• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.127-133
• /
• 2012

It is well known that if the ${\beta}$-expansion of any nonnegative integer is finite, then ${\beta}$ is a Pisot or Salem number. We prove here that $\mathbb{F}_q((x^{-1}))$, the ${\beta}$-expansion of the polynomial part of ${\beta}$ is finite if and only if ${\beta}$ is a Pisot series. Consequently we give an other proof of Scheiche theorem about finiteness property in $\mathbb{F}_q((x^{-1}))$. Finally we show that if the base ${\beta}$ is a Pisot series, then there is a bound of the length of the fractional part of ${\beta}$-expansion of any polynomial P in $\mathbb{F}_q[x]$.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.437-448
• /
• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• The korean journal of orthodontics
• /
• v.28 no.1 s.66
• /
• pp.165-174
• /
• 1998

The turnover of collagen is controlled by the balance between collagen synthesis and degradation. The production of collagenase (matrix metalloproteinase-1) and its inhibitor, tissue inhibitor of matrix metallopmteinase-1 (TIMP-1) are one of the substances which regulate this balance. The periodontal ligament fibroblast plays an important role in collagen metabolism during orthodontic treatment and is believed to be an origin of the osteoblast in the alveolar bone. The collagenase secreted by the periodontal ligament fibroblast and the osteoblast initiates the bone resorption by removing the osteoid layer in the alveloar bone. The interleukin-$1{\beta}$ is secreted by the macrophage during orthodontic treatment. The present study was undertaken to assess the effect of mechanical stress and interleukin-$1{\beta}$ on the expression of collagenase and TIMP-1 in the periodontal ligament fibroblasts using reverse transcription polymerase chain reaction and immunohistochemical staining. The periodontal ligament fibroblasts were stitched by placing the $Petriperm dish^{\circledR}$ dish on the top of spheroidal convex watch glass ($5\%$ surface increase) and tented with interleukin-$1{\beta}$ (1.0 ng/ml), or treated with both of them. Treatment with mechanical stress and/or interleukin-$1{\beta}$ resulted in increased collagenase mRNA expression. The mechanical stress treated group (1.61, 1.62, 1.37 fold increase), the interleukin-$1{\beta}$, tented group (1.68, 1.60, 3.78 fold increase), the mechanical stress and interleukin-$1{\beta}$ treated group (1.89, 1.72, 5.48 fold increase) induced increases in collagenase mRNA compared with the control group after 2, 4, 8 hours respectively. But TIMP-1 mRNA expressions at experimental groups were decreased after 2, 4 hours and increased after 8 hours. The mechanical stress treated group (0.16, 0.49 fold decrease and 3.77 fold increase), the interleukin-$1{\beta}$ treated group (0.15,0.44 fold decrease and 4.46 fold increase), the mechanical stress and interleukin-$1{\beta}$ tented group (0.15, 0.69 fold decrease and 4.81 fold increase) induced changes in TIMP-1 mRNA compared with the control group after 2, 4, 8 hours, respectively. Immunohistochemical stain showed that increased collagenase and TIMP-1 staining of the mechanical stress tented group, the interleukin-$1{\beta}$ treated group, and the mechanical stress and interleukin-$1{\beta}$ treated group compared with that of the control group after 8 hours. These findings suggest that mechanical stress and interleukin-$1{\beta}$ regulate expression of collagenase and TIMP-1.

• Journal of Dairy Science and Biotechnology
• /
• v.26 no.1
• /
• pp.11-19
• /
• 2008

Milk from dairy cows has long provided a high quality source of protein and selected micronutrients as calcuim to most populations. Recently, a relationship between disease risk and consumption of specific bovine ${\beta}$-casein fraction either A1 or A2 genetic variants has identified. Populations, which consume milk contain high containing high levels of ${\beta}$-casein A2 variants, have a lower incidence of cardiovascular disease and type 1 diabetes. Furthermore, consumption of milk with the A2 variants may be associated with less severe symptoms of autism and schizophrenia. The mechanism of action focuses on ${\beta}$-casein A1 and related forms preferentially that are able to produce a bioactive opioid peptide, ${\beta}$-casomorphin-7(${\beta}$-CM-7) during digestion. Infants may absorb ${\beta}$-CM-7 due to an immature gastrointestinal tract. Adult, on the other hand, appear to reap the biological activity locally on the intestinal brush boarder. ${\beta}$-CM-7 can potentially affect numerous opioid receptors in the nervous, endocrine, and immune system. Whether there is a definite health benefit to milk containing the A2 genetic variant is unknown and requires further investigation.

