• 자원환경지질
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• 제29권4호
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• pp.523-528
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• 1996

In Korean topography the behaviors of random fractals and multifractality are analytically and numerically studied on the mountain heights shown between $128{\sim}129^{\circ}E$ and $37{\sim}38^{\circ}N$. The phase transitions on the fractal structure are approximately found at the critical length $N_c=2000m$ from the values of standard deviations that it varies with both the longitudinal and latitudinal lengths. In the multifractal structure we assume that the mountain heights divided by the intervals of 20 m are located on the horizontal plane in two dimensional square lattice, and estimate the values of the generalized dimension and the scaling exponents by using the the box counting method for the three cases of square area ($1{\times}1km^2$, $2{\times}2km^2$, $4{\times}4km^2$).

• 한국농공학회논문집
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• 제58권5호
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• pp.91-99
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• 2016

High resolution rainfall data at 1-hour or a finer scale are essential for reliable flood analysis and forecasting; nevertheless, many observations, forecasts, and climate projections are still given at coarse temporal resolutions. This study aims to evaluate a chaotic method for disaggregation of 6-hour rainfall data sets so as to apply operational 6-hour rainfall forecasts of the Korean Meteorological Association to flood models. We computed parameters of a state-of-the-art multiplicative random cascade model with two combinations of cascades, namely uniform splitting and diversion, using rainfall observations at Seoul station, and compared statistical performance. We additionally disaggregated 6-hour rainfall time series at 58 stations with the uniform splitting and evaluated temporal transferability of the parameters and changes in multifractal properties. Results showed that the uniform splitting outperformed the diversion in reproduction of observed statistics, and hence is better to be used for disaggregation of 6-hour rainfall forecasts. We also found that multifractal properties of rainfall observations has adequate temporal consistency with an indication of gradually increasing rainfall intensity across South Korea.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.157-163
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• 2008

Using informations of subsets of divergence points and the relation between members of spectral classes, we give another complete decomposition of spectral classes generated by lower(upper) local dimensions of a self-similar measure on a self-similar Cantor set with full information of their dimensions. We note that it is a complete refinement of the earlier complete decomposition of the spectral classes. Further we study the packing dimension of some uncountable union of distribution sets.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.497-503
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• 2007

We consider a non-empty subset having same local dimension of a self-similar measure on a most generalized Cantor set. We study trans-formed lower(upper) local dimensions of an element of the subset which are local dimensions of all the self-similar measures on the most generalized Cantor set. They give better information of Hausdorff(packing) dimension of the afore-mentioned subset than those only from local dimension of a given self-similar measure.

• 대한수학회논문집
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• 제30권1호
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• pp.7-21
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• 2015

We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

• 대한수학회보
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• 제51권1호
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• pp.157-171
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• 2014

We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let $E_{{\alpha},{\beta}}$ be the set of points with lower and upper recurrence rates ${\alpha},{\beta}$, ($0{\leq}{\alpha}{\leq}{\beta}{\leq}{\infty}$), we prove that all the sets $E_{{\alpha},{\beta}}$, are of full Hausdorff dimension. Then the recurrence sets $E_{{\alpha},{\beta}}$ have constant multifractal spectra.

• International Journal of Aeronautical and Space Sciences
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• 제15권4호
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• pp.419-433
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• 2014

The Mars Exploration Rover Opportunity investigated plains at Meridiani Planum, where laminated sedimentary rocks are present. The Opportunity rover's Athena morphological investigation showed microstructures organized in intertwined filaments of microspherules: a texture we have also found on samples of terrestrial (biogenic) stromatolites and other microbialites. We performed a quantitative image analysis to compare images (n=45) of microbialites with the images (n=30) photographed by the rover (corresponding, approximately, to 25,000/15,000 microstructures). Contours were extracted and morphometric indexes were obtained: geometric and algorithmic complexities, entropy, tortuosity, minimum and maximum diameters. Terrestrial and Martian textures present a multifractal aspect. Mean values and confidence intervals from the Martian images overlapped perfectly with those from the terrestrial samples. The probability of this occurring by chance is $1/2^8$, less than p<0.004. Terrestrial abiogenic pseudostromatolites showed a simple fractal structure and different morphometric values from those of the terrestrial biogenic stromatolite images or Martian images with a less ordered texture (p<0.001). Our work shows the presumptive evidence of microbialites in the Martian outcroppings: i.e., the presence of unicellular life on the ancient Mars.

