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Journal articles on the topic 'Heptagon'

Author: Grafiati

Published: 28 June 2021

Last updated: 17 February 2022

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1

Meunier, V., and P. Lambin. "Propriétés structurales des jonctions de nanotubes de carbone." Canadian Journal of Physics 77, no. 9 (February 1, 2000): 667–75. http://dx.doi.org/10.1139/p99-004.

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The junction between two different nanotubes can be realized by the simple insertion of a pentagon-heptagon pair defect while preserving the triple coordination of each C atom. This insertion bends the structure to an angle depending on the distance between the pentagonand heptagon. The atomic structure of several of these junctions was optimized with the help of empirical potentials, the nanotubes on both sides of the junctions being considered as infinitely long. Local densities of σ + π electronic states were evaluated in the interfacial regions from a tight-binding Hamiltonian. From there, the electronic energy of these junctions was calculated and compared with that of the isolated nanotubes. It was established that the energy associated with the pentagon-heptagone pair in a graphitic tubule is of the order of 6 eV. An automatic generation algorithm for connecting any two tubules was developed. By restricting the Hamiltonian to the sole π orbitals, this algorithm made it feasible to study the energetics of the pentagon-heptagon defect in a systematical way.

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2

Zukrianto, Zukrianto, Rima Erfianti, Rahmawati Rahmawati, and Ade Novia Rahma Ade Novia Rahma. "Pengembangan Teorema Ceva pada Heptagon Nonkonveks." Jurnal Sains Matematika dan Statistika 7, no. 1 (February 26, 2021): 20. http://dx.doi.org/10.24014/jsms.v7i1.11579.

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Teorema Ceva pada dasarnya merupakan suatu teorema yang berlaku pada segitiga. Dalam penelitian ini teorema Ceva dikembangkan pada heptagon nonkonveks dalam dua kasus. Kasus satu menunjukkan kekonkurenan tujuh buah garis di dalam heptagon nonkonveks dan kasus dua menunjukkan kekonkurenan tujuh buah garis di luar heptagon nonkonveks. Proses ini dimulai dengan pengkontruksian heptagon nonkonveks menggunakan aplikasi Geogebra, selanjutnya pembuktian teorema Ceva dilakukan dengan menggunakan prinsip perbandingan luas pada segitiga. Hasil yang diperoleh dari penelitian ini adalah eksistensi tujuh buah garis dari masing-masing titik sudut pada heptagon nonkonveks berpotongan di satu titik (konkuren) yaitu titik yang berada di dalam dan di luar heptagon nonkonveks.Kata Kunci: Segitiga, Teorema Ceva, Heptagon nonkonveks

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3

Belitsky, A. V. "Resummed tree heptagon." Nuclear Physics B 929 (April 2018): 113–36. http://dx.doi.org/10.1016/j.nuclphysb.2018.01.031.

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4

Porter, A. F. "THE REGULAR HEPTAGON." Survey Review 31, no. 245 (July 1992): 409–12. http://dx.doi.org/10.1179/sre.1992.31.245.409.

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5

Douce, J. L. "THE REGULAR HEPTAGON." Survey Review 32, no. 248 (April 1993): 121. http://dx.doi.org/10.1179/sre.1993.32.248.121.

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6

Cawthorne, Stephanie, and Judy Green. "Harold and the Purple Heptagon." Math Horizons 17, no. 1 (September 2009): 5–9. http://dx.doi.org/10.1080/10724117.2009.11974834.

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7

Crompton, T. O. "CONSTRUCTION FOR A REGULAR HEPTAGON." Survey Review 32, no. 248 (April 1993): 122. http://dx.doi.org/10.1179/sre.1993.32.248.122.

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8

Cawthorne, Stephanie, and Judy Green. "Harold and the Purple Heptagon." Math Horizons 17, no. 1 (September 1, 2009): 5–9. http://dx.doi.org/10.4169/194762109x468283.

