• Korean Journal of Mathematics
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• 제18권2호
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권2호
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• pp.63-73
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• 2002

The influence of unsteady boundary layer magnetohydrodynamic flow with thermal relaxation of perfectly conducting fluid, past a semi-infinite plate, is considered. The governing non linear partial differential equations are solved using the method of successive approximations. This method is used to obtain the solution for the unsteady boundary layer magnetohydrodynamic flow in the special form when the free stream velocity exponentially depends on time. The effects of Alfven velocity $\alpha$ on the velocity is discussed, and illustrated graphically for the problem.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.619-630
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• 2015

This paper is devoted to investigate the multiple solutions for a class of the cooperative elliptic system involving subcritical Sobolev exponents on the bounded domain with smooth boundary. We first show the uniqueness and the negativity of the solution for the linear system of the problem via the direct calculation. We next use the variational method and the mountain pass theorem in the critical point theory.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.211-218
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• 2009

We investigate the multiple solutions for a suspending beam equation with jumping nonlinearity crossing three eigenvalues, with Dirichlet boundary condition and periodic condition. We show the existence of at least six nontrivial periodic solutions for the equation by using the finite dimensional reduction method and the geometry of the mapping.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.107-116
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• 2012

We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.181-189
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• 2017

A method for recovering Chui-Lian's orthogonal symmetric/antisymmetric multiwavelets of order 2 from orthogonal two-direction wavelets of order 2 was proposed by Yang and Xie. In this paper we pursue the converse, that is, we propose a method for constructing orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets of order 2.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.65-73
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• 2003

In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of $0(N^2)$, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제10권1호
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• pp.29-34
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• 2021

실시간 화상교육은 원격지에서 강의자와 학습자의 면대면 교육을 대체하는 효과적인 수업 운영방식으로 활용되고 있다. 하지만 기존의 영상통화 및 화상회의 시스템을 활용하는 형태가 주를 이루고 있으며 이는 영상을 통한 강의에 치중하게 되어 어학교육에서 효과성을 보이고 있다. 그러나 그 외의 교육에서는 활용도가 미비한 실정이다. 최근 코로나로 인해 영상 중심의 화상 교육이 있으면서 화상 회의 시스템이 가지는 영상 중심 화상교육의 제한점을 개선하여 강의자와 학습 참여자 모두에게 수업 중 활용할 수 있는 기능을 제공한다. 본 논문에서는 수학교육에서 효과성을 향상시킬 수 있는 실시간 화상 시스템의 설계 모델을 제시한다.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.471-489
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• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권4호
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• pp.305-313
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• 2019

Using the fixed point method, we prove the Hyers-Ulam stability of 3-Lie homomorphisms and 3-Lie derivations in 3-Lie algebras for Cauchy-Jensen functional equation.