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Journal articles on the topic 'Heptagon'

Author: Grafiati

Published: 28 June 2021

Last updated: 21 June 2025

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1

Sánchez-Bernabe, Francisco J. "Study of fullerenes C₁₂₆ and C₁₅₆ with seven heptagon rings." Journal of Physics: Conference Series 2321, no. 1 (2022): 012028. http://dx.doi.org/10.1088/1742-6596/2321/1/012028.

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Abstract We consider fullerenes C126 and C156, both of them with seven heptagon rings. The first of them is C126 with 19 pentagons, and 39 hexagons. It is also considered C156 with 19 pentagons, and 54 hexagons. From previous work, a couple of fullerenes, C130 and C134, are mentioned for comparative reasons. These two fullerenes also contain seven heptagon rings. Fullerene C130 is constituted of 19 pentagons, and 41 hexagons. On the other hand, fullerene C134 has 19 pentagons, and 43 hexagons. Therefore, the four fullerenes considered, with seven heptagon rings, also share the property that, the number of pentagons in each of them, is 19. This fact is a consequence of a couple of equations that relates the number of pentagons, hexagons, and heptagons contained in a fullerene. Classical fullerenes contain only pentagons and hexagons, and the more familiar example is C60 with 20 hexagons, and 12 pentagons. Actually, all classical fullerenes have 12 pentagons, regardless of how many hexagons are involved. Besides this type of molecules, there exists nonclassical fullerenes, where another type of ring is presented, like squares, or heptagons. In this paper, fullerenes with 126, 130, 134, and 156 carbons are considered, with seven heptagons, and as a consequence, all them contain 19 pentagons, and they have 39, 41, 43, and 54 hexagons, respectively. Future work would focus on finding fullerenes with a different number of carbons, and hexagons, but with 7 heptagons, and 19 pentagons. Thus, fullerene C128 of this type, should contain 40 hexagons.

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2

Meunier, V., and P. Lambin. "Propriétés structurales des jonctions de nanotubes de carbone." Canadian Journal of Physics 77, no. 9 (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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3

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 (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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4

Porter, A. F. "THE REGULAR HEPTAGON." Survey Review 31, no. 245 (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 (1993): 121. http://dx.doi.org/10.1179/sre.1993.32.248.121.

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6

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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7

Prianasari, Eka Ningrum, and Isnaini Rosyida. "Nilai Ketakteraturan Sisi Total pada Graf Rantai Heptagon dan Graf Rantai Heptagon dengan Dua Sisi Pendant." Unnes Journal of Mathematics 11, no. 1 (2022): 38–43. http://dx.doi.org/10.15294/ujm.v11i1.35333.

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Diketahui sebuah graf G dengan himpunan titik tak kosong V(G) dan himpunan sisi E(G). Suatu pelabelan dikatakan pelabelan-k total tak teratur sisi jika setiap dua sisi berbeda memenuhi bobot sisi yang berbeda, dengan bobot suatu sisi adalah jumlah dari label sisi tersebut ditambah jumlah semua titik yang terkait pada sisi tersebut. Nilai ketakteraturan sisi total (total edge irregularity strength) graf G, yang dinotasikan dengan tes(G) adalah minimum k atau label terbesar minimum yang digunakan untuk melabeli titik dan sisi graf G dengan pelabelan total tak teratur sisi. Pada artikel ini, penulis menyelidiki nilai ketakteraturan sisi total pada graf rantai heptagon dan graf rantai heptagon dengan dua sisi pendant . Hasil dari penelitian ini yaitu nilai ketakteraturan sisi total pada graf rantai heptagon adalah batas atas dari 7r ditambah 2 kemudian dibagi 3, dan nilai ketakteraturan sisi total pada graf rantai heptagon dengan dua sisi pendant adalah batas atas dari 9r ditambah 2 kemudian dibagi 3.

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8

Prayogi, Gusti Dian, and Widiar Onny Kurniawan. "The Influence of the Fraud Heptagon on Fraud Levels in Indonesian State-Owned Enterprises: The Moderating Role of the Whistleblowing System." Majalah Ekonomi 31, no. 1 (2025): 49–59. https://doi.org/10.36456/majeko.vol31.no1.a10143.

