• Journal of applied mathematics & informatics
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• 제30권1_2호
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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.

• 대한수학회보
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• 제57권3호
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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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• 제32권5_6호
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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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• 제34권4호
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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.

• 충청수학회지
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• 제31권2호
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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.

• 대한수학회보
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• 제50권4호
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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.

• 대한수학회지
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• 제58권1호
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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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• 제38권5호
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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.

• 한국수소및신에너지학회논문집
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• 제29권5호
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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.

• 한국패류학회지
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• 제29권2호
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• pp.121-127
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• 2013

본 연구에서는 신석기시대의 서산 대죽리 패총에서 출토된 말백합의 패각에 나타난 윤문을 판독하여 성장식을 추정하고 현재의 말백합 개체군과의 성장을 비교하였다. 패총 출토 패각의 수는 총 206개체였다. 각 연령군별로 각장과 윤경 간에 대응성을 보였고, 각 윤문군이 비교적 뚜렷이 구분되어 윤문판독의 타당성이 확인되어 판독된 윤문을 연륜으로 간주하였다. 패총 출토 말백합의 윤문은 2-5개까지 확인되어 2-5세군으로 구성되었음을 알 수 있었다. 패총 개체군의 성장식은 $SL_t=102.9025[1-e^{-0.18657(t+1.0906)}]$ 이었으며, 현생 개체군은 $SL_t=104.2583[1-e^{-0.2277(t+0.7499)}]$ 이었다. 각장 (SL) 과 각고 (SH) 간의 상대성장식은 패총 개체군 SH = 0.7791SL + 3.6636 ($R^2$ = 0.946) 이었으며, 현생 개체군은 SH = 0.8103SL + 0.5145 ($R^2$ = 0.991) 이었다. 두 개체군의 성장계수 (k) 는 차이가 없었고 (p < 0.05), 극한각장 ($SL_{\infty}$) 은 차이가 있었으나 (p > 0.05) 전체적으로 두 개체군의 상대성장식의 차이는 크지 않아 성장의 차이는 없다고 할 수 있다. 이는 두 개체군의 서식 환경이 비슷하다는 것을 의미한다. 따라서 신석기시대의 대죽리 패총이 형성될 당시 인근 연안의 해수온은 현재의 김제 연안지역과 비슷하게 높았을 가능성이 있는 것으로 추정된다.