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Relevant bibliographies by topics / Sextic Equations

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Academic literature on the topic 'Sextic Equations'

Author: Grafiati

Published: 29 July 2024

Last updated: 30 July 2024

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Journal articles on the topic "Sextic Equations"

1

Gaál, István, Borka Jadrijević, and László Remete. "Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields." International Journal of Number Theory 15, no. 01 (February 2019): 11–27. http://dx.doi.org/10.1142/s1793042118501695.

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The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known, see G. Lettl, A. Pethő and P. Voutier, Simple families of Thue inequalities, Trans. Amer. Math. Soc. 351 (1999) 1871–1894, On the arithmetic of simplest sextic fields and related Thue equations, in Number Theory: Diophantine, Computational and Algebraic Aspects, eds. K. Győry et al. (de Gruyter, Berlin, 1998), pp. 331–348. The family of simplest cubic Thue equations was already studied in the relative case, over imaginary quadratic fields. In the present paper, we give a similar extension of simplest quartic and simplest sextic Thue equations over imaginary quadratic fields. We explicitly give the solutions of these infinite parametric families of Thue equations over arbitrary imaginary quadratic fields.

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2

Hurley, A. C., and A. K. Head. "Explicit Galois resolvents for sextic equations." International Journal of Quantum Chemistry 31, no. 3 (March 1987): 345–59. http://dx.doi.org/10.1002/qua.560310306.

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3

Lee, Yang-Hi. "On the Hyers-Ulam-Rassias Stability of a General Quintic Functional Equation and a General Sextic Functional Equation." Mathematics 7, no. 6 (June 4, 2019): 510. http://dx.doi.org/10.3390/math7060510.

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The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation.

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4

Gaál, István, and László Remete. "Power integral bases in a family of sextic fields with quadratic subfields." Tatra Mountains Mathematical Publications 64, no. 1 (September 1, 2015): 59–66. http://dx.doi.org/10.1515/tmmp-2015-0041.

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Abstract Let M = Q(i √d) be any imaginary quadratic field with a positive square-free d. Consider the polynomial f(x) = x3 − ax2 − (a + 3)x − 1 with a parameter a ∈ ℤ. Let K = M(α), where α is a root of f. This is an infinite parametric family of sextic fields depending on two parameters, a and d. Applying relative Thue’s equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields.

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5

Togbé, Alain. "A parametric family of sextic Thue equations." Acta Arithmetica 125, no. 4 (2006): 347–61. http://dx.doi.org/10.4064/aa125-4-4.

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Hagedorn, Thomas R. "General Formulas for Solving Solvable Sextic Equations." Journal of Algebra 233, no. 2 (November 2000): 704–57. http://dx.doi.org/10.1006/jabr.2000.8428.

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7

Hu, Shuangnian, and Rongquan Feng. "On the number of solutions of two-variable diagonal sextic equations over finite fields." AIMS Mathematics 7, no. 6 (2022): 10554–63. http://dx.doi.org/10.3934/math.2022588.

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<abstract><p>Let $ p $ be a prime, $ k $ a positive integer, $ q = p^k $, and $ \mathbb{F}_q $ be the finite field with $ q $ elements. In this paper, by using the Jacobi sums, we give an explicit formula for the number of solutions of the two-variable diagonal sextic equations $ x_1^6+x_2^6 = c $ over $ \mathbb{F}_q $, with $ c\in\mathbb{F}_q^* $ and $ p\equiv1({\rm{mod}} \ 6) $. Furthermore, by using the reduction formula for Jacobi sums, the number of solutions of the diagonal sextic equations $ x_1^6+x_2^6+\cdots+x_n^6 = c $ of $ n\geq3 $ variables with $ c\in\mathbb{F}_q^* $ and $ p\equiv1({\rm{mod}} \ 6) $, can also be deduced.</p></abstract>

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Bilu, Yuri, István Gaál, and Kálmán Győry. "Index form equations in sextic fields: a hard computation." Acta Arithmetica 115, no. 1 (2004): 85–96. http://dx.doi.org/10.4064/aa115-1-7.

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9

Hoshi, Akinari. "On the simplest sextic fields and related Thue equations." Functiones et Approximatio Commentarii Mathematici 47, no. 1 (September 2012): 35–49. http://dx.doi.org/10.7169/facm/2012.47.1.3.

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10

Kulkarni, Raghavendra G. "Insert a Root to Extract a Root of Quintic Quickly." Annales Mathematicae Silesianae 33, no. 1 (September 1, 2019): 153–58. http://dx.doi.org/10.2478/amsil-2018-0013.

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AbstractThe usual way of solving a solvable quintic equation has been to establish more equations than unknowns, so that some relation among the coefficients comes up, leading to the solutions. In this paper, a relation among the coefficients of a principal quintic equation is established by effecting a change of variable and inserting a root to the quintic equation, and then equating odd-powers of the resulting sextic equation to zero. This leads to an even-powered sextic equation, or equivalently a cubic equation; thus one needs to solve the cubic equation.We break from this tradition, rather factor the even-powered sextic equation in a novel fashion, such that the inserted root is identified quickly along with one root of the quintic equation in a quadratic factor of the form, u2− g2 = (u + g)(u − g). Thus there is no need to solve any cubic equation. As an extra benefit, this root is a function of only one coefficient of the given quintic equation.

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Book chapters on the topic "Sextic Equations"

1

Gaál, István. "Sextic Fields." In Diophantine Equations and Power Integral Bases, 97–112. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0085-7_8.

