• 대한수학회지
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• 제45권3호
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• pp.645-681
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• 2008

The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain ${\Omega}{\subset}R^3$. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of ${\Omega}$ or decay at infinity when ${\Omega}$ is unbounded.

• 한국항공운항학회지
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• 제14권4호
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• pp.60-65
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• 2006

An aeronautical study is a study of an aeronautical problem to identify possible solutions and select a solution that is acceptable without degrading safety. ICAO and the member states have established the standards regarding the obstacle limitation and regulated the construction of the man-made structures in and beyond the standards. Any obstacles that extend above a standards should as far as practicable be removed except after aeronautical study it is determined that the object would not adversely affect the safety or significantly affect the regularity of operations of airplanes. However ICAO and most member states does not established provisions of the scope and implement procedures of aeronautical study. Recently, Civil Aviation Regulations in Korea specify the provisions relevant to aeronautical study. The Prime objectives of this comparative study are to improve the domestic provisions for aeronautical study caused by obstacle limitation through the investigate the international standards and regulations.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.363-372
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• 2023

In this paper, we consider two functional equations: (1) h(𝓕(x, y, z) + 2x + y + z) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) + 2x + y) + h(xy) + yh(x + z) + 2h(z), (2) h(𝓕(x, y, z) - y + z + 2e) + 2h(x + y) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) - y + 2e) + 2h(x + y + z) + h(xy) + yh(x + z), without any regularity assumption for all x, y, z in a unital algebra A, where 𝓕 : A³ → A is defined by 𝓕(x, y, z) := h(x + y + z) - h(x + y) - h(z) for all x, y, z ∈ A. Also, we find general solutions of these equations in unital algebras. Finally, we prove the Hyers-Ulam stability of (1) and (2) in unital Banach algebras.

• Macromolecular Research
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• 제10권6호
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• pp.359-364
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• 2002

A series of PLA-PEO-PLA triblock stereo-copolymers with varying PLA/PEO and L-DL-LA ratios were synthesized via ring opening pelymerizations. Aqueous solutions of these copolymers undergo thermo-responsive phase transitions as the temperature monotonically increases. Further study shows that there is a critical gel concentration (CGC), and also lower and upper critical gel temperatures (CGTs), at which the thermo-responsive phase transition occurs. The CGC and CGTs are affected by various factors such as block length, as well as the compositions of the PLA blocks and of the additives. In particular, the changes in the phase diagram produced by varying the L-/DL-LA ratio in the PLA blocks were determined to be mainly due to consequent stereo-regularity changes in the PLA blocks.

• 대한수학회지
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• 제56권1호
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• pp.239-263
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• 2019

The $Calder{\acute{o}}n$-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity $a({\xi},x_1,x^{\prime})$ is assumed to be only measurable in one spatial variable $x_1$ and has locally small BMO semi-norm in the other spatial variables x', uniformly in ${\xi}$ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.

• 대한수학회지
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• 제59권5호
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• pp.869-890
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• 2022

We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case.

• 공업화학
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• 제20권2호
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• pp.201-207
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• 2009

Dodecanol 합성을 위한 methyl dodecanoate의 수소화반응을 위하여 copper chromite를 세라믹법, 공침법 및 개량된 공침법으로 합성하였다. 입자의 형상은 SEM 및 XRD로 확인하였으며 수소화 반응후 얻어진 생성물은 GC, GC/MSD 및 NMR로 분석하였다. 합성된 입자는 (1) 3.2에서 $7.0{\mu}m$ 크기의 구형형태(세라믹법), (2) 50에서 500 nm 크기의 구형이 혼재한 판형태(공침법) 및 (3) 작고 균일한 구형형태(개량된 공침법)를 보였다. 입자의 크기를 제어하기 위하여 PEG, Span 80 및 polyacrylate등 다양한 분산제 용액에서 copper chromite를 합성하였다. PEG (Mw = 4000) 수용액에서 합성한 입자가 30~50 nm 크기로 가장 작고 균일하였으며, $280^{\circ}C$ 및 100 atm에서 촉매의 반응성을 테스트한 결과, dodecanol의 수율은 79.9%로 얻어졌다. 수소화반응에서 촉매의 반응성은 촉매의 크기가 작고 균일할수록 높아지는 경향을 보였다. 최적화된 반응조건인 $280^{\circ}C$ 및 240 atm에서 dodecanol의 수율은 95.5%였다.