• Journal for History of Mathematics
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• v.28 no.2
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• pp.85-102
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• 2015

Elliptic curves are a common theme among various fields of mathematics, such as number theory, algebraic geometry, complex analysis, cryptography, and mathematical physics. In the history of elliptic curves, we can find number theoretic problems on the one hand, and complex function theoretic ones on the other. The elliptic curve theory is a synthesis of those two indeed. As an overview of the history of elliptic curves, we survey the Diophantine equations of 3rd degree and the congruent number problem as some of number theoretic trails of elliptic curves. We discuss elliptic integrals and elliptic functions, from which we get a glimpse of idea where the name 'elliptic curve' came from. We explain how the solution of Diophantine equations of 3rd degree and elliptic functions are related. Finally we outline the BSD conjecture, one of the 7 millennium problems proposed by the Clay Math Institute, as an important problem concerning elliptic curves.

• The Journal of the Korea Contents Association
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• v.19 no.5
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• pp.147-162
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• 2019

This study investigates the relationship between the online WOMs(such as volume of blogs, articles, reviews, searches) and the number of audience of successful film.The results are as follow: Frist, using a curve-estimation method, the results show that the longitudinal trends of the online WOMs can be best described by a cubic indicating. Second, using panel analysis in model(t) the volume of blogs, reviews, and searches is positively associated with the number of audience. All of the variables' coefficient are significant. However the volume of articles is negatively related to the number of audience with a significant coefficient.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.2
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• pp.130-136
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• 2015

In this paper, we propose a robust curved lane marking detection method. Several lane detection methods have been proposed, however most of them have considered only straight lanes. Compared to the number of straight lane detection researches, less number of curved-lane detection researches has been investigated. This paper proposes a new curved lane detection and tracking method which is robust to various illumination conditions. First, the proposed methods detect straight lanes using a robust road feature image. Using the geometric relation between a vehicle camera and the road plane, several circle models are generated, which are later projected as curved lane models on the camera images. On the top of the detected straight lanes, the curved lane models are superimposed to match with the road feature image. Then, each curve model is voted based on the distribution of road features. Finally, the curve model with highest votes is selected as the true curve model. The performance and efficiency of the proposed algorithm are shown in experimental results.

• Journal of Korean Society of Water and Wastewater
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• v.32 no.2
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• pp.107-113
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• 2018

Maintaining adequate residual chlorine concentration is an important criteria to provide secure drinking water. The chlorine decay can be influenced by unstable flow due to the transient event caused by operation of hydraulic devices in the pipeline system. In order to understand the relationship between the transient event and the chlorine decay, the probability density function based on the water demand curve of a hypothetical water distribution system was used. The irregular transient events and the same number of events with regular interval were assumed and the fate of chlorine decay was compared. The chlorine decay was modeled using a generic chlorine decay model with optimized parameters to minimize the root mean square error between the experimental chlorine concentration and the simulated chlorine concentration using genetic algorithm. As a result, the chlorine decay can be determined through the number of transients regardless of the occurrence intervals.

• Journal of the Korea Society of Computer and Information
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• v.8 no.4
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• pp.104-110
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• 2003

In this paper, we proposed hybrid cryptosystem of Diffie-Hellman base in Elliptic Curve, and explained for specific protocol design. The proposed system is efficient hybrid cryptosystems system that offer implicit key authentication about sender and receiver unlike existing hybrid system. This system increased safety generating session key using pseudo-random number generator by cryptographic. Because the system is hybrid system, it is more efficient in calculation amount aspect supplementing merit and fault of public key system and secret key system. Also, the system can not get right plaintext except receiver even if sender's secret key is revealed and impersonation attack is impossible. And the system offers security on known keys without influencing in safety of other session's cryptogram even if session key is exposed. And the system is provided safety about mutual entity authentication and replay attack.

