• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.13-32
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• 1994

Let A(n) and B(n) be sequences of $m \times m$ random matrices with a joint asymptotic distribution as $n \to \infty$. The asymptotic distribution of the ordered roots of $$\mid$A(n) - f B(n)$\mid$ = 0$ depends on the multiplicity of the roots of a determinatal equation involving parameter roots. This paper treats the asymptotic distribution of the roots of the above determinantal equation in the case where some of parameter roots are zero. Furthermore, we apply our results to deriving the asymptotic distributions of the eigenvalues of the MANOVA matrix in the noncentral case when the underlying distribution is not multivariate normal and some parameter roots are zero.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권2호
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• pp.185-188
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• 2010

In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations.

• The Korean Journal of Ecology
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• 제17권2호
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• pp.113-119
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• 1994

Vertical and horizontal distribution and seasonal changes of fine roots as well as inorganic nitrogen content in soil were determined in Quercus mongolica and Quercus acutissima stands in Mt. Taemosan, Seoul. The vertical distribution of fine rooth phytomass showed a power-functional decrease as descending soil depth. Fine root phytomass was 170 g $DM/m^2$(46%) and 225 g $DM/m^2$(47%) in top soil of 5 cm depth, and 370 g $DM/m^2$ and 480 g $DM/m^2$ from soil surface to 50 cm depth in Q. mongolica and Q. acutissima stands, respectively. Fine roots in relation to the distance from the nearest tree were evenly distributed horizontally in both stands. Fine roots phytomass in top soil of 5 cm depth reached a peak in June, and thereafter decreased gradually in both stands. Patterns of seasonal changes in fine root phytomass were closely related to inorganic nitrogen and moisture content.

• Industrial Engineering and Management Systems
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• 제12권3호
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• pp.281-287
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• 2013

In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

• Journal of Forest and Environmental Science
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• 제11권1호
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• pp.22-39
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• 1995

본 연구는 "강원도(江原道) 소나무임(林)의 특성(特性)에 관한 종합적(綜合的) 연구(硏究)(III) - 강원대학교(江原大學校) 구내림(構內林)의 근계(根系) 형태(形態)와 분포(分布)에 대하여-"에 이어 강원도(江原道) 명주군(溟州郡) 왕산면(旺山面) 송현리(松峴里) 사유임내(私有林內) 소나무임(林)의 근계(根系) 형태(形態) 및 분포(分布)에 대하여 규명하였다. 5개의 공시목(供試木)에 대하여 조사한 결과, 뿌리의 형태(形態)는 주근(主根) 및 수평근(水平根)이 수직(垂直)으로 잘 발달하였다. 뿌리의 분포(分布)에 있어서 크기별로는 세근(細根)은 대부분 점재(点在)(+)하였지만, 세근지수(細根指數) 1(+~20%)의 방형구(方形區)도 7개소나 분포하였으며, 태근(太根)의 크기는 직경이 대부분 0.20cm였다. 깊이별로는 태근(太根), 세근(細根) 모두 지표(地表)의 10~30cm 부근에 50%이상 집중되어 있었다.

• Mycobiology
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• 제31권1호
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• pp.1-8
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• 2003

Detailed structures of ectomycorrhizae formed in Pinus roots were observed with various microscopes: light, fluorescence, and scanning electron microscopes. The mantles and Hartig nets commonly found in the structure of ectomycorrhiza were newly observed according to developmental stage by various staining. The mycelia were observed to be composed of coiled types on the surface of epidermal root during early stage and fused to form mantles of smooth fungal layers, loosing mycelia with some viscous liquid secreted. The ectomycorrhizal hyphae in anatomical roots penetrated the cortical layer and formed obviously mantle and Hartig net. The round spots of ectomycorrhizal mycelia were observed morphological distribution from the cortical layer to vascular bundle of stele in the ectomycorrhizal roots of Pinus species and especially scattered at the area of meristem at the root tip as longitudinal sections. Those mycelia penetrated seemed to move into other roots by means of vascular bundle of ectomycorrhizal roots and newly form ectomycorrhizal roots of dichotomous branches.

• 한국작물학회지
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• 제43권1호
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• pp.38-43
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• 1998

This study examined root growth and distribution under the direct seeding of rice cultivars developed in Korea, Japan, and the U.S. Cultivars from the U.S., especially 'M202' and 'Caloro', had a high ratio of the dry matter partitioning for root and top plant components. Caloro had high root and top growth. 'Koshihikari' from Japan showed the lowest ratio of R/T (root/total dry matter) due to the small amount of root and top plant growth. Most Japanese cultivars except transplanted 'Hatsuboshi' showed low ratio of R/T. Patterns of root distribution for each soil block were recorded by the root box-pin board method. Roots of all cultivars were distributed in blocks A, C, and E in the middle of box, i.e., just below the plant base. Roots of 'Dongjin', M202, and Caloro were distributed deeper than the others. Roots of transplanted Hatsuboshi developed much better than direct seeded Hatsuboshi. Total root weight density was highest in Caloro followed by Dongjin, 'Gancheok', 'Calrose', and the others. The root density of Caloro was twice as much as those of the others except Dongjin. According to cumulative percentages of root distribution on each soil layer, roots of most cultivars were distributed below 20cm. The U.S. cultivars showed vertically well developed root systems as compared to others. A large amount of roots were distributed in the top 15cm of soil layer for Hatsuboshi and Koshinikari, and their root systems appeared to be shallow. In contrast, the rates of root distribution in the top 10cm of soil layer were low for Dongjin, Calrose, and Caloro. These cultivars had relatively deep root systems.

