• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• Archives of Pharmacal Research
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• v.26 no.9
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• pp.739-746
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• 2003

Ultraviolet B (UVB) is known to induce apoptosis in human melanocytes. Here we show the cytoprotective effect of sphingosine-1-phosphate (S1P) against UVB-induced apoptosis. We also show that UVB-induced apoptosis of melanocytes is mediated by caspase-3 activation and poly(ADP-ribose) polymerase (PARP) cleavage, and that S1P prevents apoptosis by inhibiting this apoptotic pathway. We further investigated three major mitogen-activated protein (MAP) kinases after UVB irradiation. UVB gradually activated c-Jun N-terminal kinase (JNK) and p38 MAP kinase, while extracellular signal-regulated protein kinase (ERK) was inactivated transiently. Blocking of the p38 MAP kinase pathway using SB203580 promoted cell survival and inhibited the activation of caspase-3 and PARP cleavage. These results suggest that p38 MAP kinase activation may play an important role in the UVB-induced apoptosis of human melanocytes. To explain this cytoprotective effect, we next examined whether S1P could inhibit UVB-induced JNK and p38 MAP kinase activation. However, S1P was not found to have any influence on UVB-induced JNK or p38 MAP kinase activation. In contrast, S1P clearly stimulated the phosphorylation of ERK, and the specific inhibition of the ERK pathway using PD98059 abolished the cytoprotective effect of S1P. Based on these results, we conclude that the activation of p38 MAP kinase plays an important role in UVB-induced apoptosis, and that S1P may show its cytoprotective effect through ERK activation in human melanocytes.

• The Korean Journal of Physiology and Pharmacology
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• v.6 no.3
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• pp.165-169
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• 2002

We have previously demonstrated that phytoestrogens isolated from safflower seeds significantly attenuated bone loss in ovariectomized rats, and directly stimulated proliferation and differentiation of cultured osteoblastic cells. In an attempt to elucidate underlying cellular mechanisms, in the present study we investigated effects of $17{\beta}-estradiol\;(E_2)$ and phytoestrogens such as matairesinol and acacetin, a type of lignan and flavonoid, respectively, on activation of mitogen activated protein (MAP) kinases, extracellular signal-regulated kinase 1 (ERK1) and ERK2, in cultured osteoblastic ROS 17/2.8 cells. Western blot analysis with anti-MAP kinase antibody showed that a wide range concentrations $(10^{-14}\;to\;10^{-6}\;M)\;of\;E_2$ as well as both phytoestrogens induced rapid and transient activation of ERK1/2 through phosphorylation within minutes. Maximum activation of MAP kinases by $E_2$ and phytoestrogens were observed at 10 and 15 min, respectively. $E_2-induced$ phosphorylation of ERK1/2 returned to the control level at 30 min, whereas phytoestrogen-induced phosphorylation was maintained at high level until 30 min. PD-98059, a highly selective inhibitor of MAP kinase, prevented phosphorylation of ERK1/2 in the cells treated either with $E_2$ or phytoestrogens. To examine a possible involvement of estrogen receptor in the activation process of MAP kinase, Western blot analysis was performed in the presence and absence of the estrogen receptor antagonists, ICI 182,780 and tamoxifen. These antagonists blocked MAP kinase phosphorylation induced not only by $E_2,$ but also by the phytoestrogens. To the best our knowledge, this study is the first to demonstrate that phytoestrogens such as flavonoid and lignan extracted from safflower seeds produce a rapid activation of MAP kinase, at least partially via membrane estrogen receptor of the cultured osteoblastic cells.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.67-72
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• 2003

The purpose of this paper is to prove flow induced by a covering map. Lee and Park had studied semiflows induced by a covering map in 1997 [1]. This proof differs from the proof of Lee and Park. Notice that for the proof of this paper, we use the fact that $\mathbb{R}$ is connected space.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1309-1318
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• 2020

In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.105-115
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• 2003

It is well known that there exists a regular branched covering map from T$^2$ onto $\={C}$ iff the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3). In this paper we construct (count-ably many) chaotic homeomorphisms induced by hyperbolic toral automorphism and regular branched covering map corresponding to the ramification indices (2,2,2,2). And we also gave an example which shows that the above construction of a chaotic map is not true in general if the ramification indices is (2,4,4) and also show that there are no chaotic homeomorphisms induced by hyperbolic toral automorphism and regular branched covering map corresponding to the ramification indices (2,3,6) and (3,3,3).

• Proceedings of the SAREK Conference
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• 2008.06a
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• pp.957-963
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• 2008

The refrigerant-induced noise of the air conditioner is one of the irregular noises which occurs at the indoor unit. Because the air-conditioner makers are always trying to reduce the sound pressure level radiated from indoor unit, reducing the refrigerant-induced noise at low cooling mode is very important problem. But it is very difficult to estimate whether the refrigerant-induced noise occurs or not before it becomes problem. In this paper, a method to predict the refrigerant-induced noise is suggested using flow pattern map. It is estimated that the irregular noise from the refrigerant comes from the slug flow in a pipe.

• Proceedings of the PSK Conference
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• 2003.04a
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• pp.117.1-117.1
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• 2003

We investigated whether experimental esophagitis and IL-1$\beta$ could induce the activation of MAP kinases in esophageal smooth muscle. With two models of experimental esophagitis, we assessed the activity of p38 MAP kinase, p44/42 MAP kinase and JNK. In feline acute experimental esophagitis, immunoblotting of normal and esophagitis-induced smooth muscle with each types of MAP kinase antibodies revealed the slight increase of phosphorylated form of p38 MAP kinase, especially in membrane fraction. (omitted)

• BMB Reports
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• v.41 no.6
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• pp.479-484
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• 2008

In the present study, we demonstrate that ephrin-A5 is able to induce a transient increase of MAP kinase activity in PC12 cells. However, the effects of ephrin-A5 on the MAP kinase signaling pathway are about three-fold less than that of EGF. In addition, we demonstrate that EphA4 is the only Eph member expressed in PC12 cells, and that tyrosine phosphorylation induced by ephrin-A5 treatment is consistent with the magnitude and longevity of MAP kinase activation. Experiments using the Ras dominant negative mutant N17Ras reveal that Ras plays a pivotal role in ephrin-A5-induced MAP kinase activation in PC12 cells. Importantly, we found that the EphA4 receptor is rapidly internalized by endocytosis upon engagement of ephrin-A5, leading to a subsequent reduction in the MAP kinase activation. Together, these data suggest a novel regulatory mechanism of differential Ras-MAP kinase signaling kineticsexhibited by the forward signaling of EphA4 in PC12 cells.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.409-421
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• 2011

We study a natural map from the braid group to the mapping class group which is called Harer map. It is rather new and different from the classical map which was studied in 1980's by F. Cohen, J. Harer et al. We show that this map is homologically trivial for most coefficients by using the fact that this map factors through the symmetric group.