• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• East Asian mathematical journal
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• v.40 no.3
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• pp.287-293
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• 2024

For a nondegenerate irreducible projective variety, it is a classical problem to describe its defining equations and the syzygies among them. In this paper, we precisely determine a minimal generating set and the minimal free resolution of defining ideals of some rational curves of maximal genus in ℙ³.

• East Asian mathematical journal
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• v.40 no.1
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• pp.75-83
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• 2024

For a reduced, irreducible and nondegenerate curve C ⊂ ℙ^r of degree d, it was shown that the arithmetic genus g of C has an upper bound π₀(d, r) by G. Castelnuovo. And he also classified the curves that attain the extremal value. These curves are arithmetically Cohen-Macaulay and contained in a surface of minimal degree. In this paper, we investigate the arithmetic genus of curves lie on a surface of minimal degree - the Veronese surface, smooth rational normal surface scrolls and singular rational normal surface scrolls. We also provide a construction of curves on singular rational normal surface scroll S(0, 2) ⊂ ℙ³ which attain the maximal arithmetic genus.

• The Journal of Korean Medicine
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• v.25 no.1
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• pp.60-71
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• 2004

Objectives : We have examined the relaxational response to the water extract of genus Panax in rat thoracic aorta and mesenteric artery. Methods : Segments of thoracic aorta and mesenteric artery obtained from rats immediately after delivery were mounted in organ baths superfused on a polygraph. Results : We found that the thoracic aorta segments responded to the water extract of genus Panax with a dose-dependent vasorelaxation. At $10^{-5}m$ 5-hydroxytrptamine (5-HT), the maximal contraction force were 94.9% of the maximum KCl-response. At $10^{-5}m$ 5-HT - induced contraction, The contractile response of thoracic aortic rings were inhibited by 54.7%, 36.3% and 31.3% after addition of the high concentration (100 mg/ml) of water extract of Panax ginseng, Panax japonicus and Panax quinquefolium. The contractile response of mesenteric arteries were inhibited by 88.3%, 87.7%, and 70.3% after addition of the high concentration (100 mg/ml) of water extract of Panax ginseng, Panax japonicus and Panax quinquefolium. Conclusions : In conclusion, water extract of genus Panax - induced relaxation in the isolated rat thoracic aorta and mesenteric artery were composed of endothelium - independent relaxation and dose - dependent relaxation.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.965-976
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• 2008

In this article, we constructively prove that on a surface S with genus g$\geq$2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.

• The Korean Journal of Food And Nutrition
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• v.8 no.4
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• pp.275-279
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• 1995

A bacterium L-10 which produce mush of glutamic acid was Isolated from soil and identified as the genus Pserdomonas. The maximal glutamic acid production was obtained when the strain was cultured at 3$0^{\circ}C$ for 30 hrs in the optimal medium containing 5% glucose, 0.5% each of urea and yeast extract, 0.1% K2HP04, 0.02% MgSO4.7H20, 0.3% (NH, )rHP04, 0.5ug/l biotin and Initial pH 7.0, and then final glutamic acid production under the above conditions was 1.2mg/ml of cell cultures.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.593-610
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• 2010

We consider a degeneration of genus 2 curves, which is opposite to maximal degeneration in a sense. Such a degeneration of curves yields a variation of mixed Hodge structure with monodromy weight filtration. The mixed Hodge structure at each fibre, which is different from the limit mixed Hodge structure of Schmid and Steenbrink, can be realized as $H^1$ of a noncompact singular elliptic curve. We also prove that the pull back of the above variation of mixed Hodge structure to a double cover of the base space comes from a family of noncompact singular elliptic curves.

• Korean Journal of Agricultural Science
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• v.25 no.1
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• pp.124-130
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• 1998

An alkalophilic bacterium, the strain AC-711 as a potent producer of alkaline cellulase, was selected among many isolates from soil environments. Morphological, physiological and chemical characteristics of the strain AC-711 suggested that it belongs to the genus Pseudomonas according to the Bergey's Manual of Systematic Bacteriology, however the G+C mol% (54.43) of its chromosomal DNA is lower than the normal values of the genus. The major cell wall fatty acids were determined as 15:0 and 17:0 anteiso. The production of alkaline CMCase by the strain was maximal when grown on the mediun containing 1% carboxymethyl cellulose, 0.1% $KH_2PO_4$, 0.02% $CoCl_2$, 0.02% Tween 80, 0.5% $Na_2CO_3$, 0.8% yeast extract, pH 10.3 at $30^{\circ}C$ for 3 days, and the most of enzyme was excreted into culture mediun.

• The Journal of Korean Medicine
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• v.24 no.4
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• pp.87-91
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• 2003

Objectives: To examine the relaxational response to the water extract of Rheum palmatum L. and Rheum undulatum L. on rat thoracic aorta and abdominal aorta. Methods: Segments of thoracic aorta and abdominal aorta obtained from rats immediately after delivery were mounted in organ baths superfused on a polygraph. Results : We found that the thoracic aorta segments responded to the water extract of genus Rheum with a dose-dependent vasorelaxation. At $10^{-4}$ M 5-HT, the maximal contraction force was 93.5% of the maximum KCI-response. The 5-HT induced contractions at $10^{-4}$ M were inhibited by 86.4% and 62.1 % after addition of the high concentrations of R. palmatum root (RPR) and leaf (RPL) and R. undulatum root (RUR) and leaf (RUL). At 10 mg/ml RPR and RUR, the relaxational response at thoracic aorta and abdominal aorta with and without endothelium were 86.4%, 83.2%, 85.8%, and 62.1% of the maximum 5-HT induced contraction. Conclusion: Our result showed that RPL and RUL induced dose-dependent vasorelaxation on rat thoracic aorta and abdominal aorta, and that RPL and RUL roots have more potent effects than the leaves.