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This study aims to explore the correlation between the theoretical construct of the Fraud Heptagon and the intensity of fraudulent practices in Indonesian State-Owned Enterprises (SOEs), as well as the moderating role of the whistleblowing system in this relationship. The Fraud Heptagon is a concept that expands upon previous theories, such as the Fraud Triangle and Fraud Diamond, by incorporating additional elements that influence fraud occurrence, namely financial pressure, opportunity, rationalization, capability, arrogance, and greed. The whistleblowing system is identified as a control mechanism that can mitigate fraud risks within organizations by enhancing transparency and accountability. This research adopts a quantitative approach, systematically analyzing data to identify patterns in the relationships between variables. The analysis method employed is Moderated Regression Analysis (MRA), a statistical technique that allows for testing interaction effects between the independent variable and the moderating variable in influencing the dependent variable. Data processing is conducted using SPSS version 26, which provides advanced analytical capabilities for estimating regression coefficients and testing the significance of relationships. Data collection is carried out through a survey targeting SOE auditors using purposive sampling. The findings indicate that the Fraud Heptagon has a positive and significant influence on the level of fraud (β = 0.42; Sig. 0.001), suggesting that the more complex the factors within the Fraud Heptagon, the higher the potential for fraudulent practices. The whistleblowing system is found to have a negative and significant impact on fraud (β = -0.35; Sig. 0.002), demonstrating that an effective reporting system can suppress fraudulent activities within an organization. Moreover, the moderating effect of the whistleblowing system on the relationship between the Fraud Heptagon and fraud is also significant and negative (β = -0.28; Sig. 0.004), indicating that the more effective the whistleblowing system, the weaker the relationship between the Fraud Heptagon and fraud levels

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9

White, Tony. "The Life Script Heptagon." International Journal of Transactional Analysis Research & Practice 13, no. 1 (2022): 53–61. http://dx.doi.org/10.29044/v13i1p53.

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The life script heptagon, developed by the author, is described to show how seven elements, all seven aspects of human personality – behaviour, feelings, thoughts, body holding patterns, habits, beliefs and attitudes, and early decisions – fit together geometrically so that they reinforce and support each other and make it hard for people to change their life scripts. These elements are then related to the ways in which different psychotherapies tend to work with them, and explanations are given of why the geometric nature of the model means that several aspects need to change because otherwise the remaining elements are reinforcing the unhelpful patterns. Editorial Note: This is an example of the saying ‘great minds think alike’ – this version of a heptagon was being developed over several years and the author was unaware that Benedetti, Benelli and Zanchetta (2020) had been developing a similar geometrical shape with different elements. Benedetti et al. were also unaware that the version described in this article was being developed. (Benedetti et al article is in this journal, Vol. 11, Issue 1 at https://doi.org/10.29044/v11i1p13)

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10

Lestari, Sari, and Siti Mutmainah. "Academic Fraud Enigma among Accounting Vocational School Students: Insights from Heptagon Framework and Relevance of Artificial Intelligence." Jurnal Dinamika Akuntansi dan Bisnis 11, no. 2 (2024): 207–28. https://doi.org/10.24815/jdab.v11i2.37442.

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This study aims to investigate the influence of heptagon theory elements, including pressure, opportunity, rationalization, competency, arrogance, greed, and ignorance, on academic fraud. Additionally, the study seeks to assess the moderating effect of Chat GPT usage, an artificial intelligence application, on the relationship between each element of heptagon theory and academic fraud. Employing a quantitative approach, the study focuses on the population of accounting students in vocational high schools, with a sample of 120 respondents meeting representativeness criteria calculated using the Cochran formula. Primary data is collected through respondents' responses obtained via a Google Form questionnaire. The results indicate that rationalization, competency, and greed exert has a significant influence on academic fraud among accounting students, whereas pressure, opportunity, arrogance, and ignorance do not exhibit a significant impact. Chat GPT, representing artificial intelligence, does not moderate the relationship between heptagon theory elements and academic fraud.

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11

Čerin, Zvonko. "Regular Heptagon’s Midpoints Circle." Sarajevo Journal of Mathematics 2, no. 1 (2024): 119–31. http://dx.doi.org/10.5644/sjm.02.1.13.

