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1

Chichak, K. S. "Molecular Borromean Rings." Science 304, no. 5675 (2004): 1308–12. http://dx.doi.org/10.1126/science.1096914.

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2

Zhang, Hai-Ning, Wen-Xi Gao, Yu-Xin Deng, Yue-Jian Lin, and Guo-Xin Jin. "Stacking-interaction-induced host–guest chemistry and Borromean rings based on a polypyridyl ligand." Chemical Communications 54, no. 13 (2018): 1559–62. http://dx.doi.org/10.1039/c7cc09448e.

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3

Lu, Ye, Yuejian Lin, Zhenhua Li, and Guoxin Jin. "Highly Stable Molecular Borromean Rings." Chinese Journal of Chemistry 36, no. 2 (2017): 106–11. http://dx.doi.org/10.1002/cjoc.201700590.

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4

O'Keeffe, Michael, and Michael M. J. Treacy. "On Borromean links and related structures." Acta Crystallographica Section A Foundations and Advances 77, no. 5 (2021): 379–91. http://dx.doi.org/10.1107/s2053273321005568.

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The creation of knotted, woven and linked molecular structures is an exciting and growing field in synthetic chemistry. Presented here is a description of an extended family of structures related to the classical `Borromean rings', in which no two rings are directly linked. These structures may serve as templates for the designed synthesis of Borromean polycatenanes. Links of n components in which no two are directly linked are termed `n-Borromean' [Liang & Mislow (1994). J. Math. Chem. 16, 27–35]. In the classic Borromean rings the components are three rings (closed loops). More generally
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5

Klosterman, Jeremy K., Janis Veliks, Derik K. Frantz, et al. "Conformations of large macrocycles and ring-in-ring complexes." Organic Chemistry Frontiers 3, no. 6 (2016): 661–66. http://dx.doi.org/10.1039/c6qo00024j.

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6

Suzaki, Yuji. "Molecular Borromean Rings and Solomon’s Knot." Bulletin of Japan Society of Coordination Chemistry 50 (2007): 40–41. http://dx.doi.org/10.4019/bjscc.50.40.

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7

Singh, Nem, Dongwook Kim, Dong Hwan Kim, et al. "Selective synthesis of iridium(iii)-derived molecular Borromean rings, [2]catenane and ring-in-ring macrocycles via coordination-driven self-assembly." Dalton Transactions 46, no. 2 (2017): 571–77. http://dx.doi.org/10.1039/c6dt04512j.

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Unprecedented iridium(iii) derived molecular Borromean rings, 2[catenane] and ring-in-ring metallacycles were synthesizedviacoordination driven self-assembly using an iridium(iii)-based acceptor and dipyridyl donors.
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8

Markiewicz, Marcin, Marcin Karczewski, and Pawel Kurzynski. "Borromean states in discrete-time quantum walks." Quantum 5 (August 16, 2021): 523. http://dx.doi.org/10.22331/q-2021-08-16-523.

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In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong inter-particle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discrete-time quantum walk of many interacting partic
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9

Veliks, Janis, Helen M. Seifert, Derik K. Frantz, et al. "Towards the molecular Borromean link with three unequal rings: double-threaded ruthenium(ii) ring-in-ring complexes." Organic Chemistry Frontiers 3, no. 6 (2016): 667–72. http://dx.doi.org/10.1039/c6qo00025h.

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10

Richard, J. M. "Borromean Bound States." Few-Body Systems 38, no. 2-4 (2006): 79–84. http://dx.doi.org/10.1007/s00601-005-0148-5.

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11

Lu, Ye, Yu-Xin Deng, Yue-Jian Lin, et al. "Molecular Borromean Rings Based on Dihalogenated Ligands." Chem 3, no. 1 (2017): 110–21. http://dx.doi.org/10.1016/j.chempr.2017.06.006.

