• Title/Summary/Keyword: ${\tau}_m$

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ON INTEGRAL GRAPHS WHICH BELONG TO THE CLASS $\overline{aK_{a}\;{\bigcup}\;{\beta}K_{b}}$

  • Lepovic, Mirko
    • Journal of applied mathematics & informatics
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    • v.14 no.1_2
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    • pp.39-49
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    • 2004
  • Let G be a simple graph and let $\={G}$ denotes its complement. We say that G is integral if its spectrum consists entirely of integers. If $\overline{aK_{a}\;{\bigcup}\;{\beta}K_{b}}$ is integral we show that it belongs to the class of integral graphs $[\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;z}\;K_{(t+{\ell}n)+{\ell}m}\;\bigcup\;[\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t\;+\;{\ell}n)k\;+\;{\ell}m}{\tau}\;z]n\;K_{em)$, where (i) t, k, $\ell$, m, $n\;\in\;\mathbb{N}$ such that (m, n) = 1, (n,t) = 1 and ($\ell,\;t$) = 1 ; (ii) $\tau\;=\;((t\;+\;{\ell}n)k\;+\;{\ell}m,\;mt)$ such that $\tau\;$\mid$kt$; (iii) ($x_0,\;y_0$) is a particular solution of the linear Diophantine equation $((t\;+\;{\ell}n)k\;+\;{\ell}m)x\;-\;(mt)y\;=\;\tau\;and\;(iv)\;z\;{\geq}\;{z_0}$ where $z_{0}$ is the least integer such that $(\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;{z_0})\;\geq\;1\;and\;(\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t+{\ell}n)k+{\ell}m}{\tau}\;{z_0})\;\geq\;1$.

On the numerical computation of the matrix exponential

  • Yu, Dong-Won
    • Journal of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.633-643
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    • 1994
  • Let us consider the initial-value problem of dimension m: $$ \frac{d\tau}{d}y(\tau) = f(\tau, Y(\tau)), y(0) = y_0, \tau \geq 0, (1.1) $$ Where $ = (f_1, f_2, \cdots, f_m) and y = (y_1, y_2, \cdots, y_m)$.

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The C-terminal Region of Human Tau Protein with Ability of Filament Formation

  • Chung, Sang-Ho
    • Animal cells and systems
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    • v.1 no.2
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    • pp.317-321
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    • 1997
  • Tau protein is one of the microtubule-associated proteins in the mammalian brain. In Alzheimer's disease, tau protein is immobilized in the somatodendritic compartment of certain nerve cells, where it forms a part of the paired helical filament (PHF). To understand the role of tau protein in the formation of PHF, a recombinant human tau protein expressed in Escherichia coli and five synthetic peptide fragments (peptide 1 to peptide 5), corresponding to the C-terminal region of tau protein, were prepared and their ability in self-assembly to form filamentous structures was examined. The recombinant human tau protein formed short rod-like structures in 0.1M MES buffer containing 1 mM $MgCI_2$, while a synthetic peptide fragment 1 containing 55 amino acid residues could assemble into a lot of long filamentous structures in water and particularly twisted helical structures in 0.1M MES buffer containing 1 mM $MgCI_2$. This suggests that the C-terminal region possesses a filament-forming ability and may be related to the formation of the helical structure by providing a powerful filament-forming driving force.

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RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF THE WEIBULL DISTRIBUTION BY RECORD VALUES

  • Chang, Se-Kyung
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.471-477
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    • 2007
  • In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

A Laboratory Study on Erosional Properties of the Deposit Bed of Kaolinite Sediments (고령토 퇴적저면의 침식특성에 대한 실험적 연구)

  • Kim, Yong-Muk;Kim, Hyun-Min;Hwang, Kyu-Nam;Yang, Su-Hyun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.34 no.4
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    • pp.1181-1190
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    • 2014
  • In this study, the erosional parameters for deposit beds were quantitatively estimated domestically for the first time through the erosion tests using an annular flume. Four erosion tests were carried out for the deposit beds with different consolidation structures, which were obtained by consolidating the kaolinite slurries for a given time durations. Results of erosion tests showed that the bed shear strength ${\tau}_s$ increased with the consolidation time and bed depth. The erosion rate ${\epsilon}$ was also shown to be related well with the excess shear stress ${\tau}_b-{\tau}_s$ which was given by the difference between flow shear stress ${\tau}_b$ and bed shear strength ${\tau}_s$. While the logarithm of the erosion rate was linearly related with the excess shear stress as ${\tau}_b-{\tau}_s{\geq}0.1N/m^2$, however, the erosion rate decreased rapidly with it when ${\tau}_b-{\tau}_s{\leq}0.1N/m^2$. These erosion test results were also shown to be good enough to verify by comparing with the test results from previous studies and a new equation was suggested to describe the erosion rate more well in the region of ${\tau}_b-{\tau}_s{\leq}0.1N/m^2$.

