• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.709-715
• /
• 1997

For a fibration (E,B,p) with fiber F and a fiber map f, we show that if the inclusion $i : F \to E$ has a left homotopy inverse, then $G^f_n(E,F)$ is isomorphic to $G^f_n(F,E) \oplus \pi_n(B)$. In particular, by taking f as the identity map on E we have $G_n(E,F)$ is isomorphic to $G_n(F) \oplus \pi_n(B)$.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.129-139
• /
• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.457-464
• /
• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.63-72
• /
• 1999

We introduce a concept of fuzzy linearity: A function $F:L^0(X){\rightarrow}\mathbb{R}$ is fuzzy linear if $F[({\alpha}{\wedge}f){\vee}(b{\wedge}g)]=[a{\wedge}F(f)]{\vee}[b{\wedge}F(g)]$ for $f,g{\in}L^0(X)$ and a, b > 0. We show that a fuzzy integral is fuzzy linear if the measure is fuzzy c-additive.

• 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.

• Clinical and Experimental Reproductive Medicine
• /
• v.20 no.2
• /
• pp.157-160
• /
• 1993

The human follicular f1uids(F.F.) may be considered to contribute the maturation of the oocytes on the in vitro culture. To investigate the effects of epidermal growth factor (E.G.F.), which is present in mature and immature follicular fluids, we had experiments of mouse oocytes maturation in vitro. The endpoints assayed were rated as percentage of oocytes undergoing germinal vesicle breakdown(G.V.B.D.) and polar body(P.B.) formation at 12 hours after in vitro culture. The rates of G.B.B.D. were 87% in mature F.F. 68% in immature F.F. and 78% in Ham's F-10 medium respectively. And overall the mature F.F. seem to stimulate on in vitro oocyte maturation compared with either immature F.F. or Ham's F-10 medium. As the concentration of addition of E.G.F. in immature F.F., the rates of G.V.B.D. and P.B. formation were 82 %, 23% in addition with 2 ng/ml while 84%, 32% in addition with 4 ng/ml respectivly. And at the concentration of addition of E.G.F. in Ham's F-10 media as well, the rates of G.V.B.D. and P.B. formation were 84%, 40% and 82%, 44% in addition with each 2ng, 4ng. AccordinglY there was no influence on the oocytes maturation at the addition of E.G.F. to each immature F.F. and Ham's F-10 medium. In conclusion, the E.G.F. is not able to induce oocyte maturation independent of it's effects in immature F.F. and Ham's F-10 media.

• Korean Journal of Microbiology
• /
• v.32 no.2
• /
• pp.120-125
• /
• 1994

The genes, trpB, trpA and 3’ trpC(F) of Vibrio metschnikovii strain RH530 were cloned and sequenced. The trpB and trpA genes had open reading frames of 1,173 bp and 804 bp encoding 391 and 268 amino acids, respectively. The trpB and trpA genes had conventional ribosome-binding sequences and overlapped with each other by one nucleotide, suggesting that these two genes are translationally coupled. 115 nucleotide upstream the trpB start codon, tjere was an incomplete open reading frame of the 3’-end of the trpC(F). The amino acid sequences of trpB, trpA and trpC(F) of V. metschnikovii RH530 had identities of 64.2%, 82.4% and 73.7% respectively, for those of V. parahaemolyticus; 58.7%, 72.3% and 54.9%, respectively, for Salmonella typhimurium; and 42.6%. 54.1% and 12.5%, respectively, for brevibacterium lactofermentum. The genetic organization of these genes, especially in the noncoding region between trpC(F) and trpB, was distinct from that of Enterobacteriaceae.

• The Journal of Korean Obstetrics and Gynecology
• /
• v.21 no.1
• /
• pp.83-98
• /
• 2008

Purpose: This study was performed to determine the inhibitory effect of Soyosangagamhwajae(SYG) on melanin synthesis in B16F10 mouse melanoma cell. Methods: The Inhibitory effects of Soyosangagamhwajae(SYG) on melanin synthesis were determined by in-vitro assay. To elucidate inhibitory effects of SYG on melanin synthesis, we determined the melanin release in B16F10 cell. And to investigate the action mechanism, we assessed the gene expression of tyrosinase, TRP-1, TRP-2. PKA, $PKC{\beta}$ in B16F10 cell. Results: 1. SYG significantly inhibited melanin-release in B16F10 cell. 2. SYG significantly inhibited mushroom tyrosinase activity in vitro. 3. SYG significantly suppressed the expression of tyrosinase in B16F10 cell. 4. SYG significantly suppressed the expression of TRP-1, TRP-2 in B16F10 cell. 5. SYG significantly suppressed the expression of PKA, $PKC{\beta}$ in B16F10 cell. Conclusion: From these results, it may be concluded that SYG has the antimelanogenetic effect.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.113-119
• /
• 2010

If f is M-harmonic and integrable with respect to a weighted radial measure $\upsilon_{\alpha}$ over the unit ball $B_n$ of $\mathbb{C}^n$, then $\int_{B_n}(f\circ\psi)d\upsilon_{\alpha}=f(\psi(0))$ for every $\psi{\in}Aut(B_n)$. Equivalently f is fixed by the weighted Berezin transform; $T_{\alpha}f = f$. In this paper, we show that if a function f defined on $B_n$ satisfies $R(f\circ\phi){\in}L^{\infty}(B_n)$ for every $\phi{\in}Aut(B_n)$ and Sf = rf for some |r|=1, where S is any convex combination of the iterations of $T_{\alpha}$'s, then f is M-harmonic.