyen. "Rank 2 affine manifolds in genus $3$." Journal of Differential Geometry 116, no. 2 (October 2020): 205–80. http://dx.doi.org/10.4310/jdg/1603936812.

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44

Biliotti, Mauro, and Norman L. Johnson. "The Non-Solvable Rank 3 Affine Planes." Journal of Combinatorial Theory, Series A 93, no. 2 (February 2001): 201–30. http://dx.doi.org/10.1006/jcta.2000.3074.

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45

Lee, Kyungyong, Li Li, and Ralf Schiffler. "Newton polytopes of rank 3 cluster variables." Algebraic Combinatorics 3, no. 6 (December 4, 2020): 1293–330. http://dx.doi.org/10.5802/alco.141.

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46

Fomin, A. A. "TORSION-FREE ABELIAN GROUPS OF RANK 3." Mathematics of the USSR-Sbornik 68, no. 1 (February 28, 1991): 1–17. http://dx.doi.org/10.1070/sm1991v068n01abeh001195.

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47

Dempwolff, U. "Affine Rank 3 Groups on Symmetric Designs." Designs, Codes and Cryptography 31, no. 2 (February 2004): 159–68. http://dx.doi.org/10.1023/b:desi.0000012444.37411.1c.

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48

Belabas, Karim. "On quadratic fields with large 3-rank." Mathematics of Computation 73, no. 248 (January 30, 2004): 2061–75. http://dx.doi.org/10.1090/s0025-5718-04-01632-1.

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49

Björner, Anders, and Kimmo Eriksson. "Extendable shellability for rank 3 matroid complexes." Discrete Mathematics 132, no. 1-3 (September 1994): 373–76. http://dx.doi.org/10.1016/0012-365x(94)90246-1.

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50

Nesin, Ali. "Non-solvable groups of Morley rank 3." Journal of Algebra 124, no. 1 (July 1989): 199–218. http://dx.doi.org/10.1016/0021-8693(89)90159-2.

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