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9

Jiménez, Vicente G., Rubén Tapia, Miguel A. Medel, Inês F. A. Mariz, Tânia Ribeiro, Victor Blanco, Juan M. Cuerva, Ermelinda Maçôas, and Araceli G. Campaña. "Aggregation-induced emission of [3]cumulenes functionalized with heptagon-containing polyphenylenes." Chemical Communications 54, no. 27 (2018): 3359–62. http://dx.doi.org/10.1039/c8cc00386f.

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10

Márquez, Irene R., Noelia Fuentes, Carlos M. Cruz, Virginia Puente-Muñoz, Lia Sotorrios, M. Luisa Marcos, Duane Choquesillo-Lazarte, et al. "Versatile synthesis and enlargement of functionalized distorted heptagon-containing nanographenes." Chemical Science 8, no. 2 (2017): 1068–74. http://dx.doi.org/10.1039/c6sc02895k.

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11

Deng, X. Q., and R. Q. Sheng. "Electronic and thermal spin effect of molecular nanowires between graphene electrodes." RSC Advances 8, no. 60 (2018): 34182–91. http://dx.doi.org/10.1039/c8ra06852f.

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12

Lluis i Ginovart, Josep, Gerard Fortuny Anguera, Agustí Costa Jover, and Pau de Sola-Morales Serra. "Gothic Construction and the Traça of a Heptagonal Apse: The Problem of the Heptagon." Nexus Network Journal 15, no. 2 (May 22, 2013): 325–48. http://dx.doi.org/10.1007/s00004-013-0152-x.

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13

Deng, Qingming, and Alexey A. Popov. "Prato and Bingel–Hirsch cycloaddition to heptagon-containing LaSc2N@Cs(hept)-C80: importance of pentalene units." Chemical Communications 51, no. 26 (2015): 5637–40. http://dx.doi.org/10.1039/c5cc00296f.

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In heptagon-containing LaSc₂N@C₈₀both thermodynamically controlled Prato addition and kinetically-controlled Bingel–Hirsch reaction are predicted to functionalize pentalene fragments.

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14

Cheung, Kwan Yin, Shuaijun Yang, and Qian Miao. "From tetrabenzoheptafulvalene to sp2 carbon nano-rings." Organic Chemistry Frontiers 4, no. 5 (2017): 699–703. http://dx.doi.org/10.1039/c6qo00828c.

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15

Ushakov, V. N., and M. V. Pershakov. "On estimation of Hausdorff deviation of convex polygons in $\mathbb{R}^2$ from their differences with disks." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 4 (December 2020): 585–603. http://dx.doi.org/10.35634/vm200404.

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We study a problem concerning the estimation of the Hausdorff deviation of convex polygons in $\mathbb R^2$ from their geometric difference with circles of sufficiently small radius. Problems with such a subject, in which not only convex polygons but also convex compacts in the Euclidean space $\mathbb R^n$ are considered, arise in various fields of mathematics and, in particular, in the theory of differential games, control theory, convex analysis. Estimates of Hausdorff deviations of convex compact sets in $\mathbb R^n$ in their geometric difference with closed balls in $\mathbb R^n$ are presented in the works of L.S. Pontryagin, his staff and colleagues. These estimates are very important in deriving an estimate for the mismatch of the alternating Pontryagin’s integral in linear differential games of pursuit and alternating sums. Similar estimates turn out to be useful in deriving an estimate for the mismatch of the attainability sets of nonlinear control systems in $\mathbb R^n$ and the sets approximating them. The paper considers a specific convex heptagon in $\mathbb R^2$. To study the geometry of this heptagon, we introduce the concept of a wedge in $\mathbb R^2$. On the basis of this notion, we obtain an upper bound for the Hausdorff deviation of a heptagon from its geometric difference with the disc in $\mathbb R^2$ of sufficiently small radius.

