• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.105-123
• /
• 2015

Let $f_{\beta}=h_{\beta}+\bar{g}_{\beta}$ and $F_a=H_a+\bar{G}_a$ be harmonic mappings obtained by shearing of analytic mappings $h_{\beta}+g_{\beta}=1/(2isin{\beta})log\((1+ze^{i{\beta}})/(1+ze^{-i{\beta}})\)$, 0 < ${\beta}$ < ${\pi}$ and $H_a+G_a=z/(1-z)$, respectively. Kumar et al. [7] conjectured that if ${\omega}(z)=e^{i{\theta}}z^n({\theta}{\in}\mathbb{R},n{\in}\mathbb{N})$ and ${\omega}_a(z)=(a-z)/(1-az)$, $a{\in}(-1,1)$ are dilatations of $f_{\beta}$ and $F_a$, respectively, then $F_a\tilde{\ast}f_{\beta}{\in}S^0_H$ and is convex in the direction of the real axis, provided $a{\in}[(n-2)/(n+2),1)$. They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture, in the affirmative, for ${\beta}={\pi}/2$ and for all $n{\in}\mathbb{N}$.

• Korean Journal of Materials Research
• /
• v.9 no.12
• /
• pp.1155-1159
• /
• 1999

Thin film solar cells on a glass/$SnO_2$ substrate with p-SiC/i-Si/n-Si heterojunction structures were fabricated using a plasma-enhanced chemical-vapor deposition system. The photovoltaic properties of the solar cells were examined with varying the gas phase composition, x=$CH_4/\;(SiH_4+CH_4)$, during the deposition of the p-SiC layer. In the range of x=0~0.4, the efficiency of solar cell increased because of the increased band gap of the p-SiC window layer. Further increase in the gas phase composition, however, led to a decrease in the cell efficiency probably due to in the increased composition mismatch at the p-SiC/i-Si layers. As a result, the efficiency of a glass/$SnO_2$/p-SiC/i-SiC/i-Si/n-Si/Ag thin film solar cell with $1cm^2$ area was 8.6% ($V_{oc}$=0.85V, $J_{sc}$=16.42mA/$cm^2$, FF=0.615) under 100mW/$cm^2$ light intensity.

• Journal for History of Mathematics
• /
• v.24 no.4
• /
• pp.1-6
• /
• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Biomolecules & Therapeutics
• /
• v.24 no.4
• /
• pp.410-417
• /
• 2016

Quercetin is a flavonoid usually found in fruits and vegetables. Aside from its antioxidative effects, quercetin, like other flavonoids, has a various neuropharmacological actions. Quercetin-3-O-rhamnoside (Rham1), quercetin-3-O-rutinoside (Rutin), and quercetin-3-(2(G)-rhamnosylrutinoside (Rham2) are mono-, di-, and tri-glycosylated forms of quercetin, respectively. In a previous study, we showed that quercetin can enhance ${\alpha}7$ nicotinic acetylcholine receptor (${\alpha}7$ nAChR)-mediated ion currents. However, the role of the carbohydrates attached to quercetin in the regulation of ${\alpha}7$ nAChR channel activity has not been determined. In the present study, we investigated the effects of quercetin glycosides on the acetylcholine induced peak inward current ($I_{ACh}$) in Xenopus oocytes expressing the ${\alpha}7$ nAChR. $I_{ACh}$ was measured with a two-electrode voltage clamp technique. In oocytes injected with ${\alpha}7$ nAChR copy RNA, quercetin enhanced $I_{ACh}$, whereas quercetin glycosides inhibited $I_{ACh}$. Quercetin glycosides mediated an inhibition of $I_{ACh}$, which increased when they were pre-applied and the inhibitory effects were concentration dependent. The order of $I_{ACh}$ inhibition by quercetin glycosides was Rutin${\geq}$Rham1>Rham2. Quercetin glycosides-mediated $I_{ACh}$ enhancement was not affected by ACh concentration and appeared voltage-independent. Furthermore, quercetin-mediated $I_{ACh}$ inhibition can be attenuated when quercetin is co-applied with Rham1 and Rutin, indicating that quercetin glycosides could interfere with quercetin-mediated ${\alpha}7$ nAChR regulation and that the number of carbohydrates in the quercetin glycoside plays a key role in the interruption of quercetin action. These results show that quercetin and quercetin glycosides regulate the ${\alpha}7$ nAChR in a differential manner.

• Korean Chemical Engineering Research
• /
• v.49 no.3
• /
• pp.338-341
• /
• 2011

Thin silicon ribbon was used for fabricating flexible silicon p-i-n junction devices, consisting of 100${\times}$100 arrays of pixels in 1 inch on the diagonal. Those passive matrix devices exhibited the rectification ratio $>10^{4}$ owing to smaller cross-talking current than that of p-n junction devices. P-i-n devices fabricated on silica/silicon substrates are easily detached by treatment with hydrofluoric acid and are subsequently transferred onto both PDMS and flexible PET film.

