• 대한수학회지
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• 제34권4호
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Radiation Oncology Journal
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• 제3권2호
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• pp.131-136
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• 1985

성문암은 술, 담배가 주 원인적 인자로 밝혀져 있다. 성문암은 쉰목소리 등으로 조기발견이 용이하며 대부분 분화도가 좋은 편평상피암이고 해부학적 위치상 조직생검 및 치료경과 관찰이 용이하며, 성운에는 임파절이 없으므로 전이가 적다. 국소 치료인 방사선치료와 수술이 치료의 주종을 이루며 방사선치료는 음성보전 측면에서 효과적이므로 초기병변에는 방사선치료를 진행된 병변의 경우 수술 혹은 수출 및 방사선 복합요법을 사용하고 있다. 저자들은 1979년 3월부터 1982년 9월까지 서울대학교병원 치료방사선과에서 성문암으로 치료받은 환자들을 추적 조사하여 다음과 같은 결과를 얻었다. 1. 방사선치료 후 3년 무병 생존율이 $T_1N_0 :\;78\%T_1N_0;\;60\%T_3N_0:\;50\%$, 2 구제적 수술후 3년 무병생존율이 $T_1N_0 :\;89\%T_2N_0;\;80\%T_3N_0:\;50\%$ 3. 재발은 대개 3년 이내에 하였다.

• Journal of Gastric Cancer
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• 제1권1호
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• pp.32-37
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• 2001

Purpose: Three subgroups of stage II stomach cancer (T1N2M0, T2N1M0, T3N0M0) by UICC-TNM staging system show obvious survival difference to each other, which becomes the pitfall of the current staging system. We analyzed the survival and relapse pattern of stage II stomach cancer patients in three subgroups retrospectively to prove the need for change in staging system. Materials and Methods: From July 1989 to December 1995, curative gastric resection was performed in 1,037 patients with gastric adenocarcinoma, and among them 268 patients ($26\%$) were in stage II. The number in each of subgroups (T1N2M0, T2N1M0, and T3N0M0) were 17, 139 and 112 respectively. Survival and relapse pattern were analyzed and median follow up period was 46 months. Results: The 3-year cumulative survival rates of T1N2M0, T2N1M0, and T3N0M0 were $50\%,\;80\%,\;and\;76\%$ respectively (p=0.001). And the 3-year cumulative survival rates of T1N2M0 was comparable to those of 2 subgroups of stage IIIa (T2N2M0, T3N1M0), $47\%\;and\;45\%$ (p>0.05). Peritoneal recurrence was the most frequent in T3N0M0. And hematogenous spread was more frequent in T2N1M0 while nodal spread was more frequent in T1N2M0. Ten out of 17 cases of T1N2M0 died of recurrence. Most of them showed submucosal tumor with depressed lesion and mean tumor size was 3.3 cm. Conclusions: Up-staging of T1N2M0 should be considered because it has the lowest survival rate and the worst prognosis among the three subgroups of Stage II stomach cancer patients. In early gastric cancer patients with high-risk factors (large tumor size, invasion into the submucosal layer, and lymphatic vessel involvement), lymph node dissection and postoperative adjuvant therapy is recommended in an attempt to prevent recurrence in the form of lymph node metastasis.

• 한국물환경학회지
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• 제22권5호
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• pp.846-850
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• 2006

The biological nutrient removal from domestic wastewater with low C/N ratio is difficult. Therefore, this study was performed to increase influent C/N ratio by ammonia stripping without required carbon source and for improving treatment efficiencies of sewerage by the combination process of ammonia stripping and BNR (StripBNR). The results of this study were summarized as follows. BOD removal efficiencies of BNR and StripBNR were 95.3% and 93.2%, respectively. T-N and T-P removal efficiencies of BNR were 53.3% and 40.8%, respectively. T-N and T-P removal efficiencies of StripBNR were 72.8% and 62.9%, respectively. Concentrations of $NH_3-N$, $NO_2-N$ and $NO_3-N$ at BNR effluent were 0.03 mg/L, 0.08 mg/L and 9.12 mg/L, respectively. On the other hands, concentrations of $NH_3-N$, $NO_2-N$ and $NO_3-N$ at StripBNR effluent were 5.79 mg/L, 0.01 mg/L and 0.14 mg/L, respectively. Consequently, influent C/N ratio of BNR process was increased by ammonia stripping. Removal efficiency of T-N and T-P was improved about 20% by the process of StripBNR.

