• The Pure and Applied Mathematics
• /
• v.18 no.1
• /
• pp.87-95
• /
• 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.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.20 no.5
• /
• pp.461-471
• /
• 2008

An analytical solution of one dimensional mild slope equation is derived by use of the WKB method, which has a form similar to Porter's solution(2003). The present solution is so general in the sense of application that it is comparable to the corresponding numerical solutions. In the derivation we also presented the solution of refraction equation in terms of surface displacement. Some numerical results of the present solution by use of Bremmer's method are presented which agree with existing numerical solutions.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.19 no.6
• /
• pp.55-61
• /
• 1982

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.

• Journal of the Korean institute of surface engineering
• /
• v.37 no.6
• /
• pp.344-349
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.2
• /
• pp.109-115
• /
• 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.

• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.219-225
• /
• 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.

• Journal for History of Mathematics
• /
• v.17 no.1
• /
• pp.61-68
• /
• 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.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.5 no.4
• /
• pp.279-287
• /
• 1993

Three dimensional linear transient wave propagation over a constant depth is presented using Green's function method. Present solution is proved to be a more general solution from which the existing solutions are obtained by using the appropriate assumptions. The effect of dispersion on wave height attenuation is shown and discussed on the numerical results of the solution.

• Structural Engineering and Mechanics
• /
• v.6 no.5
• /
• pp.529-542
• /
• 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
• /
• v.16 no.3
• /
• pp.259-269
• /
• 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.