• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1087-1107
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• 2023

Let E be an elliptic curve defined over ℚ of conductor N, c the Manin constant of E, and m the product of Tamagawa numbers of E at prime divisors of N. Let K be an imaginary quadratic field where all prime divisors of N split in K, P_K the Heegner point in E(K), and III(E/K) the Shafarevich-Tate group of E over K. Let 2u_K be the number of roots of unity contained in K. Gross and Zagier conjectured that if P_K has infinite order in E(K), then the integer c · m · u_K · |III(E/K)| $\frac{1}{2}$ is divisible by |E(ℚ)_tor|. In this paper, we prove that this conjecture is true if E(ℚ)_tor ≅ ℤ/2ℤ or ℤ/4ℤ except for two explicit families of curves. Further, we show these exceptions can be removed under Stein-Watkins conjecture.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

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

• Journal of Satellite, Information and Communications
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• v.2 no.2
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• pp.64-68
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• 2007

This paper describes the development of RF front.end equipment of a wide band high precision satellite navigation receiver to be able to receive the currently available GPS navigation signal and the GALILEO navigation signal to be developed in Europe in the near future. The wide band satellite navigation receiver with high precision performance is composed of L - band antenna, RF/IF converters for multi - band navigation signals, and high performance baseband processor. The L - band satellite navigation antenna is able to be received the signals in the range from 1.1 GHz to 1.6 GHz and from the navigation satellite positioned near the horizon. The navigation signal of GALILEO navigation satellite consists of L1, E5, and E6 band with signal bandwidth more than 20 MHz which is wider than GPS signal. Due to the wide band navigation signal, the IF frequency and signal processing speed should be increased. The RF/IF converter has been designed with the single stage downconversion structure, and the IF frequency of 140 MHz has been derived from considering the maximum signal bandwidth and the sampling frequency of 112 MHz to be used in ADC circuit. The final output of RF/IF converter is a digital IF signal which is generated from signal processing of the AD converter from the IF signal. The developed RF front - end has the C/N0 performance over 40dB - Hz for the - 130dBm input signal power and includes the automatic gain control circuits to provide the dynamic range over 40dB.

• Journal of Korean Medicine Rehabilitation
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• v.21 no.4
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• pp.23-40
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• 2011

Objectives: This study was designed to examine the effects of extracts of Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) on the lipid lowering, anti-oxidation and concentration of proinflammatory cytokines and was investigated on hyperlipidemic rats. Methods: Male rats weighing $182.39{\pm}4.71g$ were fed high fat diet for 8 weeks and 36 rats(above 400 g) were divided into 4 groups. Each of 9 rats was divided a control group and experimental groups. We fed a control group of rats a basal diet and administered normal saline(100 mg/kg, 1 time/1 day) for 4 weeks. And we fed each experimental group of rats basal diet and administered an extract of Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) extracts(100 mg/kg, 200mg/kg, 300 mg/kg, 300 mg/kg, 1 time/1 day) for 4 weeks. At the end of the experiment, the rats were sacrificed to determine their chemical composition. We measured lipid of plasma and liver, concentration of proinflmmatory cytokines, anti-oxidative activity and $TNF-{\alpha}$, Apo-B, Apo-E and leptin gene expression. Results: 1. Concentration of plasma free fatty(FFA) showed no significant difference in all the treatment groups. Concentration of plasma triglyceride(TG) showed a significant decrement in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. 2. Concentration of plasma total cholesterol showed a significant decrement in the 200 and 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. Concentration of plasma low density lipoprotein(LDL)-cholesterol showed a Significant decrement in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. Concentration of plasma high density lipoprotein(HDL)-cholesterol showed a significant increment in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) group. 3. Concentration of liver total cholesterol showed a tendence to decrease in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups. Concentration of liver TG showed a significant decrement in all Ojeoksangamibang groups than that of control group. 4. Concentration of plasma and liver thiobarbituric acid reactive substance(TBARS) showed a tendence to decrease in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups. 5. The values of glutathione peroxidase(GSH-Px), superoxide dismutase(SOD) and catalase(CAT) activity showed a significant increment in all Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups than that of control group. 6. The values of plasma aspartate aminotransferase(AST) and alanine aminotransferase(ALT) activity showed no significant different in all treatment group. 7. Concentration of plasma $interleukin(IL)-1{beta}$ showed no significant difference in all the treatment groups. Concentration of plasma IL-6 showed a significant decrement in the 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) group than that of control group. Concentration of plasma tumor necrosis $factor-{\alpha}(TNF-{\alpha})$ a siginifant decrement in the 200 and 300 mg/kg in Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) group than that of control group. However the concentration of plasma IL-10 in the 300 mg/kg Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups showed a significant increment than that of control group. 9. In the analysis of reverse transcription-polymerase chain reaction(RT-PCR), gene expression of $TNF-{\alpha}$, Apo-B and Apo-E in the Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups showed a lower expression than that of control group. However the gene expression of leptin showed no difference in the treatment groups. 10. The ratio of $TNF-{\alpha}$, Apo-B, and Apo-E per ${\beta}-actin$ expression in the Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) groups showed a significant decrement than that of control group. However The ratio of leptin expression per ${\beta}-actin$ expression showed no significant difference among all the treatment groups. Conclusions: According to above results, in lowering lipid effect, anti-oxidation and control of pro-inflammatory cytokines production, Ojeoksangamibang($W{\check{u}}j\bar{i}s\check{a}nji\bar{a}w\grave{e}if\bar{a}ng$) gives effect.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1997.10a
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• pp.183-189
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• 1997