• 대한수학회논문집
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• 제10권1호
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• pp.109-113
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• 1995

For a Hilbert space H, let L(H) denote the algebra of all bounded operators on H. For an $n \in N$, it is well known that any element $T \in L(\oplus^n H)$ is expressed as an $n \times n$ matrix each of whose entries lies in L(H) so that T is written as $$ (1) T = (T_{ij}), i, j = 1, 2, ..., n, T_{ij} \in L(H), $$ where $\oplus^n H$ is the direct sum Hilbert space of n copies of H.

• 대한수학회지
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• 제58권3호
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• pp.609-631
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• 2021

Let C[0, T] denote a generalized analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. Define $Z_{\vec{e},n}$ : C[0, T] → ℝⁿ⁺¹ by $$Z_{\vec{e},n}(x)=\(x(0),\;{\int}_0^T\;e_1(t)dx(t),{\cdots},\;{\int}_0^T\;e_n(t)dx(t)\)$$, where e₁,…, e_n are of bounded variations on [0, T]. In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function $Z_{\vec{e},n}$ which has an initial weight and a kind of drift. As applications of the formula, we evaluate the Radon-Nikodym derivatives of various functions on C[0, T] which are of interested in Feynman integration theory and quantum mechanics. This work generalizes and simplifies the existing results, that is, the simple formulas with the conditioning functions related to the partitions of time interval [0, T].

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.168-171
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• 2000

This paper is concerned with fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E$\_$N/ We study continuously initial observability for the following fuzzy system. x(t)=a(t)x(t)+f(t,x(t)), x(0)=x$\_$0/, y(t)=$\_$${\alpha}$/∏(x(t)), where a: [0, T]\longrightarrowE$\_$N/ is fuzzy coefficient, initial value x$\_$0/$\in$E$\_$N/ and nonlinear funtion f: [0, T]${\times}$E$\_$N/\longrightarrowE$\_$N/ satisfies a Lipschitz condition. Given fuzzy mapping ∏: C([0, T]: E$\_$N/)\longrightarrowY and Y is an another E$\_$N/.

• 한국동물학회지
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• 제39권1호
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• pp.1-11
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• 1996

GABA antagonist인 SR 95531이 닭의 pretectum nuclei (nucleus Superficialis Synencephali nSS) 또는 nBOR (nucleus Ectomammilaris nEM)속에 미량 주입되었다. 단안의 optokinetic nystagmus는 한쪽 뇌의 내부에 약품을 주입하기 전후에 탐색 코일 테크닉에 의해서 기록되었다. 한쪽 nSS 또는 nEM 속에 SR 95531를 미량 주입하면 자극의 양방향에 대하여 반대쪽 눈에 의해서 유도된 단안의 OKN속도 게인이 가역적으로 증가하였다. 이때 nSS속에 주입하면 N-T 성분의 속도 게인보다 T-N 성분의 속도 게인을 더욱 강하게 증가시킴으로써 방향적 불균형성이 더욱 증가되었다. 한편 nEM 속에 약품을 주입하게 되면 T-N 성분의 속도 게인보다 N-T 성분의 속조 게인이 더욱 강하게 증가함으로써 방향적 불균형성을 제거했다. 이것으로부터 우리는 nSS 특히 N-T 자극에 방응에 단안의 OKN이 관련되어 있고, nEM은 N-T 자극에 대한 OKN 반응에 더욱 관련되어 있는 것으로 유추할 수 있었다. 이 결과는 그 약품이 중뇌 수준에서 OKN에 관련된 GABAergic 메카니즘의 억제작용을 제거한다는 것을 암시한다. 미량 주입된 핵에 대하여 같은쪽 눈에 의해서 유도된 OKN의 게인의 증가는 수평적 OKN에 관련된 이들 중뇌 구조들 사이에 강한 상호작용이 존재한다는 것으로 설명된다.

• 대한수학회논문집
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• 제9권4호
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• pp.881-889
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• 1994

Let ($X, \Beta, \mu$) be a measure space with the $\sigma$-algebra $\Beta$ and the probability measure $\mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $\mu(T^{-1}E) = \mu(E)$ for $E \in B$. It is said to be ergodic if $\mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E \in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x \in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set E\ulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n \to \infty}(1/N)\sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/\mu(X)) \int_X f(x)d\mu(x)$. In the special case when f is the characteristic function $\chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N \to \infty} \frac{$\mid${n : T^n x \in E, 0 \leq n $\mid$}{N} = \mu(E) $$ for almost all $x \in X$ where $$\mid$\cdot$\mid$$ denotes cardinality of a set. For the details, see [8], [10].

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.