• Biomedical Science Letters
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• v.11 no.2
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• pp.129-134
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• 2005

Three different deconvolution techniques for quantifying cerebral blood flow (CBF) from whole brain $T2^{\ast}-weighted$ bolus tracking images were implemented (parametric Fourier transform P-FT, parametric single value decomposition P-SVD and nonparametric single value decomposition NP-SVD). The techniques were tested on 206 regions from 38 hyperacute stroke patients. In the P-FT and P-SVD techniques, the tissue and arterial concentration time curves were fit to a gamma variate function and the resulting CBF values correlated very well $(CBF_{P-FT}\;=\;1.02{\cdot}CBF_{p-SVD},\;r^2\;=\;0.96)$. The NP-SVD CBF values correlated well with the P-FT CBF values only when a sufficient number of time series volumes were acquired to minimize tracer time curve truncation $(CBF_{P-FT}\;=\;0.92{\cdot}CBF_{NP-SVD},\;r^2\;=\;0.88)$. The correlation between the fitted CBV and the unfitted CBV values was also maximized in regions with minimal tracer time curve truncation $(CBV_{fit}\;=\;1.00{\cdot}CBV_{ Unfit},\;^r^2\;=\;0.89)$. When a sufficient number of time series volumes could not be acquired (due to scanner limitations) to avoid tracer time curve truncation, the P-FT and P-SVD techniques gave more reliable estimates of CBF than the NP-SVD technique.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.1
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• pp.80-89
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• 1992

This paper presents algorithms which are region labeling and data structure of a boundary segmentation as image intermediate description process. In the method, the algorithms are region labeling, boundary segmentation, line and curve fitting and extracting data structure of each segment. As a result, a data structure of image is described by a set of region number, segment number, line or curve, starting point and end point of each segment and coefficient of line or curve. These data structures would serve for higher level processing as object recognition. For example we will use this data structure to solve the correspondence problem of stereoscopic image information. And we verified these algorithms through the image reconstruction of data structure.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.123-132
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• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.287-299
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• 2022

In radiation epidemiology, the excess relative risk (ERR) model is used to determine the dose-response relationship. In general, the dose-response relationship for the ERR model is assumed to be linear, linear-quadratic, linear-threshold, quadratic, and so on. However, since none of these functions dominate other functions for expressing the dose-response relationship, a Bayesian semiparametric method using splines has recently been proposed. Thus, we improve the Bayesian semiparametric method for the selection of the tuning parameters for splines as the number and location of knots using a Bayesian knot selection method. Equally spaced knots cannot capture the characteristic of radiation exposed dose distribution which is highly skewed in general. Therefore, we propose a nonparametric Bayesian knot selection method based on a Dirichlet process mixture model. Inference of the spline coefficients after obtaining the number and location of knots is performed in the Bayesian framework. We apply this approach to the life span study cohort data from the radiation effects research foundation in Japan, and the results illustrate that the proposed method provides competitive curve estimates for the dose-response curve and relatively stable credible intervals for the curve.

• Nuclear Engineering and Technology
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• v.55 no.8
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• pp.2844-2853
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• 2023

A sophisticated Bayesian multilevel model for estimating group bias was developed to improve the utility of the ASTM E900-15 embrittlement trend curve (ETC) to assess the conditions of nuclear power plants (NPPs). For multilevel model development, the Baseline 22 surveillance dataset was basically classified into groups based on the NPP name, product form, and notch orientation. By including the notch direction in the grouping criteria, the developed model could account for TTS differences among NPP groups with different notch orientations, which have not been considered in previous ETCs. The parameters of the multilevel model and biases of the NPP groups were calculated using the Markov Chain Monte Carlo method. As the number of data points within a group increased, the group bias approached the mean residual, resulting in reduced credible intervals of the mean, and vice versa. Even when the number of surveillance test data points was less than three, the multilevel model could estimate appropriate biases without overfitting. The model also allowed for a quantitative estimate of the changes in the bias and prediction interval that occurred as a result of adding more surveillance test data. The biases estimated through the multilevel model significantly improved the performance of E900-15.