• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.469-480
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• 2019

A generalized tiling is defined as a generalization of the properties of tiling a region of ${\mathbb{Z}}^2$ with dominoes, and comprises tiling with rhombus and any other tilings that admits height functions which can be ordered into a distributive lattice. By using properties of the distributive lattice, we prove that the Markov chain consisting of moving from one height function to the next by a flip is fast mixing and the mixing time ${\tau}({\epsilon})$ is given by ${\tau}({\epsilon}){\leq}(kmn)^3(mn\;{\ln}\;k+{\ln}\;{\epsilon}^{-1})$, where mn is the area of the grid ${\Gamma}$ that is a k-regular polycell. This result generalizes the result of the authors (T-tetromino tiling Markov chain is fast mixing, Theor. Comp. Sci. (2018)) and improves on the mixing time obtained by using coupling arguments by N. Destainville and by M. Luby, D. Randall, A. Sinclair.

• Journal of the Korean Home Economics Association
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• v.50 no.5
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• pp.125-138
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• 2012

The purpose of this study was to analyze the research literature on play therapy intervention for children with ADHD. Thirty-nine studies, conducted from 1995 to 2010, were analyzed. The results of the literature review are as follows: The most commonly studied subjects were elementary school children in grades 1-3. The most common subject selection method was to select ADHD tendency children. The most typical intervention setting used was a counseling center. The most frequent intervention was 11-15 sessions of group counseling. Pre-post experimental-control research designs were the most commonly used. In the analyzed studies, play therapy-game play therapy, CBPT, CCPT, sand play therapy, and theraplay- was used for ADHD children. The studies found that game play therapy and cognitive-behavior play therapy are effective for improving ADHD children's attention, impulsiveness, and self-control. The major game play therapy activities used were dart games, "Simon says" games, fishing games, dominoes, Jenga, Beat the Clock, the board game "Stop," and "Ice, break., ice, break." Based on these findings, this article presents implications and discussion for play therapy intervention for ADHD children.