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16

FENG, C., P. F. HE, K. M. LIEW, and W. XU. "PREDICTED MECHANICAL PROPERTIES OF CARBON NANOTUBE-BASED STRUCTURES." International Journal of Applied Mechanics 06, no. 03 (May 6, 2014): 1450027. http://dx.doi.org/10.1142/s1758825114500276.

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Carbon nanoring (CNR) with heptagon–pentagon defects is formed by single-walled carbon nanotubes (SWCNTs) (5, 5) and (9, 0) and each junction is constructed by connecting a heptagonal and a pentagonal carbon-atom ring. Then cutting the ring into two pieces along the junction, one pitch of carbon nanocoil will be obtained by constraining one end and stretching the other end along the helical axis. Molecular mechanics (MM) simulations are employed to investigate the mechanical characteristics of CNRs and nanocoils with and without defects. The Young's modulus of the nanoring with defects is about 282 GPa, which is larger than that of perfect nanorings with the similar ring radii, such as (5, 5) and (9, 0). The spring stiffness of the carbon nanocoil is calculated with a maximum value of 2.08 N/m, and it is found to be nonlinear and decreases with the increase in the relative elongation.

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17

Gleason, Andrew M. "Angle Trisection, the Heptagon, and the Triskaidecagon." American Mathematical Monthly 95, no. 3 (March 1988): 185. http://dx.doi.org/10.2307/2323624.

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18

Steinbach, Peter. "Golden Fields: A Case for the Heptagon." Mathematics Magazine 70, no. 1 (February 1, 1997): 22. http://dx.doi.org/10.2307/2691048.

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19

Knorr, Wilbur R. "On Archimedes' Construction of the Regular Heptagon." Centaurus 32, no. 3 (October 1989): 257–71. http://dx.doi.org/10.1111/j.1600-0498.1989.tb00848.x.

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20

Gleason, Andrew M. "Angle Trisection, the Heptagon, and the Triskaidecagon." American Mathematical Monthly 95, no. 3 (March 1988): 185–94. http://dx.doi.org/10.1080/00029890.1988.11971989.

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21

Steinbach, Peter. "Golden Fields: A Case for the Heptagon." Mathematics Magazine 70, no. 1 (February 1997): 22–31. http://dx.doi.org/10.1080/0025570x.1997.11996494.

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22

Rezaei, Ali Asghar. "Tiling Fullerene Surface with Heptagon and Octagon." Fullerenes, Nanotubes and Carbon Nanostructures 23, no. 12 (June 26, 2015): 1033–36. http://dx.doi.org/10.1080/1536383x.2015.1057817.

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23

Ma, Chuanxu, Haifeng Sun, Hongjian Du, Jufeng Wang, Aidi Zhao, Qunxiang Li, Bing Wang, and J. G. Hou. "Structural and electronic properties of an ordered grain boundary formed by separated (1,0) dislocations in graphene." Nanoscale 7, no. 7 (2015): 3055–59. http://dx.doi.org/10.1039/c4nr06789d.

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We present an investigation of the structural and electronic properties of a linear periodic chain of pentagon-heptagon pairs in single-layer graphene/SiO₂ using scanning tunneling microscopy/spectroscopy, joint with density functional theory calculations.

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24

Reynolds, Mark A. "From Pentagon to Heptagon: A Discovery on the Generation of the Regular Heptagon from the Equilateral Triangle and Pentagon." Nexus Network Journal 3, no. 2 (September 2001): 139–46. http://dx.doi.org/10.1007/s00004-001-0028-3.

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25

Kuzmar, Isaac E., Mercedes Rizo, and Ernesto Cortés. "How to create a telemedicine service: telemedicine heptagon." ACTUALIDAD MEDICA 99, no. 791 (April 30, 2014): 44–45. http://dx.doi.org/10.15568/am.2014.791.cd03.

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26

Boatto, Stefanella, and Carles Simó. "Thomson’s Heptagon: A case of bifurcation at infinity." Physica D: Nonlinear Phenomena 237, no. 14-17 (August 2008): 2051–55. http://dx.doi.org/10.1016/j.physd.2008.02.030.

