• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.359-366
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• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.1
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• pp.585-594
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• 2021

This Quasi-experimental study was started under the assumption that the stress of students who participated in Buddhism and Mind Healing Lectures based on an understanding of the scriptures will be relieved through the lectures, thereby enhancing their psychological stability, thinking ability, and enhancing understanding. Stress can be confirmed through a self-report test, but in this study, quantitative EEG was measured to evaluate the stress level and secure objectivity. To this end, the difference between the 1st week as pre and 15th week as post quantitative EEG was verified for the experimental group taking the Buddhism and Mind Healing Lecture held from March to June 2019 at S University in G-gu, Seoul, and the control group who did not. The Mann Whitney U test and Wilcoxon code ranking test were used as analysis methods because the number of subjects was 14. As a result, there was a significant difference in the beta wave (F7, T3, 4, T5) and the high beta wave (F7, F8, T3, T4) in the experimental group. The coherence was also improved, while there was no significant difference in the control group. Buddhism and Mind Healing Lectures improved stress.

• Geotechnical Engineering
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• v.6 no.1
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• pp.7-14
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• 1990

The two degree of freedom model is proposed to study the effects of imperfect fixing at the active end of spring-top resonant column apparatus. A computer program using the SYMPHONY spreadsheet is developed to calculate the dimensionless frequency, F, from which modulug can be determined. It is found that the effect of reaction mass through the parameter Tr on dimensionless frequency, F, can not be ignored if Tr$\leq$20. As To increases, the variation of F increases. But for Tr$\geq$ 20, the effect of To becomes small. It is recommended that T. be greater than 20 if single degree of freedom model is rosed to determine modulus of soil. It also is found that damping ratios of specimen and apparatus do not strongly affect the dimensionless frequency, F.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• ETRI Journal
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• v.31 no.2
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• pp.129-139
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• 2009

This paper provides an efficient algorithm for computing the ${\eta}_T$ pairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy a modified multiplication in $F_{2^{4n}}$ using the Vandermonde matrix. For F, G ${\in}$ $F_{2^{4n}}$ the proposed multiplication method computes ${\beta}{\cdot}F{\cdot}G$ instead of $F{\cdot}G$ with some ${\beta}$ ${\in}$ $F^*_{2n}$ because ${\beta}$ is eliminated by the final exponentiation of the ${\eta}_T$ pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in $F_{2^n}$ as n ${\rightarrow}$ ${\infty}$, while the cost of the previously fastest Karatsuba method is 9 multiplications in $F_{2^n}$. Consequently, the cost of the ${\eta}_T$ pairing computation is reduced by 14.3%.

• Journal of the Korean Society of Food Science and Nutrition
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• v.39 no.8
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• pp.1126-1131
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• 2010

The antiobesity effect of soymilks fermented with Bacillus subtilis KC-3 (KCCM 42923) from cheonggukjang was compared with other sources of B. subtilis KCCM 11316 and B. subtilis MYCO. The antiobesity effect was investigated by measuring the release of leptin, Oil red O staining, glycerol secretions and adipogenic transcription factor by reverse transcription-polymerase chain reaction (RT-PCR) in the 3T3-L1 adipocytes. Fermented soymilk with B. subtilis KC-3 (F-KC) led to decrease levels of leptin secretion and increase levels of glycerol secretion in the cells. In addition, F-KC reduced contents of Oil red O dye in the 3T3-L1 adipocytes. Also, mRNA expression levels of both SREBP-1c (sterol regulatory element-binding protein 1-c) and PPAR-$\gamma$ (peroxisome proliferator-activated receptor-$\gamma$), which are adipogenic transcription factor, in cells treated with F-KC were markedly down regulated. These results demonstrate that the Bacillus subtillis fermented soymilk (F-KC) decreased lipid content in 3T3-L1 adipocytes by inhibiting lipogenesis. All B. subtilis fermented soymilks had shown antiobesity activities, however, F-KC exhibited the strongest antiobesity effect in the 3T3-L1 adipocytes. Our study suggests that especially F-KC increased the potential of antiobesity effects.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.5
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• pp.11-16
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• 1998

We analyze the software reliability growth models for the specified period from the viewpoint of theory of differential equations. we defien a genralized form of reliability growth models as follws: dN(t)/dt = b(t)f(N(t)), Where N(t) is the number of remaining faults and b(t) is the failure rate per software fault at time t. We show that the well-known three software reliability growth models - Goel - Okumoto, s-shaped, and Musa-Okumoto model- are special cases of the generalized form. We, also, extend the generalized form into an extended form being dN(t)/dt = b(t, .gamma.)f(N(t)), The genneralized form can be obtained if the distribution of failures is given. The extended form can be used to describe a software reliabilit growth model having weibull density function as a fault exposure rate. As an application of the generalized form, we classify three mentioned models according to the forms of b(t) and f(N(t)). Also, we present a case study applying the generalized form.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.545-556
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• 2005

Hjort(1990) obtained the nonparametric Bayes estimator $\^{F}_{c,a}$ of $F_0$ with respect to beta processes in the random censorship model. Let $X_1,{\cdots},X_n$ be i.i.d. $F_0$ and let $C_1,{\cdot},\;C_n$ be i.i.d. G. Assume that $F_0$ and G are continuous. This paper shows that {$\^{F}_{c,a}$(u){\|}0 < u < T} converges weakly to a Gaussian process whenever T < $\infty$ and $\~{F}_0({\tau})\;<\;1$.