• Korean Journal of Mathematics
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• v.12 no.1
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• pp.15-22
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the power distribution. Let {$X_n$, $n{\geq}1$} be a sequence of independent an identically distributed random variables with a common continuous distribution function(cdf) $F(x)$ and probability density function(pdf) $f(x)$. Let $Y_n=max\{X_1,X_2,{\cdots},X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of {$X_n$, $n{\geq}1$}, if $Y_j$ > $Y_{j-1}$, $j$ > 1. The indices at which the upper record values occur are given by the record times {$u(n)$}, $n{\geq}1$, where $u(n)=min\{j{\mid}j>u(n-1),X_j>X_{u(n-1)},n{\geq}2\}$ and $u(1)=1$. Suppose $X{\in}POW(0,1,{\theta})$ then $$E\left(\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}\right)=\frac{\theta}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{(s-\theta)}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}\right)\;and\;E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}\right)=\frac{\theta}{n+1}\left[E\left(\frac{X^{r+1}_{u(m-1)}}{X^s_{u(n+1)}}\right)-E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{r+1}{\theta}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}}\right)\right]$$.

• Journal of the Korean Chemical Society
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• v.55 no.5
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• pp.765-775
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• 2011

Novel analogs of bortezomib were designed, synthesized and in vitro biological evaluation was carried out using human tumor cell lines A549 and PC3. Docking studies of these analogs of bortezomib was discussed. According to biological investigations, the inhibitors 4, 6, and 8 were found to be more potent than reference drug candidate bortezomib. A549 cell line showed significant sensitivity towards 4, 6, and 8 with $IC_{50}$ values 14.03, 18.5, and 12.4 nM, respectively, and PC3 cell line showed IC50 values 26.1, 37.0, and 21.2 nM, respectively. The $IC_{50}$ values of bortezomib in these cell lines are 27.3 nM and 42.0 nM.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.561-568
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• 2017

Hurwitz zeta function occurs in various parts of mathematics. In particular, it plays an important role in some area of number theory. In this paper, using a certain transformation formula, we find some identities of relations between ${\zeta}(2n+1)$ and ${\zeta}(2n+1,{\alpha})$ for special values of ${\alpha}$.

• Bulletin of the Korean Chemical Society
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• v.8 no.3
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• pp.200-202
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• 1987

Various useful relations involving Hammett's and $Br{\phi}nsted's$ coefficients are derived for cross interactions between identical groups: ${\rho}_{ii}={\rho}^N+{\rho}^L$, ${\rho}^L-{\rho}^N=1$, ${\beta}_{ii}={\beta}_N+{\beta}_L$ and ${\beta}_N-{\beta}_L=1$. The use of these relations enable us to correctly interprete the transition state structure. Another advantage of the use of these relations is to use ${\rho}/{\rho}_e$ for the determination of corresponding ${\beta}$ values instead of plotting log k vs $pK_{lg}$, once ${\rho}_e$ values for standardizing equilibria are obtained.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.97-102
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛$X_n,n\qeq1$｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$＞$Y_{j-1}$,j＞1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j｜j ＞u(n-l), $X_{j}$＞$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

• Journal of Power System Engineering
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• v.14 no.2
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• pp.71-77
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• 2010

This paper was studied on microstructure, mechanical properties and corrosion characteristics of 316L stainless steel pipe welds was fabricated by orbital welding process. S-Ar specimen was fabricated by using Ar purge gas and S-$N_2$ specimen was fabricated by using $N_2$ purge gas. Ferrite was not detected in weld metal of S-$N_2$ specimen but the order of 0.13 Ferrite number(FN) was detected in weld metal of S-Ar specimen. Oxygen and Nitrogen concentration of S-$N_2$ specimen was higher than S-Ar specimen on HAZ and inner bead. The welds microstructural characteristics of S-Ar and S-$N_2$ specimens are similar. The microvickers hardness values of S-Ar and S-$N_2$ specimens welds were similar and average values of each regions were in the range of 174~194. The microstructures of S-Ar and S-$N_2$ weld metal were full austenite by primary austenite solidification. The Solidification structures of S-Ar and S-$N_2$ weld metal were formed directional dendrite toward bead center. The potentiodynamic polarization curve of STS 316L pipe welds exhibited typical active, passive, transpassive behaviour. Corrosion current density$(I_{corr.})$ and corrosion rate values of S-Ar specimen in 0.1M HCl solution were $0.95{\mu}A/cm^2$ and $0.31{\mu}A$/year respectively. The values of S-$N_2$ specimen were $1.4{\mu}A/cm^2$ and $0.45{\mu}m$/year.

