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Journal articles on the topic 'Octic'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Lee, Yang-Hi, and Jaiok Roh. "Some Remarks Concerning the General Octic Functional Equation." Journal of Mathematics 2023 (May 16, 2023): 1–15. http://dx.doi.org/10.1155/2023/2930056.

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In this article, we study the stability of various forms for the general octic functional equation ∑ i = 09 9 C i − 1 9 − i f x + i y = 0 . We first find a special way of representing a given mapping as the sum of eight mappings. And by using the above representation, we will investigate the hyperstability of the general octic functional equation. Furthermore, we will discuss the Hyers–Ulam–Rassias stability of the general octic functional equation.

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2

Cederwall, Martin, and Jakob Palmkvist. "The octic E8 invariant." Journal of Mathematical Physics 48, no. 7 (2007): 073505. http://dx.doi.org/10.1063/1.2748615.

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3

Jones, John W., and David P. Roberts. "Octic 2-adic fields." Journal of Number Theory 128, no. 6 (2008): 1410–29. http://dx.doi.org/10.1016/j.jnt.2007.12.014.

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4

Chou, Wun-Seng. "Binomial permutations of finite fields." Bulletin of the Australian Mathematical Society 38, no. 3 (1988): 325–27. http://dx.doi.org/10.1017/s0004972700027659.

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5

Kwon, Soonhak. "A remark on rational octic reciprocity." Proceedings of the Japan Academy, Series A, Mathematical Sciences 78, no. 2 (2002): 22–25. http://dx.doi.org/10.3792/pjaa.78.22.

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6

Kulkarni, Raghavendra G. "On the Solution to Octic Equations." Mathematics Enthusiast 4, no. 2 (2007): 193–209. http://dx.doi.org/10.54870/1551-3440.1071.

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7

Sun, Zhi-Hong. "Quartic, octic residues and Lucas sequences." Journal of Number Theory 129, no. 3 (2009): 499–550. http://dx.doi.org/10.1016/j.jnt.2008.09.019.

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8

Dudka, Alexander. "Instrumental drift correction by nonparametric statistics." Journal of Applied Crystallography 42, no. 2 (2009): 354–55. http://dx.doi.org/10.1107/s0021889809002271.

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A program for instrumental drift correction by nonparametric statistics using a point-detector diffractometer is described. The correction improves structural results such as merging and refinementRfactors. The kernels available are as follows: uniform, Epanechnikov, quartic, octic, Gaussian.

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9

Abuaf, Roland, and Laurent Manivel. "Gradings of Lie algebras, magical spin geometries and matrix factorizations." Representation Theory of the American Mathematical Society 25, no. 18 (2021): 527–42. http://dx.doi.org/10.1090/ert/573.

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We describe a remarkable rank 14 14 matrix factorization of the octic S p i n 14 \mathrm {Spin}_{14} -invariant polynomial on either of its half-spin representations. We observe that this representation can be, in a suitable sense, identified with a tensor product of two octonion algebras. Moreover the matrix factorisation can be deduced from a particular Z \mathbb {Z} -grading of e 8 \mathfrak {e}_8 . Intriguingly, the whole story can in fact be extended to the whole Freudenthal-Tits magic square and yields matrix factorizations on other spin representations, as well as for the degree seven i

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10

AGBOOLA, DAVIDS, and YAO-ZHONG ZHANG. "EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL." Modern Physics Letters A 27, no. 20 (2012): 1250112. http://dx.doi.org/10.1142/s021773231250112x.

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We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

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11

Rath, Biswanath, Jihad Asad, Rabab Jarrar, Hussein Shanak, and Rania Wannan. "Nonlinear T-symmetry Quartic, Sextic, Octic Oscillator Models under Real Spectra." Symmetry 15, no. 3 (2023): 573. http://dx.doi.org/10.3390/sym15030573.

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We propose nonlinear model T-symmetry operators having quartic, sextic, octic anharmonicity and inverse quadratics under real spectra. In fact, the model operator is non-Hermitian but real in nature. A comparison with the corresponding hermitian counterpart shows higher energy levels (ET ≫ Ehermitian).

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12

Altmann, Anna, Chad Awtrey, Sam Cryan, Kiley Shannon, and Madeleine Touchette. "Galois groups of doubly even octic polynomials." Journal of Algebra and Its Applications 19, no. 01 (2019): 2050014. http://dx.doi.org/10.1142/s0219498820500140.

