Journal articles: 'Chain ring' – Grafiati (2024)

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Relevant bibliographies by topics / Chain ring / Journal articles

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Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

ALEKSEEV,V.V., K.N.ZELENIN, P.B.TERENT'EV, V.V.LASHIN, L.A.KHORSEEVA, and G.A.BULAKHOV. "ChemInform Abstract: Ring-Chain and Ring-Chain-Ring Tautomerism of Thiocarbonohydrazones." ChemInform 25, no.17 (August19, 2010): no. http://dx.doi.org/10.1002/chin.199417026.

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2

Gopinath,S., P.Narayanan, K.Sethusankar, Jeyachandran Karunakaran, Meganathan Nandakumar, and ArasambattuK.Mohanakrishnan. "Crystal structures of three 1-oxo-1,2-dihydronaphthalene derivatives: dimethyl 4-(4-methoxyphenyl)-2-(4-methylphenyl)-1-oxo-1,2-dihydronaphthalene-2,3-dicarboxylate, dimethyl 1-oxo-2-(pyren-4-yl)-4-(thiophen-2-yl)-1,2-dihydronaphthalene-2,3-dicarboxylate and ethyl 1-oxo-2-phenyl-2,4-bis(thiophen-2-yl)-1,2-dihydronaphthalene-3-carboxylate." Acta Crystallographica Section E Crystallographic Communications 73, no.2 (January13, 2017): 177–82. http://dx.doi.org/10.1107/s2056989017000469.

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In the title 1-oxo-1,2-dihydronaphthalene derivatives, C28H24O6, (I), C34H22O5S, (II), and C27H20O3S2, (III), the cyclohexa-1,3-diene rings of the 1,2-dihydronaphthalene ring systems adopt half-chair, boat and half-chair conformations, respectively. The carbonyl O atoms attached to the dihydronaphthalene ring systems are each significantly deviated from the mean plane of the 1,2-dihydronaphthalene ring system, by 0.6162 (12) Å in (I), 0.6016 (16) Å in (II) and 0.515 (3) Å in (III). The mean planes of the 1,2-dihydronaphthalene ring systems make dihedral angles of 85.83 (3), 88.19 (3) and 81.67 (8)°, respectively, with the methylphenyl ring in (I), the pyrene ring in (II) and the phenyl ring in (III). In (I), the molecular structure is stabilized by an intramolecular C—H...O hydrogen bond, generating anS(6) ring motif. In the crystal of (I), molecules are linked by an intermolecular C—H...O hydrogen bond, which generates aC(8) zigzag chain running along [100]. Adjacent chains are further connected by C—H...π and offset π–π interactions [centroid–centroid distance = 3.6572 (9) Å], forming a double-chain structure. In the crystals of (II) and (III), molecules are linked into chain structures by offset π–π interactions with centroid–centroid distances of 3.5349 (12) and 3.8845 (13) Å for (II) and 3.588 (2) Å for (III). In (II) and (III), the thiophene rings are orientationally disordered over two sites, with occupancy ratios of 0.69:0.31 for (II), and 0.528 (4):0.472 (4) and 0.632 (5):0.368 (5) for (III).

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3

Wang, Dagang, Jun Zhang, Zhencai Zhu, Shen Gang, and Li Xiang. "Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads." Advances in Mechanical Engineering 11, no.9 (September 2019): 168781401988036. http://dx.doi.org/10.1177/1687814019880366.

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Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads were investigated in this study. The dynamic tension of ring chain of the heavy-duty scraper conveyor was obtained using the time-varying dynamic analysis. Finite element analyses of three-dimensional contacts between adjacent chain rings at straight and bending segments were carried out to explore three-dimensional stress distributions of chain rings. The crack initiation life of chain ring was predicted employing the multiaxial fatigue theory. The results show that the ring chain is subjected to time-varying dynamic tensions during operation. During tension-tension contact fatigue, as compared to the straight segment of ring chain, the bending segment engaging in the sprocket presents an overall lower (or higher) equivalent stress distribution in the case of flat (or vertical) chain ring, respectively. Maximum equivalent stresses at the contact regions of adjacent chain rings both present time-varying dynamic characteristics similar to evolutions of dynamic tension. During tension-torsion contact fatigue, an increase in torsion angle level causes unobvious difference between equivalent stress distributions at contact regions of adjacent rings. Predicted crack initiation lives of chain rings during tension-tension contact fatigue indicates more severe fatigue damages of the vertical chain ring at the straight segment and of the flat chain ring at the right bending segment.

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4

Aguirre Hernández, Gerardo, Ratnasamy Somanathan, and Sylvain Bernès. "Pelanserin: 3-[3-(4-phenylpiperazin-1-yl)propyl]quinazoline-2,4(1H,3H)-dione." Acta Crystallographica Section E Structure Reports Online 70, no.8 (July23, 2014): o878. http://dx.doi.org/10.1107/s160053681401602x.

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The title compound, C21H24N4O2, is a potent serotonin 5-HT2and α1-adrenoceptor antagonist. Then-propyl chain links the quinazolinedione heterocycle and the phenylpiperazine group in which the benzene ring is equatorially located and the piperazine ring has the expected chair conformation. The dihedral angle between the planes of the benzene ring and the quinazolinedione ring system is 74.1 (1)°. In the crystal, molecules form centrosymmetric dimers throughR22(8) hydrogen-bonded rings involving the amine and one carbonyl group of the quinazolinedione moiety. These dimers are extended into chains extending along thea-axis direction through expanded centrosymmetric cyclic C—H...O associations involving the second carbonyl group, givingR22(20) andR12(7) motifs.

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5

Fernandez, Antonio, Eufemio Moreno Pineda, Jesùs Ferrando-Soria, EricJ.L.McInnes, GrigoreA.Timco, and RichardE.P.Winpenny. "A hybrid organic–inorganic molecular daisy chain." Chemical Communications 51, no.55 (2015): 11126–29. http://dx.doi.org/10.1039/c5cc02216a.

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A hybrid daisy-chain has been made, involving an organic thread for an inorganic ring, where the organic thread for the ring also acts as a ligand for a second ring. The ring contains six chromium(iii) and two zinc(ii) ions, and two isomers of the rings are found in the daisy-chain.

