• Honam Mathematical Journal
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• v.4 no.1
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• pp.75-84
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• 1982

Let M be a complete and orientable hypersurface of an odd-dimensional sphere $S^{2n+1}$ with quasi-integrable $(f,\;g,\;u,\;{\nu},\;{\lambda})$ -structure. The purpose of the present paper is to prove the following two theorems. (I) If the scalar curvature of M is constant and the function $\lambda$ is not locally constant, then M is a great sphere $S^{2n}$(1) or a product of two spheres with the same dimension $S^{n}(1/\sqrt{2}){\times}S^{n}(1/\sqrt{2})$. (II) Suppose that the sectional curvature of the section $\gamma(u,\;{\nu})$ spanned by u and $\nu$ is constant on M and M is compact. If the second fundamental tensor H of M is positive semi-definite and satisfies trace $$^{t}HH{\leq_-}{2n}$$, then M is a great sphere $S^{2n}$ (1) or a product of two spheres $S^{n}{\times}S^{n}$ or $S^{p}{\times}S^{2n-p}$, p being odd.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1037-1049
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• 2015

It is well-known that the spectrum of a $spin^{\mathbb{C}}$ Dirac operator on a closed Riemannian $spin^{\mathbb{C}}$ manifold $M^{2k}$ of dimension 2k for $k{\in}{\mathbb{N}}$ is symmetric. In this article, we prove that over an odd-dimensional Riemannian product $M^{2p}_1{\times}M^{2q+1}_2$ with a product $spin^{\mathbb{C}}$ structure for $p{\geq}1$, $q{\geq}0$, the spectrum of a $spin^{\mathbb{C}}$ Dirac operator given by a product connection is symmetric if and only if either the $spin^{\mathbb{C}}$ Dirac spectrum of $M^{2q+1}_2$ is symmetric or $(e^{{\frac{1}{2}}c_1(L_1)}{\hat{A}}(M_1))[M_1]=0$, where $L_1$ is the associated line bundle for the given $spin^{\mathbb{C}}$ structure of $M_1$.

• Korean Journal of Environment and Ecology
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• v.12 no.4
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• pp.361-372
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• 1999

Thirty-two plots have been set up and surveyed to investigate the plant community structure and distribution density of Pinus thunbergii-P. densiflora forest in Kojedo District, Hallyo-Haesang National Park. By DCA ordination technique P. thunbergii-P. densiflora forest was classified into P. thunbergii community, P. thunbergii-P. densiflora community, and P. densiflora community. The trend of plant community succession was invalid. The results of simple regression analysis between mean DBH(cm), mean distribution distance(m), and number of individual of P. thunbergii and P. densiflora were as follows: Distribution distance(m) = 0.094$\times$DBH(cm)-0.1248, Number of individual=1,820.1$\times$(cm)$DBH^{-1.6734}$ , Distribution distance(m)=6.6805$\times$Number of $individual^{-0.5425}$ .

• Journal of Plant Biology
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• v.25 no.3
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• pp.123-133
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• 1982

The tropic structure and the function of a small pone ecosystem under the tree stand were studied in terms of energy flow. About 28% of total solar radiation was intercepted by the tree canopy over the pond. Primary producers converted 1.1%(3,382 kcal$\cdot$$m^{-2}$$\cdot$$y^{-1}$) of solar radiation (320,000 kcal$\cdot$$m^{-2}$$\cdot$$y^{-1}$) into gross primary production. The amount of energy availble to the pond snail was 1,683 kcal.m-2.y-1 of the net production by primary producers and 1,033 kcal$\cdot$$m^{-2}$$\cdot$$y^{-1}$ of the litter fallen into the pond. The amount of gross secondary production by the pond snail was 245 kcal$\cdot$$m^{-2}$$\cdot$$y^{-1}$. Judging from these, supply of both net primary production and the litter was indispensable for the maintenance of the pond ecosystem. The total amont of energy as gross primary production plus litter was 4,415 kcal$\cdot$$m^{-2}$$\cdot$$y^{-1}$(100%). Since the total respiration loss was calculated to be 1,917 kcal$\cdot$$m^{-2}$$\cdot$$y^{-1}$(43.4%), the rate of energy accumulation in the pond estimated to 56.6%.

• Korean Journal of Soil Science and Fertilizer
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• v.31 no.4
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• pp.334-341
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• 1998

Sodium hydroxide concentrations were adjusted to 2.0, 2.5, 3.0 and 3.5M by dissolution in seawater. The fly ash was hydrothermally reacted with sodium hydroxide solutions (1:8, W:V) at $100^{\circ}C$ under the closed system. X-ray diffractogram proved that Na-P1 type zeolite was produced from bituminous coal fly ash. It is different from the X-ray of artificial zeolite produced by using sodium hydroxide solution dissolving in distilled water. Solid sieve structure was developed well by hydrothermal reaction with the ash and 3.0M sodium hydroxide. However chinks were observed in the structure of the product by 3.5M sodium hydroxide. CEC of the artificial zeolite was $244.5cmol^+\;kg^{-1}$ at 2.0M, 259.8 at 3.0M, 263.4 at 3.0M and 179.8 at 3.5M after 24 hours hydrothermal reaction; Artificial zeolite having high CEC, above $244.5cmol^+\;kg^{-1}$ could produce by using lower concentration of NaOH prepared in seawater than other production methods.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.34 no.5
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• pp.493-501
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• 2001

