• Journal of Korea Water Resources Association
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• v.47 no.9
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• pp.839-852
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• 2014

This study analyzed the applicability of a rainfall downscaling algorithm in space-time multifractal framework (RDSTMF) in Korean Peninsula. To achieve this purpose, the 8 heavy rainfall events that occurred in Korea during the period between 2008 and 2012 were analyzed using the radar rainfall imagery. The result of the analysis indicated that there is a strong tendency of the multifractality for all 8 heavy rainfall events. Based on the multifractal exponents obtained from the analysis, the parameters of the RDSTMF were obtained and the relationship between the average intensity of the rainfall events and the parameters of the RDSTMF was developed. Based on this relationship, the synthetic space-time rainfall fields were generated using the RDSTMF. Then, the generated synthetic space-time rainfall fields were compared to the observation. The result of the comparison indicated that the RDSTMF can accurately reproduce the multifractal exponents of the observed rainfall field up to 3rd order and the cumulative density function of the observed space-time rainfall field with a reasoable accuracy.

• The Korean Journal of Financial Management
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• v.20 no.2
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• pp.95-126
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• 2003

This paper introduces multifractal processes and presents the empirical investigation of the multifractal asset pricing. The multifractal stock price process contains long-tails which focus on Levy-Stable distributions. The process also contains long-dependence, which is the characteristic feature of fractional Brownian motion. Multifractality introduces a new source of heterogeneity through time-varying local reqularity in the price path. This paper investigates multifractality in stock prices. After finding evidence of multifractal scaling, the multifractal spectrum is estimated via the Legendre transform. The distinguishing feature of the multifractal process is multiscaling of the return distribution's moments under time-resealing. More intensive study is required of estimation techniques and inference procedures.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.357-364
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• 2006

We study Hausdorff and packing dimensions of subsets of a general coding space with a generalized ultra metric from a multifractal spectrum induced by a self-similar measure on a self-similar Cantor set using a function satisfying a H${\ddot{o}}$older condition.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.447-454
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• 2004

We study the Hausdorff and packing dimensions of subsets composing multifractal spectrum generated by a quasi-self-similar probability measure on a perturbed Cantor set.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.1-5
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• 2004

We study Hausdorff and packing dimensions of subsets of a coding space with an ultra metric from a multifractal spectrum induced by a self-similar measure on a Cantor set using a function satisfying a H$\ddot{o}$lder condition.

• Journal of Korea Water Resources Association
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• v.47 no.10
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• pp.959-972
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• 2014

In this study, a space-time rainfall grid field generation model based on multifractal theory was verified using nine flood events in the upstream watershed of Chungju dam in South Korea. For this purpose, KMA radar rainfall data sets were analyzed for the space-time multifractal characteristics. Simulated rainfall fields that represent the multifractal characteristics of observed rainfall field were reproduced using the space-time rainfall grid field generation model with log-Poisson distribution and three-dimension wavelet function. Simulated rainfall fields were applied to the S-RAT model as input data and compared with both observed rainfall fields and low-resolution rainfall field runoff. Error analyses using RMSE, RRMSE, MAE, SS, NPE and PTE indicated that the peak discharge increases about 20.03% and the time to peak decreases about 0.81%.

• Geomechanics and Engineering
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• v.14 no.2
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• pp.107-113
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• 2018

Coal samples with different joints morphology were subjected to uniaxial compression experiments, cracks evolution was recorded by Nikon D5300 and acoustic emission (AE) energy signals were collected by AEwin Test for Express-8.0. During loading process, coal samples deformed elastically with no obvious cracks changes, then they expanded gradually along the trace of the original cracks, accompanied by the formation of secondary cracks, and eventually produced a large-scale fracture. It was more interesting that the failure mode of samples were all shear shape, whatever the original cracks morphology was. With cracks and damage evolution, AE energy radiated regularly. At the early loading stage, micro damage and small scale fracture events only induced a few AE events with less energy, while large scale fracture leaded to a number of AE events with more energy at the later stage. Based on the multifractal theory, the multifractal spectrum could explain AE energy signals frequency responses and the causes of AE events with load. Multifractal spectrum width (${\Delta}{\alpha}$), could reflect the differences between the large and small AE energy signals. And another parameter (${\Delta}f$) could reflect the relationship between the frequency of the least and greatest signals in the AE energy time series. This research is helpful for us to understand cracks evolution and AE energy signals causes.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.157-163
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• 2008

We study essentially disjoint one dimensionally indexed classes whose members are distribution sets of a self-similar Cantor set. The Hausdorff dimension of the union of distribution sets in a same class does not increases the Hausdorff dimension of the characteristic distribution set in the class. Further we study the Hausdorff dimension of some uncountable union of distribution sets.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.695-702
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• 2005

We study the transformed measures with respect to the real parameters of a self-similar measure on a self-similar Can­tor set to give a simple proof for some result of its multifractal spectrum. A transformed measure with respect to a real parameter of a self-similar measure on a self-similar Cantor set is also a self­similar measure on the self-similar Cantor set and it gives a better information for multifractals than the original self-similar measure. A transformed measure with respect to an optimal parameter deter­mines Hausdorff and packing dimensions of a set of the points which has same local dimension for a self-similar measure. We compute the values of the transformed measures with respect to the real parameters for a set of the points which has same local dimension for a self-similar measure. Finally we investigate the magnitude of the local dimensions of a self-similar measure and give some correlation between the local dimensions.

• Journal of the korean society of oceanography
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• v.35 no.1
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• pp.11-15
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• 2000

The scaling behavior of random fractals and multifractals is investigated numerically on the seabottom depth in the seabottom topography. In the self-affine structure the critical length for the crossover can be found from the value of standard deviations for the seabottom depth. The generalized dimension and the spectrum in the multifractal structure are discussed numerically, as it is assumed that the seabottom depth is located on a two-dimensional square lattice. For this case, the fractal dimension D$_0$ is respectively calculated as 1.312476, 1.366726, and 1.372243 in our three regions, and our result is compared with other numerical calculations.