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Let [Formula: see text] be an irreducible polynomial with rational coefficients, [Formula: see text] the number field defined by [Formula: see text], and [Formula: see text] the Galois group of [Formula: see text]. Let [Formula: see text], and let [Formula: see text] be the Galois group of [Formula: see text]. We investigate the extent to which knowledge of the conjugacy class of [Formula: see text] in [Formula: see text] determines the conjugacy class of [Formula: see text] in [Formula: see text]. We show that, in general, knowledge of [Formula: see text] does not automatically determine [For

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13

Borcea, Ciprian. "Nodal quintic threefolds and nodal octic surfaces." Proceedings of the American Mathematical Society 109, no. 3 (1990): 627. http://dx.doi.org/10.1090/s0002-9939-1990-1021895-0.

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14

Nijsse, Pieter G. J. "Clemens' conjecture for octic and nonic curves." Indagationes Mathematicae 6, no. 2 (1995): 213–21. http://dx.doi.org/10.1016/0019-3577(95)91244-p.

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15

T. Shivalingaswamy, T. Shivalingaswamy, and B. A. Kagali B. A. Kagali. "Ground States of Sextic and Octic Anharmonic Oscillators." Paripex - Indian Journal Of Research 3, no. 7 (2012): 1–4. http://dx.doi.org/10.15373/22501991/july2014/67.

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16

Stahl, W., H. Dreizler, L. Jörissen, and W. A. Kreiner. "The Microwave Q-branch Spectrum of Germane in the Vibrational Ground State." Zeitschrift für Naturforschung A 41, no. 5 (1986): 747–51. http://dx.doi.org/10.1515/zna-1986-0510.

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We present an analysis of the rotational spectra of 70GeH4, 72GeH4 and 74GeH4 in the vibrational ground state measured by microwave Fourier transform (MWFT) spectroscopy. All quartic, sextic and octic tensor centrifugal distortion constants have been determined. A discussion of spin-rotation and spin-spin interactions will be given in a subsequent paper.

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17

Gaál, István, and László Remete. "Non-monogenity in a family of octic fields." Rocky Mountain Journal of Mathematics 47, no. 3 (2017): 817–24. http://dx.doi.org/10.1216/rmj-2017-47-3-817.

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18

Crass, Scott. "Solving the octic by iteration in six dimensions." Dynamical Systems 17, no. 2 (2002): 151–86. http://dx.doi.org/10.1080/14689360210125057.

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19

Sun, Zhi-Hong. "New reciprocity laws for octic residues and nonresidues." Journal of Number Theory 147 (February 2015): 694–707. http://dx.doi.org/10.1016/j.jnt.2014.08.015.

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20

Pohst, M., J. Martinet, and F. Diaz y Diaz. "The minimum discriminant of totally real octic fields." Journal of Number Theory 36, no. 2 (1990): 145–59. http://dx.doi.org/10.1016/0022-314x(90)90069-4.

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21

Kühnel, Marco. "A Note on Octic Hypersurfaces with Many Nodes." Geometriae Dedicata 109, no. 1 (2004): 189–95. http://dx.doi.org/10.1007/s10711-004-1775-6.

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22

Sarka, K. "The reduced octic rotational Hamiltonian for C3v molecules." Journal of Molecular Spectroscopy 134, no. 2 (1989): 354–61. http://dx.doi.org/10.1016/0022-2852(89)90322-6.

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23

Cohen, H., F. Diaz y Diaz, and M. Olivier. "Tables of octic fields with a quartic subfield." Mathematics of Computation 68, no. 228 (1999): 1701–17. http://dx.doi.org/10.1090/s0025-5718-99-01074-1.

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24

Omar, Sami. "On Artin L-Functions for Octic Quaternion Fields." Experimental Mathematics 10, no. 2 (2001): 237–45. http://dx.doi.org/10.1080/10586458.2001.10504445.

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25

Cynk, Sławomir. "Double coverings of octic arrangements with isolated singularities." Advances in Theoretical and Mathematical Physics 3, no. 2 (1999): 217–25. http://dx.doi.org/10.4310/atmp.1999.v3.n2.a2.

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26

Schütt, Matthias. "Modularity of Maschke’s octic and Calabi–Yau threefold." Communications in Number Theory and Physics 5, no. 4 (2011): 827–47. http://dx.doi.org/10.4310/cntp.2011.v5.n4.a3.

