• 대한수학회보
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• 제47권4호
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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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• 제21권1호
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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 $d\sigma={\sigma}d,\;d\tau={\tau}d$.

• 한국수자원학회논문집
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• 제33권S1호
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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.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2000년도 학술발표회 논문집
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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.

• 대한수학회논문집
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• 제16권4호
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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)

• 응용통계연구
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• 제29권3호
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• pp.425-435
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• 2016

본 논문에서는 1973년부터 2014년까지 42년 간, 12개 지역의 일일 강수량 데이터의 역통계(inverse statistics) 분석을 실시하였다. 구체적으로 일일 강수량 x의 확률밀도함수 f(x)를 도출하였고, 특정 강수량 ${\rho}$를 처음으로 넘어서는 기간 ${\tau}_{\rho}$의 분포 $f({\tau}_{\rho})$를 도출하였다. 최종적으로 ${\tau}_{\rho}$의 대푯값인 ${\tau}_{mean}({\rho})$와 ${\rho}$의 관계를 도출하였다. 분석 결과 x와 ${\tau}_{\rho}$는 확장된 지수분포(stretched exponential distribution)를 이루는 것을 확인하였다. 더불어 ${\rho}$와 ${\tau}_{mean}({\rho})$도 확장된 지수함수의 관계를 이루는 것을 알 수 있었다. 이들 분포를 바탕으로 형태 모수(shape parameter) ${\beta}$ 값을 도출하고, 12개 지역의 강수 특성을 분석하였다.

• The Korean Journal of Physiology and Pharmacology
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• 제15권2호
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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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• 제18권2호
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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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• 제11권1호
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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.

• 한국광학회지
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• 제3권3호
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• pp.161-166
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• 1992

회전하는 거친금속표면에 s-편극된 레이저광을 $-30^{\circ}$로 입시시켜 생긴 후방산란파중 입사광과 동일한 편극을 가지는 후방산란파에 대하여 세기의 시간상관함수 $g_{s}^{(2)}(\tau)$를 측정하였다. 이 과정에서 광전신호로부터 $g_{s}^{(2)}(0)$의 측정을 할 때 수반되는 shot noise의 영향을 제하여 줌으로써 정확한 $g_{s}^{(2)}(0)$ 값을 얻었다. 각 산란각$\theta_{s}$에서$g_{s}^{(2)}(\tau)$는 {1+exp($-\tau^2/\tau_0^2$)}함수와 거의 일치하였는데, 이는 등속으로 회전하는 간유리를 투과하여 형성된 레이저 스펙클의 경우와 같은 결과이다. 또한, 산란각에 따른 $\tau_0$의 분포에서는 $\theta_s=34^{\circ}$에서 예리하게 최대값을 가지는 것이 관찰되었다. 이 연구에서, 다중산란이 10%를 넘는 금속판산란과 다중산란이 무시될 수 있는 간유리판산란이 같은 함수꼴의 세기의 시간상관함수를 갖는다는 사실이 확인되었다.