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6

Chinnakali,K., D.Sudha, M.Jayagopi, R.Raghunathan, and Hoong-Kun Fun. "4,4-Dimethyl-2-tosyl-2,3,3a,4-tetrahydro-1H,10H-pyrrolo[3,4-c]pyrano[6,5-b]indan-10-one." Acta Crystallographica Section E Structure Reports Online 63, no.11 (October26, 2007): o4438. http://dx.doi.org/10.1107/s1600536807052233.

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The molecule of the title compound, C23H23NO4S, adopts a folded conformation, with the cyclopentadienone ring and tosyl groups arranged in an almost face-to-face fashion. The pyrrolidine ring has an envelope conformation and the dihydropyran ring is in a half-chair conformation. The pyrrolidine and dihydropyran rings are cis-fused. The indenone ring system is essentially planar, and the indene plane forms a dihedral angle of 25.12 (3)° with the sulfonyl-bound benzene ring. In the crystal structure, molecules translated by one unit cell along the a-axis direction are linked into a chain by C—H...O hydrogen bonds. The inversion-related molecules of adjacent chains are linked along the c axis by C—H...O hydrogen bonds into a sheet-like structure parallel to the ac plane.

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7

Kubono, Koji, Ryuma Kise, Yukiyasu Kashiwagi, Keita Tani, and Kunihiko Yokoi. "Crystal structure of 7-hydroxy-8-[(4-methylpiperazin-1-yl)methyl]-2H-chromen-2-one." Acta Crystallographica Section E Crystallographic Communications 72, no.12 (November4, 2016): 1751–53. http://dx.doi.org/10.1107/s2056989016017217.

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In the title compound, C15H18N2O3, the coumarin ring is essentially planar, with an r.m.s. deviation of 0.012 Å. An intramolecular O—H...N hydrogen bond forms anS(6) ring motif. The piperazine ring adopts a chair conformation. In the crystal, a C—H...O hydrogen bond generates aC(4) chain motif running along thecaxis. The chain structure is stabilized by a C—H...π interaction. The chains are linked by π–π interactions [centroid–centroid distance of 3.5745 (11) Å], forming a sheet structure parallel to thebcplane.

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8

Ourhriss, Najia, Noureddine Mazoir, Jean-Claude Daran, Moha Berraho, and Ahmed Benharref. "(1S,3R,6S,7R)-3,7-Dichloro-trans-himachalane." Acta Crystallographica Section E Structure Reports Online 63, no.3 (February28, 2007): o1497—o1499. http://dx.doi.org/10.1107/s1600536807008409.

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The molecule of the title compound, C15H26Cl2, is built up from two fused six-membered and seven-membered rings. The six-membered ring has a perfect chair conformation, whereas the seven-membered ring displays a twist-chair conformation. A weak C—H...Cl hydrogen-bonding interaction links the molecule into a chain parallel to the a axis.

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9

Ee, Gwendoline Cheng Lian, Soek Sin Teh, Huey Chong Kwong, Mohamed Ibrahim Mohamed Tahir, and Siau Hui Mah. "rac-[3-Hydroxy-6,9-dimethyl-6-(4-methylpent-3-en-1-yl)-6a,7,8,9,10,10a-hexahydro-6H-1,9-epoxybenzo[c]chromen-4-yl](phenyl)methanone." Acta Crystallographica Section E Structure Reports Online 68, no.4 (March17, 2012): o1091—o1092. http://dx.doi.org/10.1107/s1600536812010756.

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The title compound congestiflorone, C28H32O4, which was isolated from the stem bark ofMesua congestiflora, consists of a benzophenone skeleton with two attached pyran rings to which a cyclohexane ring and a C6 side chain are bonded. The benzene ring is significantly distorted from planarity (r.m.s. deviation = 0.0007 Å) due to the constraints imposed by junctions with the two pyran rings. The cyclohexane ring is in a chair conformation, one pyran ring is in a boat conformation, while the other is a distorted chair. The phenyl and benzene rings make a dihedral angle of 55.85 (9)°. An intramolecular O—H...O hydrogen bond is observed. In the crystal, molecules are linkedviaC—H...O interactions.

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10

Carvalho, Paulo, EdwardB.FurrIII, and Christopher McCurdy. "(E)-Methyl 2-[(2S,3S,12bR)-3-ethyl-8-methoxy-1,2,3,4,6,7,12,12b-octahydroindolo[2,3-a]quinolizin-2-yl]-3-methoxyacrylate ethanol solvate." Acta Crystallographica Section E Structure Reports Online 65, no.6 (May29, 2009): o1441—o1442. http://dx.doi.org/10.1107/s1600536809017309.

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In the title compound, C23H30N2O4·C2H6O, the indole derivative has four fused rings, forming an indolo[2-3a]quinolizine system, in which one six-membered ring is directly connected to the indole unit and has a distorted chair conformation. The fourth ring is also a six-membered ring, depicting a regular chair conformation. In the crystal, the molecules are linked by N—H...O and O—H...N interactions, forming aC(7) chain.

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11

Feng, Juan, Jian-Long Zhang, Rong-Rong Zhang, Li-Jun Ruan, and Ren-Wang Jiang. "1-Deacetoxy-1-oxocaesalmin." Acta Crystallographica Section E Structure Reports Online 70, no.6 (May17, 2014): o662. http://dx.doi.org/10.1107/s1600536814011040.

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The title compound, C24H30O7, is a diterpenoid isolated from the seeds ofCaesalpinia minax. It consists of two cyclohexane rings (AandB), one unsaturated six-membered ring (C) and one furan ring (D). The stereochemistry of the ring junctures isA/B transandB/C trans. RingsAandBhave normal chair conformations whileCadopts a twisted half-chair conformation due to fusion to the furan ring which is planar [r.m.s. deviation = 0.0009 (2) Å]. In the crystal, hydroxyl O—H...Ocarbonylhydrogen bonds link the molecules into a chain structure extending along thea-axis direction.

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12

Ahmad, Matloob, Hamid Latif Siddiqui, Naveed Ahmad, Sana Aslam, and Masood Parvez. "2-(3,4-Dimethyl-5,5-dioxo-2H,4H-pyrazolo[4,3-c][1,2]benzothiazin-2-yl)-N-(2-fluorobenzyl)acetamide." Acta Crystallographica Section E Structure Reports Online 68, no.8 (July18, 2012): o2470—o2471. http://dx.doi.org/10.1107/s160053681203187x.

