• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.815-823
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• 2010

Let ${\tau}\;{\neq}\;\delta_0$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\;=\;1$ such that there is a $\delta$ > 0 so that ${\mid}\hat{\tau}(s){\mid}\;{\neq}\;1$ for every $s\;{\in}\;\Sigma(\delta)$ \ {0,1}, or just a radial probability measure on D. Here, we provide a decomposition of the set X = {$h\;{\in}\;L^{\infty}(D)\;{\mid}\;lim_{n{\rightarrow}{\infty}}\;h\;*\;\tau^n$ exists}. Let $\tau_1$, ..., $\tau_n$ be measures on D with above mentioned properties. Here, we prove that if $f\;{in}\;L^{\infty}(D^n)$ satisfies an invariant volume mean value property with respect to $\tau_1$, ..., $\tau_n$, then f is n-harmonic.

• East Asian mathematical journal
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• v.21 no.1
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• pp.1-7
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• 2005

The object of this paper is to study($\sigma,\;\tau$)-Lie ideals in semi-prime rings with derivation. Main result is the following theorem: Let R be a semi-prime ring with 2-torsion free, $\sigma$ and $\tau$ two automorphisms of R such that $\sigma\tau=\tau\sigma$=, U be both a non-zero ($\sigma,\;\tau$)-Lie ideal and subring of R. If $d^2(U)=0$, then d(U)=0 where d a non-zero derivation of R such that $d\sigma={\sigma}d,\;d\tau={\tau}d$.

• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.37-47
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• 2000

The method of delays is widely used for reconstruction chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau}_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau}_w$ instead. Unfortunately, ${\tau}_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau}_w$ has yet emerged. However, a new technique, called the C-C method, can be used to estimate either ${\tau}_d\;or\;{\tau}_w$. Using this method, we show that, for small data sets, fixing ${\tau}_w$, rather than ${\tau}_d$, does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m in increased.

• Proceedings of the Korea Water Resources Association Conference
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• 2000.05a
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• pp.37-47
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• 2000

The method of delays is widely used fur reconstructing chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau}_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau}_w$ instead. Unfortunately, ${\tau}_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau}_w$has yet emerged. However, a new technique, called the C-C method, can be used to estimate either ${\tau}_d{\;}or{\;}{\tau}_w$. Using this method, we show that, for small data sets, fixing ${\tau}_w$, rather than ${\tau}_d$, does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m is increased.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.585-594
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• 2001

Let η be the complex upper half plane, let h($\tau$) be a cusp form, and let $\tau$ be an imaginary quadratic in η. If h($\tau$)$\in$$\Omega$( $g_{2}$($\tau$)$^{m}$ $g_{3}$ ($\tau$)$^{ι}$with $\Omega$the field of algebraic numbers and m. l positive integers, then we show that h($\tau$) is integral over the ring Q[h/$\tau$/n/)…h($\tau$+n-1/n)] (No Abstract.see full/text)

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.425-435
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• 2016

In this paper, we analyze the inverse statistics of rainfall for 12 regions from 1973 to 2014. We obtain a probability density function f(x) of daily rainfall x, and $f({\tau}_{\rho})$ of the first passage time ${\tau}_{\rho}$ for a given ${\rho}$. Lastly, we derive the relation between ${\rho}$ and ${\tau}_{mean}({\rho})$, i.e., the averaged value of ${\tau}_{\rho}$. The analyses result in the x and ${\tau}_{\rho}$ have stretched exponential distributions. Also, ${\tau}_{mean}({\rho})$ has the form of a stretched exponential function. We derive the shape parameter ${\beta}$ of the distribution, and analyze the characteristics of 12 regional rainfalls.

• The Korean Journal of Physiology and Pharmacology
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• v.15 no.2
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• pp.107-114
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• 2011

Neurofibrillary tangle (NFT) is a characteristic hallmark of Alzheimer's disease. GSK3β has been reported to play a major role in the NFT formation of tau. Dysfunction of autophagy might facilitate the aggregate formation of tau. The present study examined the role of GSK3${\beta}$-mediated phosphorylation of tau species on their autophagic degradation. We transfected wild type tau (T4), caspase-3-cleaved tau at Asp421 (T4C3), or pseudophosphorylated tau at Ser396/Ser404 (T4-2EC) in the presence of active or enzyme-inactive GSK3${\beta}$. Trehalose and 3-methyladenine (3-MA) were used to enhance or inhibit autophagic activity, respectively. All tau species showed increased accumulation with 3-MA treatment whereas reduced with trehalose, indicating that tau undergoes autophagic degradation. However, T4C3 and T4-2EC showed abundant formation of oligomers than T4. Active GSK3${\beta}$ in the presence of 3-MA resulted in significantly increased formation of insoluble tau aggregates. These results indicate that GSK3${\beta}$-mediated phosphorylation and compromised autophagic activity significantly contribute to tau aggregation.

