• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.267-296
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• 2018

This paper studies the Cauchy problem and blow-up phenomena for a new generalized Camassa-Holm equation with cubic nonlinearity in the nonhomogeneous Besov spaces. First, by means of the Littlewood-Paley decomposition theory, we investigate the local well-posedness of the equation in $B^s_{p,r}$ with s > $max\{{\frac{1}{p}},\;{\frac{1}{2}},\;1-{\frac{1}{p}}\},\;p,\;r{\in}[0,{\infty}]$. Second, we prove that the equation is locally well-posed in $B^s_{2,r}$ with the critical index $s={\frac{1}{2}}$ by virtue of the logarithmic interpolation inequality and the Osgood's Lemma, and it is shown that the data-to-solution mapping is $H{\ddot{o}}lder$ continuous. Finally, we derive two kinds of blow-up criteria for the strong solution by using induction and the conservative property of m along the characteristics.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.447-470
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• 2016

Limit cycle oscillations (LCO) as well as nonlinear aeroelastic analysis of a swept aircraft wing with cubic restoring moments in the pitch degree of freedom is investigated. The unsteady aerodynamic loading applied on the wing is modeled by using the strip theory. The harmonic balance method is used to calculate the LCO frequency and amplitude for the swept wing. Finally the super and subcritical Hopf bifurcation diagrams are plotted. It is concluded that the type of bifurcation and turning point location is sensitive to the system parameters such as wing geometry and sweep angle.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.67-76
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• 2008

Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.

• Journal of Communications and Networks
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• v.1 no.2
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• pp.81-85
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• 1999

The regrowth of OQPSK power spectral sidelobes from AM/AM and AM/PM amplifier nonlinearity is analyzed. The time-domain expression for amplifier output shows how spectral re-growth will depend on the cubic coefficient of the Taylor's series of the amplifier nonlinearity as well as input amplitude ripple. Closed form spectrum calculations show that the spectral sidelobes produced by AM/PM take the same form as those produced by AM/AM. The rate of growth of AM/PM sidelobes is, however, not as great as for AM/AM.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.3
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• pp.156-160
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• 1992

The evolution of leading waves generated by a wavemaker in a two-dimensional tank has been studied. The front of wave trains can be described in general by the Schrodinger equation. In particular, when the slope of the carrier waves is steep, and hence nonlinearity becomes important, the cubic Schrodinger equation is proved to be an appropriate mathematical model. Computations are made by using the Crank-Nicolson algorithm and compared with experimental data. It is found that the numerical result predicts the evolution of leading waves fairly well and the evolution is significantly affected by nonlinearity for steep waves when kh＞1.36.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Computers and Concrete
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• v.20 no.4
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• pp.503-509
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• 2017

In this study, fire-damaged concrete was investigated by a nonlinear resonance vibration (NRV) technique, in order to evaluate its residual material properties. For the experiments, five cubic concrete specimens were prepared and four of them were damaged at different temperatures using a furnace. With a thermal insulator wrapped at the sides of specimen, thermal gradation was applied to the samples. According to the peak temperatures and depths of the samples, nonlinearity parameters were calculated with the NRV technique before the tendency of the parameters was evaluated. In addition, compressive strength and dynamic elastic modulus were measured for each sample and a comparison with the nonlinearity parameter was carried out. Through the experimental results, the possibility of the NRV technique as a method for evaluating residual material properties was evaluated.

• Selected Papers of The Society of Naval Architects of Korea
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• v.1 no.1
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• pp.45-51
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• 1993

By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.5
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• pp.463-470
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• 2005

This paper describes a method aimed at improving dead-reckoning accuracy with gyroscopes in mobile robots. The method is a precision calibration procedure for gyroscopes, which effectively reduces the ill effects of nonlinearity of the scale-factor and temperature dependency. This paper also describes the methods of gyro data collection fur all ambient temperature$(-40^{\circ}C{\~}+80^{\circ}C)$ using cubic spline interpolation and defining the error function. The sensor used was a vibrating gyroscope called the EWTS82NA21, which is low lost and commonly used in car navigation system, made by Panasonic. This angular rate sensor utilizes Coriolis force generated by a vibrating tuning fork. The paper also provides experimental results to check the performance and the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1065-1078
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• 2007

We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u)=(V*{\mid}u{\mid}^2)u$. Here V is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential V we show the global existence and scattering of solutions.