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In the title molecule, C20H19FN4O3S, the heterocyclic thiazine ring adopts a half-chair conformation with the S atom displaced by 0.668 (4) Å from the mean plane formed by the remaining ring atoms. The mean planes of the benzene and pyrazole rings are inclined with respect to each other at a dihedral angle of 17.4 (3)°. The acetamide chain (O/N/C/C/C) linking the pyrazole and 2-fluorobenzyl rings is essentially planar (r.m.s. deviation = 0.030 Å) and forms dihedral angles with the mean planes of these rings of 78.8 (2) and 78.89 (14)°, respectively. The crystal structure is stabilized by N—H...O and C—H...O hydrogen-bonding interactions, resulting in a six-membered ring with anR21(6) motif, while C—H...O and C—H...F hydrogen-bonding interactions result in chains of molecules lying along thecaxis in a zigzag fashion.

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13

Wilkinson,J.C. "Quotient rings, chain conditions and injective ring endomorphisms." Glasgow Mathematical Journal 31, no.2 (May 1989): 173–81. http://dx.doi.org/10.1017/s0017089500007709.

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In this paper, the situation we shall be concerned with is that of a ring R, with a ring monomorphism α: R → R, which will not be assumed to be surjective.Much work has been done on the skew polynomial ring R[x, α] and the skew Laurent polynomial ring R[x, x-1, α], where α is an automorphism—see [3] for example. However, the fact that α is not surjective renders the study of these objects much more difficult.

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14

Killilea,S.D., and P.O'Carra. "Structure and apoprotein linkages of phycourobilin." Biochemical Journal 226, no.3 (March15, 1985): 723–31. http://dx.doi.org/10.1042/bj2260723.

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R-Phycoerythrin contains two covalently bound bilin prosthetic groups, phycoerythrobilin and phycourobilin. The two chromophore types were separated as their peptide-bound derivatives by subjecting tryptic digests of R-phycoerythrin to adsorption chromatography on Sephadex G-25. The structure and apoprotein linkages of the bound phycoerythrobilin were found to be identical with those previously reported for this phycobilin [Killilea, O'Carra & Murphy (1980) Biochem. J. 187, 311-320]. Phycourobilin is a tetrapyrrole, containing no oxo bridges and has the same order of side chains as IX alpha bilins. The chromophore is linked to the peptide through two and possibly three of its pyrrole rings. One linkage possibly consists of an ester bond between the hydroxy group of a serine residue and the propionic acid side chain of one of the inner rings. The second linkage is a labile thioether bond between a cysteine residue and the C2 side chain of pyrrole ring A. The third linkage is a stable thioether bond between a cysteine residue and the alpha-carbon atom of the C2 side chain of pyrrole ring D. Ring D is unsaturated and is attached to ring C through a saturated carbon bridge. Rings B and C have a conjugated system of five bonds, as found in other urobilinoid pigments. Ring A is attached to ring B via a saturated carbon bridge. Both of the alpha-positions of ring A are in the reduced state, but the ring does contain an unsaturated centre (probably a double bond between the beta-carbon and the ring nitrogen atom). The presence of this double bond and its isomerization into the bridge position between rings A and B would explain the extension of the conjugated system of phycourobilin to that of a phycoerythrobilinoid/rhodenoid pigment in acid or alkali.

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15

Meneghetti, Fiorella, Daniela Masciocchi, Arianna Gelain, and Stefania Villa. "Crystal structure of 3-(3-oxo-2,3,4,4a,5,6-hexahydrobenzo[h]cinnolin-2-yl)propionic acid." Acta Crystallographica Section E Structure Reports Online 70, no.10 (September6, 2014): o1088—o1089. http://dx.doi.org/10.1107/s1600536814019850.

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The asymmetric unit of the title compound, C15H16N2O3, contains two independent molecules, which present a different conformation of the carboxylic acid side chain [C—C—C—OH torsion angles = 65.3 (7) and −170.1 (5)°]. In both molecules, the dihydropyridazinone ring adopts a geometry intermediate between a twisted-boat and a half-chair conformation, while the central six-membered ring is almost in a half-boat conformation. In the crystal, molecules are linked by O—H...Ok(k = ketone) hydrogen bonds, generating [01-1] chains. Aromatic π–π stacking contacts between the benzene and the dihydropyridazinone rings [centroid–centroid distance [3.879 (9) Å] are also observed.

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16

Gul, Waseem, Ahmed Galal, MahmoudA.ElSohly, and Paulo Carvalho. "Crystal structure of (9S,10S)-10-ethoxy-9-hydroxy-6,6,9-trimethyl-3-pentyl-7,8,9,10-tetrahydro-6H-benzo[c]chromen-1-yl 4-methylbenzenesulfonate." Acta Crystallographica Section E Crystallographic Communications 71, no.12 (December1, 2015): o1082—o1083. http://dx.doi.org/10.1107/s2056989015024044.

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In the structure of the title compound, C30H40O6S, the cyclohexene and heterocyclic rings are linked by a double bond. The cyclohexene ring has a half-chair conformation (the methylene group adjacent to the hydroxy substituent lies above the remaining atoms) and the hydroxy and ethoxy groups have equatorial and bisectional dispositions, respectively. The heterocyclic ring has an envelope conformation (with the CMe2C atom being the flap). The dihedral angle between the aromatic rings is 53.88 (10)°. A long intramolecular C—H...S interaction is noted. In the molecular packing, hydroxy-O—H...O(sulfonate) hydrogen bonds lead to a helical chain along [010]. Connections between chains are of the type methyl-C—H...O(sulfonate) and lead to supramolecular layers that lie parallel to (001). The studied crystal was an inversion twin.

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17

Oishi, Takeshi, Keisuke Fukaya, Yu Yamaguchi, Tomoya Sugai, Ami Watanabe, Takaaki Sato, and Noritaka Chida. "Crystal structures of (±)-(1SR,5SR,6SR,7SR,10SR,11SR,13RS,14SR)-13-hydroxy-7-methoxymethoxy-11,15,18,18-tetramethyl-3-oxo-2,4-dioxatetracyclo[12.3.1.01,5.06,11]octadec-15-en-10-yl benzoate, its 13-epimer and 13-one derivative." Acta Crystallographica Section E Crystallographic Communications 71, no.5 (April9, 2015): 466–72. http://dx.doi.org/10.1107/s2056989015006854.

