• Korean Journal of Mathematics
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• 제21권4호
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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.

• East Asian mathematical journal
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• 제34권5호
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• pp.643-649
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• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1115-1123
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• 2016

Let $D{\subseteq}E$ be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D and let H(D, E) and H(D, I) (resp., h(D, E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this paper, we show that H(D, E) satisfies the ascending chain condition on principal ideals if and only if h(D, E) satisfies the ascending chain condition on principal ideals, if and only if ${\bigcap}_{n{\geq}1}a_1{\cdots}a_nE=(0)$ for each infinite sequence $(a_n)_{n{\geq}1}$ consisting of nonzero nonunits of We also prove that H(D, I) satisfies the ascending chain condition on principal ideals if and only if h(D, I) satisfies the ascending chain condition on principal ideals, if and only if D satisfies the ascending chain condition on principal ideals.

• 대한의생명과학회지
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• 제15권2호
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• pp.167-170
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• 2009

Nitric oxide is an important factor to regulate the biochemical reactions in the body such as expansion of blood vessel, neural conduction and antimicrobial activity. There are two forms of nitric oxide synthase and iNOS has attracted most attention because it is involved in the development of diabetes and cardiac disease condition. There are several regulatory sequences in the promoter region of iNOS gene. One of them is (CCTTT)n. It has been reported that the number of tandem repeat of (CCTTT)n varies from population to population. So, we analyzed (CCTTT)n polymorphism in Korean genome for the purpose of comparison. According to our present study Koreans are different from other Asians reported previously because $(CCTTT)_{10}$ is the highest incidence as opposed to $(CCTTT)_{12}$ for other countries. This study should facilitate the understanding of the expression of iNOS gene in different population.

• Archives of Pharmacal Research
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• 제19권1호
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• pp.66-70
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• 1996

Aliphatic esters of protocatechuic acid (PA, 1), vanillic acid (VA, 9) and gallic acid (GA, 18) were prepared and their anti-thrombotic effects were evaluated in the mouse model of thrombosis. The aliphatic groups included methyl, ethyl, n-propyl, i-propyl, n-butyl, i-butyl, n-amyl and cyclohexyl. n-Amyl ester of PA (7), i-propyl and cyclohexyl esters of VA (13 and 17 respectively) and ethyl ester of GA (20) treatment significantly lowered the death rate and increased the recovery from paralysis due to the thrombotic challenge. From the limited analogs available, it was tentatively concluded that the structural conformation, where carboxy oxygen (=O or -O) of the carboxyl group (COOH) at $C_1$ and the oxygen function at $C_3(either\; OH\; or\; OCH_3)$ are closely situated, is favorable for the esters of PA, VA and GA to be more antithrombotic.

• Bulletin of the Korean Chemical Society
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• 제29권11호
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• pp.2157-2160
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• 2008

• 충청수학회지
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• 제20권1호
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• pp.23-29
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• 2007

Let X and Y be vector spaces. In this paper we prove that a mapping $f:X{\rightarrow}Y$ satisfies the following functional equation $${\large}\sum_{1{\leq}k<l{\leq}n}\;(f(x_k+x_l)+f(x_k-x_l))-2(n-1){\large}\sum_{i=1}^{n}f(x_i)=0$$ if and only if the mapping f is quadratic. In addition we investigate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.

• 대한수학회논문집
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• 제23권4호
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• pp.597-606
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• 2008

Let {$Y_{ij}-{\infty}\;<\;i\;<\;{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables with zero means and finite variances and {$a_{ij}-{\infty}\;<\;i\;<\;{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {${\sum}^n_{k=1}\;{\sum}^{\infty}_{i=-{\infty}}\;a_{i+k}Y_i/n^{1/p}$; $n\;{\geq}\;1$} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191.197.] to the ${\rho}^*$-mixing case.

• Journal of Microbiology and Biotechnology
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• 제18권3호
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• pp.591-599
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• 2008

A murine model immunized by systemic and mucosal delivery of plasmid DNA vaccine expressing glycoprotein B (pCIgB) of pseudorabies virus (PrV) was used to evaluate both the nature of the induced immunity and protection against a virulent virus. With regard to systemic delivery, the intramuscular (i.m.) immunization with pCIgB induced strong PrV-specific IgG responses in serum but was inefficient in generating a mucosal IgA response. Mucosal delivery through intranasal (i.n.) immunization of pCIgB induced both systemic and mucosal immunity at the distal mucosal site. However, the levels of systemic immunity induced by i.n. immunization were less than those induced by i.m. immunization. Moreover, i.n. genetic transfer of pCIgB appeared to induce Th2-biased immunity compared with systemic delivery, as judged by the ratio of PrV-specific IgG isotypes and Th1- and Th2-type cytokines produced by stimulated T cells. Moreover, the immunity induced by i.n. immunization did not provide effective protection against i.n. challenge of a virulent PrV strain, whereas i.m. immunization produced resistance to viral infection. Therefore, although i.n. immunization was a useful route for inducing mucosal immunity at the virus entry site, i.n. immunization did not provide effective protection against the lethal infection of PrV.

• 대한수학회보
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• 제39권4호
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• pp.607-615
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• 2002

Let (X, $X_{n}$, n$\geq$1) be a sequence of i.i.d. random variables and { $a_{ni}$ , 1$\leq$i$\leq$n, n$\geq$1} be an array of constants. Let ø($\chi$) be a positive increasing function on (0, $\infty$) satisfying ø($\chi$) ↑ $\infty$ and ø(C$\chi$) = O(ø($\chi$)) for any C > 0. When EX = 0 and E[ø(｜X｜)]〈$\infty$, some conditions on ø and { $a_{ni}$ } are given under which (equation omitted).).