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27

Udomvech, A., and Teerakiat Kerdcharoen. "Electronic Structure of Straight and T-Shape Singled-Wall Carbon Nanotube Junctions: A Molecular Quantum Mechanics Study." Advanced Materials Research 55-57 (August 2008): 565–68. http://dx.doi.org/10.4028/www.scientific.net/amr.55-57.565.

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In this paper, the straight and T-shape single-walled carbon nanotube intramolecular junction (SWCNT-IMJ) were studied theoretically. The geometries of topological defect can be constructed by fusing two nanotubes having different helicities and diameters. For straight IMJ, the armchair (5,5) and (8,8) nanotubes segments were fused with the zigzag (n,0) segment varying from (6,0) to (10,0). T-junctions were constructed by joining a zigzag (n,0) tube, varying from n = 5 to 10, onto a fixed zigzag (9,0) tube sidewall. These junctions are composed of one or more pentagon and heptagon rings, and mixed pentagon-heptagon pairs as defects in the perfect hexagonal lattice. The study shows that the occurrence of defects geometries on SWCNT-IMJ and T-shape structures depends on the variation of tube helicity and diameter of combining nanotubes. The HOMO-LUMO energy levels exhibit the even-odd “quantum size” oscillation. The decreasing energy gap depends on variation of tube helicity and diameter of carbon nanotube. This study can be helpful as a knowledge base in the field of carbon nanotube molecular electronics.

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28

Saito, Yahachi, and Masatomo Maida. "Square, Pentagon, and Heptagon Rings at BN Nanotube Tips." Journal of Physical Chemistry A 103, no. 10 (March 1999): 1291–93. http://dx.doi.org/10.1021/jp983510c.

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29

Buring, Ricardo, Arthemy V. Kiselev, and Nina J. Rutten. "The heptagon-wheel cocycle in the Kontsevich graph complex." Journal of Nonlinear Mathematical Physics 24, sup1 (December 21, 2017): 157–73. http://dx.doi.org/10.1080/14029251.2017.1418060.

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30

Wünsche, A. "Construction of Regular Heptagon by Rhombic Bicompasses and Ruler." Applied Mathematics 05, no. 15 (2014): 2370–80. http://dx.doi.org/10.4236/am.2014.515229.

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31

Milewski, Jan, Grzegorz Banaszak, Tadeusz Lulek, Mirosław Łabuz, and Ryszard Stagraczyński. "Galois Actions on the Eigenproblem of the Heisenberg Heptagon." Open Systems & Information Dynamics 19, no. 02 (June 2012): 1250012. http://dx.doi.org/10.1142/s1230161212500126.

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We analyse the exact solution of the eigenproblem for the Heisenberg Hamiltonian of magnetic heptagon, i.e. the ring of N = 7 nodes, each with spin 1/2, within the XXX model with nearest neighbour interactions, from the point of view of finite extensions of the field ℚ of rationals. We point out, as the main result, that the associated arithmetic structure of these extensions makes natural an introduction of some Galois qubits. They are two-dimensional subspaces of the Hilbert space of the model, which admit a quantum informatic interpretation as elementary memory units for a (hypothetical) computer, based on their distinctive properties with respect to the action of related Galois group for indecomposable factors of the secular determinant. These Galois qubits are nested on the lattice of subfields which involves several minimal fields for determination of eigenstates (the complex Heisenberg field), spectrum (the real Heisenberg field), and Fourier transforms of magnetic configurations (the cyclotomic field, based on the simple 7th root of unity). The structure of the corresponding lattice of Galois groups is presented in terms of Kummer theory, and its physical interpretation is indicated in terms of appropriate permutations of eigenstates, energies, and density matrices.

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32

Frederickson, Greg N. "The heptagon to the square, and other wild twists." Mathematical Intelligencer 29, no. 4 (September 2007): 23–33. http://dx.doi.org/10.1007/bf02986173.

