• East Asian mathematical journal
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• v.32 no.5
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• pp.717-728
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• 2016

In this paper, we give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.

• The KSFM Journal of Fluid Machinery
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• v.14 no.4
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• pp.38-44
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• 2011

This paper deals with the detail rotordynamic analysis for BB5 eight stages pump as development of API 610 BB5 type pump. Dry-run analytical model, not considering operating fluid, and wet-run analytical model, considering operating fluid are established. In addition, plain circular and pressure dam bearings are chosen and it was discussed that each bearing has an effect on dynamic characteristics of pump rotor system. A rotordynamic analysis includes the critical speed map, Campbell diagram, stability, and unbalance response. As results, it was predicted that rated speed of the pump rotor passes through 1st critical speed in dry-run condition regardless of bearings, however, it was verified that, in wet-run condition, the rotor system doesn't have critical speeds even if more than twice rated speed. Hence the resonance problem caused by the critical speeds does not happen since actual operating is in wet-run condition including operating fluid. As a result of unbalance response analysis, the pump rotor has stable vibration response at rated speed, regardless of operating fluid and the proposed bearing types.