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The title compounds, C29H38O8·0.25C5H12, (A), C29H38O8, (B), and C29H36O8, (C), are tetracyclic benzoates possessing a taxane skeleton with a fused dioxolane ring as the core structure. In the asymmetric unit of (A), there are two independent benzoate molecules (A and A′) and a half molecule of solvent pentane disordered about an inversion center. The molecular conformations of (A), (B) and (C) are similar except for the flexible methoxymethoxy group. The cyclohexane, cyclohexene and central cyclooctane rings adopt chair, half-chair and chair–chair (extended crown) forms, respectively. The dioxolane rings are essentially planar, while the dioxolane ring of A′ is slightly twisted from the mean plane. In the crystal of (A), intermolecular O—H...O, C—H...O and C—H...π interactions link the independent benzoates alternately, forming a chain structure. In the crystals of (B) and (C), molecules are linked through O—H...O and C—H...π interactions, and C—H...O hydrogen bonds, respectively, into similar chains. Further, weak intermolecular C—H...O interactions connect the chains into a three-dimensional network in (A) and a sheet in (B), whereas no other interactions are observed for (C).

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18

Benková, Zuzana, and Peter Cifra. "Comparison of linear and ring DNA macromolecules moderately and strongly confined in nanochannels." Biochemical Society Transactions 41, no.2 (March21, 2013): 625–29. http://dx.doi.org/10.1042/bst20120279.

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Understanding the mechanism of DNA extension in nanochannels is necessary for interpretation of experiments in nanofluidic channel devices that have been conducted recently with both linear and ring chains. The present article reviews the situation with linear chains and analyses the experimental results and simulations for channel-induced extension (linearization) of ring chains. Results for confined rings indicate a transition between moderate and strong confinement similar to that of linear chains. Owing to stronger self-avoidance in confined rings, the transition and chain extension is shifted relative to linear DNA. We suggest that a relationship similar to that used for the extension of linear chains may also be used for circular DNA.

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19

Guo, Fuchen, Ke Li, Jiaxin Wu, Linli He, and Linxi Zhang. "Effects of Topological Constraints on Penetration Structures of Semi-Flexible Ring Polymers." Polymers 12, no.11 (November11, 2020): 2659. http://dx.doi.org/10.3390/polym12112659.

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The effects of topological constraints on penetration structures of semi-flexible ring polymers in a melt are investigated using molecular dynamics simulations, considering simultaneously the effects of the chain stiffness. Three topology types of rings are considered: 01-knot (the unknotted), 31-knot and 61-knot ring polymers, respectively. With the improved algorithm to detect and quantify the inter-ring penetration (or inter-ring threading), the degree of ring threading does not increase monotonously with the chain stiffness, existing a peak value at the intermediate stiffness. It indicates that rings interpenetrate most at intermediate stiffness where there is a balance between coil expansion (favoring penetrations) and stiffness (inhibiting penetrations). Meanwhile, the inter-ring penetration would be suppressed with the knot complexity of the rings. The analysis of effective potential between the rings provides a better understanding for this non-monotonous behavior in inter-ring penetration.

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20

Jeong, Seung Heum, Soowon Cho, Tae Yong Ha, Eun Jung Roh, and Chunggi Baig. "Structural and Dynamical Characteristics of Short-Chain Branched Ring Polymer Melts at Interface under Shear Flow." Polymers 12, no.12 (December21, 2020): 3068. http://dx.doi.org/10.3390/polym12123068.

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We present a detailed analysis of the interfacial chain structure and dynamics of confined polymer melt systems under shear over a wide range of flow strengths using atomistic nonequilibrium molecular dynamics simulations, paying particular attention to the rheological influence of the closed-loop ring geometry and short-chain branching. We analyzed the interfacial slip, characteristic molecular mechanisms, and deformed chain conformations in response to the applied flow for linear, ring, short-chain branched (SCB) linear, and SCB ring polyethylene melts. The ring topology generally enlarges the interfacial chain dimension along the neutral direction, enhancing the dynamic friction of interfacial chains moving against the wall in the flow direction. This leads to a relatively smaller degree of slip (ds) for the ring-shaped polymers compared with their linear analogues. Furthermore, short-chain branching generally resulted in more compact and less deformed chain structures via the intrinsically fast random motions of the short branches. The short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone, which is mostly aligned in the flow direction, thereby enhancing the dynamic wall friction of the moving interfacial chains toward the flow direction. These features afford a relatively lower ds and less variation in ds in the weak-to-intermediate flow regimes. Accordingly, the interfacial SCB ring system displayed the lowest ds among the studied polymer systems throughout these regimes owing to the synergetic effects of ring geometry and short-chain branching. On the contrary, the structural disturbance exerted by the highly mobile short branches promotes the detachment of interfacial chains from the wall at strong flow fields, which results in steeper increasing behavior of the interfacial slip for the SCB polymers in the strong flow regime compared to the pure linear and ring polymers.

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21

Galushchinskiy, Aleksei, Pavel Slepukhin, and Konstantin Obydennov. "Crystal structures of two (Z)-2-(4-oxo-1,3-thiazolidin-2-ylidene)acetamides." Acta Crystallographica Section E Crystallographic Communications 73, no.12 (November10, 2017): 1850–54. http://dx.doi.org/10.1107/s2056989017016061.

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The crystal structures of two (oxothiazolidin-2-ylidene)acetamides, namely (Z)-2-[2-(morpholin-4-yl)-2-oxoethylidene]thiazolidin-4-one, C9H12N2O3S, (I), and (Z)-N-(4-methoxyphenyl)-2-(4-oxothiazolidin-2-ylidene)acetamide, C12H12N2O3S, (II), are described and compared with a related structure. TheZconformation was observed for both the compounds. In (I), the morpholin-4-yl ring has a chair conformation and its mean plane is inclined to the thiazolidine ring mean plane by 37.12 (12)°. In (II), the benzene ring is inclined to the mean plane of the thiazolidine ring by 20.34 (14)°. In the crystal of (I), molecules are linked by N—H...O hydrogen bonds, formingC(6) chains along theb-axis direction. The edge-to-edge arrangement of the molecules results in short C—H...O and C—H...S interactions, which consolidate the chain into a ribbon-like structure. In the crystal of (II), two N—H...O hydrogen bonds result in the formation ofC(8) chains along theb-axis direction andC(6) chains along thec-axis direction. The combination of these interactions leads to the formation of layers parallel to thebcplane, enclosingR44(28) rings involving four molecules.

