• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.749-762
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• 2017

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.

• Computers and Concrete
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• v.12 no.4
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• pp.431-442
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• 2013

This study attempted to find a proper method applicable to simulating practical equifield lines of two-dimensional Accelerate Lithium Migration Technique (ALMT), and evaluate the feasibility of using the theoretical ion migration model of one-dimensional ALMT to predict the ion migration behavior of two-dimensional ALMT. The result showed that the electrolyte or carbon plate can be used as matrix to draw equifield line graph similar to that by using mortar as matrix. Using electrolyte electrode module for simulation has advantages of simple production, easy measurement, rapidness, and economy. The electrolyte module can be used to simulate the equifield line distribution diagram in practical two-dimensional electrode configuration firstly. Then, several equifield line zones were marked, and several subzones under one-dimensional ALMT were separated from various equifield line zones. The theoretical free content distribution of alkali in concrete under two-dimensional electric field effect could be obtained from duration analysis.