• 대한수학회보
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• 제52권5호
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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.

• 대한수학회지
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• 제41권5호
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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.

• 대한수학회보
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• 제49권5호
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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.

• 한국임상수의학회지
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• 제17권1호
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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.

• 응용통계연구
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• 제23권5호
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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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• 제25권5호
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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.

• 한국통신학회논문지
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• 제19권6호
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• pp.1140-1148
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• 1994

본 논문에서는 음성신호의 프랙탈 차원을 이용하여 한국어 모음인식 실험을 수행하였다. 프랙탈 차원은 Minkowski-Bouligand 차원을 사용하였으며, 형태학적 커버링(morphological covering) 방법을 이용하여 구하였다. 프렉탈 차원과 더불어 기존에 우수한 음성 인식 파라메타로 알려져 있는 LPC 켐스트럼(cepstrum)을 함께 사용하였으며, 프랙탈 차원의 음성인식에의 유용성 여부를 조사하였다. 다양한 자음환경에서의 모음인식 실험결과, LPC 켐스트럼 만을 사용하는 경우 및 프렉탈 차원과 LPC 켐스트럼을 함께 사용하는 경우의 모음 오인식율이 각각 5.6% 및 3.2%로 얻어졌다. 이는 LPC 켑스트럼에 프렉탈 차원을 추가함으로써 오인식되는 데이터가 40%이상 감소되는 결과이며, 프랙탈 차원이 음성인식에 있어서 유용한 특징 파라메터임을 보여준다.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2013년도 춘계학술대회
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• pp.407-410
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• 2013

본 논문에서는 비인가 대안학교인 벨 국제아카데미에서 5차원 전면교육 커리큘럼을 통하여 모든 교과목에 수업을 적용하여 실시하고 있다. 5차원 전면교육과 로봇 교육을 접목하여 로봇동아리에서 학생들에게 5차원적으로 로봇 교육을 통해 대회에서 입상은 물론 동기부여로 인한 대학 진학에 상당한 영향을 주며, 각종 대회수상 실적 등의 우수한 사례를 입증한다.

• 구강회복응용과학지
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• 제17권4호
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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%).

• 대한수학회보
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• 제47권5호
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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.