• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.783-800
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• 2002

Let B denote the unit ball in $C^n$, and ν the normalized Lebesgue measure on B. For $\alpha$ > -1, define $dv_\alpha$(z) ＝ $c_\alpha$$(1-\midz\mid^2)^{\alpha}$dν(z), z $\in$ B. Here $c_\alpha$ is a positive constant such that $v_\alpha$(B) ＝ 1. Let H(B) denote the space of all holomorphic functions in B. For $p\geq1$, define the Bergman-Privalov space $(AN)^{p}(v_\alpha)$ by $(AN)^{p}(v_\alpha)$ = ${f\inH(B)$ : $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function $f\inH(B)$ is in $(AN)^{p}$$(v_\alpha)$ if and only if $(1+\midf\mid)^{-2}{log(1+\midf\mid)}^{p-2}\mid\nablaf\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case 1＜p＜$\infty$, or $(1+\midf\mid)^{-2}\midf\mid^{-1}\mid{\nabla}f\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case p ＝ 1, where $nabla$f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].

• Animal Systematics, Evolution and Diversity
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• v.8 no.1
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• pp.35-56
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• 1992

The systematic studyof freshwater rotifers was conducted on the materials collected from 205 sites in South Korea. As a result, 1 species, 9 subspecies, 2 varieties and 6 forms of two genera. Brachionus and platyas in Family Brachionidae were identified, of Which , 1 subspecies and 4 forms are new to the Korean fauna: Brachionus urceolaris bennini , B. angularis f. bidens , B. quadridentatus, f. rhenanus, B. forficula f. minor, and B. forficula f. angularis. Total 134 speices, 15 subspecies, 9 varieties and 9 forms representing 14 families 40 genera are now recorded from Korea by adding the 1 subspecies and 4 forms newly described in the present paper.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.483-494
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• 2017

In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: $$T_{\lambda}(f;x)={\int_a^b}{\sum^n_{m=1}}f^m(t)K_{{\lambda},m}(x,t)dt,\;{\lambda}{\in}{\Lambda},\;x{\in}(a,b)$$, where ${\Lambda}$ is an index set consisting of the non-negative real numbers, and $n{\geq}1$ is a finite natural number, at ${\mu}$-generalized Lebesgue points of integrable function $f{\in}L_1(a,b)$. Here, $f^m$ denotes m-th power of the function f and (a, b) stands for arbitrary bounded interval in ${\mathbb{R}}$ or ${\mathbb{R}}$ itself. We also handled the indicated problem under the assumption $f{\in}L_1({\mathbb{R}})$.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.17-24
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• 1995

We begin with a brief survey of some of the known results dealing with Bloch constants. Bloch's theorem asserts that there is a constant B$\_$1.C/(1, 0) such that if f is holomorphic in the open unit disk D and normalized by │f'(0)│$\geq$1, then the Riemann surface of f contains an unramified disk of radius at least B$\_$1.C/(1, 0) (see[7,p.14]).(omitted)

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.383-388
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• 2007

A (g, f)-factor F of a graph G is Called a Hamiltonian (g, f)-factor if F contains a Hamiltonian cycle. The binding number of G is defined by $bind(G)\;=\;{min}\;\{\;{\frac{{\mid}N_GX{\mid}}{{\mid}X{\mid}}}\;{\mid}\;{\emptyset}\;{\neq}\;X\;{\subset}\;V(G)},\;{N_G(X)\;{\neq}\;V(G)}\;\}$. Let G be a connected graph, and let a and b be integers such that $4\;{\leq}\;a\;<\;b$. Let g, f be positive integer-valued functions defined on V(G) such that $a\;{\leq}\;g(x)\;<\;f(x)\;{\leq}\;b$ for every $x\;{\in}\;V(G)$. In this paper, it is proved that if $bind(G)\;{\geq}\;{\frac{(a+b-5)(n-1)}{(a-2)n-3(a+b-5)},}\;{\nu}(G)\;{\geq}\;{\frac{(a+b-5)^2}{a-2}}$ and for any nonempty independent subset X of V(G), ${\mid}\;N_{G}(X)\;{\mid}\;{\geq}\;{\frac{(b-3)n+(2a+2b-9){\mid}X{\mid}}{a+b-5}}$, then G has a Hamiltonian (g, f)-factor.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• The Journal of the Acoustical Society of Korea
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• v.19 no.5
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• pp.60-64
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• 2000

This paper studies the relation between the Fundamental Frequency (F0) and the formants of simple vowels in the Korean language sung by sopranos. It is hewn that, in soprano singing, the F0 of a vowel affects its formants. For this reason the formants of simple vowels sung by sopranos must be considered in all over the soprano singing range. We recorded the five simple vowel sounds /a/, /e/, /i/, /o/, and /u/ sung by five professional sopranos from A3 (220.0Hz) to A5 (880.0Hz) in the major scale and compared the formants of the sung vowels with those of spoken vowels. We observed that F1 and F2 of sung vowels were stable in low F0 (lower than B4) but in high F0 (higher than B4), F1 and F2 lost their stabilities. In the case of /a/, /o/, and /u/, the slope of the F1-F2 graph was about 2.6, and those of the F0-F2 and F0-Fl graphs were 2.2-2.5 and 0.7-1.0, respectively. And as the F0 increases, the F1 and F2 of sung vowels /a/, /e/, /i/, /o/, and /u/ were almost the same. At A5, the Fl and F2 of five sung vowels had the same values. This results suggest that the relation between the F0 and the formants be used to synthesize soprano's singing vowels.

• 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.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.8
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• pp.3795-3802
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• 2012

Cochinchina momordica seeds (CMS) have been widely used due to antitumor activity by Mongolian tribes of China. However, the details of the underlying mechanisms remain unknown. In the present study, we found that an EtOAc (ethyl ester) extract of CMS (CMSEE) induced differentiation and caused growth inhibition of melanoma B16 F1 cells. CMSEE at the concentration of $5-200{\mu}g/ml$ exhibited strongest anti-proliferative effects on B16 F1 cells among other CMS fractions (water or petroleum ether). Moreover, CMSEE induced melanoma B16 F1 cell differentiation, characterized by dendrite-like outgrowth, increasing melanogenesis production, as well as enhancing tyrosinase activity. Western blot analysis showed that sustained phosphorylation of p38 MAP accompanied by decrease in ERK1/2 and JNK dephosphorylation were involved in CMSEE-induced B16 F1 cell differentiation. Notably, 6 compounds that were isolated and identified may be responsible for inducing differentiation of CMSEE. These results indicated that CMSEE contributes to the differentiation of B16 F1 cells through modulating MAPKs activity, which may throw some light on the development of potentially therapeutic strategies for melanoma treatment.