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22

Chinnakali,K., D.Sudha, M.Jayagopi, R.Raghunathan, and Hoong-Kun Fun. "cis-4,4,10-Trimethyl-2-tosyl-1,2,3,3a,4,11b-hexahydro-11H-pyrrolo[3,4-c]pyrano[5,6-c]quinolin-11-one hemihydrate." Acta Crystallographica Section E Structure Reports Online 63, no.11 (October31, 2007): o4489—o4490. http://dx.doi.org/10.1107/s1600536807053287.

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The asymmetric unit of the title compound, C24H26N2O4S·0.5H2O, contains two independent molecules, A and B, with similar conformations, and a water molecule. The pyrrolidine ring adopts an envelope conformation in molecule A and a twist conformation in molecule B. In both molecules, the pyrrolidine and dihydropyran rings are cis-fused, and the dihydropyran ring has a half-chair conformation. Each of the independent molecules adopts a folded conformation, with the sulfonyl-bound benzene ring lying over the pyridinone ring. The two independent molecules, A and B, are linked together via C—H...O hydrogen bonds and C—H...π interactions. The A–B pairs are linked into a chain along the a axis by O—H...O and C—H...O hydrogen bonds, as well as C—H...π interactions. The inversion- and screw-related molecules in adjacent chains are cross-linked via C—H...O and C—H...N interactions, forming a three-dimensional framework.

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23

Jespers,E. "Chain conditions and semigroup graded rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no.3 (December 1988): 372–80. http://dx.doi.org/10.1017/s1446788700031086.

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AbstractThe following questions are studied: When is a semigroup graded ring left Noetherian, respectively semiprime left Goldie? Necessary sufficient conditions are proved for cancellative semigroup-graded subrings of rings weakly or strongly graded by a polycyclic-by-finite (unique product) group. For semigroup rings R[S] we also give a solution to the problem in case S is an inverse semigroup.

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24

Benhissi, Ali. "Chain Condition on Annihilators and Strongly Hopfian Property in Hurwitz Series Ring." Algebra Colloquium 21, no.04 (October6, 2014): 635–46. http://dx.doi.org/10.1142/s1005386714000583.

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In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its annihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.

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25

Landjev, Ivan, and Peter Vandendriessche. "Chain ring analogs of designs." Electronic Notes in Discrete Mathematics 40 (May 2013): 211–15. http://dx.doi.org/10.1016/j.endm.2013.05.038.

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26

Zelenin,K.N., V.V.Alekseyev, T.YeGabis, S.I.Yakimovitch, and T.J.Pehk. "Ring-chain tautomerism of thiocarbohydrazones." Tetrahedron Letters 31, no.27 (January 1990): 3927–30. http://dx.doi.org/10.1016/s0040-4039(00)97508-7.

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27

Nguyen, Minh Tho, Luc Landuyt, and L.G.Vanquickenborne. "Ring–chain rearrangements of phosphirane." J. Chem. Soc., Faraday Trans. 90, no.12 (1994): 1771–81. http://dx.doi.org/10.1039/ft9949001771.

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28

Tronchet,J.M.J., M.Zsély, L.Brenas, O.Lassout, E.Grand, P.Seuret, M.Grigorov, E.Rivara-minten, and M.Geoffroy. "Bicyclonucleosides and Ring-Chain Interconversion." Nucleosides and Nucleotides 18, no.4-5 (April 1999): 1077–78. http://dx.doi.org/10.1080/15257779908041651.

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29

Fulop, Ferenc, Kalevi Pihlaja, Kari Neuvonen, Gabor Bernath, Gyula Argay, and Alajos Kalman. "Ring-chain tautomerism in oxazolidines." Journal of Organic Chemistry 58, no.7 (March 1993): 1967–69. http://dx.doi.org/10.1021/jo00059a065.

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30

Singh, Surjeet, and Yousef Alkhamees. "Automorphisms of a chain ring." Annali di Matematica Pura ed Applicata 186, no.2 (August18, 2006): 289–301. http://dx.doi.org/10.1007/s10231-006-0006-1.

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31

BRUNGS,H.H., and G.TÖRNER. "I-COMPACT RIGHT CHAIN DOMAINS." Journal of Algebra and Its Applications 10, no.06 (December 2011): 1107–39. http://dx.doi.org/10.1142/s0219498811005105.

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Generalizing the concept of convergency to valued fields, Ostrowski in the 1930s introduced pseudo-convergent sequences. In the present paper we classify pseudo-convergent sequences in right chain domains R according to the prime ideal P associated to the breadth I of the sequence using an ideal theory developed for right cones in groups. The ring R is I-compact if every pseudo-convergent sequence in R with breadth I has a limit in R, and we construct right chain domains R which are I-compact only for right ideals I in particular subsets [Formula: see text] of the set of all right ideals of R. Krull's perfect valuation rings and then Ribenboim's notion of a valuation ring complete par étages, where [Formula: see text] is the minimal set containing the completely prime ideals in a commutative valuation ring, is a special case. For a non-discrete right invariant rank-one right chain domain R there are exactly two possibilities for the set [Formula: see text] if the value group of R is the group of real numbers under addition, and there are infinitely many possibilities for [Formula: see text] in all other cases.

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32

Bohrisch, Jörg, Michael Pätzel, Jürgen Liebscher, and Gerhard Maas. "Ring Chain Transformations; X:1Synthesis of Condensed (ω -Aminoalkyl)imidazoles by Ring Chain Transformation." Synthesis 1993, no.05 (1993): 521–24. http://dx.doi.org/10.1055/s-1993-25897.

