• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.137-150
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• 2016

We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.587-593
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• 2011

We find concrete necessary and sufficient conditions for the existence of contractive completions of Stochastic Hankel partial contractions of size $4{\times}4$, extremal type.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1003-1021
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• 2015

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

• Journal of the Korean Society of Costume
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• v.22
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• pp.333-344
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• 1994

In this study an experiment was made using the function of computer simulation os to whether the phenomenon of optical illusion takes place also in clothing on the human body three-dimensional space through the case study of the Gestalt illusion of planar con-traction and expension by amodal completion in perceptual organization. One woman of latter 30s was selected as the experimental subject. She was made to wear the experimental clothing and then the frontal picture was projected of in the experimental clothing which was scanned into the com-puter. For the sake of the contractive experiment 5 stages were divided by 5-15cm the thick-nes of the black vertical line in the center of the upper garmet as the variable and for the sake of the expansive experiment the skirt length was set as the variable. It length measured 50-90cm which was divided by 10cm into 5 stages and simulated using the CAD. The basic design and the experimental de-sign were made one pair and the pictures totalled 20 pictures such as ten pictures save the human body for the estimation of the up-per garmet alone and ten pictures for the ob-servation of the effect on the human body. The extimating panel consisting of 20 panellers estimated contraction/expansion in the estimation of the upper garmet and the tall effect/the slim effect in the estimation of optical illusion as the estimating factors on the 9-point scale. All the date from experiment were analyzed by ANOVA(analysis of variance) and DUNCAN'S multiple range. As a result the experimental designs all showed a significant optical illusion in comparision with the basic design.