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12

Vaagen, J. S., D. K. Gridnev, H. Heiberg-Andersen, et al. "Borromean Halo Nuclei." Physica Scripta T88, no. 1 (2000): 209. http://dx.doi.org/10.1238/physica.topical.088a00209.

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13

Sun, Junling, Marco Frasconi, Zhichang Liu, et al. "Formation of ring-in-ring complexes between crown ethers and rigid TVBox8+." Chemical Communications 51, no. 8 (2015): 1432–35. http://dx.doi.org/10.1039/c4cc08053j.

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An octacationic tetraviologen-based cyclophane—so called TVBox<sup>8+</sup>—can form a ring-in-ring complex with bis-1,5-dinaphtho[50]crown-14, which represents a key intermediate for constructing molecular Borromean rings in a stepwise manner.
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14

Lu, Ye, Dong Liu, Yue-Jian Lin, Zhen-Hua Li та Guo-Xin Jin. "Self-assembly of metalla[3]catenanes, Borromean rings and ring-in-ring complexes using a simple π-donor unit". National Science Review 7, № 10 (2020): 1548–56. http://dx.doi.org/10.1093/nsr/nwaa164.

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Abstract Despite extensive research and several stunning breakthroughs in the synthesis of interlocked molecular species, [3]catenanes, Borromean rings and ring-in-ring complexes are exceedingly rare and their targeted synthesis remains a formidable challenge. Herein, a series of Cp*Rh-based homogeneous and heterogeneous interlocked structures have been prepared by coordination-driven self-assembly, not only including metalla[2]catenanes and molecular Borromean rings, but also linear metalla[3]catenanes and ring-in-ring complexes. The interlocked structures are all based on bithiophenyl groups
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15

Lu, Ye, Hai-Ning Zhang, and Guo-Xin Jin. "Molecular Borromean Rings Based on Half-Sandwich Organometallic Rectangles." Accounts of Chemical Research 51, no. 9 (2018): 2148–58. http://dx.doi.org/10.1021/acs.accounts.8b00220.

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16

Wang, Yuping, and J. Fraser Stoddart. "Molecular Borromean Rings: From Controlled Construction to Potential Applications." Chem 3, no. 1 (2017): 17–18. http://dx.doi.org/10.1016/j.chempr.2017.06.009.

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17

Tomio, L., M. T. Yamashita, T. Frederico, and F. Bringas. "Borromean three-body heteroatomic resonances." Laser Physics 21, no. 8 (2011): 1464–69. http://dx.doi.org/10.1134/s1054660x11150229.

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18

Ghoshal, Arijit, and Y. K. Ho. "Borromean bindings in muonic molecular ions with screened Coulomb potentials." Journal of Physics B: Atomic, Molecular and Optical Physics 43, no. 11 (2010): 115007. http://dx.doi.org/10.1088/0953-4075/43/11/115007.

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19

Huang, Sheng-Li, Yue-Jian Lin, Zhen-Hua Li, and Guo-Xin Jin. "Self-Assembly of Molecular Borromean Rings from Bimetallic Coordination Rectangles." Angewandte Chemie 126, no. 42 (2014): 11400–11404. http://dx.doi.org/10.1002/ange.201406193.

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20

Meyer, Cari D., Ross S. Forgan, Kelly S. Chichak, et al. "The Dynamic Chemistry of Molecular Borromean Rings and Solomon Knots." Chemistry – A European Journal 16, no. 42 (2010): 12570–81. http://dx.doi.org/10.1002/chem.201001806.

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21

Huang, Sheng-Li, Yue-Jian Lin, Zhen-Hua Li, and Guo-Xin Jin. "Self-Assembly of Molecular Borromean Rings from Bimetallic Coordination Rectangles." Angewandte Chemie International Edition 53, no. 42 (2014): 11218–22. http://dx.doi.org/10.1002/anie.201406193.

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22

Souza, L. A., F. F. Bellotti, T. Frederico, M. T. Yamashita, and Lauro Tomio. "Scaling Limit Analysis of Borromean Halos." Few-Body Systems 57, no. 5 (2016): 361–70. http://dx.doi.org/10.1007/s00601-016-1086-0.