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33

Wills, Jörg M. "A locally regular heptagon–dodecahedron embedded in 3-space." European Journal of Combinatorics 29, no. 8 (November 2008): 1952–55. http://dx.doi.org/10.1016/j.ejc.2008.01.014.

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34

Gouda, Osama E., Salah H. El-Hoshy, and Hassan H. El-Tamaly. "Proposed heptagon graph for DGA interpretation of oil transformers." IET Generation, Transmission & Distribution 12, no. 2 (January 30, 2018): 490–98. http://dx.doi.org/10.1049/iet-gtd.2017.0826.

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35

Iragavarapu, S. N. AR G. Bharat. "Computational Approach for Finding Pythagoras Heptagon Using Programming language Java." International Journal for Research in Applied Science and Engineering Technology V, no. IX (September 30, 2017): 347–51. http://dx.doi.org/10.22214/ijraset.2017.9052.

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36

HU, H. "Electronic properties of carbon nanotubes with pentagon?heptagon pair defects." Diamond and Related Materials 10, no. 9-10 (September 2001): 1818–23. http://dx.doi.org/10.1016/s0925-9635(01)00428-9.

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37

Jiménez, Vicente G., Arthur H. G. David, Juan M. Cuerva, Victor Blanco, and Araceli G. Campaña. "A Macrocycle Based on a Heptagon‐Containing Hexa‐ peri ‐hexabenzocoronene." Angewandte Chemie International Edition 59, no. 35 (June 15, 2020): 15124–28. http://dx.doi.org/10.1002/anie.202003785.

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38

Deng, Shun-Liu. "(Invited) Capturing the Double-Heptagon-Containing C70 with Negative Curvature." ECS Meeting Abstracts MA2020-01, no. 9 (May 1, 2020): 776. http://dx.doi.org/10.1149/ma2020-019776mtgabs.

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39

Lei, Hongchuan, and Hung-Lin Fu. "The Hamilton–Waterloo Problem for Triangle-Factors and Heptagon-Factors." Graphs and Combinatorics 32, no. 1 (April 21, 2015): 271–78. http://dx.doi.org/10.1007/s00373-015-1570-1.

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40

Bernassau, A. L., F. Gesellchen, P. G. A. MacPherson, M. Riehle, and D. R. S. Cumming. "Direct patterning of mammalian cells in an ultrasonic heptagon stencil." Biomedical Microdevices 14, no. 3 (February 13, 2012): 559–64. http://dx.doi.org/10.1007/s10544-012-9633-z.

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41

Jiménez, Vicente G., Arthur H. G. David, Juan M. Cuerva, Victor Blanco, and Araceli G. Campaña. "A Macrocycle Based on a Heptagon‐Containing Hexa‐ peri ‐hexabenzocoronene." Angewandte Chemie 132, no. 35 (June 15, 2020): 15236–40. http://dx.doi.org/10.1002/ange.202003785.

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42

Prihanto, Hendi. "FACTORS AFFECTING THE PREVENTION OF CORRUPTION USING FRAUD HEPTAGON APPROACH." Moestopo International Review on Social, Humanities, and Sciences 1, no. 1 (February 28, 2021): 36–43. http://dx.doi.org/10.32509/mirshus.v1i1.9.

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This study aims to obtain evidence of the factors affecting the prevention of corruption in Indonesia by using the fraud Heptagon approach by analyzing the factors causing corruption through organizational culture, leadership, code of ethics, information technology, and governance as intervening variables. The population of the study is government agencies such as ministries, high state institutions, local governments, and other government organizations, obtained randomly through several activities of government agencies such as surveys and coordination meetings using google form and paper-based questionnaires. The results of the study show that information technology has a direct and significant effect on preventing corruption, while organizational culture and code of ethics has a significant indirect effect on good governance.

