• Honam Mathematical Journal
• /
• v.32 no.1
• /
• pp.167-176
• /
• 2010

Let (B, $\check{g}$) and (N, $\hat{g}$) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold $B\;{\times}_f\;N\;:=\;(B\;{\times}\;N,\;\check{g}\;+\;f{\hat{g}}$) to be Einstein, and obtain a complete condition for the Einstein warped product manifold $B\;{\times}_f\;N$ to be weakly stable. Moreover, we get a complete condition for the map i : ($B,\;\check{g})\;{\times}\;(N,\;\hat{g})\;{\rightarrow}\;B\;{\times}_f\;N$, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for $B\;{\times}_f\;N$ to be Einstein.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.343-358
• /
• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• Proceedings of the Polymer Society of Korea Conference
• /
• 2006.10a
• /
• pp.224-225
• /
• 2006

The Ethylene polymerization behavior of a series of polymethylene bridged dinuclear CGC $[Zr({\eta}^{5}:{\eta}^{1}-C_{9}H_{5}SiMe_{2}NCMe_{3})Me_{2}]_{2}[(CH_{2})_{n}]\;[_{n}=6(1),\;9(2),\;12(3)]$ in the cocatalytic activation with $Ph_{3}C^{+}B^{-}(C_{6}F_{5})_{4}\;(B_{1})\;or\;Ph_{3}C^{+}(C_{6}F_{5})_{3}B^{-}C_{6}F_{4}B^{-}(C_{6}F_{5})_{3}Ph_{3}C^{+}\;(B_{2})\;or\;B(C_{6}F_{5})_{3}\;(B_{3})$ were investigated to study the nuclearity effects as well as the counteranion effects. The ethylene polymerization and ethylene/1-hexene copolymerization were conducted at $30^{\circ}C$ It was found that both in ethylene polymerization and ethylene/1-hexene copolymerization, activities increased in the order of 1 < 2 < 3, which indicates the presence of longer bridge between two active sites contributes more efficiently to facilitate the polymerization activity.

• Honam Mathematical Journal
• /
• v.15 no.1
• /
• pp.75-85
• /
• 1993

For A and B, $-1{\leq}B<A{\leq}1$, let P[A, B] be the class of functions p analytic in the unit disk E with P(0) = 1 and subordinate to $\frac{1+Az}{1+Bz}$. We introduce the class $T_{\alpha}[A,B]$ of functions $f:f(z)=z+\sum\limits_{n=2}^{{\infty}}a_nz^n$ which are analytic in E and for $z{\in}E$, ${\alpha}{\geq}0$, $[(1-{\alpha}){\frac{f(z)}{z}}+{\alpha}f^{\prime}(z)]{\in}P[A,B]$. It is shown that, for ${\alpha}{\geq}1$, $T_{\alpha}[A,B]$ consists entirely of univalent functions and the radius of univalence for $f{\in}T_{\alpha}[A,B]$, $0<{\alpha}<1$ is obtained. Coefficient bounds and some other properties of this class are studied. Some radii problems are also solved.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.737-743
• /
• 2016

Let a and b be two ideals of a commutative Noetherian ring R, M a finitely generated R-module and i an integer. In this paper we study formal local cohomology modules with respect to a pair of ideals. We denote the i-th a-formal local cohomology module M with respect to b by ${\mathfrak{F}}^i_{a,b}(M)$. We show that if ${\mathfrak{F}}^i_{a,b}(M)$ is artinian, then $a{\subseteq}{\sqrt{(0:{\mathfrak{F}}^i_{a,b}(M))$. Also, we show that ${\mathfrak{F}}^{\text{dim }M}_{a,b}(M)$ is artinian and we determine the set $Att_R\;{\mathfrak{F}}^{\text{dim }M}_{a,b}(M)$.

• Biomedical Science Letters
• /
• v.10 no.2
• /
• pp.153-161
• /
• 2004

Antibiotic resistance is often associated with the production of inner membrane proteins (for example, AcrAB/TolC efflux pump) that are capable to extrude antibiotics, detergents, dyes and organic solvents. In order to evaluate the unknown MarB function of Escherichia coli, especially focused on the function of OmpF porin, several mutants were construted by T4GT7 transduction. MarA plays a major roles in mar (multiple antibiotic resistance) phenotype with AcrAB/TolC efflux pump in E. coli K-12. Futhermore, MarA decreases OmpF porin expression via micF antisense RNA. Expression of acrAB is increased in strains containing mutation in marR, and in those carrying multicopy plasmid expressing marA. MarB protein of E. coli K-12 showed its activity at OmpF porin & TolC protein as target molecule. Some paper reported MarB positively regulates OmpF function. MarA shows mar phenotype, and MarB along with MarA show decreased MIC through OmpF function. By this experiment, MarB could decrease MIC through the OmpF porin & TolC protein as target.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.875-883
• /
• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

• Toxicological Research
• /
• v.22 no.4
• /
• pp.349-356
• /
• 2006

Diallyl disulfide (DADS), an oil-soluble organosulfur compound in garlic has been reported to suppress tumor growth and to induce apoptosis in cancer. In the present study, we investigated the effects of DADS on pulmonary metastasis of B16-F10 murine melanoma cells. DADS (i.p. 40 mg/kg) significantly (p<0.05) reduced the number of pulmonary metastatic nodules (48%) in experimental pulmonary metastasis assay. We also found that DADS inhibited adhesion, invasion and migration of B16-F10 melanoma cells in a dose-dependent manner. To study the antimetastatic potential of DADS, we performed the effects of DADS on matrix metalloproteinase activity. DADS significantly inhibited the expression of matrix metalloproteinase-2 activity in B16-F10 cells by gelatin zymography. These results suggest that DADS prevent metastasis in part through suppression of migration of B16-F10 melanoma cells by Inhibiting matrix metalloproteirase-2 responsible for degradation of extracellar matrix.

• Korean Journal of Pharmacognosy
• /
• v.52 no.1
• /
• pp.13-18
• /
• 2021

This study was performed to clarify the whitening effects of anthricin on the B16F10 cell line. In order to elucidate the whitening effects of anthricin on the B16F10 cell line, cell viability, messenger ribonucleic acid (mRNA) expressions, tyrosinase activity assay, and melanin production assay were measured. The effects of anthricin on tyrosinase-related protein 1(TYRP1)/TYRP2/tyrosinase (TYR)/microphthalmia-associated transcription factor (MITF) mRNA expressions and melanin content were determined. Quantitative real-time RT-PCR showed that anthricin decreased the mRNA expression level of TYRP1/TYRP2/TYR/MITF genes and melanin production contents than α-MSH-treated B16F10 cells. The tyrosinase activity assay revealed that anthricin decreased the melanin production on the B16F10 cells. These data show that anthricin increases the whitening effects on the B16F10 cells; thus, anthricin is a potent ingredient for skin whitening. Thus, further research on the mechanism of action of anthricin for the development of not only cosmetics, but also healthy food and medicine should be investigated.

• The Journal of the Korea Contents Association
• /
• v.2 no.4
• /
• pp.93-98
• /
• 2002

Functional equations are useful in the experimental science because they play very important role for researchers to formulate mathematical models in general terms, through some not very restrictive equations that only stipulate basic properties of functions showing in these equations, without postulating the exact forms of such functions. Of lots of such functional equations, in this paper we adopt and solve some generalized quadratic functional equation a$^2$f((x+y/a))+b$^2$f((x-y/b)) = 2f(x)+2f(y)