• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.17-26
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• 2014

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of genus 3 hyperelliptic curves of type $y^2=x^7+ax$ over finite prime fields. The problem of determining the group order of the Jacobian varieties of algebraic curves defined over finite fields is important not only arithmetic geometry but also curve-based cryptosystems in order to find a secure curve. Based on this, we provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety of hyperelliptic curve $y^2=x^7+ax$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ modulo 12. Moreover, we also introduce some implementation results by using our algorithm.

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.4
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• pp.1-11
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• 2012

This paper is the study on the development of a torque precision measuring system using the curve fitting algorithm. This system can be divided into the hardware part and the software part. The hardware part consists of the main base board, the DAQ(Data Aquisition) board and Calibration parts. The software part consists of the software filter module and the curve fitting algorithm module. We have tested the torque transducer including the strain gauge for 200 Nm range and have analyzed the data acquired with the curve fitting algorithm by using this system. The DAQ board converts the electric signal induced by the transducer to the digital value precisely by using the shunt calibration procedure. The main board including the curve fitting algorithm calculates the exact digital torque value by using the digital value from the DAQ board. In this study, we confirmed that the result of the appropriate high-order power-series polynomial function is more accurate than the result of the low-order power-series polynomial through the system.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.307-314
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• 2009

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1669-1675
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• 2017

The group of automorphisms of the first Weyl algebra acts on commuting ordinary differential operators with polynomial coefficient. In this paper we prove that for fixed generic spectral curve of genus two the set of orbits is infinite.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.45-72
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• 2022

In this work, we study Bernstein-Walsh-type estimations for the derivative of an arbitrary algebraic polynomial in regions with piecewise smooth boundary without cusps of the complex plane. Also, estimates are given on the whole complex plane.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.211-219
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• 2010

Let P be a Jacobian polynomial such as deg P = $deg_y$ P. Suppose the Jacobian polynomial P satisfies the intersection condition satisfying $dim_C$ C[x, y]/$P_y$> = deg P - 1, we can prove that the Keller map which has P as one of coordinate polynomial always has its inverse.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2004.05b
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• pp.255-258
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• 2004

Efficient finite field operation in the elliptic curve (EC) public key cryptography algorithm, which attracts much of latest issues in the applications in information security, is very important. Traditional serial finite multipliers root from Mastrovito's serial multiplication architecture. In this paper, we adopt the polynomial basis and propose a new finite field multiplier, inducing numerical expressions which can be applied to exhibit 3 times as much performance as the Mastrovito's. We described the proposed multiplier with HDL to verify and evaluate as a proper hardware IP. HDL-implemented serial GF (Galois field) multiplier showed 3 times as fast speed as the traditional serial multiplier's adding only Partial-sum block in the hardware.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1211-1226
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• 2021

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.49 no.1
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• pp.63-73
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• 2021

This paper presents a algorithm for automatic target recognition robust to the influence of the flame in order to track the target by EOTS(Electro-Optical Targeting System) equipped on UAV(Unmanned Aerial Vehicle) when there is aerial target or marine target with flame at the same time. The proposed method converts infrared images of targets and flames into a gradient vector field, and applies each gradient magnitude to a polynomial curve fitting technique to extract polynomial coefficients, and learns them in a shallow neural network model to automatically recognize targets and flames. The performance of the proposed technique was confirmed by utilizing the various infrared image database of the target and flame. Using this algorithm, it can be applied to areas where collision avoidance, forest fire detection, automatic detection and recognition of targets in the air and sea during automatic flight of unmanned aircraft.

• East Asian mathematical journal
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• v.37 no.5
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• pp.585-590
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• 2021

This paper consider the Jacobian variety of a hyperelliptic curve over a finite field with the formal structure of the mixed type. We present the Newton polygon of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety. It gives an useful tool for finding the local decomposition of the Jacobian variety into isotypic components.