• Steel and Composite Structures
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• v.36 no.1
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• pp.87-101
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• 2020

A multi-scale epoxy/CNT/fiberglass annular sector plate is studied in this paper in the view of determining nonlinear forced vibration characteristics. A 3D Mori-Tanaka model is employed for evaluating multi-scale material properties. Thus, all of glass fibers are assumed to have uni-direction alignment and CNTs have random diffusion. The geometry of annular sector plate can be described based on the open angle and the value of inner/outer radius. In order to solve governing equations and derive exact forced vibration curves for the multi-scale annular sector, Jacobi elliptic functions are used. Obtained results demonstrate the significance of CNT distribution, geometric nonlinearity, applied force, fiberglass volume, open angle and fiber directions on forced vibration characteristics of multi-scale annular sector plates.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1365-1388
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• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• Steel and Composite Structures
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• v.38 no.5
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• pp.523-531
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• 2021

The generalized thermoelastic analysis problem of a two-dimension porous medium with and without energy dissipation are obtained in the context of Green-Naghdi's (GNIII) model. The exact solutions are presented to obtain the studying fields due to the pulse heat flux that decay exponentially in the surface of porous media. By using Laplace and Fourier transform with the eigenvalues scheme, the physical quantities are analytically presented. The surface is shocked by thermal (pulse heat flux problems) and applying the traction free on its outer surfaces (mechanical boundary) through transport (diffusion) process of temperature to observe the analytical complete expression of the main physical fields. The change in volume fraction field, the variations of the displacement components, temperature and the components of stress are graphically presented. Suitable discussion and conclusions are presented.

• East Asian mathematical journal
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• v.39 no.3
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• pp.271-278
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• 2023

We consider a 1-dimensional reaction diffusion equation with the following boundary conditions arising in a theory of the thermal explosion {-u"(t) = λf(u(t)), t ∈ (0, l), -u'(0) + C(0)u(0) = 0, u'(l) + C(l)u(l) = 0, where C : [0, ∞) → (0, ∞) is a continuous and nondecreasing function, λ > 0 is a parameter and f : [0, ∞) → (0, ∞) is a continuous function. We establish the extension of Quadrature method introduced in [8]. Using this extension, we provide numerical results for models with a typical function of f and C in a thermal explosion theory, which verify the existence, uniqueness and multiplicity results proved in [6].

• Journal of the Korean Magnetic Resonance Society
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• v.3 no.2
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• pp.71-83
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• 1999

The dynamics of the dipolar demagnetizing field is investigated by numerical simulation. The effects of radiation damping, molecular diffusion, and relaxation processes on the dipolar demagnetizing field are examined in terms of the modulation pattern of the z-magnetization and the signal intensity variation. Simulations for multi-components suggest applications for sensitivity enhancement in favorable conditions.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• IE interfaces
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• v.9 no.3
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• pp.44-51
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• 1996

The purpose of this paper is to develop a modeling framework for analyzing the effect of price on the PCS (Personal Commununications Service) demand. To achieve this aim, a nonlinear regression model was derived to capture the income effect on the PCS demand and then was combined into an integrated Bass diffusion model. The model was then applied to the emerging PCS market in Korea and the market demands up to the year 2006 were estimated. The results were reviewed and evaluated in various aspects. Finally, the possibilities of model enhancement and model extensions were explored.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2007.11a
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• pp.506-507
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• 2007

Lateral Information Propagation Neural Networks (LIPN) is proposed for on-line interpolation. The proposed neural network technique is the real time computation method through the inter-node diffusion. In the network, a node corresponds to a state in the quantized input space. Through several simulation experiments, real time reconstruction of the nonlinear image information is processed.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.659-670
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• 2023

In this paper, we study the distributed optimal control problem of a coupled system of the host-pathogen model. The system consists of the density of the susceptible host, the density of the infected host, and the density of pathogen particles. Our main goal is to minimize the infected density and also to decrease the cost of the drugs administered. First, we prove the existence and uniqueness of solutions for the proposed problem. Then, the existence of the optimal control is established and necessary optimality conditions are also derived.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.669-683
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• 2003

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.