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23

Lu, Ye, Yuejian Lin, Zhenhua Li, and Guoxin Jin. "Cover Picture: Highly Stable Molecular Borromean Rings (Chin. J. Chem. 2/2018)." Chinese Journal of Chemistry 36, no. 2 (2018): 85. http://dx.doi.org/10.1002/cjoc.201880021.

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24

Volosniev, A. G., D. V. Fedorov, A. S. Jensen, and N. T. Zinner. "Borromean ground state of fermions in two dimensions." Journal of Physics B: Atomic, Molecular and Optical Physics 47, no. 18 (2014): 185302. http://dx.doi.org/10.1088/0953-4075/47/18/185302.

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25

Sun, Jian-Ke, Qing-Xia Yao, Yu-Yang Tian, et al. "Borromean-Entanglement-Driven Assembly of Porous Molecular Architectures with Anion-Modified Pore Space." Chemistry - A European Journal 18, no. 7 (2012): 1924–31. http://dx.doi.org/10.1002/chem.201102938.

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26

Loren, Jon C., Michito Yoshizawa, Richard F. Haldimann, Anthony Linden, and Jay S. Siegel. "Synthetic Approaches to a Molecular Borromean Link: Two-Ring Threading with Polypyridine Templates." Angewandte Chemie 115, no. 46 (2003): 5880–83. http://dx.doi.org/10.1002/ange.200352562.

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27

Loren, Jon C., Michito Yoshizawa, Richard F. Haldimann, Anthony Linden, and Jay S. Siegel. "Synthetic Approaches to a Molecular Borromean Link: Two-Ring Threading with Polypyridine Templates." Angewandte Chemie International Edition 42, no. 46 (2003): 5702–5. http://dx.doi.org/10.1002/anie.200352562.

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28

Pentecost, Cari D., Nicholas Tangchaivang, Stuart J. Cantrill, Kelly S. Chichak, Andrea J. Peters, and J. Fraser Stoddart. "Making Molecular Borromean Rings. A Gram-Scale Synthetic Procedure for the Undergraduate Organic Lab." Journal of Chemical Education 84, no. 5 (2007): 855. http://dx.doi.org/10.1021/ed084p855.

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29

Seeman, Nadrian C. "DNA enables nanoscale control of the structure of matter." Quarterly Reviews of Biophysics 38, no. 4 (2005): 363–71. http://dx.doi.org/10.1017/s0033583505004087.

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1. Introduction 3632. Motif and sequence design 3643. Structural and topological constructions 3664. Nanomechanical devices 3675. Conclusions, applications and challenges 3706. Acknowledgments 3717. References 371Structural DNA nanotechnology consists of constructing objects, lattices and devices from branched DNA molecules. Branched DNA molecules open the way for the construction of a variety of N-connected motifs. These motifs can be joined by cohesive interactions to produce larger constructs in a bottom-up approach to nanoconstruction. The first objects produced by this approach were stick
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30

Kim, Taegeun, Nem Singh, Jihun Oh, et al. "Selective Synthesis of Molecular Borromean Rings: Engineering of Supramolecular Topology via Coordination-Driven Self-Assembly." Journal of the American Chemical Society 138, no. 27 (2016): 8368–71. http://dx.doi.org/10.1021/jacs.6b04545.

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31

Zhang, Hai‐Ning, Wei‐Bin Yu, Yue‐Jian Lin, and Guo‐Xin Jin. "Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties." Angewandte Chemie 133, no. 28 (2021): 15594–99. http://dx.doi.org/10.1002/ange.202103264.

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32

Zhang, Hai‐Ning, Wei‐Bin Yu, Yue‐Jian Lin, and Guo‐Xin Jin. "Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties." Angewandte Chemie International Edition 60, no. 28 (2021): 15466–71. http://dx.doi.org/10.1002/anie.202103264.

