• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.209-224
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• 2013

The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.10C
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• pp.614-620
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• 2011

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.469-497
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• 2016

In this research, we develop a systematic learning the materials on constructibility of cubic roots. We propose two sets of materials: one is based on concepts of field, vector space, minimal polynomial in abstract algebra, another based on properties of cubic roots in elementary algebra. We assess the validity, applicability, defects and merits of developed materials through prospective teachers, in-service teachers, and professionals. It could be expected that materials be used for advanced secondary students, mathematics majoring college students and mathematics teachers. Furthermore, we may expect the materials be useful for understanding and solving the (un)constructibility problems.

• Textile Coloration and Finishing
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• v.2 no.2
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• pp.20-32
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• 1990

In this paper, a new method by Cubic Spline to analyze Munsell Value Function is proposed. The values calculated by this method are compared with ones by Judd's Polynomial and Cube Root Functions, etc. For performing these computation algorithms have been developed.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.505-514
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• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

• Journal of Information Processing Systems
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• v.10 no.3
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• pp.395-411
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• 2014

Temporal medical data is often collected during patient treatments that require personal analysis. Each observation recorded in the temporal medical data is associated with measurements and time treatments. A major problem in the analysis of temporal medical data are the missing values that are caused, for example, by patients dropping out of a study before completion. Therefore, the imputation of missing data is an important step during pre-processing and can provide useful information before the data is mined. For each patient and each variable, this imputation replaces the missing data with a value drawn from an estimated distribution of that variable. In this paper, we propose a new method, called Newton's finite divided difference polynomial interpolation with condition order degree, for dealing with missing values in temporal medical data related to obesity. We compared the new imputation method with three existing subspace estimation techniques, including the k-nearest neighbor, local least squares, and natural cubic spline approaches. The performance of each approach was then evaluated by using the normalized root mean square error and the statistically significant test results. The experimental results have demonstrated that the proposed method provides the best fit with the smallest error and is more accurate than the other methods.

• Journal of Bio-Environment Control
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• v.31 no.4
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• pp.409-415
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• 2022

Plant growth and development are also affected by root-zone environment. Therefore, it is important to consider the variables of the root-zone environment when establishing an irrigation strategy. The purpose of this study is to analyze the relationship between the volumetric moisture content (VWC), Bulk EC (ECb), and Pore EC (ECp) used by plant roots using FDR sensors in two types of rockwool media with different water transmission characteristics, using the method above this was used to establish a method for collecting and correcting available root-zone environmental data. For the experiment, two types of rockwool medium (RW1, RW2) with different physical characteristics were used. The moisture content (MC) and ECb were measured using an FDR sensor, ECp was measured after extracting the residual nutrient solution from the medium using a disposable syringe in the center of the medium at a volumetric moisture content (VWC) of 10-100%. Then, ECb and ECp are measured by supplying nutrient solution having different concentration (distilled water, 0.5-5.0) to two types of media (RW1, RW2) in each volume water content range (0 to 100%). The relationship between ECb and ECp in RW1 and RW2 media is best suited for cubic polynomial. The relationship between ECb and ECp according to volume moisture content (VWC) range showed a large error rate in the low volume moisture content (VWC) range of 10-60%. The correlation between the sensor measured value (ECb) and the ECp used by plant roots according to the volumetric water content (VWC) range was the most suitable for the Paraboloid equation in both media (RW1, RW2). The coefficient of determination the calibration equation for RW1 and RW2 media were 0.936, 0.947, respectively.