• 대한수학회지
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• 제15권2호
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• pp.139-148
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• 1979

• 대한수학회지
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• 제22권1호
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• pp.1-8
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• 1985

• 대한수학회보
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• 제52권2호
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• pp.409-419
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• 2015

The concept of Cayley-symmetric semigroups is introduced, and several equivalent conditions of a Cayley-symmetric semigroup are given so that an open problem proposed by Zhu [19] is resolved generally. Furthermore, it is proved that a strong semilattice of self-decomposable semigroups $S_{\alpha}$ is Cayley-symmetric if and only if each $S_{\alpha}$ is Cayley-symmetric. This enables us to present more Cayley-symmetric semi-groups, which would be non-regular. This result extends the main result of Wang [14], which stated that a regular semigroup is Cayley-symmetric if and only if it is a Clifford semigroup. In addition, we discuss Cayley-symmetry of Rees matrix semigroups over a semigroup or over a 0-semigroup.

• Applied Microscopy
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• 제36권spc1호
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• pp.25-33
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• 2006

Nanofabrication with finely focused ion and electron beams is reviewed, and position and size controlled fabrication of nano-metals and -semiconductors is demonstrated. A focused ion beam (FIB) interface attached to a column of 200keV transmission electron microscope (TEM) was developed. Parallel lines and dots arrays were patterned on GaAs, Si and $SiO_2$ substrates with a 25keV $Ga^+-FIB$ of 200nm beam diameter at room temperature. FIB nanofabrication to semiconductor specimens caused amorphization and Ga injection. For the electron beam induced chemical vapor deposition (EBI-CVD), we have discovered that nano-metal dots are formed depending upon the beam diameter and the exposure time when decomposable gases such as $W(CO)_6$ were introduced at the beam irradiated areas. The diameter of the dots was reduced to less than 2.0nm with the UHV-FE-TEM, while those were limited to about 15nm in diameter with the FE-SEM. Self-standing 3D nanostructures were also successfully fabricated.