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33

Pawlak, Mariusz, Mirosław Bylicki, Jayanta K. Saha, and Prasanta K. Mukherjee. "Borromean states of three-particle exotic systems with screened Coulomb interactions." Journal of Physics B: Atomic, Molecular and Optical Physics 42, no. 21 (2009): 215701. http://dx.doi.org/10.1088/0953-4075/42/21/215701.

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34

VAAGEN, J. S., B. V. DANILIN, and S. N. ERSHOV. "CONTINUUM SPECTROSCOPY OF HALO NUCLEI." International Journal of Modern Physics E 16, no. 04 (2007): 1033–45. http://dx.doi.org/10.1142/s0218301307006484.

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Halo nuclei represent a new type of structure found in extremely neutron rich light nuclei, at the limits of nuclear existence. Of particular interest are Borromean nuclei, where none of the binary substructures can bind. Similar structures, Efimov states, have now also been produced in traps in molecular physics. Nuclear physics has in recent years taken further steps to also explore the nature of the halo continuum, in fact the major part of the spectrum since halo nuclei support only one or a few bound states. Since 3 → 3 scattering is prohibitively difficult to perform, the halo continuum
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35

Dutta, Sayantan, Jayanta K. Saha, Sukhamoy Bhattacharyya, Prasanta K. Mukherjee, and Tapan K. Mukherjee. "Exotic systems under screened Coulomb interactions: a study on Borromean windows." Physica Scripta 89, no. 1 (2013): 015401. http://dx.doi.org/10.1088/0031-8949/89/01/015401.

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36

Zhang, Hai‐Ning, Yue‐Jian Lin, and Guo‐Xin Jin. "Selective Construction of Trefoil knots and a Molecular Borromean Ring Induced by Steric Hindrance of Thioether Ligands." Chemistry – An Asian Journal 16, no. 14 (2021): 1918–24. http://dx.doi.org/10.1002/asia.202100450.

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37

Kar, Sabyasachi, Yu-Shu Wang, Yang Wang, and Yew Kam Ho. "Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z." Atoms 7, no. 2 (2019): 53. http://dx.doi.org/10.3390/atoms7020053.

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The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system ( Z e + , e − , e − ) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter μ C as a function of the continuously varied nuclear charge Z , the critical nuclear charge Z C as a function of the screening parameter μ , and the ionization
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38

Zhang, Hai‐Ning, Wei‐Bin Yu, Yue‐Jian Lin, and Guo‐Xin Jin. "Innenrücktitelbild: Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties (Angew. Chem. 28/2021)." Angewandte Chemie 133, no. 28 (2021): 15791. http://dx.doi.org/10.1002/ange.202105978.

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39

Pawlak, Mariusz, Mirosław Bylicki, and Prasanta K. Mukherjee. "On the limit of existence of Borromean binding in three-particle systems with screened Coulomb interactions." Journal of Physics B: Atomic, Molecular and Optical Physics 47, no. 9 (2014): 095701. http://dx.doi.org/10.1088/0953-4075/47/9/095701.

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40

Zhang, Hai‐Ning, Wei‐Bin Yu, Yue‐Jian Lin, and Guo‐Xin Jin. "Inside Back Cover: Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties (Angew. Chem. Int. Ed. 28/2021)." Angewandte Chemie International Edition 60, no. 28 (2021): 15659. http://dx.doi.org/10.1002/anie.202105978.

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41

Rachmawati, Meike, Herry Yulianti, Bethy S. Hernowo, et al. "The Correlation of KRAS Gene Expression and P53 Immunoexpression In Colorectal Adenocarcinoma." Open Access Macedonian Journal of Medical Sciences 7, no. 12 (2019): 1940–45. http://dx.doi.org/10.3889/oamjms.2019.549.

