• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.173-187
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• 2014

In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.219-230
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• 2012

In the paper, a symbolic construction is considered to define generalized Cantor-like sets. Lower and upper bounds for the correlation dimension of the sets with a regular condition are obtained with respect to a probability Borel measure. Especially, for some special cases of the sets, the exact formulas of the correlation dimension are established and we show that the correlation dimension and the Hausdorff dimension of some of them are the same. Finally, we find a condition which guarantees the positive correlation dimension of the generalized Cantor-like sets.

• Journal of The Korean Society of Agricultural Engineers
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• v.54 no.2
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• pp.127-135
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• 2012

The processes of chemical and physical weathering occur simultaneously. The objective of this study was to estimate the degree weathered using fractal dimension through comparison with chemical characteristic of soil samples from Pohang (PH) and Kimpo (KP). Comparing chemical characteristics with fractal dimension, $SiO_2$, $Na_2O$, $K_2O$ content decreased and loss of ignition increased as fractal dimension increased. And fractal dimension showed high correlation with CWI while ATI, STI CIW, PI, CIA and RR demonstrated different degrees of correlation with fractal dimension. The tendency of the changes in oxide content and chemical weathering index with increasing fractal dimension appeared to be similar with the chemical changes due to weathering. Therefore, fractal dimension could be a good indicator representing the extent of weathering and chemical changes.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2001.11a
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• pp.53-58
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• 2001

Fractal dimension is the method to measure the roughness and the irregularity of something that cannot be defined obviously by Euclidean dimension. And the analysis method of this dimension don't need perfect, accurate boundary and color like analysis lot diameter, perimeter, aspect or reflectivity of wear particles or surface. If we arranged the morphological characteristic of various wear particle by using the characteristic of fractal dimension, it might be very efficient to the diagnosis of driving condition. In order to describe morphology of various wear particle, the wear test was carried out under friction experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing system. These descriptors to analyze shape and surface wear particle are boundary fractal dimension and surface fractal dimension.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.2
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• pp.522-539
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• 2021

In order to solve the problems of the existing audio fingerprint method when extracting audio fingerprints from long speech segments, such as too large fingerprint dimension, poor robustness, and low retrieval accuracy and efficiency, a robust audio fingerprint retrieval method based on feature dimension reduction and feature combination is proposed. Firstly, the Mel-frequency cepstral coefficient (MFCC) and linear prediction cepstrum coefficient (LPCC) of the original speech are extracted respectively, and the MFCC feature matrix and LPCC feature matrix are combined. Secondly, the feature dimension reduction method based on information entropy is used for column dimension reduction, and the feature matrix after dimension reduction is used for row dimension reduction based on energy feature dimension reduction method. Finally, the audio fingerprint is constructed by using the feature combination matrix after dimension reduction. When speech's user retrieval, the normalized Hamming distance algorithm is used for matching retrieval. Experiment results show that the proposed method has smaller audio fingerprint dimension and better robustness for long speech segments, and has higher retrieval efficiency while maintaining a higher recall rate and precision rate.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.13-18
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• 2004

We defined Cantor dimensions of a perturbed Cantor set, and investigated a relation between these dimensions and Hausdorff and packing dimensions of a perturbed Cantor set. In this paper, we introduce another expressions of the Cantor dimensions. Using these, we study some informations which can be derived from power equations induced from contraction ratios of a perturbed Cantor set to give its Hausdorff or packing dimension. This application to a deranged Cantor set gives us an estimation of its Hausdorff and packing dimensions, which is a generalization of the Cantor dimension theorem.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1173-1183
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• 2017

We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.

• Speech Sciences
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• v.4 no.2
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• pp.25-39
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• 1998

This paper deals with fuzzy correlation dimension for an appropriate speech recognition. The proposed fuzzy correlation dimension has absorbed time variation value of strange attractor as utilizing fuzzy membership function at calculation of integral correlation when the results of proposed dimension are applied to speech recognition fuzzed correlation dimension is superior to speech recognition, and correlation dimension is superior to speaker discrimination.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1523-1537
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• 2023

Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.