• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1489-1493
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• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.933-944
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• 2004

Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper Renyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1041-1055
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• 2012

The parameter lower (upper) distribution set corresponds to the cylindrical lower or upper local dimension set for a self-similarmeasure on a self-similar set satisfying the open set condition.

• Journal of Veterinary Clinics
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• v.17 no.1
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• pp.187-193
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• 2000

Fifteen adult Korea Jin-do dogs were studied by echocardiography to obtain the basic data of the imaging planes and normal references ranges to the aorta and pulmonary artery internal dimension. Measurements of aortic root internal dimension(AOID) and right pulmonary artery internal dimension (RPAID) were made at modified pulmonary arteries level short-axis view and left ventricular outflow tract long-axis view. The aortic root internal dimension and right pulmonary artery internal dimension at modified pulmonary arteries level short-axis view were 18.7$\pm$1.3mm (mean$\pm$SD) and 10.1$\pm$0.8mm, respectively. And RPAID/AOID was 0.5$\pm$0.1mm. The aortic root internal dimension and right pulmonary artery internal dimension at left ventricular outflow tract long-axis view were 19.3$\pm$1.6 mm and 10.7$\pm$1.3mm, respectively. And RPAID/AOID was 0.5$\pm$0.1mm. These results indicate that modified pulmonary arteries level short-axis view is useful planes to examine the aortic root and pulmonary arteries, and aortic root internal dimension is significantly higher(40~50%)than the right pulmonary artery internal dimension. Therefore measurements of aortic root internal and right pulmonary artery internal dimension can be used for monitoring dilation of pulmonary artery.

• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.977-985
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• 2010

In this paper, we propose an approach to conduct partial sufficient dimension reduction with heavily unbalanced categorical predictors. For this, we consider integrated categorical predictors and investigate certain conditions that the integrated categorical predictor is fully informative to partial sufficient dimension reduction. For illustration, the proposed approach is implemented on optimal partial sliced inverse regression in simulation and data analysis.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.513-521
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• 2018

The goal of sufficient dimension reduction (SDR) is to replace original p-dimensional predictors with a lower-dimensional linearly transformed predictor. The sliced inverse regression (SIR) (Li, Journal of the American Statistical Association, 86, 316-342, 1991) is one of the most popular SDR methods because of its applicability and simple implementation in practice. However, SIR may yield different dimension reduction results for different numbers of slices and despite its popularity, is a clear deficit for SIR. To overcome this, a fused sliced inverse regression was recently proposed. The study shows that the dimension-reduced predictors is robust to the numbers of the slices, but it does not investigate how robust its dimension determination is. This paper suggests a permutation dimension determination for the fused sliced inverse regression that is compared with SIR to investigate the robustness to the numbers of slices in the dimension determination. Numerical studies confirm this and a real data example is presented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.6
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• pp.1140-1148
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• 1994

In this paper, we carried out some experiments on the Korean vowel recognition using the fractal dimension of the speech signals. We chose the Minkowski-Bouligand dimension as the fractal dimension, and computed it using the morphological covering method. For our experiments, we used both the fractal dimension and the LPC cepstrum which is conventionally known to be one of the best parameters for speech recognition, and examined the usefulness of the fractal dimension. From the vowel recognition experiments under various consonant contexts, we achieved the vowel recognition error rates of 5.6% and 3.2% for the case with only LPC cepstrum and that with both LPC cepstrum and the fractal dimension, respectively. The results indicate that the incorporation of the fractal dimension with LPC cepstrum gives more than 40% reduction in recognition errors, and indicates that the fractal dimension is a useful feature parameter for speech recognition.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.05a
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• pp.407-410
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• 2013

This paper has been written to apply the lessons of this course through a 5-dimension education curriculum from BELL International Academy, an alternative school. By integration a 5-dimension education in the school, teachers may be able to have an impact on their students, A robot club in a 5-dimension educated school migh help motivate students to take the necessary steps to accomplish their goals.

• Journal of Dental Rehabilitation and Applied Science
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• v.17 no.4
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• pp.231-244
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• 2001

This study was conducted to observe the effect on appendage muscle strength according to increase in occlusal vertical dimension. For this study, ten males with a mean age of 21 were selected. The subjects had a complete or almost complete set of natural teeth and reported no subjected symptoms of pain or dysfunction in the masticatory system. The tested occlusal splints were made at the position of increased occlusal vertical dimension of 2mm, 3.5mm, and 5mm from the ICP. Before and after wearing occlusal splints, the appendage muscle strength were tested by CybexII Dynamometer in each subject. The results were as follows : 1. When occlusal vertical dimension was increased, most of mean muscular strength values were increased except for those of supination and pronation of forearm at the position of 5mm increased occlusal vertical dimension. 2. The statistical analyses demonstrated that the increased occlusal vertical dimension position to be significantly stronger than intercuspal position for the muscle strength of the flexion and extension of hip, supination of forearm, external and internal rotation of knee, dorsiflexion and plantarflexion of ankle (p<0.05). 3. At the position of 3.5mm increased vertical dimension displayed the highest mean muscluar strength value than other positions. 4. Statistically demonstrated values, except for supination of forearm, internal rotation of shoulder, were related to lower appendage. Therefore splint was more effective on lower appendage than upper appendage to make muscle strength increased. 5. The mean increased rate of muscular strength tested on knee(57%), ankle(42%), and wrist(20%) were higher than hip(31%), elbow(14%), and shoulder(17%).

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1041-1052
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• 2010

In this paper, strongly cotorsion (torsion-free) modules are studied and strongly cotorsion (torsion-free) dimension is introduced. It is shown that every module has a special $\mathcal{SC}_n$-preenvelope and an ST $\mathcal{F}_n$-cover for any $n\;{\in}\;\mathbb{N}$ based on some results of cotorsion pairs from [9]. Some characterizations of strongly cotorsion (torsion-free) dimension of a module are given.