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This paper explores the geometry of the regular heptagon $ABCDEFG$. We start from a classical result by Thébault and Demir that six midpoints of sides and diagonals lie on a cirlce m with diameter equal to the side of the square inscribed in the circumcircle of $ABCDEFG$. Then we discover eight more midpoints of segments on $m$ and show that they are vertices of two regular heptagons inscribed in the circle $m$. Extending further this idea we show that midpoints of many other segments also lie on the circle $m$ so that it deserves the name – the midpoints circle of $ABCDEFG$. In the proofs we use the complex numbers and perform our calculations with the help of computers in Maple V. 2000 Mathematics Subject Classification. Primary 51N20, 51M04, Secondary 14A25, 14Q05

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12

Prayogi, Gusti Dian. "Pengaruh Fraud Heptagon terhadap Tingkat Fraud dalam Pengelolaan Keuangan Daerah: Peran Whistleblowing System di DPPKAD Jawa Timur." Behavioral Accounting Journal 6, no. 2 (2023): 1–16. https://doi.org/10.33005/baj.v6i2.368.

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The purpose of this study was to examine the effect of Fraud heptagon components on the level of fraud in regional financial management by considering the moderating effect of the whistleblowing system. The East Java Province Revenue, Financial Management, and Regional Asset Service (DPPKAD) which has 38 work units was the location of the study. A total of 150 employees were selected using a purposive sampling method based on factors of position, work experience, and involvement in regional financial management. Data were collected using a questionnaire and the results were analyzed using the Statistical Package for the Social Sciences (SPSS) 26. Multiple linear regression analysis, moderation interaction test, validity and reliability test, and classical assumption test were used to evaluate the effect of the whistleblowing system on the relationship between the Fraud heptagon variables and the level of fraud. Financial pressure, opportunity, rationalization, ability, arrogance, egoism, and external circumstances are the seven components of the Fraud heptagon, and the results show that these factors have a significant impact on the level of fraud in regional financial management. Furthermore, the relationship between fraud in regional financial management and fraud in Heptagon has been shown to be moderated by the violation disclosure system, which weakens it. According to the study's conclusion, increasing transparency, strengthening internal control systems, and improving disclosure systems can all be useful tactics to stop public sector fraud. It is hoped that this study will provide useful information for local governments to improve financial management and accountability.

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13

Mühlhölzer, Felix. "Witigenstein and the Regular Heptagon." Grazer Philosophische Studien 62, no. 1 (2001): 215–47. http://dx.doi.org/10.1163/18756735-06201011.

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The later Wittgenstein holds that the sole function of mathematical propositions is to determine the concepts they invoke. In the paper this view is discussed by means of a single example: Wittgenstein's investigation of the concept of a regular heptagon as used in Euclidean geometry (i.e., the Euclidean construction game with ruler and compass) and in Cartesian analytic geometry. Going on from some well-known passages in Wittgenstein’s Lectures on the Foundations of Mathematics, and completing these passages, it is shown that Wittgenstein’s view makes perfectly good sense and can be very well defended.

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14

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

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15

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

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16

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

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17

Jiménez, Vicente G., Rubén Tapia, Miguel A. Medel, et al. "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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18

Márquez, Irene R., Noelia Fuentes, Carlos M. Cruz, 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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19

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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20

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 (2013): 325–48. http://dx.doi.org/10.1007/s00004-013-0152-x.

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21

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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22

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 LaSc<sub>2</sub>N@C<sub>80</sub>both thermodynamically controlled Prato addition and kinetically-controlled Bingel–Hirsch reaction are predicted to functionalize pentalene fragments.

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23

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 (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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24

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 (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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25

Ma, Chuanxu, Haifeng Sun, Hongjian Du, et al. "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/SiO<sub>2</sub> using scanning tunneling microscopy/spectroscopy, joint with density functional theory calculations.

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26

Achmad, Tarmizi, Chen-Yuan Huang, Mukhlas Adi Putra, and Imang Dapit Pamungkas. "Strategy Model for Detecting Potential Fraudulent Financial Statements of State-Owned Enterprises in Indonesia: Fraud Heptagon Theory Analysis with Big Data Analytics, Risk Management, and Sustainable Development Goals (SDGS)." Journal of Lifestyle and SDGs Review 5, no. 2 (2024): e03659. https://doi.org/10.47172/2965-730x.sdgsreview.v5.n02.pe03659.