• Journal of the Korean Society for Heat Treatment
• /
• v.2 no.4
• /
• pp.1-10
• /
• 1989

To investigate the influence of temperature on the TiN film, it was deposited on the STC-3 steel and Si-wafer from $TiCl_4/N_2/H_2$ gas mixture by using the radio frequency plasma assisted chemical vapor deposition. The deposition was performed at temperature of $400^{\circ}C-500^{\circ}C$. The results showed that crystalline TiN film was deposited over $480^{\circ}C$, and all specimens showed the crystalline TiN X-ray diffraction peaks after vacuum heat treatment for 3 hrs, at $1000^{\circ}C$, $10^{-5}torr$. While the film thickness was increased above $480^{\circ}C$, it was decreased under $480^{\circ}C$ as temperature increased. And the contents of titanium were increased and it of chlorine were decreased as temperature increased. Because temperature increase was attributed to the increase in the density of TiN film, surface hardness of TiN film was increased with temperature.

• Journal of Preventive Medicine and Public Health
• /
• v.27 no.4 s.48
• /
• pp.677-691
• /
• 1994

To evaluate the validity of serum pepsinogen levels as a screening tool for gastric cancer and adenoma, immunoradiometric assays of serum pepsinogen I level (PG I), II level (PG II) and esphagogastroduodenal endoscopies were done in 757 health examinees. Serum PG I level was higher in subjects with active duodenal ulcer (n=45, $75.2{\pm}34.3{\mu}g/l(mean{\pm}standard\;deviation)$, p<0.01) and gastroduodenal ulcers (n=8, $75.6{\pm}19.8{\mu}g/l$, p<0.05), and was lower in those with gastric adenoma(n=4, $37.7{\pm}37.2{\mu}g/l$, p<0.2) than those with normal, mild gastritis findings or ulcer scars (n=378, $56.6{\pm}24.9{\mu}g/l$. Serum PG II level was higher in subjects with active duodenal ulcer($17.2{\pm}13.8{\mu}g/l$, p<0.2), active gastro-duodenal ulcers ($18.3{\pm}7.4{\mu}g/l$, p<0.2) and gastric carcinoma (n=3, $23.8{\pm}10.9{\mu}g/l$, p<0.05) than those with normal, mild gastritis findings or ulcer scars $(14.5{\pm}7.9{\mu}g/l)$. Serum PG I/PG II ratio was higher in subjects with active duodenal ulcer($5.1{\pm}1.6$, p<0.05) and was lower in those with chronic gastritis(n=107, $4.1{\pm}1.7$, p<0.05), gastric polyp(n=19, $3.9{\pm}1.4$, p<0.2), gastric adenoma(n=4, $2.1{\pm}1.9$, p<0.01) and gastric carcinoma(n=3, $2.7{\pm}1.2$, p<0.1) than those with normal, mild gastritis findings or ulcer scars ($4.5{\pm}1.7$). Serum PG II level increased with age until 6th decade, whereas serum PG I/PG II ratio decreased with age in 378 subjects with normal, mild gastritis findings or ulcer scars. The screening criteria of serum PG I<$70{\mu}g/l$ and PG I/PG II ratio<3.0 for detecting gastric cancer and adenoma gave a positive rate of 15.7%, sensitivity of 57.1% and specificity of 84.7%.

• Honam Mathematical Journal
• /
• v.26 no.4
• /
• pp.411-421
• /
• 2004

A digital $(k_0,\;k_1)$-homotopy is induced from digital $(k_0,\;k_1)$-continuity with the n kinds of $k_i$-adjacency relations in ${\mathbb{Z}}^n$, $i{\in}\{0,\;1\}$. The k-fundamental group, ${\pi}^k_1(X,\;x_0)$, is derived from the pointed digital k-homotopy, $k{\in}\{3^n-1(n{\geq}2),\;3^n-{\sum}^{r-2}_{k=0}C^n_k2^{n-k}-1(2{\leq}r{\leq}n-1(n{\geq}3)),\;2n(n{\geq}1)\}$. In this paper two kinds of digital 8-pseudotori stemmed from the minimal simple closed 4-curve and the minimal simple closed 8-curve with 8-contractibility or without 8-contractibility, e.g., $DT_8$ and $DT^{\prime}_8$, are introduced and their digital topological properties are studied by the calculation of the k-fundamental groups, $k{\in}\{8,\;32,\;64,\;80\}$.

• Bulletin of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.105-113
• /
• 1994

In the course of study of dendroids, Czuba [3] introduced a notion of $R^{i}$ -continua which is a generalization of R-arc [1]. He showed a new class of non-contractible dendroids, namely of dendroids which contain an $R^{i}$ -continuum. Subsecequently Charatonik [2] attempted to extend the notion into hyperspace C(X) of metric continuum X. In so doing, there were some oversights in extending some of the results relating $R^{i}$ -continua of dendroids for metric continua. In fact, Proposition 1 in [2] is false (see example C below) and his proof of Theorem 6 in [2] is not correct (Take Example 4 in [4] with K = [e,e'] as an $R^{1}$-continuum of X and work it out. Then one seens that K not .mem. K as he claimed otherwise.). The aims of this paper are to introduce a notion of w-regular convergence which is weaker than 0-regular convergence and to prove that the w-regular convergence of a sequence {Xn}$^{\infty}$$_{n=1}$ to $X_{0}$ of subcontinua of a metric continuum X is a necessary and sufficient for the sequence {C( $X_{n}$)}$^{\infty}$$_{n=1}$ to converge to C( $X_{0}$ ), and also to prove that if a metric continuum X contains an $R^{i}$ -continuum with w-regular convergence, then the hyperspace C(X) of X contains $R^{i}$ -continuum.inuum.uum.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2001-2011
• /
• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.