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33

Wang, Hai-Ying, Jian-Ping Ma, Ru-Qi Huang, and Yu-Bin Dong. "3,5-Bis(4-methoxyphenyl)-1H-1,2,4-triazole monohydrate." Acta Crystallographica Section E Structure Reports Online 65, no.6 (May14, 2009): o1260. http://dx.doi.org/10.1107/s160053680901695x.

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In the title compound, C16H15N3O2·H2O, the two benzene rings and the triazole ring lie almost in the same plane, the triazole ring forming dihedral angles of 5.07 (9) and 5.80 (8)° with the benzene rings. In the crystal, there are three relatively strong intermolecular O—H...N and N—H...O hydrogen bonds, which lead to the formation of a one-dimensional double chain running parallel to theaaxis. Weak π—π interactions between the benzene rings of neighboring chains with a centroid–centroid distance of 3.893 (4) Å result in the formation of layers parallel to theacplane.

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34

Syed, Khajamohiddin, Aleksey Porollo, Ying Wai Lam, PaulE.Grimmett, and JagjitS.Yadav. "CYP63A2, a Catalytically Versatile Fungal P450 Monooxygenase Capable of Oxidizing Higher-Molecular-Weight Polycyclic Aromatic Hydrocarbons, Alkylphenols, and Alkanes." Applied and Environmental Microbiology 79, no.8 (February15, 2013): 2692–702. http://dx.doi.org/10.1128/aem.03767-12.

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ABSTRACTCytochrome P450 monooxygenases (P450s) are known to oxidize hydrocarbons, albeit with limited substrate specificity across classes of these compounds. Here we report a P450 monooxygenase (CYP63A2) from the model ligninolytic white rot fungusPhanerochaete chrysosporiumthat was found to possess a broad oxidizing capability toward structurally diverse hydrocarbons belonging to mutagenic/carcinogenic fused-ring higher-molecular-weight polycyclic aromatic hydrocarbons (HMW-PAHs), endocrine-disrupting long-chain alkylphenols (APs), and crude oil aliphatic hydrocarbonn-alkanes. A homology-based three-dimensional (3D) model revealed the presence of an extraordinarily large active-site cavity in CYP63A2 compared to the mammalian PAH-oxidizing (CYP3A4, CYP1A2, and CYP1B1) and bacterial aliphatic-hydrocarbon-oxidizing (CYP101D and CYP102A1) P450s. This structural feature in conjunction with ligand docking simulations suggested potential versatility of the enzyme. Experimental characterization using recombinantly expressed CYP63A2 revealed its ability to oxidize HMW-PAHs of various ring sizes, including 4 rings (pyrene and fluoranthene), 5 rings [benzo(a)pyrene], and 6 rings [benzo(ghi)perylene], with the highest enzymatic activity being toward the 5-ring PAH followed by the 4-ring and 6-ring PAHs, in that order. Recombinant CYP63A2 activity yielded monohydroxylated PAH metabolites. The enzyme was found to also act as an alkane ω-hydroxylase that oxidizedn-alkanes with various chain lengths (C9to C12and C15to C19), as well as alkyl side chains (C3to C9) in alkylphenols (APs). CYP63A2 showed preferential oxidation of long-chain APs and alkanes. To our knowledge, this is the first P450 identified from any of the biological kingdoms that possesses such broad substrate specificity toward structurally diverse xenobiotics (PAHs, APs, and alkanes), making it a potent enzyme biocatalyst candidate to handle mixed pollution (e.g., crude oil spills).

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35

Choi, Hong Dae, and Uk Lee. "Crystal structure of 2,5-dimethyl-3-(2-methylphenylsulfonyl)-1-benzofuran." Acta Crystallographica Section E Structure Reports Online 70, no.11 (October24, 2014): o1181—o1182. http://dx.doi.org/10.1107/s1600536814022788.

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The title compound, C17H16O3S, crystallized with two independent molecules (AandB) in the asymmetric unit. The dihedral angle between the benzofuran ring system [r.m.s. deviation of 0.013 (1) forAand 0.009 (1) Å forB] and the 2-methylphenyl ring is 83.88 (5) forAand 86.94 (5)° forB. In the crystal, theBmolecules are linked into a chain along theb-axis direction by C—H...O hydrogen bonds. TheAmolecules are connected on either side of this chain by further C—H...O hydrogen bonds. These chains are linkedviaC—H...π interactions, forming sheets parallel to (100). There are also very weak π–π interactions present [centroid–centroid distance = 3.925 (11) Å] involvingthe 2-methylphenyl rings of neighbouringAandBmolecules.

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36

Heatherly, Henry, and Altha Blanchet. "N-th root rings." Bulletin of the Australian Mathematical Society 35, no.1 (February 1987): 111–23. http://dx.doi.org/10.1017/s0004972700013083.

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A ring for which there is a fixed integer n ≥ 2 such that every element in the ring has an n-th in the ring is called an n-th root ring. This paper gives numerous examples of diverse types of n-th root rings, some via general construction procedures. It is shown that every commutative ring can be embedded in a commutative n-th root ring with unity. The structure of n-th root rings with chain conditions is developed and finite n-th root rings are completely classified. Subdirect product representations are given for several classes of n-th root rings.

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37

Fun, Hoong-Kun, Chin Wei Ooi, S.Samshuddin, B.Narayana, and B.K.Sarojini. "[2,6-Bis(biphenyl-4-yl)-4-hydroxy-4-(pyridin-2-yl)cyclohexane-1,3-diyl]bis[(pyridin-2-yl)methanone]–butan-2-one (1/1)." Acta Crystallographica Section E Structure Reports Online 68, no.6 (May5, 2012): o1633—o1634. http://dx.doi.org/10.1107/s1600536812019241.

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In the title solvate, C47H37N3O3·C4H8O, the cyclohexane ring adopts a chair conformation and the plane through its near coplanar atoms forms dihedral angles of 82.58 (7), 89.27 (7), 60.30 (8), 54.54 (7) and 72.03 (7)°, respectively, with the three pyridine rings and the two attached benzene rings. The rings of the biphenyl units are twisted from each other, making dihedral angles of 35.27 (7) and 45.41 (7)°. All the rings are in equatorial orientations in the cyclohexane ring, except for the C=O-bonded pyridine ring in position 1, which is axial. Intramolecular O—H...N and C—H...O hydrogen bonds form one S(5) and three S(6) ring motifs. In the crystal, molecules are linked via C—H...O hydrogen bonds into a chain along the c axis. The crystal structure also features weak C—H...π interactions and aromatic π–π stacking [centroid–centroid distances = 3.5856 (10) and 3.7090 (9) Å].