• Journal of Forest and Environmental Science
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• 제10권1호
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• pp.8-24
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• 1994

수목(樹木)의 뿌리는 수목(樹木)의 생장(生長)과 토양(土壤)의 구조개선(構造改善)에 밀접한 관계가 있음에도 불구하고 지하부(地下部)에 위치하고 있으므로 연구가 미진한 상태이다. 따라서 각 수종(樹種)의 근계(根系)의 발달상태를 파악하는 것은 그 수종(樹種)의 특성 파악과 뿌리가 지표고정(地表固定)에 미치는 영향을 파악하는데 기초자료로 활용할 수 있다. 본 연구에서는 강원도(江原道) 소나무림(林)의 특성을 파악하기 위한 기초연구의 일부로서 일차적으로 강원대학교(江原大學校) 구내(構內) 소나무림(林)의 근계(根系) 형태(形態) 및 분포(分布)에 대하여 규명하였다. 5개의 공시목(供試木)에 대해 조사한 결과 뿌리의 형태(形態)는 수평근(水平根)이 잘 발달되어 있었다. 뿌리의 분포(分布)에 있어서 크기별로는 세근(細根)은 대부분이 점재(点在)(+)하고 있었음, 태근(太根)은 0.2cm가 대부분이었다. 깊이별로는 태근(太根), 세근(細根) 모두가 10~30cm에서 60~70% 이상 집중되었으며, 태근(太根)은 주로 0.9cm 이하였고, 세근(細根)은 대부분이 점재(点在)(+)하고 있었다.

• The Korean Journal of Ecology
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• 제17권3호
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• pp.261-275
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• 1994

수도권과 그 주변의 33장소의 리기다소나무 숲에서 연륜생장과 잔뿌리의 수직분포를 조사하였다. 생리적 연령이 16년과 20년 사이의 연륜의 생장은 전원지보다 도심지에서 불량하였다. 그리고 최근 5년간 (1985~1989)의 연륜생장은 연령 11년~20년, 연령 21년~30년 및 연령 31년~40년 그룹 모두에서 도심지에서 거리가 멀어짐에 따라 양호하였다. 리기다소나무 잔뿌리의 양은 도심지, 주변지 및 전원지 모두에서 토양의 깊이가 깊어짐에 따라 지수함수적으로 감소하였고, 그 양은 전원지에 비해 도심지에서 매우 적었다. 그리고 전원지의 잔뿌리의 수직분포와 비교해 볼 때, 도심지에서 잔뿌리는 토양층보다 낙엽층에 많이 분포하였다. 그리고 낙엽층 속의 잔뿌리 양과는 유의한 음의 상관이 있었다. 이들 결과로부터 도심지에서 리기다소나무 생장감소는 잔뿌리 생장감소와 잔뿌리의 비정상적인 수직분포에 원인이 있는 것으로 판단되었다.

• Journal of Ecology and Environment
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• 제32권3호
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• pp.159-165
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• 2009

The purpose of this study was to investigate the effects of thinning on fine root biomass and vertical distribution. and litterfall amount in a 50 year old Pinus koraiensis plantation in Chuncheon, Kangwon Province. Fine root (< 2 mm in diameter) biomass ($367\;g/m^2$) in the site 'OC_75', thinning once in 1975, was 68% of those in the site 'CON', no thinning after planting, and in the site 'TC_00', thinning twice in 1975 and 2000. There were no significant differences of dead roots among treatments. Diameter $0{\sim}1\;mm$ roots were vertically decreased only in the TC_00 site. The litterfall was very similar between OC_75 ($5.2\;Mg\;ha^{-1}\;yr^{-1}$) and TC_00 ($4.7\;Mg\;ha^{-1}\;yr^{-1}$), but the composition of litterfall was different: The proportion of leaves and branches was 80% and 13% in OC_75 and 56% and 36% in TC_00, respectively. Reduction of P. koraiensis density by thinning decreased leaf litter as well as fine roots of P. koraiensis, but increased fine roots production by neighboring understory plants offset the reduction of fine roots of P. koraiensis. We suggest that belowground as well as aboveground responses, including both over- and understory vegetation, should be considered to measure the responses of trees in thinned forest ecosystems.