• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.415-427
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• 2015

In this paper, we investigate bounds for solutions of the non-linear functional differential systems.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.201-211
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• 2010

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.1-12
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• 2000

We explore the structure and usefulness of CERES plot as a basic tool for dealing with curvature as a function of the new predictor in nonlinear regression. If a predictor has a nonlinear effect and there are nonlinear relationships among the predictors the partial residual plot and augmented partial residual plot are not able to display the correct functional form of the predictor. Unlike these plots the CERES plot can show the correct from. In situations where nonlinearity exists in two predictors we extend the idea of CERES plot to three dimensions, This is illustrated by simulated data.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.72-76
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• 1990

A new statistical linearization technique for nonlinear system called covariance matching method is proposed in this paper. The covariance matching method makes the mean and variance of an approximated output be identical real functional output, and the distribution of the approximated output have identical shape with a given random input. Also, the covariance matching method can be easily implemented for statistical analysis of nonlinear systems with a combination of linear system covariance analysis.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.15-33
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• 2024

In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

• Advances in nano research
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• v.15 no.2
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.6
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• pp.573-580
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• 2009

In this paper, we develop a functional test model for magnetic bearing wheels. The functional test model is an electromagnetic levitation system that has three degree of freedom, which consists of one axial suspension from gravity and two axes gimbaling capability to small angels. A nonlinear controller with high-gain observers is proposed and the real-time experiment results show that the rotor is accurately levitated at the desired position and well-balanced, which is a suitable result for the potential use an magnetic bearing wheels. Also, the proposed scheme exhibits better performance when it is compared with the conventional PID control method.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.547-564
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• 1994

Let X be a real Banach space. We consider the existence of solutions of the abstract nonlinear functional evolution equation : $$ (E) \frac{du(t)}{dt} + A(t)u(t) + F(u)(t) \ni h(t), $$ $$ u(s) = x_o \in D(A(s)), 0 \leq s \leq t \leq T, $$ where u : $[s, T] \to x$ is an unknown function, ${A(t) : 0 \leq t \leq T}$ is a given family of nonlinear (possibly multivalued) operators in X, and $F : C([s, t];X) \to L^{\infty}([s, X];X)$ and $h : [s, T] \to X$ are given functions.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• Journal of the Korean Ceramic Society
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• v.56 no.1
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• pp.1-23
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• 2019

Dielectric materials with inherently high power densities and fast discharge rates are particularly suitable for pulsed power capacitors. The ongoing multifaceted efforts on developing these capacitors are focused on improving their energy density and storage efficiency, as well as ensuring their reliable operation over long periods, including under harsh environments. This review article summarizes the studies that have been conducted to date on the development of high-performance dielectric ceramics for employment in pulsed power capacitors. The energy storage characteristics of various lead-based and lead-free ceramics belonging to linear and nonlinear dielectrics are discussed. Various strategies such as mechanical confinement, self-confinement, core-shell structuring, glass incorporation, chemical modifications, and special sintering routes have been adopted to tailor the electrical properties and energy storage performances of dielectric ceramics. In addition, this review article highlights the challenges and opportunities associated with the development of pulsed power capacitors.