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Permanence of a Three-species Food Chain System with Impulsive Perturbations
Baek, Hunki,Lee, Hung-Hwan Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.3
We investigate a three-species food chain system with Lotka-Volterra functional response and impulsive perturbations. In [23], Zhang and Chen have studied the system. They have given conditions for extinction of lowest-level prey and top predator and considered the local stability of lower-level prey and top predator eradication periodic solution. However, they did not give a condition for permanence, which is one of important facts in population dynamics. In this paper, we establish the condition for permanence of the three-species food chain system with impulsive perturbations. In addition, we give some numerical examples.
PERTURBED TYPE RANDOM CANTOR SET
Baek, In Soo,Lee, Hung Hwan 경북대학교 위상수학 기하학연구센터 1999 硏究論文集 Vol.8 No.-
We define the perturbed type random Cantor set which is a variation of Falconer's random Cantor set, and calculate its Hausdorff dimension by using game fairer with time. It is a generalization of a Falconer's result about random Cantor set.
A medium-maturing, disease resistant and good-quality rice variety Geumanbyeo
Hung-goo Hwang,Yeon-gyu Kim,Ha-cheol Hong,Yong-hwan Choi,Man-kee Baek,Im-soo Choi,Young-chan Cho,Chang-in Yang,Hong-yeol Kim,Jong-doo Yea,Young-seop Shin,Kyung-ho Kang,Sang-nag Ahn 한국육종학회 2007 한국육종학회지 Vol.39 No.4
“Geumanbyeo” is a new japonica rice variety developed by the rice breeding team of National Institute of Crop Science, RDA in 2002, which was derived from a cross between SR11878-14-4-1 of good eating-quality and high yield potential, and Suweon345 of lodging tolerance and resistance to diseases. Geumanbyeo is a medium-maturing variety with heading date of August 12 on ordinary planting in the middle plain area. It has a semi-erect plant type with culm length of 82cm, erect pubescent leaf blade and slightly tough culm with good canopy architecture. Geumanbyeo has a little bit fewer tillers per hill, and more spikelets per panicle than Hwaseongbyeo. It is slightly less tolerant to the cold stress in terms of both heading delay and spikelet fertility than Hwaseongbyeo. This variety shows delayed leaf senescence and considerable tolerance to viviparous germination at ripening stage. It shows moderately resistant to leaf blast and K1 race of bacterial blight, but susceptible to virus diseases and insect pests. The milled rice of Geumanbyeo exhibits translucent, relatively clear non-glutinous endosperm and medium-short grain. It showed lower amylose content of 18.6% and similar gelatinization temperature and better palatability of cooked rice compared to Hwaseongbyeo. The milled rice yield of this variety is about 5.32 MT/ha at ordinary culture in local adaptability test for three years. Geumanbyeo would be highly adaptable to the central lowland and mid-southern mountainous areas in Korea. “Geumanbyeo” is a new japonica rice variety developed by the rice breeding team of National Institute of Crop Science, RDA in 2002, which was derived from a cross between SR11878-14-4-1 of good eating-quality and high yield potential, and Suweon345 of lodging tolerance and resistance to diseases. Geumanbyeo is a medium-maturing variety with heading date of August 12 on ordinary planting in the middle plain area. It has a semi-erect plant type with culm length of 82cm, erect pubescent leaf blade and slightly tough culm with good canopy architecture. Geumanbyeo has a little bit fewer tillers per hill, and more spikelets per panicle than Hwaseongbyeo. It is slightly less tolerant to the cold stress in terms of both heading delay and spikelet fertility than Hwaseongbyeo. This variety shows delayed leaf senescence and considerable tolerance to viviparous germination at ripening stage. It shows moderately resistant to leaf blast and K1 race of bacterial blight, but susceptible to virus diseases and insect pests. The milled rice of Geumanbyeo exhibits translucent, relatively clear non-glutinous endosperm and medium-short grain. It showed lower amylose content of 18.6% and similar gelatinization temperature and better palatability of cooked rice compared to Hwaseongbyeo. The milled rice yield of this variety is about 5.32 MT/ha at ordinary culture in local adaptability test for three years. Geumanbyeo would be highly adaptable to the central lowland and mid-southern mountainous areas in Korea.
Mutifractal Analysis of Perturbed Cantor Sets
Baek, Hun Ki,Lee, Hung Hwan Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
Let $\left{K_{\alpha}\right}_{{\alpha}{\in}{\mathbb{R}}}$ be the multifractal spectrums of a perturbed Cantor set K. We find the set of values ${\alpha}$ of nonempty set $K_{\alpha}$ by using the Birkhoff ergodic theorem. And we also show that such $K_{\alpha}$ is a fractal set in the sense of Taylor [12].
Scaling Law of the Hausdorff Measure
Baek, Hun-Ki,Lee, Hung-Hwan Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.4
We exhibit an example that the scaling property of Hausdorff measure on $\mathbb{R}^{\infty}$ does not hold.
LEE, HUNG HWAN,BAEK, HUN KI 경북대학교 위상수학 기하학연구센터 1999 硏究論文集 Vol.9 No.-
We figure out geometric properties of the Julia set J_(a) of cubic complex polynomial C_a(z)=z^(3) + az(a ∈ C) and the smallest ellipse which surrounds J_a.
Lee, Hung-Hwan,Baek, Hun-Ki 한국전산응용수학회 1997 Journal of applied mathematics & informatics Vol.4 No.1
We figure out geometric properties of the Julia set $J_{\alpha}$ of cubic complex polynomial $C_{\alpha}(z)=z^3 + {\alpha}z(\alpha \epsilon \mathbb{C})$ and the smallest ellipse which surrounds $J_{\alpha}$.