• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.67-71
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• 2005

We call K a (1, 1)-knot in M if M is a union of two solid tori $V_1\;and\;V_2$ glued along their boundary tori ${\partial}V_1\;and\;{\partial}V_2$ and if K intersects each solid torus $V_i$ in a trivial arc $t_i$ for i = 1 and 2. Note that every (1, 1)-knot is a tunnel number one knot. In this article, we determine when a tunnel number one knot is a (1, 1)-knot. In other words, we show that any tunnel number one knot with bridge number 3 is a (1, 1)-knot.

• 대한수학회지
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• 제47권1호
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• pp.113-122
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• 2010

In [4], we gave a condition for a pair of unknotting tunnels of a non-trivial tunnel number one link to give a genus three Heegaard splitting of the link complement. In this paper we prove the corresponding result for tunnel number one knots.

• 식물병연구
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• 제7권2호
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• pp.69-79
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• 2001

Meloidogyne arenaria race 2 (59%) is widely distributed, followed by M. incognita race 1 (23%), and an unknown race of M. incognita (18 ％) in greenhouses in southern Korea. The key character to distinguish between M. arenaria and M. incognita is excretory pore in female head. When oriental melon, Cucumis melo L., grafted on Shintozoa (Cucurbit maxima x Cu. moschata) is transplanted in February in a plastic tunnel inside a greenhouse infested with M. arenaria, nematodes produced egg masses on roots at 40 days after transplanting and the soil juveniles (J2) population reach maximum in July to 3,817/100 ㎤. Juveniles are distributed relatively uniform over the 180-cm-wide row horizontally and the highest density occurs at 0-25 cm soil depth. For the control of root-knot nematodes, rice rotation, solarization, and soil addition treatments are the most effective (P=0.05); treatments reduce number of J2 over 90% and increase yield two times. Corn retation, fosthiazate, and soil drying treatment are moderately effective, while sesame and green onion rotations are not effective. The relationship between M. arenaria and yield of oriental melon is adequately described by a linear regression model. In the test with wild Cucumis genetic sources introduced from U.S.Dept. of Agriculture (USDA), one of C.heptadactylus, two of C.anguria, two of C. anguria var. longaculeatus, nine of C. metuliferus are resistant to both species of root-knot nematodes.