• Journal of the Korean Mathematical Society
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• v.34 no.4
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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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• v.3 no.2
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• pp.131-136
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• 1985

A retrospective analysis of 29 patients with glottic cancer, treated at the Department of Therapeutic Radiology, Seoul National University Hospital. $97\%$ of the patients was male. Of the 29 patients, stage $T_1N_0M_0$ comprised $31\%$, $T_2N_0M_0\;52\%$, and stage $T_3N_0M_0\;14\%$. Local control rate with radical readiotherapy was $78\%$ for stage $T_1N_0M_0,\;60\%$, for stage $T_2N_0M_0$, and $50\%$ for stage $T_3N_0M_),\;57\%$ of the patients with the radiation failure was salvaged by surgery. The overall 3 year survival rate was $89\%$ for the $T_1N_0M_0,\;80\%$ for stage $T_2N_0M_0$, and $50\%$ for stage $T_3N_0M_0$. Among the survivors: $88\%$ of $T_1N_0M_0\;75\%$ of $T_2N_0M_0,\;and\;50\%$ $T_3N_0M_0$ had an intact larynx and natural voice. It is concluded that radiotherapy is a highly effective method as the primary treatment of the early glottic cancer, emphasized on preserving of the larynx and natural voice.

• Journal of Gastric Cancer
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• v.1 no.1
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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.

• Journal of Korean Society on Water Environment
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• v.22 no.5
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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.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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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].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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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/.

• The Korean Journal of Zoology
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• v.39 no.1
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• pp.1-11
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• 1996

The SR 95531, a GABA antagonist was microinjected into either the pretectum nuclei (nucleus Superficialis Synencephali nSS) or the nBOR (nucleus Ectomammilaris nEM) of chickens. Monocular optokinetic nystagmus (01(N) was reorded by the search coil technique before and after unilateral intracerebral drug administration. Unilateral microinjections of SR 95531 into either the nSS or nEM induce a reversible increase of gain in OKN directed by contralateral eye for both directions of stimulation. The administration into the nSS increased directional asymmetry by increasing the T~ component velocity gain more strongly than the N-T component velocity gain. On the other hand, the unilateral administration of the drug into the nEM suppressed the diretional O1(N asymmetry by increasing the N-T component velocity gain more strongly than the T-N component velocity gain. The nSS seems especially involved in monocular OKN in response to a T-N stimulation, while the nEM seems more involved in the OKN response to N-T stimulation. These results indicate that the drug suppresses GABAergic inhibition at the mesencephalic level. The increase in gain of OKN directed by the ipsilateral eye to microinjeded nuclei could account for the strong interactions existing between these two mesencephalic structures responsible for horizontal OKN.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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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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• v.9 no.1
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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 $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.