• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.189-198
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• 2007

We have defined a bijective map from certain set of coinstacks onto the permutations avoiding 132-pattern and give an algorithm that finds a corresponding permutation from a given coin-stack. We also list several open problems which are similar as a CS-partition problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.1-18
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• 2019

In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn-Hilliard (vCH) equation. In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose a constrained Convex Splitting (cCS) scheme for the vCH equation, which is based on a convex splitting of the energy functional for the vCH equation under the constraint. We show analytically that the cCS scheme is mass conserving and unconditionally uniquely solvable. And it satisfies the constraint at the next time level for any time step thus is unconditionally energy stable. Numerical experiments are presented demonstrating the accuracy, energy stability, and efficiency of the proposed cCS scheme.

• Textile Coloration and Finishing
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• v.6 no.4
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• pp.72-76
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• 1994

The permselectivity of alkali metal chlorides through silk fibroin membrane was investigated at $25^{\circ}C$: The Permeability coefficients were found to increase in a sequence of LiCl < NaCl < KCl < CsCl. This sequence was explained by considering the partition and the hydrophilic membrane. The dependence of the permeability on the salts concentration was interpreted by means of TMS theory. The ionic mobility ratio of alkali metal chlorides through this membrane decreased with the increase of the Stokes radius. The Effectiveness of the charged density was found to depend on the ionic species. The greater the Stokes radius the larger the effective charge density of membrane.

• Microbiology and Biotechnology Letters
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• v.8 no.3
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• pp.167-172
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• 1980

Yellow pigments were extracted with mixture of 60% -ethanol and petroleum ether (1 : 2) by method of partition chromatography in petroleum ether phase. The absorption curve of yellow pigments solution exhibits maximum peak at wave length range of 394-403um. By thin layer chromatography yellow pigments preparation were found to consists of monascin(yellow), monascidin A (pale yellow) and one unknown (orange-yellow) compound. Isolated fat soluble yellow pigments were changed to water soluble by N-KOH (adjust pH 9). The resulted product obtained were yellow pigments of K-salt complex.