• The Korean Journal of Physiology and Pharmacology
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• v.18 no.2
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• pp.155-161
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• 2014

Overexpression of amyloid precursor protein with the Swedish mutation causes abnormal hyperphosphorylation of the microtubule-associated protein tau. Hyperphosphorylated isoforms of tau are major components of neurofibrillary tangles, which are histopathological hallmarks of Alzheimer's disease. Protein phosphatase 2A (PP2A), a major tau protein phosphatase, consists of a structural A subunit, catalytic C subunit, and a variety of regulatory B subunits. The B subunits have been reported to modulate function of the PP2A holoenzyme by regulating substrate binding, enzyme activity, and subcellular localization. In the current study, we characterized regulatory B subunit-specific regulation of tau protein phosphorylation. We showed that the PP2A B subunit PPP2R2A mediated dephosphorylation of tau protein at Ser-199, Ser-202/Thr-205, Thr-231, Ser-262, and Ser-422. Down-regulation of PPP2R5D expression decreased tau phosphorylation at Ser-202/Thr-205, Thr-231, and Ser-422, which indicates activation of the tau kinase glycogen synthase kinase 3 beta ($GSK3{\beta}$) by PP2A with PPP2R5D subunit. The level of activating phosphorylation of the $GSK3{\beta}$ kinase Akt at Thr-308 and Ser-473 were both increased by PPP2R5D knockdown. We also characterized B subunit-specific phosphorylation sites in tau using mass spectrometric analysis. Liquid chromatography-mass spectrometry revealed that the phosphorylation status of the tau protein may be affected by PP2A, depending on the specific B subunits. These studies further our understanding of the function of various B subunits in mediating site-specific regulation of tau protein phosphorylation.

• Animal cells and systems
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• v.11 no.1
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• pp.39-50
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• 2007

Tau plays a role in numerous neuronal processes, such as vesicle transport, microtubule-plasma membrane interaction and intracellular localization of proteins. SUMO (Small Ubiquitin-like Modifier) modification (SUMOylation) appears to regulate diverse cellular processes including nuclear transport, signal transduction, apoptosis, autophagy, cell cycle control, ubiquitin-dependent degradation, as well as gene transcription. We noticed that putative SUMOylation site is localized at $^{340}K$ of $Tau(^{339}VKSE^{342})$ with the consensus sequence information (${\Phi}KxE$ ; where ${\Phi}$ represents L, I, V or F and x is any amino acid). In this report, we demonstrated that $^{340}K$ of Tau is the SUMOylation site and that a point mutant of Tau S214E (an analog of the phospho $^{214}S$ Tau) promotes its SUMOylation at $^{340}K$ and its nuclear or nuclear vicinity localization, by co-immunoprecipitation and confocal microscopy analysis. Further, we demonstrate that the Tau S214E (neither Tau S214A nor Tau K340R) mutant increases its protein stability. However, the SUMOylation at $^{340}K$ of Tau did not influence cell survival, as determined by FACS analysis. Therefore, our results suggested that the phosphorylation of Tau on $^{214}S$ residue promotes its SUMOylation on $^{340}K$ residue and nuclear vicinity localization, and increases its stability, without influencing cell survival.

• Korean Journal of Optics and Photonics
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• v.3 no.3
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• pp.161-166
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• 1992

The s-polarized laser beam is incident with an angle ~$-30^{\circ}$ to a uniformly rotating rough metal surface and the degree of second order temporal coherence $g_{s}^{(2)}(\tau)$ of the backscattered wave, which has the same polarization with the incident laser beam, is measured. The contribution of shot noise involved in the measurement of $g_{s}^{(2)}(0)$ is subtracted from the photoelectric signal to obtain the accurate value of $g_{s}^{(2)}(0)$.At each scattering angle$\theta_{s}$에서$g_{s}^{(2)}(\tau)$ is almost consistent with the function {1+exp($-\tau^2/\tau_0^2$)}, which is the same result with the case of the laser speckle formed by scattering on the rotating ground glass suface. In addition, a peak in the angular distribution of $\tau_0$ is observed with the maximum at$\theta_s=34^{\circ}$.It is found that the rough metallic scattering with multiple scattering over than 10% has the same function of the degree of second order temporal coherence with that of the ground glass surface scattering where the multiple scattering is ignorably small.