• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.261-275
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• 2011

We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) singulr function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than 0 and the packing dimension of the infinite derivative points of the RNT singular function is less than 1. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the ($\tau$, $\tau$ - 1)-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.

• 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.

• Journal of Fisheries and Marine Sciences Education
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• v.29 no.2
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• pp.447-452
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• 2017

A closely associated set of characteristics was analyzed using both classical and truss dimensions to discriminate sexual dimorphism between spawning season and non spawning season in grass puffer, Takifugu niphobles. In non-spawning season, $1{\times}10/Ls$ of classical dimension was significantly different between male and female (P<0.05). In spawning season, $1{\times}9/Ls$ and $1{\times}10/Ls$ of classical dimension, $3{\times}8/Ls$, $3{\times}9/Ls$, $3{\times}10/Ls$, $4{\times}8/Ls$, $4{\times}9/Ls$ and $8{\times}9/Ls$ of truss dimension and $7{\times}9/HL$ of head part dimension were significantly different between male and female (P<0.05). The results of this study may be useful as basic information of other fish species to compare the change of sexual dimorphism between spawning season and non spawning season.

• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.187-192
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• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• Journal of Korean Society on Water Environment
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• v.26 no.2
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• pp.343-348
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• 2010

The objective of this study was to investigate the effects of starvation periods with aerobic or non-aerobic conditions on the organic removal efficiencies and physical characteristics of activated sludge for treating saline and non-saline wastewater. During the experiment, MLSS, MLVSS, sludge volume index (SVI), floc size and fractal dimension, $COD_{Mn}$ removal efficiencies were monitored. The reductions of MLSS, MLVSS and SVI with maintaining the sludge under a non-aerobic condition during starvation periods were smaller than those under a aerobic condition. Floc size, fractal dimension and $COD_{Mn}$ removal efficiencies were less decreased under non-aerobic condition than under aerobic condition. And SVI were strongly correlated with floc size and fractal dimension. Consequently, the result showed that maintaining the activated sludge under non-aerobic starvation conditions was better strategy than that under aerobic starvation conditions as it adapted and resisted to starvation.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• East Asian mathematical journal
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• v.19 no.2
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• pp.213-219
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• 2003

We study the properties of non-diffenrentiable points of a self-similar Cantor function from which we conjecture a generalization of Darst's result that the Hausdorff dimension of the non-diffenrentiable points of the Cantor function is $(\frac{ln\;2}{ln\;3})^2$.

• Communications for Statistical Applications and Methods
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• v.29 no.5
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• pp.615-627
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• 2022

Principal Fitted Component (PFC) is a semi-parametric sufficient dimension reduction (SDR) method, which is originally proposed in Cook (2007). According to Cook (2007), the PFC has a connection with other usual non-parametric SDR methods. The connection is limited to sliced inverse regression (Li, 1991) and ordinary least squares. Since there is no direct comparison between the two approaches in various forward regressions up to date, a practical guidance between the two approaches is necessary for usual statistical practitioners. To fill this practical necessity, in this paper, we newly derive a connection of the PFC to covariance methods (Yin and Cook, 2002), which is one of the most popular SDR methods. Also, intensive numerical studies have done closely to examine and compare the estimation performances of the semi- and non-parametric SDR methods for various forward regressions. The founding from the numerical studies are confirmed in a real data example.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.255-259
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• 2003

Moire topography method isa well-known non-contacting 3-D measurement method as afast non-contact test for three-dimension shape measuring method. Recently, it's important to study the automatic three-dimension measurement by moire topography because it is frequently applied to the reverse engineering , the medical , the entertainment fields. Three-dimension measurement using projection of moire topography is very attractive because of its high measuring speed and high sensitivity. In this paper, the classical moire method is computerized-so called digital moire when a virtual grating pattern is projected on a surface, the captured image by the CCD camera has three-dimension information of the objects. The moire image can be obtained through a simple image processing and a reference grating pattern. and it provides similar results without physical grating pattern. digital projection moire topography turn out to be very effective for the three-dimension measurement of objects. Using different N-bucket algorithm method of digital projection moire topography is tested to measuring object with the 2-ambiguity problem. Experimental results prove that the proposed scheme is capable of finding measurement errors that decreased more by using the four-three step algorithm method instead of the same step in the phase shifting of different pitch.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.9
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• pp.870-877
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• 2009

This study provides how the Dimension Reduction (DR) method as an efficient technique for reliability analysis can acquire its increased efficiency when it is applied to highly nonlinear problems. In the highly nonlinear engineering systems, 4N+1 (N: number of random variables) sampling is generally recognized to be appropriate. However, there exists uncertainty concerning the standard for judgment of non-linearity of the system as well as possibility of diverse degrees of non-linearity according to each of the random variables. In this regard, this study judged the linearity individually on each random variable after 2N+1 sampling. If high non-linearity appeared, 2 additional sampling was administered on each random variable to apply the DR method. The applications of the proposed sampling to the examples produced the constant results with increased efficiency.