• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1201-1219
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• 2023

We characterize the boundedness and compactness of differences of weighted composition operators acting from weighted Bergman spaces A^p_ω to Lebesgue spaces L^q(dµ) for all 0 < p, q < ∞, where ω is a radial weight on the unit disk admitting a two-sided doubling condition.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.73-95
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• 1999

We prove that if a given complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincar inequality and the finite covering condition at infinity on each end, then every positive harmonic function on the manifold is asymptotically constant at infinity on each end. This result is a direct generalization of those of Yau and of Li and Tam.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1737-1751
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• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.213-230
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• 2019

We construct new metric outer measures (multifractal analogues of the Hewitt-Stromberg measure) $H^{q,t}_{\mu}$ and $P^{q,t}_{\mu}$ lying between the multifractal Hausdorff measure ${\mathcal{H}}^{q,t}_{\mu}$ and the multifractal packing measure ${\mathcal{P}}^{q,t}_{\mu}$. We set up a necessary and sufficient condition for which multifractal Hausdorff and packing measures are equivalent to the new ones. Also, we focus our study on some regularities for these given measures. In particular, we try to formulate a new version of Olsen's density theorem when ${\mu}$ satisfies the doubling condition. As an application, we extend the density theorem given in [3].

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• Microbiology and Biotechnology Letters
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• v.26 no.4
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• pp.303-308
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• 1998

A bacterial strain which utilizes phenol under denitrifying condition was isolated from the industrial waste water collected from the Chong-ju Industrial Complex. The strain was identified as Pseudomonas species from the morphological, physiological, and biochemical characteristics and designated as HL100. The strain can utilize phenol as the sole source of carbon and energy when nitrate is provided as the terminal electron acceptor. The isolated strain completely degraded 3 mM of phenol within 110 hour with concomitant reduction of nitrate to nitrite. The observed maximum doubling time was 20 hours. Under appropriate condition, complete reduction of nitrate to atmospheric N$_2$ was observed indicating that the isolated strain could perform complete steps of denitrification. The strain showed optimal growth at pH 7.0 and temperature of 37$^{\circ}C$ under denitrifying phenol-degrading condition. The strain can also utilize toluene as the sole carbon and energy source under the same growth condition. However, no growth was detected on xylene and benzene.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1597-1612
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• 2016

There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.145-153
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• 1995

A Jordan domain D in C is said to be a c-quasidisk if there exists a constant $c \geq 1$ such that each two points $z_1$ and $z_2$ in D can be joined by an arc $\tau$ in D such that $$ \ell(\tau) \leq c$\mid$z_1 - z_2$\mid$ $$ and $$ (1.1) min(\ell(\tau_1),\ell(\tau_2)) \leq c d(z, \partial D) $$ for all $z \in \tau$, where $\tau_1$ and $\tau_2$ are the components of $\tau\{z}$. Quasidisks have been extensively studied and can be characterized in many different ways [1],[2],[3].

• Radiation Oncology Journal
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• v.19 no.2
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• pp.163-170
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• 2001

Purpose : The measurement of radiation survival using a clonogenic assay, the established standard, can be difficult and time consuming. In this study, We have used the MTT assay, based on the reduction of a tetrazolium salt to a purple formazan precipitate by living cells, as a substitution for clonogenic assay and have examined the optimal condition for performing this assay in determination of radiation sensitivity. Materials and Methods : Four human cancer cell lines - PCI-1, SNU-1066, NCI-H630 and RKO cells have been used. For each cell line, a clonogenic assay and a MTT assay using Premix WST-1 solution, which is one of the tetrazolium salts and does not require washing or solubilization of the precipitate were carried out after irradiation of 0, 2, 4, 6, 8, 10 Gy. For clonogenic assay, cells in $25\;cm^2$ flasks were irradiated after overnight incubation and the resultant colonies containing more than 50 cells were scored after culturing the cells for $10\~14$ days. For MTT assay, the relationship between absorbance and cell number, optimal seeding cell number, and optimal timing of assay was determined. Then, MTT assay was performed when the irradiated cells had regained exponential growth or when the non-irradiated cells had undergone four or more doubling times. Results : There was minimal variation in the values gained from these two methods with the standard deviation generally less than $5\%$, and there were no statistically significant differences between two methods according to t-test in low radiation dose (below 6 Gy). The regression analyses showed high linear correlation with the $R^2$ value of $0.975\~0.992$ between data from the two different methods. The optimal cell numbers for MTT assay were found to be dependent on plating efficiency of used cell line. Less than 300 cells/well were appropriate for cells with high plating efficiency (more than $30\%$). For cells with low plating efficiency (less than $30\%$), 500 cells/well or more were appropriate for assay. The optimal time for MTT assay was after 6 doubling times for the results compatible with those of clonogenic assay, at least after 4 doubling times was required for valid results. In consideration of practical limits of assay (12 days, in this study) cells with doubling time more than 3 days were inappropriate for application. Conclusion : In conclusion, it is found that MTT assay can successfully replace clonogenic assay of tested cancer cell lines after irradiation only if MTT assay was undertaken with optimal assay conditions that included plating efficiency of each cell line and doubling time at least.

• Journal of Korean Society on Water Environment
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• v.22 no.2
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• pp.258-263
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• 2006

ANAMMOX (Anaerobic ammonium oxidation) reactor, which was cultivated ANAMMOX bacteria in mesophilic condition ($35^{\circ}C$), was operated to investigate the effects of temperature. In $20{\sim}30^{\circ}C$ of operation condition, which was assumed as field-temperature, total N removal and $NH_4-N$ removal rate were declined from about 2.50 and $1.27kg\;N/{m^3}_{reactor}-day$ (0.06 and 0.03 kg N/kgVSS/day) to 1.62 and $0.41kg\;N/{m^3}_{reactor}-day$ (0.04 and 0.01 kg N/kgVSS/day), In this range of temperature, ANAMMOX had very low activities but acid fermentation bacteria and denitrifiers, which were competitors of substrates, had high activities relatively. Though operation temperature was higher than inhibition condition for two months, ANAMMOX activities could not been recovered once they were inhibited by low temperature. This fact was resulted from very slow doubling time of ANAMMOX bacteria. This study shows that maintenance device of optimal temperature is necessary required in field application of ANAMMOX.