• Honam Mathematical Journal
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• v.42 no.1
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• pp.105-121
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• 2020

The main result of this article is to factorize the first (σ, τ)-cohomology group of triangular Banach algebra 𝓣 of order three with coefficients in 𝓣 -bimodule 𝓧 to the first (σ, τ)-cohomology groups of Banach algbras 𝓐, 𝓑 and 𝓒, where σ, τ are continuous homomorphisms on 𝓣. As a direct consequence, we find necessary and sufficient conditions for 𝓣 to be (σ, τ)-weakly amenable.

• Journal of the Korean Association of Geographic Information Studies
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• v.16 no.2
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• pp.141-151
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• 2013

This study presents a modeling of aerosol extinction vertical profiles in Korea by using the Moderate Resolution Imaging Spectro-radiometer(MODIS) derived aerosol optical thickness(AOT) and ground based visibility observation data. The method uses a series of physical equations for the derivation of aerosol scale height and vertical profiles from MODIS AOT and surface visibility data. The modelled results under the standard atmospheric condition showed small differences with the standard aerosol vertical profile used in the radiative transfer model. Model derived aerosol scale heights for two cases of clean(${\tau}_{MODIS}=0.12{\pm}0.07$, visibility=$21.13{\pm}3.31km$) and hazy atmosphere(${\tau}_{MODIS}=1.71{\pm}0.85$, visibility=$13.33{\pm}5.66km$) are $0.63{\pm}0.33km$ and $1.71{\pm}0.84km$. Based on these results, aerosol extinction profiles can be estimated and the results are transformed into the KML code for visualization of dataset. This has implications for atmospheric environmental monitoring and environmental policies for the future.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.2
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• pp.99-103
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• 2010

A new analytic solution was derived for the diffusion into or from an immobile zone of a rectangular 2-D pore. For a long time, the new solution converges to a traditional mobile-immobile zone (MIM) model, but only if the latter is used with an apparent initial concentration that is smaller by almost 20% than the true one. This is the tradeoff for using a simple MIM model instead of an exact model based on the diffusion equation. The mass-transfer coefficient was found to be constant for a sufficiently long time; it was proportional to the molecular diffusion and inversely proportional to the square of the pore depth. The mass-transfer coefficient was time-dependent for a sufficiently short time and may be significantly larger than its asymptotic value.