• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.215-223
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• 2009

The helicoidal surfaces with pointwise 1-type or harmonic gauss map in Euclidean 3-space are studied. The notion of pointwise 1-type Gauss map is a generalization of usual sense of 1-type Gauss map. In particular, we prove that an ordinary helicoid is the only genuine helicoidal surface of polynomial kind with pointwise 1-type Gauss map of the first kind and a right cone is the only rational helicoidal surface with pointwise 1-type Gauss map of the second kind. Also, we give a characterization of rational helicoidal surface with harmonic or pointwise 1-type Gauss map.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1119-1133
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• 2020

In this paper, we derive an upper bound for the distance from a point in the immediate basin of a root of a complex polynomial to the root itself. We establish that if z is a point in the immediate basin of a root α of a polynomial p of degree d ≥ 12, then ${\mid}z-{\alpha}{\mid}{\leq}{\frac{3}{\sqrt{d}}\(6{\sqrt{310}}/35\)^d{\mid}N_p(z)-z{\mid}$, where N_p is the Newton map induced by p. This bound leads to a new bound of the expected total number of iterations of Newton's method required to reach all roots of every polynomial p within a given precision, where p is normalized so that its roots are in the unit disk.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.303-309
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• 2009

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computational Diffie-Hellman assumption implies the bilinear Diffie-Hellman assumption or the general inversion assumption. Secondly, we show that a cryptographic useful self-bilinear map does not exist. If a self-bilinear map exists, it might be used as a building block for several cryptographic applications such as a multilinear map. As a corollary, we show that a fixed inversion of a bilinear map with homomorphic property is impossible. Finally, we remark that a self-bilinear map proposed in [7] is not essentially self-bilinear.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.544-553
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• 2013

In this paper, we propose the pattern classifier of Radial Basis Function Neural Networks(RBFNNs) for diagnosis of 3-phase partial discharge. Conventional methods map the partial discharge/noise data on 3-PARD map, and decide whether the partial discharge occurs or not from 3-phase or neutral point. However, it is decided based on his own subjective knowledge of skilled experter. In order to solve these problems, the mapping of data as well as the classification of phases are considered by using the general 3-PARD map and PA method, and the identification of phases occurring partial discharge/noise discharge is done. In the sequel, the type of partial discharge occurring on arbitrary random phase is classified and identified by fuzzy clustering-based polynomial Radial Basis Function Neural Networks(RBFNN) classifier. And by identifying the learning rate, momentum coefficient, and fuzzification coefficient of FCM fuzzy clustering with the aid of PSO algorithm, the RBFNN classifier is optimized. The virtual simulated data and the experimental data acquired from practical field are used for performance estimation of 3-phase partial discharge pattern classifier.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.22 no.4
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• pp.331-338
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• 2004

This paper describes capability of utilizing ground control points(GCPs) obtained from 1:1,000 and 1:5,000 digital vector maps to correct image coordinates which have errors due to bais rational polynomial coefficient(RPC) of IKONOS Geo-level stereo images. The accuracy of the bias-corrected images was improved to approximately 4m and 2m in planimetry and height, respectively. The accuracy was also compared with results from using GCPs obtained by GPS surveying. In consequence, bias-compensated IKONOS sereo imagery was evaluated to satisfy generating topographic map 1:10,000.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.883-914
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• 2001

We present a survey of research results obtained for infra-nilmanifolds, their fundamental groups and some of their generalizations. This is presented from two different approaches and covers achievements obtained during the past four decades and showing a remarkable amount of mathematical interdisciplinarity. We go more in depth concerning the existence and construction of polynomial structures for these manifolds and groups, a direction where significant progress was made in the past few years. The bounded-degree polynomial structures developed by the authors triggered a number of challenging open problems. Also, their study already has lead to some interesting results concerning e.g. Anosov diffeomorphisms and expanding maps.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.11-13
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• 2008

This study proposes the method to use existing digital maps as one of the technologies to exclude individual differences that occur in the process of manually determining GCP for the geometric correction of KOMPSAT images and applying it to the images and to automate the generation of ortho-images. It is known that, in case high-resolution satellite images are corrected geometrically by using RPC, first order polynomials are generally applied as the correction formula in order to obtain good results. In this study, we matched the corresponding objects between 1:25,000 digital map and a KOMPSAT image to obtain the coefficients of the zero order polynomial and showed the differences in the pixel locations obtained through the matching. We performed proximity corrections using the Boolean operation between the point data of the surface linear objects and the point data of the edge objects of the image. The surface linear objects are road, water, building from topographic map.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.3
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• pp.197-203
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• 1999

Depending on geographical features and error sources in the survey field, inaccurate data is inevitable in GPS kinematic survey for positioning with feature codes. In this study, the trimmed mean and the first order differential equation are used to develop an inaccurate positioning data detection algorithm, and a cubic spline curve and a linear polynomial are used to interpolate the inaccurate data. Based on interpolated data, a digital map for 30 km range of rural highway is produced and a corresponding GIS coverage map is obtained by analyzing and solving the problem associated with the map.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.19 no.4
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• pp.447-457
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• 2021

Graphite Isotope Ratio Method (GIRM) can be used to estimate plutonium production in a graphite-moderated reactor. This study presents verification results for the GIRM combined with a 3-D polynomial regression function to estimate cumulative plutonium production in a graphite-moderated reactor. Using the 3-D Monte-Carlo method, verification was done by comparing the cumulative plutonium production with the GIRM. The GIRM can estimate plutonium production for specific sampling points using a function that is based on an isotope ratio of impurity elements. In this study, the ¹⁰B/¹¹B isotope ratio was chosen and calculated for sampling points. Then, 3-D polynomial regression was used to derive a function that represents a whole core cumulative plutonium production map. To verify the accuracy of the GIRM with polynomial regression, the reference value of plutonium production was calculated using a Monte-Carlo code, MCS, up to 4250 days of depletion. Moreover, the amount of plutonium produced in certain axial layers and fuel pins at 1250, 2250, and 3250 days of depletion was obtained and used for additional verification. As a result, the difference in the total cumulative plutonium production based on the MCS and GIRM results was found below 3.1% with regard to the root mean square (RMS) error.

• Korean Journal of Remote Sensing
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• v.34 no.6_3
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• pp.1329-1350
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• 2018

There have been many applications to observe Earth using synthetic aperture radar (SAR) since it could acquire Earth observation data without reference to weathers or local times. However researches about digital map generation using SAR have hardly been performed due to complex raw data processing. In this study, we suggested feasibility of producing digital map using SAR stereo images. We collected two sets, which include an ascending and a descending orbit acquisitions respectively, of KOMPSAT-5 stereo dataset. In order to suggest the feasibility of digital map generation from SAR stereo images, we performed 1) rational polynomial coefficient transformation from radar geometry, 2) digital resititution using KOMPSAT-5 stereo images, and 3) validation using digital-map-derived reference points and check points. As the results of two models, root mean squared errors of XY and Z direction were less than 1m for each model. We discussed that KOMPSAT-5 stereo image could generated 1:25,000 digital map which meets a standard of the digital map. The proposed results would contribute to generate and update digital maps for inaccessible areas and wherever weather conditions are unstable such as North Korea or Polar region.