• 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 $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.129-131
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• 2001

Let $q=p^{e1}_1{\cdots}p^{em}_m$ be the product of distinct prime elements. In this short paper, we show that the largest value of M such that there exists an ($n$, M, $n-1$) $q$-ary code is $q^2$ if $n-1{\leq}p^{ei}_i$ for all $i$.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.33-39
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• 1994

The purpose of this paper prove the following property; Suppose A has many units (local global ring) and |A/m| > 5 for every maximal ideal $m{\subseteq}A$. Let(E, q) ${\in}$ Q(A) and $E=E_1{\bot}{\cdots}{\bot}E_t$ be an orthogonl decomposition of E with $t{\geq}2$ and $rk(E_i){\geq}1$, for $i=1,{\cdots},t$. Let $x{\in}E$ be a primitive vector. Then there exists ${\sigma}{\in}O(q)$ such that ${\sigma}(x)$ is transversal to this decomposition.

• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.71-79
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• 1987

The linear and quadratic log contrast model with mixtures on the strictly positive simplex, $$ x_{q-1} = {(x_1, \cdots, x_q):\sum x_, = 1 and \delta \leq \frac{x_i}{x_j} \leq \frac{1}{\delta} for all i,j},$$ are considered. Using the invariance arguments, symmetric D-optimal designs are investigated. The class of symmetric D-optimal designs for the linear log contrasts model is given. Any D-optimal design for the quadratic log contrast model is shown to metric D-optimal designs for q=3 and 4 cases are given.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.253-266
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• 2021

This work is devoted to the study of a q-harmonic analysis related to the q-analog of the Bessel-Wright integral transform [6]. We establish some important properties of this transform and we focalise our attention in studying the associated transmutation operator.

• Molecules and Cells
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• v.24 no.3
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• pp.351-357
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• 2007

Regions (about 3.7-3.8 kb) of the mitochondrial genomes (rrnL-cox1) of two tardigrades, a heterotardigrade, Batillipes pennaki, and a eutardigrade, Pseudobiotus spinifer, were sequenced and characterized. The gene order in Batillipes was $\underline{rrnL}-\underline{V}-\underline{rrnS}-\underline{Q}-\underline{I}$-M-nad2-W-$\underline{C}-\underline{Y}$-cox1, and in Pseudobiotus it was $\underline{rrnL}-\underline{V}-\underline{rrnS}-\underline{Q}$-M-nad2-W-$\underline{C}-\underline{Y}$-cox1. With the exception of the trnI gene, the two tardigrade regions have the same gene content and order. Their gene orders are strikingly similar to that of the chelicerate Limulus polyphemus (rrnL-V-rrnS-CR-I-Q-M-nad2-W-C-Y-cox1), which is considered to be ancestral for arthropods. Although the tardigrades do not have a distinct control region (CR) within this segment, the trnI gene in Pseudobiotus is located between rrnL-trnL1 and trnL2-nad1, and the trnI gene in Batillipes is located between trnQ and trnM. In addition, the 106-bp region between trnQ and trnM in Batillipes not only contains two plausible trnI genes with opposite orientations, but also exhibits some CR-like characteristics. The mitochondrial gene arrangements of 183 other protostomes were compared. 60 (52.2%) of the 115 arthropods examined have the M-nad2-W-C-Y-cox1 arrangement, and 88 (76.5%) the M-nad2-W arrangement, as found in the tardigrades. In contrast, no such arrangement was seen in the 70 non-arthropod protostomes studied. These are the first non-sequence molecular data that support the close relationship of tardigrades and arthropods.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.7
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• pp.1241-1249
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• 2002

The extent of materials deterioration can be evaluated accurately by mechanical test such as impact test or creep test. But it is almost impossible to extract a large test specimen from in-service components. Thus material degradation evaluation by non-destructive method is earnestly required. In this paper, the material degradation for virgin and several aged materials of a Cr-Mo-V steel, which is an candidated as structural material of the turbine casing components for electric power plant, is nondestructively evaluated by reactivation polarization testing method. And, the results obtained from the test are compared with those in small punch(SP) tests recommended as a semi-nondestructive testing method using miniaturized specimen. In contrast to the aged materials up to 1,000hrs which exhibit the degradation behaviors with increased ${\Delta}[DBTT]_{SP}$, the improvement of mechanical property can be observed on the 2,000hrs and 3,000hrs aged materials. This is because of the softening of material due to the carbide precipitation, the increase of ferritic structures and the recovery of dislocation microstructure by long-time heat treatment. The reactivation rates($I_R/I_{Crit},\;Q_R/Q_{Crit}$) calculated by reactivation current densityt ($I_R$) and charge($Q_R$) in the polarization curves exhibit a good correlation with ${\Delta}[DBTT]_{SP}$ behaviors.

