• Journal of the Korean Statistical Society
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• 제7권1호
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• 대한수학회보
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• 제46권2호
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• pp.331-346
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• 2009

Let ${\alpha}$ = (${\alpha}_1,\;{\alpha}_2$,...) and ${\beta}$ = (${\beta}_1,\;{\beta}_2$,...) be two sequences with ${\alpha}_1$ = ${\beta}_1$ and k and n be natural numbers. We denote by $A^{(k,{\pm})}_{{\alpha},{\beta}}(n)$ the matrix of order n with coefficients ${\alpha}_{i,j}$ by setting ${\alpha}_{1,i}$ = ${\alpha}_i,\;{\alpha}_{i,1}$ = ${\beta}_i$ for 1 ${\leq}$ i ${\leq}$ n and $${\alpha}_{i,j}=\{{\alpha}_{i-1,j-1}+{\alpha}_{i-1,j}\;if\;j{\equiv}$$2,3,4,..., k + 1 (mod 2k) $$\{{\alpha}_{i-1,j-1}-{\alpha}_{i-1,j}\;if\;j{\equiv}$$ k + 2,..., 2k + 1 (mod 2k) for 2 ${\leq}$ i, j ${\leq}$ n. The aim of this paper is to study the determinants of such matrices related to certain sequence ${\alpha}$ and ${\beta}$ and some natural numbers k.

• The Korean Journal of Physiology and Pharmacology
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• 제7권2호
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• pp.53-57
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• 2003

The glutamate receptors (GluRs) are key receptors for modulatory synaptic events in the central nervous system. It has been reported that glutamate increases the intracellular $Ca^{2+}$ concentration ($[Ca^{2+}]_i$) and induces cytotoxicity. In the present study, we investigated whether the glutamate-induced $[Ca^{2+}]_i$ increase was associated with the activation of ionotropic (iGluR) and metabotropic GluRs (mGluR) in substantia gelatinosa neurons, using spinal cord slice of juvenile rats (10${\sim}21 day). $[Ca^{2+}]_i$ was measured using conventional imaging techniques, which was combined with whole-cell patch clamp recording by incorporating fura-2 in the patch pipette. At physiological concentration of extracellular $Ca^{2+}$, the inward current and $[Ca^{2+}]_i$ increase were induced by membrane depolarization and application of glutamate. Dose-response relationship with glutamate was observed in both $Ca^{2+}$ signal and inward current. The glutamate-induced $[Ca^{2+}]_i$ increase at holding potential of -70 mV was blocked by CNQX, an AMPA receptor blocker, but not by AP-5, a NMDA receptor blocker. The glutamate-induced $[Ca^{2+}]_i$ increase in $Ca^{2+}$ free condition was not affected by iGluR blockers. A selective mGluR (group I) agonist, RS-3,5-dihydroxyphenylglycine (DHPG), induced $[Ca^{2+}]_i$ increase at holding potential of -70 mV in SG neurons. These findings suggest that the glutamate-induced $[Ca^{2+}]_i$ increase is associated with AMPA-sensitive iGluR and group I mGluR in SG neurons of rats.

• 한국세라믹학회지
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• 제41권5호
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• pp.401-405
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• 2004

순수한 SrB $i_2$T $a_2$$O_{9}$ 세라믹스와 도너와 억셉터가 치환된 S $r_{0.99}$B $i_2$(T $a_{0.99}$ $W_{0.01}$)$_2$$O_{9}$ 와 SrB $i_2$(T $a_{0.99}$ $Ti_{0.01}$)$_2$ $O_{8.99}$ 세라믹스를 제조하고 미세구조, 강유전 P-E 이력특성, 상전이 온도를 조사하였다. 입자크기는 SrB $i_2$T $a_2$$O_{9}$ 세라믹스의 강유전 이력곡선에는 영향을 주지 않았다. 도너를 치환한 S $r_{0.99}$B $i_2$(T $a_{0.99}$ $W_{0.01}$)$_2$$O_{9}$ 세라믹스는 순수한 SrB $i_2$T $a_2$$O_{9}$ 세라믹스보다 잔류 분극이 크고 더욱 포화된 강유전 P-E 이력곡선을 보였으며, 억셉터가 치환된 SrB $i_2$(T $a_{0.99}$ $Ti_{0.01}$)$_2$ $O_{8.99}$ 세라믹스는 잔류분극이 크게 감소하여 가운데가 잘록한 모양을 보였다. 도너가 치환된 S $r_{0.99}$B $i_2$(T $a_{0.99}$ $W_{0.01}$)$_2$$O_{9}$ 세라믹스의 강유전 분극이 순수한 SrB $i_2$T $a_2$$O_{9}$ 세라믹스보다 더 큰 것은 Sr 공공의 생성에 의하여 분역벽 이동이 용이해졌기 때문이다.동이 용이해졌기 때문이다.동이 용이해졌기 때문이다.동이 용이해졌기 때문이다.