Analysis of Low Field Microwave Absorption Properties in CoFe/MnIr Thin Film (CoFe/MnIr 박막 재료에서 저자장 마이크로파 흡수 특성 분석)

  • Kim, Dong Young;Yoon, Seok Soo
    • Journal of the Korean Magnetics Society
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    • v.25 no.3
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    • pp.74-78
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    • 2015
  • We measured the low field microwave absorption (LFMA) and ferromagnetic resonance (FMR) signals at various magnetic field angle in exchange biased CoFe/MnIr thin film. The LFMA signals were dominantly related to the magnetization rotation process. In order to analyze the LFMA signal, we calculated transverse magnetization ($M_{\tau}$) and permeability (${\mu}_{\tau}$) for CoFe/MnIr thin film by using S-W model, which magnetic parameters of exchange bias ($H_{ex}$ = 58.5 Oe) and uniaxial anisotropy field ($H_k$ = 30Oe) was obtained from FMR signals. The LFMA signal at hard axis showed similar behavior compared with that of $M_{\tau}$. As the magnetic field angle approach to the perpendicular to hard axis, the LFMA signals were depending on both of $M_{\tau}$ and ${\mu}_{\tau}$.

Group Based Two-Layer Mobility Management of MTC Devices in 5G Network (5G 네트워크에서 MTC 단말들의 그룹기반 2계층 이동성 관리 기술)

  • Kim, Nam-Sun
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.11 no.6
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    • pp.631-637
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    • 2018
  • In 5G mobile communication, it is necessary to provide different mobility to user equipments(UE) that do not require mobility management or need limited mobility management. In this paper, we propose a two-layer mobility management system that classifies multiple MTC devices with similar mobility levels into c-MTC and m-MTC groups. In order to improve the energy efficiency and service life by reducing the number of control signals generated when TAU is performed, the group header typically performs a Tracking Area Update(TAU) request and adjusts the periodic TAU update period according to the mobility level. The TAU update period of the m-MTC is set to 54 minutes proposed by the 3GPP standard and the c-MTC is set to 12 minutes. Compared to when the UEs perform TAU individually, it is found that the number of control signals decreases by 33% when the MME is not changed and by 49% when the MME is not changed in the m-MTC or c-MTC group.

Potential of River Bottom and Bank Erosion for River Restoration after Dam Slit in the Mountain Stream

