• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.925-934
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• 2012

In this work the sine-Gordon equation will be examined for multiple soliton solutions. The higher dimensional sine-Gordon equations will be studied for multiple soliton solutions as well. The simplified form of the Hirota's method will be employed to conduct this analytic study.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1227-1237
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• 2010

In this paper, a Klein-Gordon equation is solved by using the homotopy analysis method (HAM), homotopy perturbation method (HPM) and modified homotopy perturbation method (MHPM). The approximation solution of this equation is calculated in the form of series which its components are computed easily. The uniqueness of the solution and the convergence of the proposed methods are proved. The accuracy of these methods are compared by solving an example.

• Bulletin of the Korean Chemical Society
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• v.31 no.12
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• pp.3573-3578
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• 2010

Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schr$\ddot{o}$dinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1447-1465
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• 2019

In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_0$, we prove the existence and uniqueness of the mild solution via the iteration method.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.509-524
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• 2002

We Study the Problems Of identification for the damped sine-Gordon equations with constant parameters. That is, we establish the existence and necessary conditions for the optimal constant parameters based on the fundamental optimal control theory and the transposition method studied in Lions and Magenes [5].

• Honam Mathematical Journal
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• v.30 no.4
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• pp.631-635
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• 2008

In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.349-352
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• 2017

Since the early 2000s, many information security professionals have sought to measure the effectiveness of information security investments. Such efforts have devised a number of ways to calculate the return in ROSI (Return On Security Investment) including the Gordon & Loeb method for calculating cyber damage. However, due to the characteristics of information security structure, the lack of relate information sharing, and many qualitative factors are included, the damage calculation is inaccurate.. This study reviews related studies, analyzes the Gordon & Loeb method and the Shin-Jin method, which are considered to be the most efficient of the existing methods, and designs improved methods.

• Journal of Korean Home Economics Education Association
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• v.12 no.3
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• pp.1-17
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• 2000

The purpose of this research was to apply and conduct a class with Gordon’s Creative Problem Solving Method(Synectics) to the area of ’human development and family relations’among male students in a jr. high school. Subject matters which were appropriate for applying Gordon’s Creative Problem Solving method were selected from ’human development and family relations’area, with problem circumstances set to reflect to the highest degree the interests of individuals and families. An 8 hour teaching instructional guide was constructed with $\boxdr$strategy 1$\boxul$of Gordon’s Creative Problem Solving method in order to solve creatively the established problem. This was practically implied to 70 students(each class had 34 and 36 students respectively) in K middle school located in Seoul. The period of this application was for 3 months during March through May of 1999. The perception of this method was examined by the teachers and students through open-ended questions. The record of perception showed that 56 students out of 70(with no response from 5 students) through that the class done by the creativity problem solving method was good. The majority of reasons mentioned for the positive answers were ’being able to receive different thoughts which were unusual of daily life’. In addition the students who participated in the class were able to foster a joint experience which improved their understanding of relationships and sens of community. moreover students who did not do well n the class or were diffident were encouraged to participate which in result showed that there was even an internal effect.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.281-294
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• 2020

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.