• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.741-750
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• 2018

Antoine showed that the properties of Armendariz and NI are independent of each other. The study of Armendariz and NI rings has been doing important roles in the research of zero-divisors in noncommutative ring theory. In this article we concern a new class of rings which generalizes both Armendariz and NI rings. The structure of such sort of ring is investigated in relation with near concepts and ordinary ring extensions. Necessary examples are examined in the procedure.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.85-101
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• 2018

Let S be a polynomial ring over a field K, with a monomial order ${\prec}$, and let I be an unmixed graded ideal of S. In this paper we study two functions associated to I: The minimum distance function ${\delta}_I$ and the footprint function $fp_I$. It is shown that ${\delta}_I$ is positive and that $fp_I$ is positive if the initial ideal of I is unmixed. Then we show that if I is radical and its associated primes are generated by linear forms, then ${\delta}_I$ is strictly decreasing until it reaches the asymptotic value 1. If I is the edge ideal of a Cohen-Macaulay bipartite graph, we show that ${\delta}_I(d)=1$ for d greater than or equal to the regularity of S/I. For a graded ideal of dimension ${\geq}1$, whose initial ideal is a complete intersection, we give an exact sharp lower bound for the corresponding minimum distance function.

• Polymer(Korea)
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• v.27 no.3
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• pp.210-216
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• 2003

4-Vinyl-1-cyclohexene diepoxide (VCE)/diglycidyl ether of bisphenol-A (DGEBA) epoxy blends with benzylquinoxalinium hexafluoroanti-monate were cured using an electron-beam technique. The effect of DGEBA content to VCE on cure behavior, thermal stabilities, and mechanical properties was investigated. The composition of VCE/DGEBA blend system vaned within 100:0, 80:20, 60:40, 40:60, 20:80, and 0:100 wt%. The cure behavior and thermal stability of the cured specimens was monited by near-infrared spectroscopy and thermogravimetric analysis, respectively. Also, the critical stress intensity factor ($_{4}$) test of the cured specimens was performed to study the mechanical interfacial properties. As a result, the decreases of short side-chain structure and chain scission were observed in NIR measurements as the DGEBA content increases, resulting in varying the hydroxyl and carbonyl groups. And, the initial decomposition temperature (IDT), temperature of maximum weight loss (T$\_$max/), and decomposition activation energy (E$\_$d/) as thermal stability factors were increased with increasing the DGEBA content. These results could be explained by mean of decreasing viscosity, stable aromatic ring structure, and grafted interpenetrating polymer network with increasing of DGEBA content. Also, the maximum $_{4}$ value showed at mixing ratio of 40:60 wt% in this blend system. in this blend system.