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Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.


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Journal ArticleDOI
TL;DR: It is proved that the eigenvalues of all localized stationary solutions of the cubic-quintic (2+1) -dimensional nonlinear Schrödinger equation exhibit an upper cutoff value, and it is shown that, in the limit of eigen values close to zero, the eigens of the square root of this equation behave similarly to those of the cube nonlinear equation.
Abstract: Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic $(2+1)$-dimensional nonlinear Schr\"odinger equation exhibit an upper cutoff value. The existence of the cutoff is inferred using Gagliardo-Nirenberg and H\"older inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schr\"odinger equation behave similarly to those of the cubic nonlinear Schr\"odinger equation.

10 citations

Journal ArticleDOI
TL;DR: In this paper, a method of solving a quartic equation, which does not require extracting the roots of complex numbers is explained in details, and the solution of a cubic equation has also been presented, with the same degree of simplicity.
Abstract: A method of solving a quartic equation, which does not require extracting the roots of complex numbers is explained in details. In the process, the solution of a cubic equation has also been presented, with the same degree of simplicity.

10 citations

Journal ArticleDOI
TL;DR: In this paper , the Khater II analytical technique is used to examine novel soliton structures for the fractional nonlinear third-order Schrödinger (3-FNLS) problem.
Abstract: In this paper, the Khater II analytical technique is used to examine novel soliton structures for the fractional nonlinear third-order Schrödinger (3-FNLS) problem. The 3-FNLS equation explains the dynamical behavior of a system’s quantum aspects and ultra-short optical fiber pulses. Additionally, it determines the wave function of a quantum mechanical system in which atomic particles behave similarly to waves. For example, electrons, like light waves, exhibit diffraction patterns when passing through a double slit. As a result, it was fair to suppose that a wave equation could adequately describe atomic particle behavior. The correctness of the solutions is determined by comparing the analytical answers obtained with the numerical solutions and determining the absolute error. The trigonometric Quintic B-spline numerical (TQBS) technique is used based on the computed required criteria. Analytical and numerical solutions are represented in a variety of graphs. The strength and efficacy of the approaches used are evaluated.

10 citations

Book ChapterDOI
06 Jun 2008
TL;DR: Results on the design of quintic RRMF curves by the interpolation of G1 spatial Hermite data are presented, in which the problem is reduced to computing positive real roots of a certain univariate polynomial.
Abstract: A rotation–minimizing adapted frame (f1(t),f2(t),f3(t)) on a given space curve r(t) is characterized by the fact that the frame vector f1 coincides with the tangent t=r′/ |r′|, while the frame angular velocity ω maintains a zero component along it, ie, ω·t≡0 Such frames are useful in constructing swept surfaces and specifying the orientation of a rigid body moving along a given spatial path Recently, the existence of quintic polynomial curves that have rational rotation–minimizing frames (quintic RRMF curves) has been demonstrated These RRMF curves are necessarily Pythagorean–hodograph (PH) space curves, satisfying certain non–linear constraints among the complex coefficients of the Hopf map representation for spatial PH curves Preliminary results on the design of quintic RRMF curves by the interpolation of G1 spatial Hermite data are presented in this paper This problem involves solving a non–linear system of equations in six complex unknowns The solution is obtained by a semi–numerical scheme, in which the problem is reduced to computing positive real roots of a certain univariate polynomial The quintic RRMF G1 Hermite interpolants possess one residual angular degree of freedom, which can strongly influence the curve shape Computed examples are included to illustrate the method and the resulting quintic RRMF curves

10 citations

Journal ArticleDOI
TL;DR: In this article, the free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters.
Abstract: Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters The governing equations of motion for truncated conical shell are obtained in terms of displacement functions The displacement functions are approximated by cubic and quintic splines resulting into a generalized eigenvalue problem The parametric studies have been made and discussed

10 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202397
2022254
2021109
2020104
201993
201893