This research is a experimental study for the machining conditions of E. D. M. They were used Cu electrode and the various amplitude of current waves for the machining by E.D.M. By the analyse the characteristics of current, voltage, roughness of surface and over cut, the next results were obtained. E.D.M. machining time become to be more longer by the increasing the tensile stress. In case of NAK 55 as the composite resin, the machining time was more faster without the relationship for the tensile stress. And if it was more increased the amplitude of Ip, it has been more faster in the machining time and more poor in the surface roughness. But it was increased Ip with 5A, it has been increased 0.3 time in over cut. So, if we want to be the precision machining, the diameter of the electrode should be more smaller than the diameter of machined hole in workpiece with E.D.M.

• Microbiology and Biotechnology Letters
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• v.36 no.4
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• pp.353-359
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• 2008

Hepatitis C virus (HCV) is known as the causative agent of blood transmitted hepatitis. Two viral proteins, E2 and NS5A, are known to exert interferon resistance of HCV via PKR pathway. Here, we report a third protein, the RNA-dependent RNA polymerase (NS5B) of HCV, induced interferon resistance inhibiting p56 pathway. p56 was shown to interact with p48 subunit of eukaryotic initiation factor 3 (eIF3). This interaction inhibited formation of ternary complex in translation initiation. Using dual reporter assay system, we observed that the translation decreased when interferon alpha was added to the culture. But, in the presence of HCV NS5B, the translation partly recovered. NS5B and p48 subunit of eIF3 were shown to interact. This interaction seems to inhibit the interaction between p48 and p56. This is the first report that a virus exerts interferon resistance via p56 pathway.

• The Plant Pathology Journal
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• v.23 no.4
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• pp.281-286
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• 2007

Interactions between viral proteins and host proteins are essential for virus replication. Especially, translation of viral genes completely depends on the host machinery. In potyviruses, interactions of genome-linked viral protein (VPg) with host translation factors including eIF4E, eIF(iso)4E, and poly(A)-binding protein (PABP) has previously been characterized. In this study, we investigated interactions between Soybean mosaic virus (SMV) viral proteins and host translation factors by yeast two-hybrid system. SMV VPg interacted with eIF4E, eIF(iso)4E, and PABP in yeast two-hybrid system, while SMV helper component proteinase (HC-pro) interacted with neither of those proteins. The interaction between SMV NIb and PABP was also detected. These results are consistent with those reported previously in other potyviruses. Interestingly, we found reproducible and specific interactions between SMV coat protein (CP) and PABP. Deletion analysis showed that the region of CP comprising amino acids 116 to 206 and the region of PABP comprising amino acids 520 to 580 are involved in CP/PABP interactions. Soybean library screening with SMV NIb by yeast two-hybrid assay also identified several soybean proteins including chlorophyll a/b binding preprotein, photo-system I-N subunit, ribulose 1,5-biphosphate carboxylase, ST-LSI protein, translation initiation factor 1, TIR-NBS type R protein, RNA binding protein, ubiquitin, and LRR protein kinase. Altogether, these results suggest that potyviral replicase may comprise a multi-protein complex with PABP, CP, and other host factors.

• Communications of Mathematical Education
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• v.5
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.

• BMB Reports
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• v.44 no.3
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• pp.147-157
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• 2011

The meiotic process from the primordial stage to zygote in female germ cells is mainly adjusted by post-transcriptional regulation of pre-existing maternal mRNA and post-translational modification of proteins. Several key proteins such as the cell cycle regulator, Cdk1/cyclin B, are post-translationally modified for precise control of meiotic progression. The second messenger (cAMP), kinases (PKA, Akt, MAPK, Aurora A, CaMK II, etc), phosphatases (Cdc25, Cdc14), and other proteins (G-protein coupled receptor, phosphodiesterase) are directly or indirectly involved in this process. Many proteins, such as CPEB, maskin, eIF4E, eIF4G, 4E-BP, and 4E-T, post-transcriptionally regulate mRNA via binding to the cap structure at the 5' end of mRNA or its 3' untranslated region (UTR) to generate a closed-loop structure. The 3' UTR of the transcript is also implicated in post-transcriptional regulation through an association with proteins such as CPEB, CPSF, GLD-2, PARN, and Dazl to modulate poly(A) tail length. RNA interfering is a new regulatory mechanism of the amount of mRNA in the mouse oocyte. This review summarizes information about post-transcriptional and post-translational regulation during mouse oocyte meiotic maturation.