• Journal of Korea Water Resources Association
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• v.36 no.2
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• pp.183-193
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• 2003

A relation between the temporal variation of rainfall and direct runoff was characterized using temporal indexes of rainfall(1st, 2nd, 3rd, and 4th moment). Curve Number has a relation with 1st and 2nd moment for AMCIII condition when the rainfall duration is relative (10th quantile). Also peak runoff ratio(QP/Q) has a relation with 1st and End moment for AMCIII condition as well as 3rd and 4th moment for AMC I condition. Considering all durations of rainfall, alternatively, Curve Number has a relation with 1st and 2nd moment for AMCIIIcondition besides every moments for AMC I condition. But peak runoff ratio(QP/Q) has few relations excepting 3rd and 4th moment for AMC I condition. As a results, temporal indexes of rainfall are useful to determine curve numbers regarding the temporal variation of rainfall.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.418-418
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• 2012

현재 전 세계적으로 온실가스 농도 증가로 호우나 가뭄, 대설 등 지역에 따라 서로 상반되는 변화를 가져올 수 있다고 경고되고 있으며, 우리나라에서도 남해안지역과 경기북부지역에서 호우빈도가 증가하는 반면, 충정도 내륙지역과 경상북도에서는 호우빈도가 감소하고 5일 누적 강수량 또한 감소하여, 해당지역에서 가뭄이 발생할 경우 심화될 가능성이 높아진다고 보고된 바 있다. 기후변화 시나리오에 분석결과에서도 우리나라의 경우 평균적으로 강우일수는 작아지며, 강우강도는 커지는 결과들이 도출되었다. 이러한 결과들은 가뭄의 발생가능성이 높아지고 있음을 보여주고 있다. 본 연구에서는 우리나라에서 발생된 가뭄의 특성을 분석하고 가뭄의 특성과 기상인자간의 관계를 Quantile regression 분석을 통해 살펴보고자 한다. 가뭄의 특성과 기상인자(엘니뇨, 강수량 등)의 관계에 있어서 기상인자들의 평균을 이용하는 일반적인 회귀분석은 전체 데이터의 영향에 따른 가뭄특성인자와의 관계를 보여준다. 하지만 강수량과 가뭄과의 관계에서와 같이 강수량의 극값보다는 적은 강수량 혹은 무강우일수가 가뭄과 밀접한 관련을 보여준다. 이러한 점에서 이상치들에 영향을 배재할 수 있는 Quantile regression을 사용하여 Quantile에 따른 기상인자와 가뭄특성과의 관계를 규명하고 평가해 보고자 한다. 본 연구에서 적용한 Quantile Regression 기법은 회귀계수의 추정에 있어서 회귀인자의 신뢰성을 아래와 같은 Quantile-회귀계수 그래프를 통해 분석할 수 있으며, 로버스트 통계량의 특징인 분산이 적은 안정적인 추정량을 확보할 수 있는 장점을 갖는다. 아래식은 Quantile regression의 회귀계수 추정식을 나타낸다. $$arg\;in\;{n\\\;p(y_i-f(x_i,\;z_i,\;{\cdots}))\\ =1}$$ 여기서, $y_i$는 가뭄특성값을 $x_i$, $z_i$, $\cdots$는 기상인자를 나타낸다. $$p(y-q)={{\beta}(y-q)\;y{\geq_-}q \\ (1-{\beta})(q-y)\;y<q}$$ ${\beta}$는 quantile을 나타내며 0< ${\beta}$ <1범위를 갖는다.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.745-763
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• 2012

We use Kazhdan-Lusztig bases of representations of the symmetric group to express Pfaffians with entries $(a_i-a_j)h_{i+j}$. In the case where the parameters $a_i$ are specialized to successive powers of $q$, and the $h_i$ are complete functions, we obtain the $q$-discriminant.