• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.315-327
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• 2007

Mathematical aspects of the electromagnetic surface-wave propagation are examined for the dielectric core consisting of multiple sub-layers, which are embedded in the gap between the two bounding cladding metals. For this purpose, the linear problem with a partial differential wave equation is formulated into a nonlinear eigenvalue problem. The resulting eigenvalue is found to exist only for a certain combination of the material densities and the number of the multiple sub-layers. The implications of several limiting cases are discussed in terms of electromagnetic characteristics.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1769-1775
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• 2004

In presence of collision between two rigid bodies, they exhibit impulsive behavior to generate physically feasible state. When the frictional impulse is involved, collision resolution can not be easily made based on a simple Newton's law or Poisson's law, mainly due to possible change of collision mode during collision, For example, sliding may change to sticking, and then sliding resumes. We first examine two conventional methods: the method of mode evolution by differential equation, and the other by linear complementarity programming. Then, we propose a new method for mode evolution by solving only algebraic equations defining mode changes. Further, our method attains the original nonlinear impulse cone constraint. The numerical simulation will elucidate the advantage of the proposed method as an alternative to conventional ones.

• East Asian mathematical journal
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• 제33권5호
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• pp.495-509
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• 2017

With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.

• 한국해양공학회지
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• 제25권2호
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• pp.62-66
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• 2011

In this paper, a liquid-filled long membrane container resting on a horizontal foundation is considered. All of the quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The integration of the curvature gives the solutions, which are expressed in terms of the elliptic integrals. A method for finding the shape and characteristic values is proposed for a given cross-sectional volume. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes.

• International Journal of Ocean System Engineering
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• 제2권3호
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• pp.195-199
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• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.

• 대한수학회보
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• 제55권3호
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권3호
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• pp.269-277
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• 2014

A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.

• Computers and Concrete
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• 제20권3호
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• pp.361-368
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• 2017

Seismic response of the concrete column covered by nanofiber reinforced polymer (NFRP) layer is investigated. The concrete column is studied in this paper. The column is modeled using sinusoidal shear deformation beam theory (SSDT). Mori-Tanaka model is used for obtaining the effective material properties of the NFRP layer considering agglomeration effects. Using the nonlinear strain-displacement relations, stress-strain relations and Hamilton's principle, the motion equations are derived. Harmonic differential quadrature method (HDQM) along with Newmark method is utilized to obtain the dynamic response of the structure. The effects of different parameters such as NFRP layer, geometrical parameters of column, volume fraction and agglomeration of nanofibers and boundary conditions on the dynamic response of the structure are shown. The results indicated that applied NFRP layer decreases the maximum dynamic displacement of the structure. In addition, using nanofibersas reinforcement leads a reduction in the maximum dynamic displacement of the structure.

• 대한수학회지
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• 제36권1호
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• pp.229-241
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• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1984년도 하계학술회의논문집
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• pp.92-95
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• 1984

This paper describes a general method for the design of variable structure Model-Following Control systems (VSMFC). This design concept is developed using the theory of variable structure systems and slide mode. The feasibility and the advantages of the method are illustrated by applying it to a 1000 MWe Boiling Water Reactor. The control is studied in the range of 85 - 90 % of rated power for load-following control. A set of 12 nonlinear differential eq. are used to simulate the total plant. A 6th order linear model has been developed from these equations at 85% of rated power. The obtained controller is shown by simulations to be able to compensate for a plant parameter variation over a wide power range.