• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1683-1709
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• 2015

Let (${\Omega}$, S) be an association scheme where ${\Omega}$ is a non-empty finite set and S is a partition of ${\Omega}{\times}{\Omega}$. For a positive integer k we say that (${\Omega}$, S) is k-equivalenced if each non-diagonal element of S has valency k. In this paper we focus on 4-equivalenced association schemes, and prove that they are transitive.

• The Journal of the Petrological Society of Korea
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• v.19 no.1
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• pp.67-87
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• 2010

This article deal with petrotectonic setting and petrogenesis from petrography and chemical analyses of the Cretaceous volcanic and intrusive rocks in the Cheolwon basin. The volcanic rocks are composed of basalts in Gungpyeong Formation, Geumhaksan Andesite, and rhyolitic rocks (Dongmakgol Tuff, Rhyolite and Jijangbong Tuff), and intrusive rocks, Bojangsan Andesite, granite porphyry and dikes. According to petrochemistry, these rocks represent medium-K to high-K basalt, andesite and rhyolite series that belong to calc-alkaline series, and generally show linear compositional variations of major and trace elements with increase in $SiO_2$ contents, on many Harker diagrams. The incompatible and rare earth elements are characterized by high enrichments than MORB, and gradually high LREE/HREE fractionation and sharp Eu negative anomaly with late strata, on spider diagram and REE pattern. Some trace elements exhibit a continental arc of various volcanic arcs or orogenic suites among destructive plate margins on tectonic discriminant diagrams. These petrochemical data suggest that the basalts may have originated from basaltic calc-alkaline magma of continental arc that produced from a partial melt of upper mantle by supplying some aqueous fluids from a oceanic crust slab under the subduction environment. The andesites and rhyolites may have been evolved from the basaltic magma with fractional crystallization with contamination of some crustal materials. Each volcanic rock may have been respectively erupted from the chamber that differentiated magmas rose sequentially into shallower levels equivalenced at their densities.