• 대한수학회보
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• 제55권4호
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• pp.1007-1012
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• 2018

Let R be an integral domain. We prove that the power series ring R[[X]] is a Krull domain if and only if R[[X]] is a generalized Krull domain and t-dim $R{\leq}1$, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts "Krull domain" and "generalized Krull domain" are the same in power series rings, (2) there exists a non-t-SFT domain R with t-dim R > 1 such that t-dim R[[X]] = 1.

• 대한수학회보
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• 제51권6호
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• pp.1829-1839
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• 2014

Let (${\Omega}$, $\mathcal{S}$, ${\mu}$) be a probabilistic measure space, ${\varepsilon}{\in}\mathbb{R}$, ${\delta}{\geq}0$, p > 0 be given numbers and let $P{\subset}\mathbb{R}$ be an open interval. We consider a class of functions $f:P{\rightarrow}\mathbb{R}$, satisfying the inequality $$f(EX){\leq}E(f{\circ}X)+{\varepsilon}E({\mid}X-EX{\mid}^p)+{\delta}$$ for each $\mathcal{S}$-measurable simple function $X:{\Omega}{\rightarrow}P$. We show that if additionally the set of values of ${\mu}$ is equal to [0, 1] then $f:P{\rightarrow}\mathbb{R}$ satisfies the above condition if and only if $$f(tx+(1-t)y){\leq}tf(x)+(1-t)f(y)+{\varepsilon}[(1-t)^pt+t^p(1-t)]{\mid}x-y{\mid}^p+{\delta}$$ for $x,y{\in}P$, $t{\in}[0,1]$. We also prove some basic properties of such functions, e.g. the existence of subdifferentials, Hermite-Hadamard inequality.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• 대한수학회보
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• 제52권2호
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• pp.531-540
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• 2015

Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all $t{\leq}r$ the sets $$(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/I^n,A)))_{{\geq}k}\;and\\(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/(a_1^{n_1},{\cdots},a_l^{n_l}),A)))_{{\geq}k}$$ are independent of the choice of $n,n_1,{\cdots},n_l$ for any system of generators ($a_1,{\cdots},a_l$) of I.

• 대한수학회보
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• 제51권3호
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• pp.653-657
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• 2014

Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that $$Ext^i{_R}(R/I,H^t{_{I,J}}(M))$$ is finitely generated for i = 0, 1 where t=inf{$i{\in}\mathbb{N}_0:H^2{_{I,J}}(M)$ is not finitely generated}. Also, we prove that $H^i{_{I+J}}(H^t{_{I,J}}(M))$ is Artinian when dim(R/I + J) = 0 and i = 0, 1.

• 한국가금학회지
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• 제35권4호
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• pp.375-380
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• 2009

본 시험은 비절식 강제 환우 가 산란계의 장기 비율의 변화 및 혈액 성상에 미치는 영향을 알아보고자 60주령 Leghorn종 400수를 공시하여 34주간 실시하였다. 처리구는 관행적으로 절식한 대조구(C), 옥수수 단일사료 급여(T1), 밀기울 단일 사료 급여(T2) 및 알팔파 단일 사료를 급여(T3)한 4처리로서, 처리구당 5반복, 반복당 20수씩 철제 케이지에 완전임의 배치하였다. 시험결과, 생체중 대비 장기 비율은 환우 개시시 난소는 $2.03{\sim}2.86%$, 난관은 $2.51{\sim}3.47%$로 처리구간에 유의차를 보이지 않았으며, 환우 종료시에는 난소의 경우 $0.25{\sim}0.41%$로서 차이가 없었으나, 난관은 대조구, T1구, T2 구 및 T3구가 각각 1.15%, 0.80%, 0.46% 및 0.89%로서 T2구가 대조구, T3구보다 유의적으로 낮았다(P<0.05). 50% 산란시 난소는 $2.19{\sim}2.60%$, 난관은 $3.00{\sim}3.50%$였으며, 산란피크시에 난소의 경우 2.65{\sim}3.01%, 난관은 $3.25{\sim}3.65%$로서 절식과 비절식에 따른 처리간에 차이가 나타나지 않았다. 혈액성상에서 Cholesterol은 환우 개시시 $179.8{\sim}245.7\;mg/dL$로서 처리간에 차이가 없었고, 환우 종료시에는 대조구 353.6, T1구 229.1, T2구 261.8 및 T3구 300.6 mg/dL로서 T1구가 대조구 및 T3구보다 유의적으로 낮았으며(P<0.05), 시산시에는 $228.1{\sim}271.8\;mg/dL$, 50% 산란시에는 $236.5{\sim}284.8\;mg/dL$로서 처리간에 차이가 없었다. 산란 피크시에는 대조구, T1구, T2구 및 T3구가 각각 324.1, 591.6, 363.0 및 315.6 mg/dL로서 T1구가 다른 처리구에 비하여 유의적으로 높았다(P<0.05).

• 대한전자공학회논문지
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• 제16권3호
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• pp.9-18
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• 1979

본 논문에서는 바나디움 주화물을 사용한 새로운 반도체 소자인 C.T.R을 제조하여 그외 전기적 특성을 조사하였다. 그 실험결과는 다음과 같다. (1) 제조될 C.T.R의 저항급변계수 는 3정도였고, (2) 의 값은 환원시간과 급냉시간에 크게 의존하였으며, (3) 의 큰 값을 갖는 C.T.R은 짧은 switching현상을 갖는다.

• 대한수학회보
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• 제56권5호
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.93-96
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• 1997

An atomic integral domain R is a half-factorial domain (HFD) if whenever $\chi_1$… $\chi_{m}=y_1$…$y_n$ with each $\chi_{i},y_j \in R$ irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then $Cl_{t}(R)$ $\cong$ $Cl_{t}$(R[X]), and if $G_1$ and $G_2$ are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = $G_1\bigoplus\; G_2$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.364-368
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• 1994

Algebraic matrix Riccati equations of the form, FP+PF$^{T}$ -PRP+Q=0. are analyzed with reference to the stability of closed-loop system F-PR. Here F, R and Q are n * n real matrices with R=R$^{T}$ and Q=Q$^{T}$ .geq.0 (nonnegative-definite). Such equations have been playing key roles in optimal control and filtering problems with R .geq. 0. and also in the solutions of in H$_{\infty}$ control problems with R taking the form R=H$_{1}$$^{T}$ H$_{1}$-H$_{2}$$^{T}$ H$_{2}$. In both cases an existence of stabilizing solution, i.e. the solution yielding asymptotically stable closed-loop system, is an important problem. First, we briefly review the typical results when R is of definite form, namely either R .geq. 0 as in LQG problems or R .leq. 0. They constitute two extrence cases of Riccati to the cases H$_{2}$=0 and H$_{1}$=0. Necessary and sufficient conditions are shown for the existence of nonnegative-definite or positive-definite stabilizing solution. Secondly, we focus our attention on more general case where R is only assumed to be symmetric, which obviously includes the case for H$_{\infty}$ control problems. Here, necessary conditions are established for the existence of nonnegative-definite or positive-definite stabilizing solutions. The results are established by employing consistently the so-called algebraic method based on an eigenvalue problem of a Hamiltonian matrix.x.ix.x.