• Journal of Communications and Networks
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• 제3권4호
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• pp.383-395
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• 2001

Recent measurement and simulation studies have revealed that wide area network traffic displays complex statistical characteristics-possibly multifractal scaling-on fine timescales, in addition to the well-known properly of self-similar scaling on coarser timescales. In this paper we investigate the performance and network engineering significance of these fine timescale features using measured TCP anti MPEG2 video traces, queueing simulations and analytical arguments. We demonstrate that the fine timescale features can affect performance substantially at low and intermediate utilizations, while the longer timescale self-similarity is important at intermediate and high utilizations. We relate the fine timescale structure in the measured TCP traces to flow controls, and show that UDP traffic-which is not flow controlled-lacks such fine timescale structure. Likewise we relate the fine timescale structure in video MPEG2 traces to sub-frame encoding. We show that it is possibly to construct a relatively parsimonious multi-fractal cascade model of fine timescale features that matches the queueing performance of both the TCP and video traces. We outline an analytical method ta estimate performance for traffic that is self-similar on coarse timescales and multi-fractal on fine timescales, and show that the engineering problem of setting safe operating points for planning or admission controls can be significantly influenced by fine timescale fluctuations in network traffic. The work reported here can be used to model the relevant characteristics of wide area traffic across a full range of engineering timescales, and can be the basis of more accurate network performance analysis and engineering.

• 한국농림기상학회지
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• 제18권4호
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• pp.208-220
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• 2016

본 연구는 매년 발생하고 있는 산불, 산사태 등의 산림 재해방지를 위해 호남과 제주의 산악지역을 대상으로 최적의 산악기상관측망 입지를 선정하는 연구를 수행하였다. 먼저 적정위치 선정을 위해 고려해야 하는 항목들을 공간자료화한 후 공간 분석을 통해서 후보지를 선정하고 현장 조사를 통해 정량적 평가를 수행함으로써 최종적인 적정위치를 선정하였다. 공간자료는 과거 10년간의 산불발생 정보와 과거 7년간의 산사태위험등급 정보, 산림청의 국사경계도, 국유지의 임도와 등산로 그리고 기상청의 자동기상관측소(AWS)와 산림청의 산악기상관측소 위치정보, 30m 해상도의 수치표고모델(DEM)을 사용하였다. 공간분석은 산불과 산사태의 1-2등급의 위험지에 대한 추출 및 중첩 분석, 산림청 국유지 내에 100m 버퍼를 준 임도와 등산로의 접근성 분석, 기상관측소의 2.5km 버퍼를 준 중복성 분석, 산악기상관측 입지 환경 조성을 위한 고도 200m 이상의 지형특성 분석을 통해 종합적인 중첩분석을 수행하였다. 공간분석 결과, 총 159개의 중첩 폴리곤이 추출되었고 구글어스 등을 활용하여 능선과 정상부에 총 64개의 적정위치 후보지를 선정하였다. 선정된 후보지는 기상관측환경, 접근성, 통신 및 전력공급 환경, 기상관측소의 중복성에 대한 정량적인 현장 평가를 통해서 총점이 70점 이상인 지점을 '적합'으로 판정하여 고득점 순으로 산악기상관측망의 적정위치 26개소를 선정하였다. 따라서 적정위치 선정 기법에 의해 구축된 산악기상관측망의 기상정보는 향후 산불, 산사태 등과 같은 산림재해위험 예측력의 향상과 산림 복잡 지형에 대한 미기상 연구에 활용이 가능할 것으로 판단된다.