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38

Jagadeesan, Gajendran, Immanuel Monica Chandramalar, Jayachandran Karunakaran, Solaiappan Gopinath, and ArasambattuK.Mohanakrishnan. "Crystal structure of dimethyl 1-oxo-2,4-diphenyl-1,2-dihydronaphthalene-2,3-dicarboxylate." Acta Crystallographica Section E Crystallographic Communications 74, no.3 (February13, 2018): 349–51. http://dx.doi.org/10.1107/s2056989018002360.

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In the title compound, C26H20O5, a 1,2-dihydronaphthalene derivative, the cyclohexa-1,3-diene ring of the 1,2-dihydronaphthalene ring system adopts a half-chair conformation. The mean plane of the 1,2-dihydronapthalene ring system makes dihedral angles of 86.23 (6) and 64.80 (7)° with two phenyl rings. The carbonyl O atom attached to the dihydronaphthalene ring system deviates from the mean plane of the 1,2-dihydronaphthalene ring system by 0.618 (1) Å. In the crystal, the molecules are linked into layers parallel to thebcplaneviatwo kinds of C—H...O interactions, one of which forms aC(10) chain motif running along thec-axis direction and the other forms anR22(6) ring motif. Adjacent layers are further connected by C—H...π and offset π–π interactions [centroid–centroid distance = 3.6318 (9) Å].

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39

Gasser, Gilles, and Helen Stoeckli-Evans. "N-(2-Pyridylcarbonyl)benzamide." Acta Crystallographica Section E Structure Reports Online 63, no.3 (February23, 2007): o1455—o1456. http://dx.doi.org/10.1107/s1600536807008355.

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The title compound, C13H10N2O2, has a Z,Z (trans–trans) arrangement of the central CONHCO group and an intramolecular N—H...N hydrogen bond. The molecule has a twisted conformation; the pyridine ring, which is almost parallel to the plane of the amide function at position 2, is inclined to the phenyl ring by 50.05 (6)°. In the crystal structure, symmetry-related molecules are linked by C—H...O hydrogen bonds, forming a zigzag polymer chain extending in the a-axis direction. The chains are linked by a C—H...π interaction involving phenyl rings of adjacent chains. There is also a π–π interaction involving pyridine rings related by a center of symmetry.

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40

Singh, Abhay Kumar, Narendra Kumar, and Kar Ping Shum. "Cyclic self-orthogonal codes over finite chain ring." Asian-European Journal of Mathematics 11, no.06 (December 2018): 1850078. http://dx.doi.org/10.1142/s179355711850078x.

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In this paper, we study the cyclic self-orthogonal codes over a finite commutative chain ring [Formula: see text], where [Formula: see text] is a prime number. A generating polynomial of cyclic self-orthogonal codes over [Formula: see text] is obtained. We also provide a necessary and sufficient condition for the existence of nontrivial self-orthogonal codes over [Formula: see text]. Finally, we determine the number of the above codes with length [Formula: see text] over [Formula: see text] for any [Formula: see text]. The results are given by Zhe-Xian Wan on cyclic codes over Galois rings in [Z. Wan, Cyclic codes over Galois rings, Algebra Colloq. 6 (1999) 291–304] are extended and strengthened to cyclic self-orthogonal codes over [Formula: see text].

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41

Mohamad, Khalit, Mahfizah Yusoff, Khalijah Awang, Kartini Ahmad, and Seik Weng Ng. "Pinnatane A from the bark ofWalsura pinnataHassk." Acta Crystallographica Section E Structure Reports Online 65, no.6 (May20, 2009): o1317. http://dx.doi.org/10.1107/s1600536809015955.

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In the molecule of pinnatane A, C30H48O3, isolated from the bark ofWalsura pinnataHassk, the four cyclohexane rings adopt chair conformations; the carboxyl and hydroxy substituents occupy axial positions. The cyclohexene ring is envelope-shaped. Adjacent molecules are linked by O—H...O hydrogen bonds into a chain running along thecaxis.

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42

Al-Ezeh,H. "Two properties of the power series ring." International Journal of Mathematics and Mathematical Sciences 11, no.1 (1988): 9–13. http://dx.doi.org/10.1155/s0161171288000031.

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For a commutative ring with unity,A, it is proved that the power series ringA〚X〛is a PF-ring if and only if for any two countable subsetsSandTofAsuch thatS⫅annA(T), there existsc∈annA(T)such thatbc=bfor allb∈S. Also it is proved that a power series ringA〚X〛is a PP-ring if and only ifAis a PP-ring in which every increasing chain of idempotents inAhas a supremum which is an idempotent.

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43

Radics, Ute, Jürgen Liebscher, Burkhard Ziemer, and Viktor Rybakov. "Ring-chain transformations, IX[1] Synthesis and ring-chain tautomerism of 2-(-aminoalkyl)-1,3,4-thiadiazoles." Chemische Berichte 125, no.6 (June 1992): 1389–95. http://dx.doi.org/10.1002/cber.19921250614.

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44

Siddiqui, Sadaf, Osayemwenre Erharuyi, Abiodun Falodun, M.IqbalChoudhary, and Sammer Yousuf. "Crystal structure of (3S*,4S*,4aS*,5R*,6R*,6aS*,7R*,11aS*,11bR*)-5,6-bis(benzoyloxy)-3,4a-dihydroxy-4,7,11b-trimethyl-1,2,3,4,4a,5,6,6a,7,11,11a,11b-dodecahydrophenanthro[3,2-b]furan-4-carboxylic acid methanol monosolvate." Acta Crystallographica Section E Crystallographic Communications 71, no.10 (September12, 2015): o739—o740. http://dx.doi.org/10.1107/s2056989015016461.