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BACKGROUND: Colorectal Adenocarcinoma (ADCCR) is the third most cancer not only in the world but also in Indonesia. There were 623 cases of ADCCR at Dr Hasan Sadikin hospital within 2015-2017. Both KRAS and TP53 mutation are known as genes which involve in carcinogenesis through the same pathway, namely the chromosomal instability pathway. In West Java, researches focusing on mutation KRAS and p53 also a correlation between both biomarkers among ADCCR patients are still limited. AIM: Therefore, this research aimed to perceive a correlation between KRAS gene expression with p53 immunoexpression
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42

Volosniev, Artem G., Dmitri V. Fedorov, Aksel S. Jensen, and Nikolaj T. Zinner. "Occurrence conditions for two-dimensional Borromean systems." European Physical Journal D 67, no. 5 (2013). http://dx.doi.org/10.1140/epjd/e2013-30693-5.

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43

Segovia, Jorge, Cédric Mezrag, Lei Chang, and Craig D. Roberts. "Nucleon Viewed as a Borromean Bound-State." Few-Body Systems 59, no. 3 (2018). http://dx.doi.org/10.1007/s00601-018-1341-7.

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44

S. Forgan, Ross, Jason M. Spruell, John-Carl Olsen, Charlotte L. Stern, and J. Fraser Stoddart. "Towards the Stepwise Assembly of Molecular Borromean Rings. A Donor-Acceptor Ring-in-Ring Complex." Journal of the Mexican Chemical Society 53, no. 3 (2019). http://dx.doi.org/10.29356/jmcs.v53i3.995.

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The assembly of molecular Borromean Rings from constitutionally independent rings in a stepwise manner depends on the preparation of robust “ring-in-ring” complexes. The π-electron rich macrocycle bis-1,5-dinaphtho[50]crown-14 (1) is shown to form a donor-acceptor ring-in-ring complex with the π-electron poor cyclophane cyclobis(paraquat-4,4'-biphenylene) (24+) in solution. In the crystal superstructure of [1⊂2]·4PF6, CH···O interactions between the polyether loops of 1 and the bipyridinium units of 24+ could disfavor the threading of dialkylammonium components of a third ring.&#x0D; &#x0D;
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45

Garrido, E., D. V. Fedorov, and A. S. Jensen. "From Two-Body Resonances to Three-Body Borromean States." Few-Body-Systems 34, no. 1-3 (2004). http://dx.doi.org/10.1007/s00601-004-0044-4.

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46

Yamashita, M. T., D. V. Fedorov, and A. S. Jensen. "Universality of Brunnian (N-body Borromean) four- and five-body systems." Physical Review A 81, no. 6 (2010). http://dx.doi.org/10.1103/physreva.81.063607.

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47

Li, Yong, Wenjuan Zhang, Qingdong Gou, Hongwei Song, and Tingyun Shi. "Search for Borromean states in the He-He-Rb triatomic system." Physical Review A 82, no. 2 (2010). http://dx.doi.org/10.1103/physreva.82.022515.

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48

Lu, Ye, Dong Liu, Zheng Cui, Yue‐Jian Lin, and Guo‐Xin Jin. "Adaptive Self‐Assembly and Induced‐Fit Interconversions between Molecular Borromean Rings, Russian Dolls and Ring‐in‐Ring Complexes †." Chinese Journal of Chemistry, December 30, 2020. http://dx.doi.org/10.1002/cjoc.202000406.

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49

Zhang, Hai-Ning, Yue-Jian Lin, and Guo-Xin Jin. "Selective Construction of Very Large Stacking-Interaction-Induced Molecular 818 Metalla-knots and Borromean Ring Using Curved Dipyridyl Ligands." Journal of the American Chemical Society, December 31, 2020. http://dx.doi.org/10.1021/jacs.0c11925.

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50

Pont, Federico, and Pablo Serra. "Stability diagrams of plasma-embedded three-unit-charge systems: Borromean states and the Efimov effect." Physical Review A 79, no. 3 (2009). http://dx.doi.org/10.1103/physreva.79.032508.

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