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Objective: Fraudulent financial statements are among the least frequent types of fraud globally but result in the highest median losses for companies. This study aims to develop a strategy model for detecting potential fraudulent financial statements in Indonesia’s State-Owned Enterprises (B.U.M.N.) by analyzing the Fraud Heptagon Theory, which includes stimulus, ability, collusion, opportunity, rationalization, ego, and big data analytics. Theoretical Framework: The study incorporates risk management and the audit committee as moderating variables to evaluate their roles in mitigating fraudulent financial reporting. Fraudulent financial statements were measured using the F-Score Model, emphasizing Goal 16 of the Sustainable Development Goals (SDGs): Peace, Justice, and Strong Institutions. Method: A total of 126 samples from 2018–2022 were obtained through purposive sampling. Data analysis employed Warp PLS 7.0 with a Structural Equation Modeling (SEM-PLS) approach. Results and Discussion: The findings reveal that most Fraud Heptagon Theory elements do not significantly affect fraudulent financial statements, except for financial pressure, which acts as a stimulus proxy. While big data analytics enhances risk management, it does not directly mitigate fraudulent reporting. The audit committee moderates the collusion relationship with fraudulent financial reporting, albeit with limited overall impact. Research Implications: This study offers a framework for stakeholders to leverage innovative technologies and governance strategies to improve financial transparency and accountability, aligning corporate practices with SDGs. Originality/Value: This research integrates the Fraud Heptagon Theory with big data analytics and SDGs, proposing a novel strategy model for detecting fraudulent financial statements in State-Owned Enterprises. It highlights the dynamic role of advanced technologies and governance in fraud detection.

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27

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

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28

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

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29

Wahyuni, Nonong, Mas hadi, and Sri Gemawati. "Modification of the Japanese Theorem on Heptagon." International Journal of Mathematics Trends and Technology 68, no. 6 (2022): 205–10. http://dx.doi.org/10.14445/22315373/ijmtt-v68i6p526.

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30

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

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31

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

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32

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

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33

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

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34

Adib, Noval, Meilenia Rahma, and Areta Widya. "Financial Reporting in the Perception of Heptagon Fraud Theory." Jurnal Ilmiah Manajemen Kesatuan 12, no. 6 (2024): 2559–68. https://doi.org/10.37641/jimkes.v12i6.2984.

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This study aims to examine the effect of fraud heptagon consisting of seven elements, namely pressure, rationalization, opportunity, arrogance, ability or competence, culture, and religiosity on financial statement fraud in SMEs employees in Indonesia. This research method is quantitative with a questionnaire. Respondents who were successfully collected were 250 who were SMEs employees in the finance department in Indonesia. Data were collected through questionnaire distribution and then processed using a statistical application, namely SPSS. The results obtained from the processing were pressure, rationalization, opportunity, arrogance, ability or competence, and culture had an effect on financial statement fraud. However, this study found that religiosity had no effect on financial statement fraud. The practical contribution of the study can be the implementation of the fraud heptagon theory in financial statement fraud and a practical contribution to all State-owned enterprises (SMEs) management in Indonesia, namely it can be an evaluation of how important pressure, rationalization, opportunity, arrogance, ability or competence, and culture are in preventing fraud.

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35

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 (2001): 139–46. http://dx.doi.org/10.1007/s00004-001-0028-3.

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36

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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37

Azizah, Siti, and Reskino Reskino. "Pendeteksian Fraudulent Financial Statement: Pengujian Fraud Heptagon Theory." Jurnal Akuntansi dan Governance 4, no. 1 (2023): 17. http://dx.doi.org/10.24853/jago.4.1.17-37.

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Objectives. This study aims to examine Reskino's (2022) heptagon fraud theory, which encompasses seven dimensions: pressure, opportunity, rationalization, competence, arrogance, culture, and religiosity.Design/method/approach. Data was collected through purposive sampling, wherein questionnaires were distributed to auditors in DKI Jakarta. A total of 117 respondents completed the questionnaires, and subsequently analyzed using SEM-PLS.Result/findings. The results show that pressure, opportunity, rationalization, and competence do not have a significant impact on detecting fraudulent financial statements. On the other hand, arrogance, culture, and religiosity are revealed to exert a strong influence in this regard.Theoretical contribution. This study represents the inaugural examination of the most recent fraud theory, known as the fraud heptagon theory, formulated by Reskino (2022). The primary aim is to address the existing gap in the literature, which lacks an explanation for fraud occurrences attributed to religious and cultural factors.Practical contribution. The anticipated outcome of this research is to provide valuable insights that could serve as input for regulators in formulating regulations that consider the influence of religion and culture.Limitations. This study solely relies on primary data gathered from the perspectives of auditors operating in the DKI Jakarta region. Consequently, the research scope is limited, making it inappropriate to generalize the findings to auditors outside the DKI Jakarta area.