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Gaál, István. "Sextic Fields." In Diophantine Equations and Power Integral Bases, 169–95. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23865-0_11.

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3

Togbé, Alain. "On the Solutions of a Family of Sextic Thue Equations." In Number Theory for the Millennium III, 285–99. London: A K Peters/CRC Press, 2023. http://dx.doi.org/10.1201/9780138747022-18.

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4

Rassias, John Michael, Krishnan Ravi, and Beri V. Senthil Kumar. "Stabilities and Instabilities of Rational Functional Equations and Euler-Lagrange-Jensen (a,b)-Sextic Functional Equations." In Mathematical Analysis and Applications, 341–400. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2018. http://dx.doi.org/10.1002/9781119414421.ch10.

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Michael Rassias, John, and Narasimman Pasupathi. "Various Ulam-Hyers Stabilities of Euler-Lagrange-Jensen General (a,b;k=a+b)-Sextic Functional Equations." In Mathematical Analysis and Applications, 255–82. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2018. http://dx.doi.org/10.1002/9781119414421.ch8.

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6

"General Solution of Quintic and Sextic Functional Equations." In Series on Concrete and Applicable Mathematics, 85–88. World Scientific, 2017. http://dx.doi.org/10.1142/9789813147614_0007.

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Conference papers on the topic "Sextic Equations"

1

Xu, Tian Zhou, Wan Xin Xu, John Michael Rassias, and Matina John Rassias. "Stability of quintic and sextic functional equations in non-archimedean fuzzy normed spaces." In 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2011). IEEE, 2011. http://dx.doi.org/10.1109/fskd.2011.6019605.

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Hassan, Saleh M., D. G. Alamery, Ilias Kotsireas, Roderick Melnik, and Brian West. "Sextic B-spline collocation algorithm for the modified equal width equation." In ADVANCES IN MATHEMATICAL AND COMPUTATIONAL METHODS: ADDRESSING MODERN CHALLENGES OF SCIENCE, TECHNOLOGY, AND SOCIETY. AIP, 2011. http://dx.doi.org/10.1063/1.3663505.

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3

Mortazavi, Mansour, and Surendra Singh. "Laser with a saturable absorber as a sextic oscillator." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.tud2.

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The laser with an intracavity saturable absorber is capable of exhibiting a wide variety of fluctuation properties. By using a discharge tube containing pure Ne gas as an absorber inside a He-Ne laser cavity, we succeeded in eliminating the third-order nonlinearity from the equation of motion for the slowly varying field amplitude of the laser. This was accomplished by adjusting the pressure and the discharge current in the absorber tube. The equation of motion for the scaled field amplitude in these conditions is where a is the so-called pump parameter and q(t) represents quantum noise. This equation describes the overdamped motion of a Brownian particle in a sextic potential well under the influence of quantum noise. Statistical properties of the laser were studied experimentally as the pump parameter was varied from negative values to positive values when the time evolution of the field amplitude was governed by the above equation.

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Li, Chen, Jiadao Lin, and Cetin Cetinkaya. "Transfer Matrix Formulation With Optical Penetration for Axisymmetric Thermoelastic Wave Propagation in Films." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/nde-25808.

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Abstract Using Laplace and Hankel integral transforms in time and the radial coordinate, a fully-coupled thermoelastic formulation based on the equation of motion and heat equation is developed to study the effects of axial optical penetration on axisymmetric wave propagation in thermoelastic layers and/or layered structures. It is demonstrated that the optical penetration has no effect on the entries of the sextic transfer matrix, however it introduces an equivalent forcing term for all state variables for both surfaces of a thermoelastic layer as opposed to the surface heating case in which the heating effect is localized in the heating volume (the thermal skin). The thickness of thermal skin depends on the light intensity modulation frequency while the optical penetration typically depends only on the wavelength of the light. This additional forcing vector is a function of the light intensity modulation frequency, the radial wave number, penetration decay rate, as well as thermoelastic material properties. Complexities in wavefields due to the nature of the forcing term are demonstrated and discussed. A thin copper layer with hypothetical penetration properties is considered for the demonstration of the current formulation.

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Hu, Qiuhao, Ye Li, and Fangyi Wei. "Preliminary Results of Numerical Simulations of a Bio-Mimetic Wells Turbine." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54463.

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Wells turbine is a kind of self-rectified air turbines used in an oscillatory water column (OWC) device for wave energy conversion. In this study, a steady three-dimensional simulation of a fan-shaped Wells turbine is performed on Star CCM+ commercial software by solving the Reynolds-averaged Navier-Stokes (RANS) equations. The turbulence effects are taken into account by using the Spalart-Allmaras turbulence model. Good agreement between the numerical results and the experimental results within the operation region (5< α <11 degrees) is observed. The geometry of the turbine rotor has a significant effect on the performance of energy conversion. Inspired by the aerodynamics of low Reynolds flyer, the normal fan-shaped Wells turbine is optimized by a bio-mimetic method in which the profile of a hawk moth wing of Manduca Sexta is applied on the blades. The modified turbine has a lower torque and pressure drop coefficient with higher efficiency. The maximum efficiency for the modified turbine is 0.61, compared to 0.48 for the normal fan-shaped one. By analysis of the detailed flow-field, it has also been found that only the middle parts of the blade can effectively generate the momentum. In order to acquire a higher efficiency, further optimization is carried out by refining some blade parts in the tip and the hub which cannot effectively produce power.

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