• Journal of the Korean Mathematical Society
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• v.45 no.3
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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.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.14 no.4
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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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• v.31 no.3
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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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• v.10 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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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.

• Applied Chemistry for Engineering
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• v.20 no.2
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• pp.201-207
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• 2009

The hydrogenation reaction of methyl dodecanoate for the synthesis of 1-dodecanol has been carried out in the presence of a copper chromite catalyst. The catalysts were synthesized by ceramic method, co-precipitation, and improved co-precipitation method and the particles were characterized by SEM and XRD. Also, the products of the reaction were assigned by GC, GC/MSD and NMR. The particles synthesized by each method showed (1) a spherical shape with the size of 3.2 to $7.0{\mu}m$, (2) an agglomerated spherical shape with the size of 50 to 500 nm and (3) a spherical shape with smaller particle size, respectively. Especially, in order to control the size of particles, the particles were synthesized in various dispersant solutions as Span 80, polyacrylate, and polyethyleneglycols (PEGs). The particles synthesized in PEG (Mw = 4000) solution showed the smallest particle size of 30 to 50 nm and the regularity of the particle size distribution. Our experimental results elucidated that the activity of catalyst for hydrogenation increases with decreasing the size of catalyst particle. The highest yield of dodecanol in the hydrogenation reaction was 95.5% when copper chromite synthesized in the PEG solution was used as a catalyst in the optimized reaction condition.