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27

Louboutin, Stéphane. "Hasse Unit Indices of Dihedral Octic CM-Fields." Mathematische Nachrichten 215, no. 1 (2000): 107–13. http://dx.doi.org/10.1002/1522-2616(200007)215:1<107::aid-mana107>3.0.co;2-a.

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28

Cynk, Sławomir, and Christian Meyer. "Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds." Canadian Mathematical Bulletin 48, no. 2 (2005): 180–94. http://dx.doi.org/10.4153/cmb-2005-016-7.

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AbstractWe study Calabi–Yau manifolds constructed as double coverings of ℙ3 branched along an octic surface. We give a list of 87 examples corresponding to arrangements of eight planes defined over ℚ. The Hodge numbers are computed for all examples. There are 10 rigid Calabi–Yau manifolds and 14 families with h1,2 = 1. The modularity conjecture is verified for all the rigid examples.

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29

Reddy, Y. Rajashekhar. "OCTIC B-SPLINE COLLOCATION SOLUTION WITH NON-UNIFORM LENGTH FOR EIGHTH ORDER LINEAR DIFFERENTIAL EQUATION." International Journal of Research -GRANTHAALAYAH 5, no. 6 (2017): 53–57. http://dx.doi.org/10.29121/granthaalayah.v5.i6.2017.1995.

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Presentation of Numerical solution for eighth order linear boundary value problem using Octic B-spline collocation method with non-uniform length is the subject of this paper. In this approach recursive form of B-spline function is used as basis in collocation method. Numerical examples are considered to show the advantage of recursive of B-spline function particularly in non-fixing the length of subintervals.

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30

Dr.Y.Rajashekhar, Reddy. "OCTIC B-SPLINE COLLOCATION SOLUTION WITH NON-UNIFORM LENGTH FOR EIGHTH ORDER LINEAR DIFFERENTIAL EQUATION." International Journal of Research - Granthaalayah 5, no. 6 (2017): 53–57. https://doi.org/10.5281/zenodo.815396.

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Presentation of Numerical solution for eighth order linear boundary value problem using Octic B-spline collocation method with non-uniform length is the subject of this paper. In this approach recursive form of B-spline function is used as basis in collocation method. Numerical examples are considered to show the advantage of recursive of B-spline function particularly in non-fixing the length of subintervals.

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31

Cynk, Sławomir, Matthias Schütt, and Duco van Straten. "Hilbert modularity of some double octic Calabi–Yau threefolds." Journal of Number Theory 210 (May 2020): 313–32. http://dx.doi.org/10.1016/j.jnt.2019.09.015.

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32

Pathak, Anirban, and Swapan Mandal. "Classical and quantum oscillators of sextic and octic anharmonicities." Physics Letters A 298, no. 4 (2002): 259–70. http://dx.doi.org/10.1016/s0375-9601(02)00500-5.

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33

Watson, James K. G. "Calculated octic centrifugal distortion coefficients of non-linear molecules." Journal of Molecular Structure 795, no. 1-3 (2006): 263–70. http://dx.doi.org/10.1016/j.molstruc.2006.02.038.

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34

Rababah, Abedallah. "BEST OCTIC APPROXIMATION OF CIRCULAR ARCS WITH SEVENTEEN EQUIOSCILLATIONS." Far East Journal of Electronics and Communications 18, no. 3 (2018): 393–405. http://dx.doi.org/10.17654/ec018030393.

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35

Singh, Ram Mehar. "Quantum Mechanics of Complex Octic Potential in One Dimension." Journal of Quantum Information Science 03, no. 01 (2013): 42–49. http://dx.doi.org/10.4236/jqis.2013.31009.

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36

Vinette, Francine, Jiri Cizek, and Edward R. Vrscay. "Renormalized inner projection?a case study: The octic oscillator." International Journal of Quantum Chemistry 32, no. 6 (1987): 663–67. http://dx.doi.org/10.1002/qua.560320604.

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37

Cynk, Sławomir. "Hodge numbers of a double octic with non-isolated singularities." Annales Polonici Mathematici 73, no. 3 (2000): 221–26. http://dx.doi.org/10.4064/ap-73-3-221-226.

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38

Cynk, Sł awomir, and Christian Meyer. "Modularity of Some Non-Rigid Double Octic Calabi-Yau Threefolds." Rocky Mountain Journal of Mathematics 38, no. 6 (2008): 1937–58. http://dx.doi.org/10.1216/rmj-2008-38-6-1937.