  • Kang, Ji-Hyun;So, Kazama
    • Proceedings of the Korea Water Resources Association Conference
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    • 2011.05a
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    • pp.46-46
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    • 2011
  • Severe sediment erosion during floods occur disaster and economic losses, but general sediment erosion is basic mechanism to move sediment from upstream to downstream river. In addition, it is important process to change river form. Check dam, which is constructed in mountain stream, play a vital role such as control of sudden debris flow, but it has negative aspects to river ecosystem. Now a day, check dam of open type is an alternative plan to recover river biological diversity and ecosystem through sediment transport while maintaining the function of disaster control. The purpose of this paper is to verify sediment erosion progress of river bottom and bank as first step for river restoration after dam slit by cross-sectional shear stress and critical shear stress. Study area is upstream reach of slit check dam in mountain stream, named Wasada, in Japan. The check dam was slit with two passages in August, 2010. The transects were surveyed for four upstream cross-sections, 7.4 m, 34 m, 86 m, and 150 m distance from dam in October 2010. Sediment size was surveyed at river bottom and bank. Sediment of cobble size was found at the wetted bottom, and small size particles of sand to medium gravel composed river bank. Discharge was $2.5\;m^3/s$ and bottom slope was 0.027 m/m. Excess shear stress (${\tau}_{ex}$) was calculated for hydraulic erosion by subtracting the values of critical shear stress (${\tau}_{c}$) from the value of shear stress (${\tau}$) at river bottom and bank (${\tau}_{ex}=\tau-{\tau}_c$). Shear stress of river bottom (${\tau}_{bottom}$) was calculated using the cross-sectional shear stress, and bank shear stress (${\tau}_{bank}$) was calculated from the method of Flintham and Carling (1988). $${\tau}_{bank}={\tau}^*SF_{bank}((B+P_{bed})/(2^*P_{bank}))$$ where $SF_{bank}=1.77(P_{bed}/p_{bank}+1.5)^{-1.4}$, B is the water surface width, $P_{bed}$ and $P_{bank}$ are wetted parameter of the bed and bank. Estimated values for ${\tau}_{bottom}$ for a flow of $2.5\;m^3/s$ were lower as 25.0 (7.5 m cross-section), 25.7 (34 m), 21.3 (86 m) and 19.8 (150 m), in N/$m^2$, than critical shear stress (${\tau}_c=62.1\;N/m^2$) with cobble of 64 mm. The values were insufficient to erode cobble sediment. In contrast, even if the values of ${\tau}_{bank}$ were lower than the values for ${\tau}_{bottom}$ as 18.7 (7.5 m), 19.3 (34 m), 16.1 (86 m) and 14.7 (150 m), in N/$m^2$, excess shear stresses were calculated at the three cross-sections of 7.5 m, 34 m, and 86 m distances compare with ${\tau}_c$ is 15.5 N/$m^2$ of 16mm gravel. Bank shear stresses were sufficient for erosion of the medium gravel to sand. Therefore there is potential to erode lateral bank than downward erosion in a flow of $2.5\;m^3/s$. Undercutting of the wetted bank can causes bank scour or collapse, therefore this channel has potential to become wider at the same time. This research is about a potential of sediment erosion, and the result could not verify with real data. Therefore it need next step for verification. In addition an erosion mechanism for river restoration is not simple because discharge distribution is variable by snow-melting or rainy season, and a function for disaster control will recover by big precipitation event. Therefore it needs to consider the relationship between continuous discharge change and sediment erosion.

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Crystal structures and magnetic properties of Mn-Al-M (M=Cu, Fe) alloys (Mn-Al-M(M=Cu, Fe) 합금계의 결정구조 및 자기적 성질)

  • Choe, Won-Gyu;Go, Gwan-Yeong;Yun, Seok-Gil
    • Korean Journal of Materials Research
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    • v.5 no.1
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    • pp.22-35
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    • 1995
  • In this study, crystal structures and magnetic properties of as-ast, annealed and rapidly solidified Mn-A1-M( M=Cu, Fe) alloys have been investigated. In $Mn_{0.56}Al_{0.44}$ alloys, the largest fraction of $\tau$ phase and values of magnetic properties was obtained in Mnl, i6Alo or alloy. And this alloy was used as the basic composition. In $Mn_{0.56-X}M_{X}Al_{0.44}$ alloys, when annealed, $\tau$- and $\beta$-Mn phase appeared at x< 0.08, $\tau$- and $\kappa$ phase at 0.10 $\leq x \leq$ 0.12 and $\kappa$- phase only at 0.15 $\leq x \leq$0.20 . When rapidly solidified, specimens showed similar phases as when annealed except that $\varepsilon$ phase appeared at x=0.04. In Mnu FexAlo 44 alloys, asyast specimens showed $\tau$-, $\beta$-Mn and $\gamma_2$- phase at x<0.08 and K and $\beta$-Mn phase at x>0.10. When rapidly solidified, Mn-Fe-Al specimens showed $\varepsilon$-, $\gamma_2$- and small amount of $\tau$- and $\kappa$ phase at x<0.08 and $\kappa$- phase only at 0.$\leq x \leq$0.20. All the alloys investigated were ferromagnetic. The Curie temperature of annealed specimens and rapidly solidified of Mno 5sAlu 44 alloy were -650K and -644K. Spontaneous magnetization( UII of annealed and rapidly solidified specimens were 40-45 (emu/g) and 50-52(emu/g), respectively. Remanent (M,) to saturation magnetization( Ms) ratio was -0.7. M, of rapidly solidified specimen was about 48(emu/g). Magnetic properties of $Mn_{0.56}Al_{0.44}$ alloys were found to be determined by the relative fraction of ferromagnetic r- and K- phase. When M= Cu and x=0.15, maximum as($\sigma_{0.0}$) was obtained by about 64.3 emu/g), and when M=Fe and x=0.15, 66.4( emu/g). The Curie temperature decreased as x increased.

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Chaos and Correlation Dimension

  • Kim, Hung-Soo
    • 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.

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