• 센서학회지
• /
• 제12권1호
• /
• pp.1-9
• /
• 2003

CsI에 활성제로 Li, K, Rb를 첨가하여 CsI(Li), CsI(K) 및 CsI(Rb) 단결정을 Czochralski방법으로 육성하였다. $^{137}CS$(0.662 MeV)에 대한 CsI(Li:0.2 mole%) 섬광체의 에너지 분해능은 14.5%이었고 CsI(K:0.5 mole%) 섬광체는 15.9%이었으며 CsI(Rb:1.5 mole%) 섬광체는 17.0%이였다. 이들 CsI(Li), CsI(K) 및 CsI(Rb) 섬광체의 $\gamma$선 에너지에 대한 에너지 교정곡선은 선형적 이였다. 일정비율 시간분석법(CFT :constant-fraction timing method)으로 측정한 CsI(Li:0.2 mole%), CsI(K:0.5 mole%) 및 CsI(Rb:1.5 mole%) 성광체의 시간 분해능은 각각 9.0 ns, 14.7 ns 및 9.7 ns이였다. CsI(Li:0.2 mole%), CsI(K:0.5 mole%) 및 CsI(Rb:1.5 mole%) 섬광체의 형광감쇠시간은 각각 ${\tau}_1=41.2\;ns$, ${\tau}_2=483\;ns$, ${\tau}_1=47.2\;ns$, ${\tau}_2=417\;ns$ 및 ${\tau}_1=41.3\;ns$ 및 ${\tau}_2=553\;ns$이였다. 그리고 CsI(Li:0.2 mole%), CsI(K:0.5 mole%) 및 CsI(Rb:1.5 mole%) 단결정의 인광감쇠시간은 각각 0.51 s, 0.57 s 및 0.56 s이였다.

• 대한수학회지
• /
• 제51권2호
• /
• pp.239-250
• /
• 2014

Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim$_RH_I^i(M){\leq}k$ for ${\forall}i$ < t, then $$\displaystyle\bigcup_{i=0}^{j}(Ass_RH_I^i(M))_{{\geq}k}=\displaystyle\bigcup_{i=0}^{j}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$$ for ${\forall}j{\leq}t$ and ${\forall}n$ >0. This shows that${\bigcup}_{n>0}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$ is a finite set for ${\forall}i{\leq}t$. Also, we prove that $\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1^{n_1},x_2^{n_2},{\ldots},x_i^{n_i})M)_{{\geq}k}=\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1,x_2,{\ldots},x_i)M)_{{\geq}k}$ if $x_1,x_2,{\ldots},x_r$ is M-sequences in dimension > k and $n_1,n_2,{\ldots},n_r$ are some positive integers. Here, for a subset T of Spec(R), set $T_{{\geq}i}=\{{p{\in}T{\mid}dimR/p{\geq}i}\}$.

• 충청수학회지
• /
• 제23권4호
• /
• pp.731-739
• /
• 2010

In this paper, we prove stability of the reciprocal difference functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)-r\(\sum_{i=1}^{m}x_i\)=\frac{(m-1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ and the reciprocal adjoint functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)+r\(\sum_{i=1}^{m}x_i\)=\frac{(m+1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ in m-variables. Stability of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables were proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar [13]. We extend their result to m-variables in similar types.

• Korean Journal of Mathematics
• /
• 제18권4호
• /
• pp.395-407
• /
• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• Kyungpook Mathematical Journal
• /
• 제46권4호
• /
• pp.573-580
• /
• 2006

In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.

• 대한수학회보
• /
• 제59권1호
• /
• pp.73-82
• /
• 2022

Let K be a field of characteristic zero. We first show that images of the linear derivations and the linear 𝓔-derivations of the polynomial algebra K[x] = K[x₁, x₂, …, x_n] are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear 𝓔-derivations are not unity. In addition, we prove that the images of D and 𝛿 are Mathieu-Zhao spaces of the polynomial algebra K[x] if D = ∑ⁿ_i=1 (a_ix_i + b_i)∂_i and 𝛿 = I - 𝜙, 𝜙(x_i) = λ_ix_i + 𝜇_i for a_i, b_i, λ_i, 𝜇_i ∈ K for 1 ≤ i ≤ n. Finally, we prove that the image of an affine 𝓔-derivation of the polynomial algebra K[x₁, x₂] is a Mathieu-Zhao space of the polynomial algebra K[x₁, x₂]. Hence we give an affirmative answer to the LFED Conjecture for the affine 𝓔-derivations of the polynomial algebra K[x₁, x₂].

• 분석과학
• /
• 제11권4호
• /
• pp.248-253
• /
• 1998

수용액에서 poly-dibenzo-18-crown-6를 이용한 알칼리, 알칼리토금속이온 및 전이금속이온들의 흡착 및 분리특성을 조사하였다. 알칼리금속이온들과 알칼리토금속이온들의 흡착정도와 분포비의 순위는 각각 Li(I)

• 대한수학회보
• /
• 제46권2호
• /
• pp.331-346
• /
• 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.

• Journal of the Korean Statistical Society
• /
• 제17권2호
• /
• pp.81-92
• /
• 1988

We observe independent random variable $Y_i \sim N(\theta_i,1), i=1,2,\cdots,k$, and we are interested in detecting the treatment with the largest $\theta_i$. We consider a procedure which infers $\theta_{(k)} \geq max\theta_i (i\neq(k))$ whenever $Y_{(k)} \geq maxY_i+C (i\neq(k))$. The maximum probability of a false inference is found, and it is shown that the inference can be made with the two-sample one-sided critical value for the usual error levels. The result also holds in the case of common unknown variance.

• 한국작물학회:학술대회논문집
• /
• 한국작물학회 2007년도 춘계학술발표회
• /
• pp.78.2-78.2
• /
• 2007