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39

Shen, Yuan Yuan. "Unit groups and class numbers of real cyclic octic fields." Transactions of the American Mathematical Society 326, no. 1 (1991): 179–209. http://dx.doi.org/10.1090/s0002-9947-1991-1031243-3.

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40

Jafarpour, Mojtaba, and Tayebeh Tahamtan. "Octic Anharmonic Oscillators: Perturbed Coherent States and the Classical Limit." International Journal of Theoretical Physics 48, no. 2 (2008): 487–96. http://dx.doi.org/10.1007/s10773-008-9824-9.

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41

Vlachos, K., V. Papatheou, and A. Okopińska. "Perturbation and variational-perturbation method for the free energy of anharmonic oscillators." Canadian Journal of Physics 85, no. 1 (2007): 13–30. http://dx.doi.org/10.1139/p07-015.

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The perturbation and the variational-perturbation methods are applied for calculating the partition function of one-dimensional oscillators with anharmonicity x2n. New formally simple expressions for the free energy and for the Rayleigh–Schrodinger energy corrections are derived. It is shown that the variational-perturbation method overcomes all the deficiencies of the conventional perturbation method. The results of fifth-order numerical calculations for the free energy of the quartic, quartic–sextic, and octic anharmonic oscillator are highly accurate in the whole range of temperatures. PACS

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42

Rajashekhar, Reddy. "Comparison of Septic and Octic Recursive B spline Collocation Solutions for Seventh Order Differential Equation." International Journal of Trend in Scientific Research and Development 1, no. 5 (2017): 251–54. https://doi.org/10.31142/ijtsrd2269.

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This note is concerned of improvement in numerical solution for seventh order linear differential equation by using the higher degree B spline collocation solution than its order. Numerical examples are used to study the improvement in the accuracy of the numerical solutions with the high degree B spline base function. Rajashekhar Reddy "Comparison of Septic and Octic Recursive B-spline Collocation Solutions for Seventh Order Differential Equation" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-5 , August

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43

Czarnecki, Aleksander. "Counting points on double octic Calabi–Yau threefolds over finite fields." Annales Polonici Mathematici 125, no. 3 (2020): 215–27. http://dx.doi.org/10.4064/ap200210-30-8.

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44

Rhee, Min Surp, and Young Ik Kim. "Two triparametric families of optimal derivative-free methods with octic convergence." Applied Mathematical Sciences 7 (2013): 6621–30. http://dx.doi.org/10.12988/ams.2013.310609.

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45

Louboutin, Stéphane. "Determination of all Quaternion Octic CM-Fields with Class Number 2." Journal of the London Mathematical Society 54, no. 2 (1996): 227–38. http://dx.doi.org/10.1112/jlms/54.2.227.

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46

Sultan, Mamoona, and Toru Nakahara. "On certain octic biquartic fields related to a problem of Hasse." Monatshefte für Mathematik 176, no. 1 (2014): 153–62. http://dx.doi.org/10.1007/s00605-014-0670-y.

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47

Cynk, Slawomir, and Duco van Straten. "Picard–Fuchs operators for octic arrangements, I: The case of orphans." Communications in Number Theory and Physics 13, no. 1 (2019): 1–52. http://dx.doi.org/10.4310/cntp.2019.v13.n1.a1.

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48

Dana-Picard, Thierry, and Tomás Recio. "Dynamic construction of a family of octic curves as geometric loci." AIMS Mathematics 8, no. 8 (2023): 19461–76. http://dx.doi.org/10.3934/math.2023993.

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<abstract><p>We explore the construction of curves of degree 8 (octics) appearing as geometric loci of points defined by moving points on an ellipse and its director circle. To achieve this goal we develop different computer algebra methods, dealing with trigonometric or with rational parametric representations, as well as through implicit polynomial equations, of the given curves. Finally, we highlight the involved mathematical or computational issues arising when reflecting on the outputs obtained in each case.</p></abstract>

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49

Park, Choonkil, Madjid Eshaghi Gordji, Mohammad Ghaemi, and Hamid Majani. "Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces." Journal of Inequalities and Applications 2012, no. 1 (2012): 289. http://dx.doi.org/10.1186/1029-242x-2012-289.

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50

Witwit, M. R. M. "Energy levels of two‐dimensional anharmonic oscillators with sextic and octic perturbations." Journal of Mathematical Physics 33, no. 12 (1992): 4196–205. http://dx.doi.org/10.1063/1.529818.

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