• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.619-629
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• 1997

In this paper, we give some properties of the sets $D_z(x_o, G)P_{G, z}(x)$. We also provide the relation between $P_{G, z}(x)$ and G$\hat{a}$teaux derivatives.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.677-683
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• 2003

In multi-allelic model $X\;=\;(x_1,\;x_2,\;\cdots\;,\;x_d),\;M_f(t)\;=\;f(p(t))\;-\;{\int_0}^t\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we examine the stochastic differential equation for model X and find the properties using stochastic differential equation.

• Journal of Korean Society for Quality Management
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• v.15 no.2
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• pp.27-37
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• 1987

In life testing problem, many authors obtained the minimum variance unbiased estimator of $P_r$[X>Y] for the exponential family generally and conceptually. In this paper, we study the maximum likelihood estimator and minimum variance unbiased estimator of $P_r$[X>Y] in exponential X and normal Y.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.743-748
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• 2009

In 1970, Fernique proved that there is a positive real number $\alpha$ such that $\int_{\mathbb{B}}\exp\{\alpha{\parallel}x{\parallel}^{2}\}dP(x)$ is finite where ($\mathbb{B},\;P$) is an abstract Wiener measure space and ${\parallel}\;{\cdot}\;{\parallel}$ is a measurable norm on ($\mathbb{B},\;P$) in [2, 3]. In this article, we investigate the existence of the integral $\int_{c}\exp\{\alpha(sup_t{\mid}x(t){\mid})^p\}dm_{\varphi}(x)$ where ($\mathcal{C}$, $m_{\varphi}$) is the analogue of Wiener measure space and p and $\alpha$ are both positive real numbers.

• The Journal of Korean Academy of Prosthodontics
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• v.48 no.4
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• pp.251-258
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• 2010

Purpose: To evaluate the effect of surface conditioning on the shear bond strength of zirconium-oxide ceramic to 4 luting agents. Materials and methods: A total of 120 diskshaped zirconium-oxide ceramic blocks (3Y-TZP, Kyoritsu, Japan) were treated as follows: (1) Sandblasting with $110\;{\mu}m$ aluminum-oxide ($Al_2O_3$) particles; (2) tribochemical silica coating (Rocatec) using $110\;{\mu}m$ $Al_2O_3$ particles modified by silica; (3) no treatment. Then zirconium-oxide ceramic blocks bonded with 4 luting cements (RelyX luting (3M ESPE), Maxcem (Kerr), Nexus3 (Kerr), Rely X Unicem (3M ESPE)). Each group was tested in shear bond strengths by UTM. A 1-way analysis of variance and 2-way analysis of variance was used to analyze the data ($\alpha$ = .05). Results: RelyX unicem in combination tribochemical silica-coating produced a highest bond strength (P < .05). Air abrasion group and Rocatec treatment groups resulted in significantly higher than no conditioning group (P < .05). RelyX Luting groups showed lower bond strength than other groups. There were significant differences among groups (P < .05). Conclusion: Within the limitation of this study, RelyX Unicem cement provided the highest bond strength and Rocatec treatment enhanced the bond strength.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.787-797
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• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2003.07b
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• pp.1208-1211
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• 2003

High quality $Bi_2Sr_2Ca_nCu_{n+1}O_x$ superconducting thin films fabricated by using the evaporation method at various substrate temperatures, $T_{sub}$, and ozone gas pressures, $pO_3$. The correlation diagrams of the $Bi_2Sr_2Ca_nCu_{n+1}O_x$ phases with $T_{sub}$ and $pO_3$ are established in the 2212 and 2223 compositional films. In spite of 2212 compositional sputtering, Bi2201 and Bi2223 as well as Bi2212 phases come out as stable phases depending on $T_{sub}$ and $pO_3$. From these results, the thermodynamic evaluation of ${\Delta}H$ and ${\Delta}S$, which are related with Gibbs' free energy change for single Bi2212 or Bi2223 phase, was performed.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• Reproductive and Developmental Biology
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• v.33 no.3
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• pp.119-123
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• 2009

The two dimensional quantitative structure-activity relationships (2D-QSARs) models concerning the binding affinity constants ($p[Od.]_{50}$) between 2-cyclohexyltetrahydropyrane and 2-cyclohexyltetrahydrofurane analogues as substrates, and bovine odorant binding protein (bOBP) as receptor were derived by multiple regression analyses method and discussed. The statistical quality of the optimized 2D-QSAR model (5) was good (r=0.907). From the model, the binding affinity constants ($p[Od.]_{50}$) were dependent upon the optimal value ($(TL)_{opt.}$=2.737) of total lipole (TL) of substrate molecules. Based on these findings, the high active compounds predicted by optimized 2D-QSAR model (5) were 2-(dimethylcyclohexyl)tetrahydropyrane molecule and their isomer molecules. The binding affinity constants regarding bOBP of the tetrahydrofuryl-2-yl family compounds were dependent upon the hydrophobicity (logP) of whole substrate molecules. In any case of porcine odorant-binding proteins (pOBP), the constants were dependent upon the hydrophobicity (${\pi}x={\log}P_X-{\log}P_H$) of substituents (R) in substrate molecules. Also, from the optimal values of hydrophobic constant, the hydrophobicity for bOBP influenced ca. twice time bigger (bOBP>pOBP) than that for pOBP.