• 대한수학회보
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• 제58권5호
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• pp.1069-1078
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• 2021

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary ([4]) if for all nonunit a, b, c ∈ R such that abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. The concept of 1-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly 1-absorbing primary ideals which are generalization of weakly prime ideals and 1-absorbing primary ideals. A proper ideal I of R is called weakly 1-absorbing primary if for all nonunit a, b, c ∈ R such that 0 ≠ abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. Some properties of weakly 1-absorbing primary ideals are investigated. For instance, weakly 1-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if I is a weakly 1-absorbing primary ideal of a ring R and 0 ≠ I₁I₂I₃ ⊆ I for some ideals I₁, I₂, I₃ of R such that I is free triple-zero with respect to I₁I₂I₃, then I₁I₂ ⊆ I or I₃ ⊆ I.

• 대한수학회보
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• 제39권3호
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

• 대한수학회보
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• 제39권3호
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• pp.423-430
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• 2002

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{}i$ = $Y_{i}$ for i/ = 1,2,…, n. In this article, we obtained the following : Let X ＝ ($x_{i\sigma(i)}$ and Y ＝ ($y_{ij}$ be operators in B(H) such that $X_{i\sigma(i)}\neq\;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${\frac{\parallel{\sum^n}_{i=1}E_iYf_i\parallel}{\parallel{\sum^n}_{i=1}E_iXf_i\parallel}n\;\epsilon\;N,E_i\;\epsilon\;L and f_i\;\epsilon\;H}$ < $\infty$ and $x_{i,\sigma(i)}y_{i,\sigma(i)}$ is real for all i = 1,2, ....

• 충청수학회지
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• 제27권2호
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• pp.157-163
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• 2014

Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

• Journal of Communications and Networks
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• 제3권4호
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• pp.361-364
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• 2001

Over an additive abelian group G of order g and for a given positive integer $\lambda$, a generalized Hadamard matrix GH(g, $\lambda$) is defined as a gλ$\times$gλ matrix[h(i, j)], where 1 $\leq i \leqg\lambda and 1 \leqj \leqg\lambda$, such that every element of G appears exactly $\lambd$atimes in the list h($i_1, 1) -h(i_2, 1), h(i_1, 2)-h(i_2, 2), …, h(i_1, g\lambda) -h(i_2, g\lambda), for any i_1\neqi_2$. In this paper, we propose a new method of expanding a GH(g^m, \lambda_1) = B = [B_{ij}] over G^m$ by replacing each of its m-tuple B_{ij} with B_{ij} + GH(g, $\lambda_2) where m = g\lambda_2. We may use g^m/\lambda_1 (not necessarily all distinct) GH(g, \lambda_2$)s for the substitution and the resulting matrix is defined over the group of order g.

• 응용통계연구
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• 제18권3호
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• pp.689-699
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• 2005

우리는 모분산 ${\sigma}^2$에 대한 추정량으로서 표본분산 $S^2=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n-1}$을 주로 사용한다. 그러나, 제 7차 교육과정에 따른 고등학교 수학 교과서(10-가, 수학 I과 실용수학)에서는 표본분산의 정의를 $S^2_n=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n}$로 사용하고 있다. 이 두 표본분산들의 관계를 알아보고, 시뮬레이션을 통하여 확인하여 본다. 또한, 이 두 표본분산들을 포함하여 일반적으로 정의할 수 있는 표본분산을 제안한다.