• Journal of the Korean Society of Propulsion Engineers
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• v.17 no.1
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• pp.26-34
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• 2013

An analytic approach to determine the optimal conditions for maximizing altitude of a sounding rocket is suggested. The behavior of the one-dimensional momentum equation including thrust, gravitational force and aerodynamic drag force is investigated. For the case where an analytic solution exists, a characteristic equation for determining optimal condition for maximizing altitude at the burn-out state and that for maximizing altitude at the stationary state are developed and verified with numerical experiments.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.63-77
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• 2005

The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed curves and containing cuts is studied. The Neumann condition is given on the closed curves, while the Dirichlet condition is specified on the cuts. The existence of a classical solution is proved by potential theory. The integral representation of the unique classical solution is obtained. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. Our results hold for both interior and exterior domains.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1673-1685
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• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.83-102
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• 2024

In this paper, first we establish a unique common fixed point theorem satisfying new contractive condition on partially ordered non-Archimedean fuzzy metric spaces and give an example to support our result. By using the result established in the first section of the manuscript, we formulate a unique common coupled fixed point theorem and also give an example to validate our result. In the end, we study the existence of solution of integral equation to verify our hypothesis. These results generalize, improve and fuzzify several well-known results in the existing literature.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.387-395
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• 1998

In this article we prove a Harnack inequality for the positive solutions of the heat equation with Neumann boundary condition for a compact Riemannian manifold with possibly non-convex boundary.

• East Asian mathematical journal
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• v.19 no.2
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• pp.173-187
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• 2003

We study decay estimates of the energy for the nonlinear wave equation in the whole space. We note that the method of proof is based on the multiplier technique and on the unique continuation, and no geometrical condition is imposed on the boundary.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.1
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• pp.23-36
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• 2023

The vector wave equation is widely used in electromagnetic wave analysis. This paper solves the vector wave equation using curl-conforming finite elements. The variational problem is established from Riesz functional based on vector wave equation and the unique existence of weak solution is explored. The edge elements are used in computation and the simulation results are compared with those obtained from a commercial simulator, ANSYS HFSS (high-frequency structure simulator).

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1121-1136
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• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.

• New & Renewable Energy
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• v.2 no.2 s.6
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• pp.50-59
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• 2006

An experimental and numerical study is carried out to investigate the performance and the efficiency humidifying Membrane Electrolyte Assembly and having the double-layered catalyst in a fuel cell system which is taken into account the physical and thermal concept. Based on the principals of the problem, the equation of electronic charge conservation equation, gas-phase continuity equation, and mass balance equation are used for the numerical calculation. A unit cell for $200cm^2$ MEA is assembled and measured for finding better operational situation. After finding the optimal condition, 10 cell stacked PEMFC is fabricated. For the performance evaluation, V-I and power curves are examined in detail by changing the condition of humidity, temperature, pressure, thickness of catalyst and oxidant. It is found that the power is maximized around 500W at 80A.

• Journal of the Korean Professional Engineers Association
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• v.23 no.6
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• pp.41-46
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• 1990

First of all, Under given condition such as bit gage of 36mm Drill bit with right class of jack-logs experimental test carried out from two face of Bench, firing of each hole brought 90 degree Angle face and them measured length of Burden and charged ammount of powder as following. (equation omitted) A=Activated Area A=ndi=m S=Peripheral length of Charged. room Ca=Rock Coeffiecency d : di=Hole diameter When constructed subway of Seoul in 1980 the blasting works increased complaint of ground vibration. in order to prevent the damage to structures. Some empirical equations were made as follows on condition with Jackleg Drill (Bit Gage ø 36mm) and within 30 meter distance between blasting site and structures. V=K(D / W)$\^$-n/ N=1.60-1.78 K=48-138 Project one of contineous works to above a determination of empirical equation on the cautious blasting vibration with Crawler Drill(ø 70-75mm) in long distance. V=41(equation omitted) V=124(equation omitted).