• Journal for History of Mathematics
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• v.15 no.2
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• pp.141-160
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• 2002

We investigate the history of the research of the existence of periodic solutions of a nonlinear wave equation with jumping nonlinearity, suggested by Mckenna and Lazer (cf. [15]). We also investigate the recent research of it; a relation between multiplicity of solutions and source terms of the equation when the nonlinearity -($bu^+$-$au^-$) crosses eigenvalues and the source term f is generated by eigenfuntions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1495-1510
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• 2022

This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.

• Structural Engineering and Mechanics
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• v.50 no.4
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• pp.487-500
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• 2014

An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1021-1030
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• 2000

We formulate a pair of symmetric dual mixed integer programs with a square root term and establish the weak, strong and converse duality theorems under suitable invexity conditions. Moreover, the self duality theorem for our pair is obtained by assuming the kernel function to be skew symmetric.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.04a
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• pp.611-616
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• 2000

Numerical studies were carried out to investigate the long-term behavior of late plates in basement, subjected to combined in-plane compressive and transverse loads. For the numerical studies, a computer program of nonlinear finite element analysis was modified by adding function of creep and shrinkage analysis. This numerical method was verified by comparison with the existing experiments. Parametric studies were performed to investigate the strength variations of flat plates with three parameters; 1) loading sequence of floor load, compression and time 2) uniaxial an biaxial compression and 3) the ratio of dead to live load.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.901-908
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• 2011

In this paper, we establish a sharp condition of global existence for the solution of the Gross-Pitaevskii equation with an angular momentum rotational term. This condition is related to the ground state solution of some steady-state nonlinear Schrodinger equation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.329-337
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• 2000

An investigation has been performed to develop an analysis tool based on a nonlinear beam theory, which can be used to predict the long-term behavior of an artificial hip joint. The nonlinear behav ior of the femur arise from the coupled dependence of the bone density and the mechanical properties on each other. The beam theory together with its numerical algorithm is developed to take into account the nonlinear bone remodeling process of the femur that is long enough to be assumed as a beam. A piecewise linear curve for the bone remodeling rate is used in the bone remodeling theory and the surface area density of bone is modeled as the third order polynomial function of bone density. At each section of the beam, a constant curvature is assumed and the longitudinal strains are also assumed to vary linearly across the section. The Newton-Rhapson iteration method is used to solve the nonlinear equations for each cross section of the bone and a backward method is used to march along the time. The density and the remodeling signal ar, calculated along with time for the various time steps, and the developed beam theory has been verified by comparing with the results of finite element analysis of a remodeling bone with an artificial hip joint of titanium prosthesis subjected to uni-axial loads and pure bending moment. It is concluded that the developed beam theory can be used to predict the long-term behavior of the femur and thus to design the artificial hip prosthesis.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.21-23
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• 2005

NARX(Nonlinear AutoRegressive with eXogenous input) neural network was used for prediction of nuclear reactor behavior which was influenced by control rods in short-term period and also by xenon and boron in long-term period in load following operations. The developed model was designed to predict reactor power, xenon worth and axial offset with different burnup rates when control rod and boron were adjusted in load following operations. Data of UCN 3 were collected by ONED94 code. The test results presented exhibit the capability of the NARX neural network model to capture the long term and short term dynamics of the reactor core and seems to be utilized as a handy tool for the use of a plant simulation.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.211-216
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• 2000

Numerical studies were carried out to develop the moment magnifier method for long-term behavior of flat plates, subjected to combined in-plane compressive and transverse loads. Nonlinear finite element analyses were performed for the numerical studies. Through the numerical studies, the long term behavior of the flat plate subjected to uniform or nonuniform floor load was investigated, and creep effects on the degradation of strength and stiffness of the slabs were examined. As the result, the creep factor was developed to epitomizes with creep effect on the flat plate. The moment magnifier method using the creep factor was developed for long-term behavior of flat plates. Also, the design examples are shown for verification of proposed design method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.67-67
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• 2000

In this paper, a hybrid type fuzzy controller is proposed to maintain molten steel level stable and reliable manner in high speed continuous casting regardless of various disturbances such as casting speed change, tundish weight variation, 치ogging/undoning of SEN(Submerged Entry Nozzle), periodic bulgings, etc. To accomplish this purpose, hardware filter and software filer are carefully designed to eliminate high frequency noise and to smooth input signals from harsh environments. In order to minimize the molten steel level variations from various disturbances the controller uses hybrid type control term: fuzzy logic term, proportional term, differential term and nonlinear feedback compensation tenn. The proposed controller is applied tn commercial mini-mill plant and shows considerable improvement in minimizing the molten steel variation.