• 충청수학회지
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• 제26권2호
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• pp.259-268
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• 2013

In this paper, we define the Banach-valued strong $M_{\alpha}$-integral and study the primitive of the strong $M_{\alpha}$-integral in terms of the $M_{\alpha}$-variational measures. We also prove that every function of bounded variation is a multiplier for the strong $M_{\alpha}$-integral.

• 한국재료학회지
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• 제17권5호
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• pp.250-255
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• 2007

The alloying effects on the electronic structures of Zinc are investigated using the relativistic $DV-X{\alpha}molecular$ orbital method in order to obtain useful information for alloy design. A new parameter which is the d obital energy level(Md) and the bonder order(Bo) of alloying elements in Zinc was introduced and used for prediction of the mechanical properties. The Md correlated with the atomic radius and the electronegativity of elements. The Bo is a measure of the strength of the covalent bond between M and X atoms. First-principles calculations of electronic structures were performed with a series of models composed of a MZn18 cluster and the electronic states were calculated by the discrete variational- $X{\alpha}method$ by using the program code SCAT. The central Zinc atom(M) in the cluster was replaced by various alloying elements. In this study energy level structures of pure Zinc and alloyed Zinc were calculated. From calculated results of energy level structures in MZn18 cluster, We found Md and Bo values for various elements of Zn. In this work, Md and Bo values correlated to the tensile strength for the Zn. These results will give some guide to design of zinc based alloys for high temperature applications and it is possible the excellent alloys design.