• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.15-23
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• 1996

Let C be a category of (pointed) spaces. For $X, Y \in C$ we denote the wedge (or one point union) by $X \vee Y$ and the cartesian product by $X \times Y$. Let $Z \in C$; we say that Z cancels with respect to wedge (resp. cartesian product) and C, if for all $X, Y \in C$ the existence of a homotopy equivalence $X \vee Z \to Y \vee Z$ implies the existence of a homotopy equivalence $X \to Y$ (resp. for cartesian product). If this does not hold, we say that there is a non-cancellation phenomenon involving Z (and C).

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.407-421
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• 2004

By using a recursive algorithm, we construct edge-coloured graphs representing products of spheres and consequently we give upper bounds for the regular genus of ${\mathbb{S}}^{m}\;\times\;{\mathbb{S}}^{n}$, for each m, n > 0.

• Bulletin of the Korean Chemical Society
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• v.32 no.5
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• pp.1534-1538
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• 2011

Uniform, hollow nanosilica spheres were prepared by the chemical coating of cationic polystyrene (cPS) with tetraethylorthosilicate (TEOS), followed by calcination at 600 $^{\circ}C$ under air. cPS was synthesized by surfactant-free emulsion polymerization using 2,2'-azobis (2-methyl propionamidine) dihydrochloride as the cationic initiator, and poly(vinyl pyrrolidone) as a stabilizer. The resulting cPS spheres were 280 nm in diameter, and showed monodispersion. After coating, the hollow silica product was spherically shaped, and 330 nm in diameter, with a narrow distribution of sizes. Dispersion was uniform. Wall thickness was 25 nm, and surface area was 96.4 $m^2/g$, as determined by BET. The uniformity of the wall thickness was strongly dependent upon the cPS surface charge. The effects of TEOS and ammonia concentrations on shape, size, wall thickness, and surface roughness of hollow $SiO_2$ spheres were investigated. We observed that the wall thicknesses of hollow $SiO_2$ spheres increased and that silica size was simultaneously enhanced with increases in TEOS concentrations. When ammonia concentrations were increased, the irregularity of rough surfaces and aggregation of spherical particles were more severe because higher concentrations of ammonia result in faster hydrolysis and condensation of TEOS. These changes caused the silica to grow faster, resulting in hollow $SiO_2$ spheres with irregular, rough surfaces.

• East Asian mathematical journal
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• v.11 no.2
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• pp.351-357
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• 1995

• East Asian mathematical journal
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• v.11 no.1
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• pp.87-113
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.38-40
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• 1984

• East Asian mathematical journal
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• v.22 no.2
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• pp.223-238
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• 2006

• East Asian mathematical journal
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• v.11 no.2
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• pp.327-340
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• 1995

• Honam Mathematical Journal
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• v.5 no.1
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• pp.215-225
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• 1983

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.231-240
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• 2013

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.