• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.87-95
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• 2011

The existence of T-periodic solutions for a general class of p-Laplacian equations is investigated. By using coincidence degree theory, some existence and uniqueness results, which generalize some earlier works on this topic, are presented.

• 한국해안·해양공학회논문집
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• 제20권5호
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• pp.461-471
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• 2008

WKB 방법에 의한 일차원 완경사 파랑식의 해석해를 유도하였고 이는 Porter(2003)의 해와 유사한 형태를 갖는다. 적용적 측면에서 본 해석해는 관련 수치해에 견줄 만큼 해석상의 일반성을 갖는다. 유도과정에서 해면함수로 표현된 굴절 방정식의 해도 얻었다. Bremmer 방법을 이용한 본 해석해에 대한 수치계산 결과를 제시하였고 이들은 기존 결과와 일치한다.

• 대한전자공학회논문지
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• 제19권6호
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• pp.55-61
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• 1982

집적 광학에서 응용되는, 주기가 거의 선형으로 변하는 도파로 격자 필터의 파장에 따른 응답을 격자의 길이가 유한함을 고려하여 수식적으로 구하였다. 이 필터가 광대역 필터로서 설계되는 보편적인 경우에 대해서는 관련된 포물주면 함수를 변수의 위상에 따라 점근 근사를 취함으로써 파장에 따른 응답을 간단한 함수들로써 나타냈다. 또한 구한 결파식들이 기존 근사식들을 특별한 경우로 포함하는 일반적인 식임을 보였다. 마지막으로, 수식적인 해에 의한 결과와 RunRe-Kutta 수치 계산법에 의한 정확한 해를 비교하여 서로 잘 일치함을 확인하였다. An analytic solution for the spectral response of linearly-chirped grating filter is derived, which takes the finite physical length of filter into account. In the usual case of broad-band linearly-chirped grating filter the analytic solution is expressed in terms of elementary functions, by approximating asymptotically the involved parabolic cylinder functions over different ranges of its argument. It is also shown that derived results are general enough to include previously-available approximations as particular cases, and that they agree well with the numerical solutions based upon the Runge-Kutta method.

• 한국표면공학회지
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• 제37권6호
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• pp.344-349
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• 2004

Emulsions were formed through putting small quantity of nickel electroplating solution into supercritical carbon dioxide, and then electroplating in the $sc-CO_2$ emulsions was conducted. It is an environmental-friendly technology that can solve the treatment of a large quantity of toxic plating wastewater, which is a big problem in the existing wet plating, and also can reduce secondary waste generation fundamentally. Supercritical carbon dioxide emulsions enhanced by ultrasonic horn were formed by non-ionic surfactant and nickel solution. Plating condition within emulsions was set up as 120bar and $55^{\circ}C$ through measurement of electrical conductivity following the pressure change. Experiments were conducted respectively against supercritical carbon dioxide emulsions electroplating and general chemical electroplating, and then their results were compared and analyzed. As the experiment result utilizing emulsions, plating surface was formed very evenly even with a small quantity of electroplating solution, and fine particles were plated compactly without any pinhole or crack due to hydrogenation, which occurs in general electroplating. Used electroplating solution can be reused through recovery process. Therefore, this technology will be able to be applied as new clean technology in electro-plating.

• 충청수학회지
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• 제20권2호
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• pp.109-115
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

• 호남수학학술지
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• 제30권2호
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• pp.219-225
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• 2008

In this paper, we obtain the general solution and the stability of the 2-dimensional vector variable quadratic functional equation f( x + y, z - w) + f(x - y, z + w) = 2f(x, z ) + 2f(y, ${\omega}$). The quadratic form f( x, y) = $ax^2$ + $by^2$ without cross product terms is a solution of the above functional equation.

• 한국수학사학회지
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• 제17권1호
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• pp.61-68
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• 2004

This paper aims at investigating the algebraic solution of cubic and quartic equation and eliciting the didactical meanings of them. First, I examine the event which relates to the equation in the history of mathematics and investigate the algebraic solution of cubic and quartic equation. And then I elicit the didactical suggestions which are required of teachers and students when they investigate the algebraic solution of cubic and quartic equation. In general, the investigation of these solutions is the valuable task which requires the algebraic intuition and technique for students and certificates expert knowledge for teachers.

• 한국해안해양공학회지
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• 제5권4호
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• pp.279-287
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• 1993

일정 수심 위를 전파하는 삼차원 파낭의 시간에 따른 변화를 Green함수를 사용하여 나타내었다. 본 논문에서 구한 해에 적절한 가정을 부여하면 기존의 해가 유도되므로 본 해는 보다 일반적인 해임을 입증하였다. 유도한 해를 수치적분하여 파낭 분산효과에 의한 파고 감소를 나타내고 이를 분석하였다.

• Structural Engineering and Mechanics
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• 제6권5호
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• pp.529-542
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• 1998

Generalised plane strain solution is presented for simply supported, angle-ply laminated hybrid plate under cylindrical bending. The arbitrary constants in the general solution of the governing differential equations are obtained from the boundary and interface conditions. The response of hybrid plates to sinusoidal loads is obtained to illustrate the effect of the thickness parameter and the ply-angle. The classical lamination theory and the first order shear deformation theory are also assessed.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.259-269
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• 2008

The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals $${\Delta}u+u(a-bu+g(v))=0\;in\;{\Omega}\\{\Delta}v+v(d+h(u)-cv)=0\;in\;{\Omega}\\u=v=0\;on\;{\partial}{\Omega}$$ are investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.