• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.279-287
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• 2012

In this paper, we investigate bounds for solutions of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.781-802
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• 2020

For a fixed semi-Wakamatsu-tilting module _AT, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of ∞-T-cotorsionfree modules and a subclass of the class of T-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.697-705
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• 2014

In this paper, we investigate bounds for solutions of the nonlinear functional differential systems.

• East Asian mathematical journal
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• v.34 no.4
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• pp.359-369
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• 2018

This note, we first show that the famous Carleman's inequality can be improved if we find a positive sequence $\{c_n\}$ such that $c_n{\sum\limits_{j=n}^{\infty}}{\frac{1}{j\(\prod_{k=1}^{j}ck\)^{\frac{1}{j}}}}$ < e. Then we list a lot of known results in the literature improving Carleman's inequality by this method. These results can be a good source to a further research for interested students. We next consider about similar improvement of Polya-Knopp's inequality, which is a continuous version of Carleman's inequality. We show by a manner parallel to the case of Carleman's inequality that Polya-Knopp's inequality can be improved if we find a positive function c(x) such that $c(x){\int}_{x}^{\infty}\frac{1}{t\;{\exp}\(\frac{1}{t}{\int}_{0}^{t}{\ln}\;c(s)\;ds\)}dt$ < e. But there are no known results improving Polya-Knopp's inequality by this method. Suggesting to find a new method, we lastly show that there is no nice continuous function c(x) that satisfies the inequality.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.231-237
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• 2018

Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1087-1098
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• 2013

We find a $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on $\mathbb{R}^k$, $k{\geq}3$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the Euclidean metric on $\mathbb{R}^k$, the scalar curvatures of $g_t$ are strictly decreasing in $t$ in the open unit ball and $g_t$ is isometric to the Euclidean metric in the complement of the ball. Furthermore we extend the discussion to the Fubini-Study metric in a similar way.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.91-107
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• 2021

A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.

• Journal of Pharmaceutical Investigation
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• v.38 no.5
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• pp.335-342
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• 2008

The bioequivalence of two carbamazepine preparations was conducted. The in vivo bioequivalence study in 20 healthy male Korean volunteers was designed by using a single dose, randomized, 2-period crossover with a 3-weeks washout period between the doses. Prior to the in vivo study, an in vitro comparative dissolution test was performed by the paddle and basket method as described in the bioequivalence guidance of the Korea Food and Drug Administration (KFDA). Based on the similar dissolution pattern between two preparations in the dissolution test, the two formulations are demonstrated to be pharmaceutically equivalent. In addition, in vivo bioequivalence test was used to reconfirm the in vitro dissolution results. In the in vivo bioequivalence study, the plasma concentrations of carbamazepine up to 144 h after the administration were determined using a validated HPLC method with UV detection and the bioequivalence between the two drug products was assessed by statistical analysis of the log transformed mean ratios of $C_{max}$, $AUC_{0-t}$ and $AUC_{0-\infty}$. The mean maximum concentration ($C_{max}$) of the test and reference were found to be $1467.0{\pm}335.8\;ng/mL$ and $1465.9{\pm}310.3\;ng/mL$, respectively. The 90% confidence intervals (C.I.) of $C_{max}$ were in the range from 0.95 to 1.05. As for the $AUC_{0-t}$ and $AUC_{0-\infty}$, test values were $110027.1{\pm}27786.4\;ng/mL{\cdpt}h$, $128807.0{\pm}34563.2\;ng/mL{\cdot}h$ and $105473.6{\pm}26496.2\;ng/mL{\cdot}h$, $125448.5{\pm}35975.5\;ng/mL{\cdot}h$, respectively. The 90% C.I. of $AUC_{0-t}$ were 0.97 to 1.10 and of $AUC_{0-\infty}$, 0.99 to 1.09 and thus were within the log 0.8-log 1.25 interval proposed by the KFDA. A two-way ANOVA showed no significant difference between the two formulations. Based on these statistical analysis, it was concluded that the test formulation is bioequivalent to the reference.

• Transactions of the Korean hydrogen and new energy society
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• v.29 no.5
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• pp.512-522
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• 2018

This study was conducted to investigate on the combustion characteristic with the effects of mat thickness and fuel kinds in a metal-fiber burner. The mode transition point is confirmed by the K value, which was defined as the rate of flow velocity and laminar burning velocity. The ($T^4_{sur}-T^4_{\infty}$) is highest at methane flame with 3 T thickness. Through the measurement of the unburned mixture temperature, the possibility of submerged flame in surface combustion burner was confirmed. The rapid emission of CO occurs nearby limit blow out (LBO) because of the increase of flow velocity. In case of NOx, the trend is similar with surface temperature. However, it also considered that the NOx emission is affected by residence time with flame position.

• The Korean Journal of Malacology
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• v.29 no.2
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• pp.121-127
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• 2013

In this study, growth-line analysis was carried out on the hard clam (Meretrix petechialis) collected from the Neolithic shell middens in Daejuk-ri, Seosan, Korea, to reconstruct palaeoenvironment. Growth increments of 206 specimens of the clam were examined. The ages of the specimens were determined from the rings on the shells. The relationship between shell length and ring radius in each ring group was expressed as a regression line, indicating a correspondence in each ring formation. Growth pattern of the midden specimens was compared to that of modern ones collected from Gimje, Jeonbuk. Growth curves for shell length fitted to the von Berta anffy's growth curve were expressed respectively as follows: $SL_t=102.9025[1-e^{-0.18657(t+1.0906)}]$ in the shell midden specimens, $SL_t=104.2583[1-e^{-0.2277(t+0.7499)}]$ in the modern ones. The relationship between shell length (SL; mm) and shell height (SH; mm) was expressed by the following equations: SH = 0.7791 SL + 3.6636 ($R^2$ = 0.946) in the midden specimens, SH = 0.8103 SL + 0.5145 ($R^2$ = 0.991) in the modern ones. The results of the tests regarding the differences between regression coefficients and elevations of growth curves of these two populations demonstrate that the slopes were not significantly different (p < 0.05), but the elevations were (p > 0.05). However, overall growth curves of the midden and modern populations were not significantly different, indicating that shell growth environments of the two areas are similar. Therefore, it is likely that sea temperature near the midden area could be similar to that of present Gimje area, and thus temperature during the period of the midden formation could be higher than presently known.