• Journal of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.169-177
• /
• 2003

Recently, K. Watanabe Showed that the Hilbert-Kunz multiplicity of a toric ring is a rational number. In this paper we give an explicit formula to compute the Hilbert-Kunz multiplicity of two-dimensional toric rings. This formula also shows that the Hilbert-Kunz multiplicity of a two-dimensional non-regular toric ring is at least 3/2.

• Journal of applied mathematics & informatics
• /
• v.3 no.1
• /
• pp.65-78
• /
• 1996

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the rela-tions among the generators. Using this fact we have described explic-itly the Chow ring for a Q-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. In this paper we calculate the Chow ring for 3-dimensional Q-factorial toric varieties having one bad isolated singularity.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.761-765
• /
• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• Tribology and Lubricants
• /
• v.35 no.4
• /
• pp.222-228
• /
• 2019

As rubber products such as O-rings, which are also known as packings or toric joints, come in regular, long term contact with liquid fuel, they can eventually swell, become mechanically weakened, and occasionally crack; this diminishes both their usefulness and intrinsic lifetime and could cause leaks during the steady-state flow condition of the fuel. In this study, we evaluate the lifetime of such products through compression set tests of FKM, a family of fluorocarbon elastomer materials defined by the ASTM international standard D141; these materials have great compression, sunlight, and ozone resistance as well as a low gas absorption rate. In this process, O-rings are immersed in the liquid fuel of airtight containers that can be expressed as a compression set, and the liquid fuel leakage in a flow rig tester at variable temperatures over 12 months is investigated. Using the Power Law model, our study determined a theoretical O-ring lifetime of 2,647 years, i.e. a semi-permanent lifespan, by confirming the absence of liquid fuel leakage around the O-ring assembled fittings. These results indicate that the FKM O-rings are significantly compatible for fuel tests to evaluate long-term sealing conditions.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.331-346
• /
• 2016

The primary aim of this paper is to generalize a theorem of Hirzebruch for the complex 2-dimensional Bott manifolds, usually called Hirzebruch surfaces, to more general Bott towers of height n. To do so, we first show that all complex vector bundles of rank 2 over a Bott manifold are classified by their total Chern classes. As a consequence, in this paper we show that two Bott manifolds $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n)$ and $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n^{\prime})$ are isomorphic to each other, as Bott towers if and only if both ${\alpha}_n{\equiv}{\alpha}_n^{\prime}$ mod 2 and ${\alpha}_n^2=({\alpha}_n^{\prime})^2$ hold in the cohomology ring of $B_{n-1}({\alpha}_1,{\ldots},{\alpha}_{n-1})$ over integer coefficients. This result will complete a circle of ideas initiated in [11] by Ishida. We also give some partial affirmative remarks toward the assertion that under certain condition our main result still holds to be true for two Bott manifolds just diffeomorphic, but not necessarily isomorphic, to each other.