• Archives of Pharmacal Research
• /
• v.24 no.6
• /
• pp.564-567
• /
• 2001

The fecal ${\beta}-glucuronidase$ activity of patients with colon cancer and healthy controls were measured to determine the relationship between the fluctuation of intestinal bacterial ${\beta}-glucuronidase$ and colon cancer. The fecal ${\beta}-glucuronidase$ activity of patients with colon cancer was 1.7 times higher than that of the healthy controls. However, when these fecal specimens were sonicated, the enzyme activity of patients with colon cancer was 12.1 times higher than that of the healthy controls. The fecal ${\beta}-glucuronidase$ activity of human Intestinal bacteria was drastically induced by its substrate or the bile secreted after a subcutaneous injection of 1,2-dimethylhydrazine (DMH) and benzo[a]pyrene into rats. DMH-and benzo[a]pyrene-treated biles induced ${\beta}-glucuronidase$ activity in the human intestinal microflora by approximately 1.5- and 2.3-fold, respectively. They also induced ${\beta}-glucuronidase$ in E. coli HGU-3, which is a ${\beta}-glucuronidase$-producing bacterium from the human intestine. D-saccharic acid 1,4-lactone similarly inhibited fecal ${\beta}-glucuronidase$ in several patients with colon cancer in addition to the healthy controls. This suggests that potent ${\beta}-glucuronidase$ activity is a prime factor in the etiology of colon cancer.

• Korean Journal of Microbiology
• /
• v.35 no.2
• /
• pp.164-168
• /
• 1999

TGF-$\beta$3 is among five TGF-$\beta$ isolorms and shows 80% sequence identity to TGF-$\beta$I, a prototype of TGF--$\beta$. It has been reported that TGF-$\beta$I, particularly in the presence of IL-2 or L-5, increases the pmduction of IgA and IgG2b isoiypes by LPS-actwated murine B cells. We examined the effect of TGF-P3 on Ig synlhesis by B cells from different lymphoid origins. IgA induction by TGP-$\beta$3 was mardnal in LPS-activated spleen B cell culture, while 1gA production was markedly enhanced in the culture shulated with TGF-$\beta$P3 and L-5. In addition, number of IgA secreting cells was increased by TGF-$\beta$P3. Under the same conditions, TGP-$\beta$3 alone was enough to increase IgG2b production but IgM and 1gGl. Sirmlar patiem of IgA and IgGZb enbancement by TGF-$\beta$3 and L-5 was observed in the cullures of mesenteric lymph node B cells. Thus, overall effect of TGF-$\beta$3 on Ig synthesis was quite similar to that of TGF-$\beta$I. Nonetheless, it remains to be underslood whether TGF-$\beta$3 is an important modulator in B cell differentiation since regulation of TGF-$\beta$3 expression is considered to differ from that of TGF-$\beta$I

• Tuberculosis and Respiratory Diseases
• /
• v.58 no.3
• /
• pp.267-276
• /
• 2005

Background : The transforming growth $factor-{\beta}1$ ($TGF-{\beta}1$) plays a key role in lung fibrosis. However, the molecular mechanisms involved in $TGF-{\beta}1$-induced lung fibrosis are unclear. $TGF-{\beta}1$ is the key inducer of myofibroblast transdifferentiation via de novo synthesis of ${\alpha}-smooth$ muscle actin (${\alpha}-SMA$). Since $TGF-{\beta}1$ signals through reactive oxygen species (ROS) and ROS have been shown to induce accumulation of extracellular matrix (ECM) in various tissues, this study examined if ROS play a role in $TGF-{\beta}1$-induced fibronectin secretion and ${\alpha}-SMA$ expression in human lung fibroblasts, MRC-5 cells. Methods : Growth arrested and synchronized MRC-5 cells were stimulated with $TGF-{\beta}1$ (0.2-10 ng/ml) in the presence or absence of N-acetylcysteine (NAC) or diphenyleneiodonium (DPI) for up to 96 hours. Dichlorofluorescein (DCF)-sensitive cellular ROS were measured by FACScan and secreted fibronectin and cellular ${\alpha}-SMA$ by Western blot analysis. Results : $TGF-{\beta}1$ increased the level of fibronectin secretion and ${\alpha}-SMA$ expression in MRC-5 cells in a dosedependent manner. Both NAC (20 and 30 mM) and DPI (1 and $5{\mu}M$) significantly inhibited $TGF-{\beta}1$-induced fibronectin and ${\alpha}-SMA$ upregulation. The $TGF-{\beta}1$-induced cellular ROS level was also significantly reduced by NAC and DPI. Conclusions : The results suggest that NADPH oxidase-dependent ROS play an important role in $TGF-{\beta}1$-induced fibronectin secretion and ${\alpha}-SMA$ expression in MRC-5 cells, which leads to myofibroblast transdifferentiation and progressive lung fibrosis.