• Korean Journal of Radiology
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• v.20 no.6
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• pp.985-996
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• 2019

Objective: To determine the correlation between cerebral blood flow (CBF) on arterial spin labeling (ASL) MRI and the degree of postoperative revascularization assessed on digital subtraction angiography in children with moyamoya disease (MMD). Materials and Methods: Twenty-one children (9 boys and 12 girls; mean age, 8.4 ± 3.6 years; age range, 3-16 years) with MMD who underwent both pseudocontinuous ASL MRI at 1.5T and catheter angiography before and after superficial temporal artery encephaloduroarteriosynangiosis were included in this retrospective study. The degree of revascularization in the middle cerebral artery (MCA) territory was evaluated on external carotid angiography and was graded on a 3-point scale. On ASL CBF maps, regions of interest were manually drawn over the MCA territory of the operated side at the level of the centrum semi-ovale and over the cerebellum. The normalized CBF (nCBF) was calculated by dividing the CBF of the MCA territory by the CBF of the cerebellum. Changes in nCBFs were calculated by subtracting the preoperative nCBF values from the postoperative nCBF values. The correlation between nCBF changes measured with ASL and the revascularization grade from direct angiography was evaluated. Results: The nCBF value on the operated side increased after the operation (p = 0.001). The higher the degree of revascularization, the greater the nCBF change was: poor revascularization (grade 1), -0.043 ± 0.212; fair revascularization (grade 2), 0.345 ± 0.176; good revascularization (grade 3), 0.453 ± 0.182 (p = 0.005, Jockheere-Terpstra test). The interobserver agreement was excellent for the measured CBF values of the three readers (0.91-0.97). Conclusion: The nCBF values of the MCA territory obtained from ASL MRI increased after the revascularization procedure in children with MMD, and the degree of nCBF change showed a significant correlation with the degree of collateral formation evaluated via catheter angiography.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.375-381
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• 2006

This paper presents characterizations based on the identical distribution and the finite moments of the exponential distribution by record values. We prove that $X{\in}EXP({\sigma})$, ${\sigma}$>0, if and only if $X_{U(n+k)}-X_{U(n)}$ and $X_{U(n)}-X_{U(n-k)}$ for n > 1 and $k{\geq}1$ are identically distributed. Also, we show that $X{\in}EXP({\sigma})$, ${\sigma}$>0, if and only if $E(X_{U(n+k)}-X_{U(n)})=E(X_{U(n)}-X_{U(n-k)})$ for n>1 and $k{\geq}1$.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.439-442
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• 1995

Let ${X_n : n = 1,2,\cdots}$ be a sequence of pairwise independent identically distributed random vectors taking values in a separable Hilbert space H such that $E \Vert X_1 \Vert = \infty$. Let $S_n = X_1 + X_2 + \cdots + X_n$ and for any real $\alpha$ with $0 < \alpha < 1$ define a sequence ${\gamma_n(\alpha)}$ as $\gamma_n(\alpha) = inf {r : P(\Vert S_n \Vert \leq r) \geq \alpha}$. Then $$ lim_{n \to \infty} sup \Vert S_n \Vert/\gamma_n(\alpha) = \infty $$ holds. This is a generalization of Vvedenskaya[2].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.51-57
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• 2007

In this paper, we establish characterizations of the Pareto distribution by the independence of record values. We prove that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}-X_{U(n+1)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$. And we show that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}-X_{U(n+1)}}{X_{U(n)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$.