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43

Hoffmann, Florian, Gerrit W. Fester, and Jörg Wagler. "Die rotationsfehlgeordnete Kristallstruktur von Tropyliumbromid C7H7+Br– / The Rotationally Disordered Crystal Structure of Tropylium Bromide C7H7+Br−." Zeitschrift für Naturforschung B 65, no. 9 (September 1, 2010): 1137–42. http://dx.doi.org/10.1515/znb-2010-0913.

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The crystal structure of tropylium bromide, C7H7+Br−, was solved and refined in space group type R¯3m with rotationally disordered C7 rings. Restraints of identical 1,2- and 1,7-C-C bond lengths as well as identical 1,3- and 1,6-C-C separations within a flat C7H7 moiety were applied. The refinement converged to a regular C7 heptagon with C-C bond lengths of 139.1(1) pm. C7H7+Br− reacts with Mo(CO)3(CH3CN)3 to form C7H7Mo(CO)2Br.

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44

Zhao, Ruisheng, Zizhong Liu, and Xiang Zhao. "How to Stabilize a Heptagon-Containing C80 Cage by Endohedral Derivation." Inorganic Chemistry 59, no. 12 (June 1, 2020): 8099–107. http://dx.doi.org/10.1021/acs.inorgchem.0c00394.

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45

Hui-fang, Hu, Li Yi-bing, Zhou Wei-ya, and Tang Dong-sheng. "Electronic properties of carbon nanotubes with a pentagon-heptagon pair defect." Chinese Physics 10, no. 6 (June 2001): 531–36. http://dx.doi.org/10.1088/1009-1963/10/6/313.

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46

Gesellchen, F., A. L. Bernassau, T. Déjardin, D. R. S. Cumming, and M. O. Riehle. "Cell patterning with a heptagon acoustic tweezer – application in neurite guidance." Lab Chip 14, no. 13 (2014): 2266–75. http://dx.doi.org/10.1039/c4lc00436a.

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47

Zhong, Yuan‐Yuan, Zuo‐Chang Chen, Peng Du, Cun‐Hao Cui, Han‐Rui Tian, Xiang‐Mei Shi, Shun‐Liu Deng, et al. "Double Negatively Curved C 70 Growth through a Heptagon‐Involving Pathway." Angewandte Chemie International Edition 58, no. 40 (August 27, 2019): 14095–99. http://dx.doi.org/10.1002/anie.201902154.

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48

Zhong, Yuan‐Yuan, Zuo‐Chang Chen, Peng Du, Cun‐Hao Cui, Han‐Rui Tian, Xiang‐Mei Shi, Shun‐Liu Deng, et al. "Double Negatively Curved C 70 Growth through a Heptagon‐Involving Pathway." Angewandte Chemie 131, no. 40 (August 27, 2019): 14233–37. http://dx.doi.org/10.1002/ange.201902154.

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49

Ghobadi, Zahra Karimi, Aliasghar Shokri, and Sonia Zarei. "Effect of boron impurity in a carbon nanotube superlattice." International Journal of Modern Physics B 31, no. 14 (March 23, 2017): 1750106. http://dx.doi.org/10.1142/s0217979217501065.

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In this work, the influence of boron atom impurity is investigated on the electronic properties of a single-wall carbon nanotube superlattice which is connected by pentagon–heptagon topological defects along the circumference of the heterojunction of these superlattices. Our calculation is based on tight-binding [Formula: see text]-electron method in nearest-neighbor approximation. The density of states (DOS) and electronic band structure in presence of boron impurity has been calculated. Results show that when boron atom impurity and nanotube atomic layers have increased, electronic band structure and the DOS have significant changes around the Fermi level.

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50

Tan, Shi-Hua, Li-Ming Tang, Zhong-Xiang Xie, Chang-Ning Pan, and Ke-Qiu Chen. "Effect of pentagon–heptagon defect on thermal transport properties in graphene nanoribbons." Carbon 65 (December 2013): 181–86. http://dx.doi.org/10.1016/j.carbon.2013.08.012.

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