Results 21 to 30 of about 4,759 (244)
Stability of a Quartic Functional Equation [PDF]
The Scientific World Journal, 2014 We obtain the general solution of the generalized quartic functional equationf(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y)+f(x-y)}for a fixed positive integerm. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces.
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Cubic-quartic optical solitons with Kudryashov’s law of refractive index by F-expansions schemes
Results in Physics, 2020 This work presents cubic-quartic optical soliton solutions to Kudryashov’s equation in polarization-preserving fibers. The integration is conducted with F-expansion scheme having four independent forms.
Gokhan Genc +3 more
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On Ramanujan's Quartic Theory of Elliptic Functions
Journal of Number Theory, 2001 Let \(\varphi(q):=\sum_{n=-\infty}^\infty q^{n^2}\). In the classical theory of theta-functions, a fundamental inversion formula is \[ {}_2F_1(\tfrac 12, \tfrac 12;1;x)=\varphi^2(q_2),\tag{1} \] where the relationship between \(q_2\) and \(x\) is given by \[ q_r=q_r(x)=\exp\left(-\pi \csc(\pi/r)\frac {{}_2F_1(\frac {1}{r}, \frac{r-1}r;1;1-x)} {{}_2F_1(\
Berndt, B.C., Chan, H.H., Liaw, W.-C.
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The Stability Analysis of A-Quartic Functional Equation [PDF]
Mathematics, 2021 In this paper, we study the general solution of the functional equation, which is derived from additive–quartic mappings. In addition, we establish the generalized Hyers–Ulam stability of the additive–quartic functional equation in Banach spaces by using direct and fixed point methods.
Chinnaappu Muthamilarasi +5 more
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Landau pole in the Standard Model with weakly interacting scalar fields
Physics Letters B, 2015 We consider the Standard Model with a new scalar field X which is an nX representation of the SU(2)L with a hypercharge YX. The renormalization group running effects on the new scalar quartic coupling constants are evaluated.
Yuta Hamada +2 more
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Nuclear Physics B, 2017 We demonstrate that in non-Abelian N=1 supersymmetric gauge theories the NSVZ relation is valid for terms quartic in the Yukawa couplings independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare ...
V.Yu. Shakhmanov, K.V. Stepanyantz
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Green Functions for the Wrong-Sign Quartic [PDF]
International Journal of Theoretical Physics, 2010 It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric explicitly, by truncation of the equations.
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Chemical Engineering Transactions, 2015 Although many methods can be used to conduct platinum resistor non-linear rectification, they cannot be put into wide use because of shortcomings such as narrow temperature range and complicated calculation of rectification. This article conducts fitting
Z.X. Wu, X.C. Zhou, G. Chen
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The Mixed Cubic-Quartic Functional Equation
Annals of the Alexandru Ioan Cuza University - Mathematics, 2015 AbstractIn this paper, we obtain the general solution of the following generalized mixed cubic and quartic functional equation f(x + kx) + f(x − ky) = k2{f(x + y) + f(x−y)}−2(k2−1)f(x)−2k2(k2−1)f(y)+ 1/4 k2(k2−1)f(2y), for fixed integers k with k ≠ 0,±1. The Hyers-Ulam stability problem for the mentioned functional equation is also proved.
Bodaghi, A., Kang, D., Rassias, J. M.
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