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The title compound, C34H36O9·CH3OH, is a diterpenoid isolated from the roots ofCaesalpinia pulcherrima(L.) Swartz. The threetrans-fused six-membered rings are in chair, chair and half-chair conformations. The mean plane of this fused-ring system makes dihedral angles of 67.95 (15) and 83.72 (14)° with the two phenyl rings of the benzoyloxy groups. An intramolecular C—H...O hydrogen bond is observed. In the crystal, molecules are linkedviaO—H...O hydrogen bonds, forming an infinite chain along theb-axis direction.

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45

BISI, MARIA CRISTINA, RITA STAGNI, GIANNI GNUDI, and ANGELO CAPPELLO. "NON-CIRCULAR CHAIN RING ALLOWS A REDUCTION OF JOINT LOADING IN CYCLING." Journal of Mechanics in Medicine and Biology 10, no.01 (March 2010): 113–22. http://dx.doi.org/10.1142/s0219519410003228.

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Non-circular (NC) chain rings were primarily designed to improve the mechanical effectiveness of cycling. Their use can be investigated for application in rehabilitation: they could provide a solution to design an effective exercise reducing joint loading. The aim of this study was to analyze the differences in kinematics, energy consumption, and joint moments between circular and NC chain rings, then to identify a profile that can reduce joint loads, maintaining equal mechanical and metabolic works. Five young participants performed two tests on a cycloergometer; one with a circular chain ring and the other with an NC one. The test consisted in 15 min of cycling; during which they were asked to cycle at three different speeds and at two different powers. Stereophotogrammetric and metabolic data were acquired. Statistical analysis was applied on metabolic data. Joint angular velocities were obtained from kinematic data. A two-dimensional (2D) model of cycling was designed to estimate joint moments with both chain rings. A different ring profile was suggested to further reduce joint flexion peak moment. NC chain ring allows a reduction of flexion joint moments with respect to the circular one without significant difference in metabolic and kinematic data. The new profile proposed further decreases maximum knee flexion moment maintaining equal mechanical work.

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46

Ogoshi, Tomoki, Tomohiro Akutsu, and Tada-aki Yamagishi. "An amphiphilic pseudo[1]catenane: neutral guest-induced clouding point change." Beilstein Journal of Organic Chemistry 14 (July26, 2018): 1937–43. http://dx.doi.org/10.3762/bjoc.14.167.

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The hydrophobic/hydrophilic ratio in a molecule largely affects its assembled properties in aqueous media. In this study, we synthesized a new bicyclic compound which could dynamically change its hydrophobic/hydrophilic ratio by chemical stimulus. The bicyclic compound consisted of amphiphilic pillar[5]arene and hydrophobic alkyl chain rings, and formed a self-inclusion structure in aqueous media, which was assigned as a pseudo[1]catenane structure. The hydrophobic chain ring was hidden inside the pillar[5]arene cavity in the pseudo[1]catenane structure, thus the bicyclic compound was soluble in water at 20 °C with a clouding point at 24 °C. The pseudo[1]catenane was converted to the de-threaded structure upon addition of the neutral guest 1,4-dicyanobutane, which displaced the alkyl chain ring from the inside to the outside of the cavity. The hydrophobic alkyl chain ring was now exposed to the aqueous media, causing aggregation of the hydrophobic alkyl chain rings, which induced insolubilization of the bicyclic compound in aqueous media at 20 °C and a decrease in its clouding point.

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47

Lin, Hui-Hui, Xiao-Lin Zheng, and Sheng-Li Cao. "5-Methyl-3,3-bis(4-methylpiperazin-1-yl)-1-[2-(4-methylpiperazin-1-yl)ethyl]indolin-2-one." Acta Crystallographica Section E Structure Reports Online 68, no.6 (May23, 2012): o1855. http://dx.doi.org/10.1107/s1600536812022416.

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In the title compound, C26H43N7O, each piperazine ring adopts a chair conformation. Two 1-methylpiperazine rings bond to one Csp 3 of the pyrrole ring via the piperazine N atoms, while the third one links to the N atom of the indolin-2-one unit through a flexible ethyl group with an almost syn conformation. In the crystal, molecules are connected through methylene–carbonyl C—H...O interactions into an infinite chain along the c axis. The almost parallel arrays are stacked, forming a three-dimensional framework.

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48

Bahadur,S.Asath, M.Rajalakshmi, S.Athimoolam, R.SayeeKannan, and V.Ramakrishnan. "Chain and ring motifs in bis(creatininium) sulfate." Acta Crystallographica Section E Structure Reports Online 63, no.11 (October3, 2007): o4195. http://dx.doi.org/10.1107/s1600536807046119.

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The title compound, 2C4H8N3O+·SO4 2−, crystallizes with two creatininium cations and one sulfate anion in the asymmetric unit. Cations and anions dimerize through N—H...O hydrogen bonds forming R 2 2(8) ring motifs. Furthermore, these rings are connected via N—H...O hydrogen bonds, leading to C 2 2(6) and C 2 2(8) chain motifs. These interactions lead to a parallel set of hydrogen-bonded lamellar aggregations propagating along the c axis of the unit cell. Another cation is situated above these sheets, leading to a grid-like structure.

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49

Hagita, Katsumi, and Takahiro Murashima. "Multi-ring configurations and penetration of linear chains into rings on bonded ring systems and polycatenanes in linear chain matrices." Polymer 223 (May 2021): 123705. http://dx.doi.org/10.1016/j.polymer.2021.123705.

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50

Peng, Yin, Lei Wang, Xiao Feng Jiang, Feng Ling Zhang, and Gui Xiang Xiao. "Vision-Based Deformation Measurement of Loaded Three-Ring Chain." Advanced Materials Research 490-495 (March 2012): 865–70. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.865.

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The deformation measurement of loaded Three-Ring Chains is of great significance for production safety. In this study, a machine vision system for measuring deformation of loaded Three-Ring chains is developed. The measuring system uses a back diffuse light illumination and a CMOS industrial camera. A measurement algorithm based on sub-pixel edge extraction, contour segmentation, contour fitting is designed. The system can measure the long axis length of outer diameter (OLL) of the each ring of loaded three-ring chains. For the visual system, the absolute error is 0.004 mm, the standard deviation is 0.0024 mm. For the whole system, the absolute error is less than 0.015 mm, the relative error to the full-length of chain is less than 0.25 ‰, the relative error to the total amount of the stretching deformation is less than 2‰.

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