A study on the community structure of macrobenthos was accomplished around Kadugdo, a south coast of Korea. Sampling was performed bimonthly using a Smith-McIntyre grab ($0.05 m^2$) at ten stations from January to November, 1998. A total of 260 species was sampled with mean density of $1,729 ind./m^2$and biomass of $154.7 gwwt./m^2$during the study periods. Of these species, there were 96 species of arthropods ($37.0\%$), 89 species of annelids ($34.2\%$), 45 species of molluscs ($17.3\%$) and 30 species of others ($11.5\%$). Annelids were density-dominant faunal group with a mean density of $1,263 ind./m^2$which occupied $73.0\%$ of the total individual of benthic animals. Molluscs were represented as biomass-dominant faunal group with a mean biomass of $99.5 gwwt./m^2$ ($64.3\%$ of total biomass). The density-dominant species were a bivalvia Theora fragilis ($194 ind./m^2$) and five species of polychaetes, Lumbrineris longifolia ($177 ind./m^2$), Chaetozone setosa ($150 ind./m^2$), Sternaspis scutata ($116 ind./m^2$), Sigambra tentaculata ($106 ind./m^2$) and Hemipodus yenourensis ($94 ind./m^2$). And major biomass-dominant species was a bivalvia Ruditapes philippinarum ($45.6 gwwt./m^2$). Clustering analysis showed that the study area could be divided into two station groups and three stations: southwestern part of Kadugdo effected on Chinhae Bay, fisheries farming area and eastern part of Kadugdo effected on Nakdong River estuary.

• Journal of Korean Society of Forest Science
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• v.85 no.2
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• pp.260-270
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• 1996

Structure and dynamics of Pinus densiflora community in Mt. Kaya were studied to provide the information needed for management of Pinus densiflora forest in the southern inland of Korea. Stratification structure of Pinus densiflora community in the lower and middle slope consisted of tree layer(10~15m), subtree layer(4~10m), shrub layer(1~4m), and herb layer(below 1m), while in the rock zone of ridge and top area consisted of tree layer(7~10m), subtree layer(2~7m), shrub layer(1~2m), and herb layer(below 1m). According to the diameter distribution of tree species in Pinus densiflora community, secondary Pinus densiflora forest will gradually decline. Its forest may be replaced by Quercus mongolica, Quercus serrata, Carpinus laxiflora, C. cordata, and Fraxinus rhychophylla in the lower slope, and by Quercus mongolica in the middle slope. Pinus densiflora forest has its seedlings and saplings in ridge and top area, so it may be sustained. By taking cores from Pinus densiflora trees in research area, it could be obtained that in the lower and middle slope, age of Pinus densiflora forest was about 80~90 years old. When the age of its trees was about 72~80 years old, withering trees of standing dead occurred. Disturbance regime of Pinus densiflora community in Mt. Kaya consisted of standing dead, uprooting and limbfall, these were 70.6%, 17.6% and 11.8% respectively. It takes about 100~110 years for advance growth of Pinus densiflora in ridge and top area to reach tree layer. During the period, it has twice chances of disturbance in standing dead. Annual diameter growth of Pinus densiflora was 2.45~2.9mm in the lower and middle slope, while it was 1.75mm in ridge and top region, by measuring cores.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1069-1083
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• 2016

In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M: (1) M is e-local; (2) $Rad_e(M)$ is a maximal submodule of M and every proper essential submodule of M is contained in a maximal submodule; (3) M has a unique essential maximal submodule and every proper essential submodule of M is contained in a maximal submodule.

• 한국해양학회지
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• v.15 no.1
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• pp.58-61
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• 1980

Water movements at nine different layers were observed from July 31 to August 2, 1976 at station H, which has water depth 42 meters and 3km far from the coast of Wolsong, and dispersion coefficients were computed from these current data, then relative magnitudes of dispersion coefficients were calculated at each layers. Relative magnitudes of dispersion coefficients based on the surface value are 62% at 5m layer, 24% at 10m layer, 20% at 15m and 20m layers, 17% at 25m layer, 24% at 30m layer, 28% at 35m layer and 15% at bottom layer, respectively.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.99-107
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• 2018

This article considers a robust Kalman filter from the M-estimation point of view. Pak (Journal of the Korean Statistical Society, 27, 507-514, 1998) proposed a particular M-estimating function which has the data-based shaping constants. The Kalman filter with the proposed M-estimating function is considered. The structure and the estimating algorithm of the Kalman filter accompanying the M-estimating function are mentioned. Kalman filter estimates by the proposed M-estimating function are shown to be well behaved even when data are contaminated.