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

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

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Becker, David A. "Tending to the Facial Surfaces of a Mathematical Biology Head-Scratcher: Why Does the Head of the Sea Turtle Natator depressus Resemble a Convex Zygomorphic Dodecahedron?" Animals 15, no. 1 (2025): 100. https://doi.org/10.3390/ani15010100.

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Two convex polyhedra that markedly resemble the head of the flatback sea turtle hatchling are identified. The first example is a zygomorphic tetragonal dodecahedron, while the other, an even better matching structure, is a related tetradecahedron, herein speculated to arise from this particular dodecahedron via known mechanisms gleaned from studies of the behavior of foams. A segmented, biomorphic, convex polyhedral model to address cephalic topology is thus presented stemming from solid geometry, anatomical observations, and a recently computed densest local packing arrangement of fifteen slightly oblate spheroids in which fourteen oblate spheroids surround a central such spheroid. This particular array of oblate spheroids shares salient structural features with the aforementioned dodecahedron. Successful testing of the model has been achieved by converting this array of fifteen oblate spheroids constructed with putty to the cephaloid dodecahedron in a process involving ventral elongation induced by stretching in the anterior direction along the anteroposterior axis (convergent extension). During convergent extension, the two left most anterolateral oblate spheroids that are in direct contact with the ventral spheroid of the array merge into a single lateral facet of the incipient dodecahedron, while the corresponding two right such oblate spheroids do the same. Thus, the fourteen outer oblate spheroids of the array give rise to the twelve facets of the finalized dodecahedron, while the central oblate spheroid remnant assumes an interior dodecahedral position. The hypothetical dodecahedron to tetradecahedron transformation entails the collapse of a tetravalent vertex (which is known to occur in foams as part of a T1 transition) followed by bilateral facet splitting. Remarkably, a model stipulating that convexity is to be retained in connection with this sequence of steps necessitates that the starting dodecahedral template undergoes modification to become a tetradecahedron in possession of precisely the highly ordered feature found at the top of the head of numerous specimens of the flatback sea turtle hatchling, namely, a fused medial pentagon–heptagon pair in the form of a pentagonal frontal scute and heptagonal frontoparietal scute. Such a possible new instance of geometric biomorphy, taken together with the correct anticipation of the cephalic pentagon–heptagon pair, might serve to instill further confidence in renewed efforts to shed light on morphogenesis with foam embryo models.

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

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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 (2017): 157–73. http://dx.doi.org/10.1080/14029251.2017.1418060.

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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 (2018): 490–98. http://dx.doi.org/10.1049/iet-gtd.2017.0826.

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

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

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Lluis-Teruel, Cinta, Josep Lluis i Ginovart, Iñigo Ugalde-Blázquez, and Ricardo Gómez-Val. "The Apse of the Gothic Cathedral of Tortosa versus Augustine of Hippo’s Civitate Dei." Religions 15, no. 8 (2024): 943. http://dx.doi.org/10.3390/rel15080943.

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This research delves into the influence of St. Augustine on the construction of the Gothic cathedral of Tortosa. The canonical cathedral of Tortosa underwent re-establishment in 1155, which was carried out by Bishop Godfrey who was the abbot of Saint Rufus of Avignon and was governed by Beati Augustini rule. The presence of St. Augustine in the Capitular archives with De Civitate Dei (ACTo-20) from the XII century is examined. This, coupled with a spatial analysis of the liturgical space using laser scanning (TLS), serves to validate the historiographical thesis put forth by Wilhelm Worringer, Erwin Panofsky, and Otto von Simson for understanding the construction of the apse of the Gothic cathedral (1346–1441). This methodology establishes a bijection between patristic and Neoplatonic sources and the interpretation of the liturgical space’s dimensions using statistical systems. This approach addresses the construction of the apse through the incorporation of a heptagon, a geometric figure that is absent in Euclid’s Elementa and Ptolemy’s Almagest. In conclusion, it is determined that both the imagery and metrics employed in the design of a radial heptagonal apse, as well as its cross-section, are influenced by both St. Augustine and the metrics of the Neoplatonics, which remain present in the Chapter Archives.

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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 (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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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 (2017): 347–51. http://dx.doi.org/10.22214/ijraset.2017.9052.

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