• Applied Biological Chemistry
• /
• v.39 no.6
• /
• pp.482-487
• /
• 1996

Five barley and two oat varieties grown in Korea were investigated for soluble, insoluble, and total $(1{\to}3)$, $(1{\to}4)-{\beta}-D-glucans$. Total and insoluble ${\beta}-glucans$ after extraction of soluble ${\beta}-glucans$ with water were analyzed, and the soluble ${\beta}-glucans$ were calculated as the difference between total and insoluble ${\beta}-glucans$. The total ${\beta}-glucans$ in whole barleys were in a range of $3.3{\sim}5.6%$(average 4.4%), and those in pearled barleys were In a range of $3.3{\sim}7.1%$(average 5.2%). In whole barleys, on average, 54% of the ${\beta}-glucans$ was soluble and in pearled barley 46%. Whole oats contained $3.1{\sim}4.0%$ total ${\beta}-glucans$, and dehulling increased the groat ${\beta}-glucans$ contents to $4.0{\sim}4.8%$. Oats demonstrated considerably higher ${\beta}-glucans$ solubility of 84% than barley. ${\beta}-Glucans$ in barley and oats were rapidly extracted at the beginning of the extraction and almost all of the ${\beta}-glucans$ were extracted after $2{\sim}3 hr extraction. As extraction temperature increased from $23^{\circ}C$ to $45^{\circ}C$, more soluble ${\beta}-glucans$ were extracted. However, solubility of barley ${\beta}-glucans$ decreased at a relatively high temperature of $65^{\circ}C$. Steam-cooking reduced the analytical solubility of barley and oat ${\beta}-glucans$, while roasting seemed to render the ${\beta}-glucans$ of barley more soluble.

• East Asian mathematical journal
• /
• v.32 no.1
• /
• pp.77-84
• /
• 2016

We explicitly derive diagrams representing (1,1)-decompositions of rational pretzel knots $K_{\beta}=M((-2,\;1),\;(3,\;1),\;({\mid}6{\beta}+1{\mid},{\beta}))$ from four unknotting tunnels for ${\beta}=1,\;-2$ and 2.

• Molecules and Cells
• /
• v.19 no.3
• /
• pp.375-381
• /
• 2005

Phospholipase C-${\beta}$ (PLC-${\beta}$) hydrolyses phosphatidylinositol 4,5-bisphosphate and generates inositol 1,4,5-trisphosphate in response to activation of various G protein-coupled receptors (GPCRs). Using glial cells from knock-out mice lacking either PLC-${\beta}1$ [PLC-${\beta}1$ (-/-)] or PLC-${\beta}3$ [PLC-${\beta}3$ (-/-)], we examined which isotype of PLC-${\beta}$ participated in the cellular signaling events triggered by thrombin. Generation of inositol phosphates (IPs) was enhanced by thrombin in PLC-${\beta}1$ (-/-) cells, but was negligible in PLC-${\beta}3$ (-/-) cells. Expression of PLC-${\beta}3$ in PLC-${\beta}3$ (-/-) cells resulted in an increase in pertussis toxin (PTx)-sensitive IPs in response to thrombin as well as to PAR1-specific peptide, while expression of PLC-${\beta}1$ in PLC-${\beta}1$ (-/-) cells did not have any effect on IP generation. The thrombin-induced $[Ca^{2+}]_i$ increase was delayed and attenuated in PLC-${\beta}3$ (-/-) cells, but normal in PLC-${\beta}1$ (-/-) cells. Pertussis toxin evoked a delayed $[Ca^{2+}]_i$ increase in PLC-${\beta}3$ (-/-) cells as well as in PLC-${\beta}1$ (-/-) cells. These results suggest that activation of PLC-${\beta}3$ by pertussis toxin-sensitive G proteins is responsible for the transient $[Ca^{2+}]_i$ increase in response to thrombin, whereas the delayed $[Ca^{2+}]_i$ increase may be due to activation of some other PLC, such as PLC-${\beta}4$, acting via PTx-insensitive G proteins.