• 정보보호학회논문지
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• 제9권3호
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• pp.3-12
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• 1999

공개키 암호법은 정수 인수분해의 어려움에 바탕을 둔 RSA와 이산대수문제의 어려움에 근거한 EIGamal 암호법을 대표된다. GF(qn)*에서 index-calculus 이산대수 알고리즘을 다항식 인수분해를 필요로 한다. 최근에 Niederreiter에 의하여 유한체위에서의 다항식 인수분해 알고리즘이 제안되었다. 이 논문에서는 정규기저(normal basis)를 이용한 유한체의 연산을 c-언어로 구현하고, 이것을 이용한 Niederreiter의 알고리즘을 기반으로 유한체위에서의 다항식 인수분해 알고리즘과 구현한 결과를 제시한다. The public key crytptosystem is represented by RSA based on the difficulty of integer factorization and ElGamal cryptosystem based on the intractability of the discrete logarithm problem in a cyclic group G. The index-calculus algorithm for discrete logarithms in GF(qn)* requires an polynomial factorization. The Niederreiter recently developed deterministic facorization algorithm for polynomial over GF(qn) In this paper we implemented the arithmetic of finite field with c-language and gibe an implementation of the Niederreiter's algorithm over GF(2n) using normal bases.

• 대한수학회논문집
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• 제21권4호
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• pp.675-678
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• 2006

We show that every real polynomial of degree n can be represented by the sum of two real polynomials of degree n, each having only real zeros. As an example of this, we consider a real polynomial with even degree whose all zeros lie on the imaginary axes except the origin.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권3호
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• pp.305-325
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• 2015

In this paper, missile homing guidance laws to control the impact angle and time are proposed based on the polynomial function. To derive the guidance commands, we first assume that the acceleration command profile can be represented as a polynomial function with unknown coefficients. After that, the unknown coefficients are determined to achieve the given terminal constrains. Using the determined coefficients, we can finally obtain the state feedback guidance command. The suggested approach to design the guidance laws is simple and provides the more generalized optimal solutions of the impact angle and time control guidance.

• 대한수학회논문집
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• 제12권4호
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• pp.855-864
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• 1997

Let K be a algebraically closed field of characteristic 0 and G a cyclic group of order n. We find the units and idempotent elements of the group ring KG by using the basic group table matrix of G.

• 한국통신학회논문지
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• 제21권1호
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• pp.251-268
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• 1996

In this paper, a higher-order feedforward neural network called ridge polynomial network (RPN) which shows good approximation capability for nonlnear continuous functions defined on compact subsets in multi-dimensional Euclidean spaces, is presented. This network provides more efficient and regular structure as compared to ordinary higher-order feedforward networks based on Gabor-Kolmogrov polynomial expansions, while maintating their fast learning property. the ridge polynomial network is a generalization of the pi-sigma network (PSN) and uses a specialform of ridge polynomials. It is shown that any multivariate polynomial can be exactly represented in this form, and thus realized by a RPN. The approximation capability of the RPNs for arbitrary continuous functions is shown by this representation theorem and the classical weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental function approximation based on learning algorithm of the PSN. Simulation results on several applications such as multivariate function approximation and pattern classification assert nonlinear approximation capability of the RPN.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권9호
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• pp.430-438
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• 2001

In this study, we introduce the adaptive Polynomial Neuro-Fuzzy Networks(PNFN) architecture generated from the fusion of fuzzy inference system and PNN algorithm. The PNFN dwells on the ideas of fuzzy rule-based computing and neural networks. Fuzzy inference system is applied in the 1st layer of PNFN and PNN algorithm is employed in the 2nd layer or higher. From these the multilayer structure of the PNFN is constructed. In order words, in the Fuzzy Inference System(FIS) used in the nodes of the 1st layer of PNFN, either the simplified or regression polynomial inference method is utilized. And as the premise part of the rules, both triangular and Gaussian like membership function are studied. In the 2nd layer or higher, PNN based on GMDH and regression polynomial is generated in a dynamic way, unlike in the case of the popular multilayer perceptron structure. That is, the PNN is an analytic technique for identifying nonlinear relationships between system's inputs and outputs and is a flexible network structure constructed through the successive generation of layers from nodes represented in partial descriptions of I/O relatio of data. The experiment part of the study involves representative time series such as Box-Jenkins gas furnace data used across various neurofuzzy systems and a comparative analysis is included as well.

• 대한수학회보
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• 제29권2호
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• 한국안광학회지
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• 제14권2호
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• pp.35-39
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• 2009

목적: 본 연구는 각막지형검사기의 각막형상을 이용하여 각막수차를 구현하는 프로그램을 개발하고자 하며, 개발된 프로그램을 이용하여 저니케 다항식(Zernike Polynomial)으로 파면과 각막수차를 구현하고자 한다. 방법: 각막지형검사기인 ORBSCAN의 각막형상 데이터로부터 각막의 형상을 재구성하기 위해 저니케 다항식을 사용하였으며, 이때 동공의 유효구경은 6 mm를 고려하였다. 구현된 각막형상으로부터 광선추적을 사용하여 동일한 광학적 거리의 파면을 구현하는 프로그램을 개발하였으며, 파면으로부터 6차 28항의 저니케 계수로 각막수차를 구현하였다. 결론: 본 연구에서는 각막지형검사기의 각막형상으로부터 각막의 수차와 파면을 구현하는 프로그램을 개발하였으며, 이러한 결과는 각막지형검사기 개발과 콘택트렌즈 및 OK렌즈 처방에 유용하게 적용될 수 있으리라 사료된다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.399-402
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• 1996

The electrodynamic loudspeakers should have a wide dynamic range to reproduce various sound levels. When the input signal is small, the radiated sound from the loudspeaker is not so much distorted. However, for large input signal with low frequency component the radiated sound is significantly distorted due to the nonlinearities of the loudspeaker. The suspension, damping, and magnetic flux of loudspeaker are the main sources of the nonlinearity. Such electromechanical parameters related to harmonic distortion have been represented by a polynomial model for diaphragm displacement, while each of the polynomial coefficient is evaluated by using the principle of harmonic balance experimentally. Based on the polynomial model, we designed a compensator for nonlinear harmonic distortion of direct radiator loudspeaker. Than observer is used to estimate the displacement of the loudspeaker diaphragm, which is rather difficult to measure directly in the conventional setting. The usefulness of the designed compensator is demonstrated by numerical simulations. Simulation results show about 30db decrease at the second and third higher harmonic distortions. We carry out an experiment on speaker to verify designed controller and nonlinear observer.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2004년도 Asia Navigation Conference
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• pp.29-36
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• 2004

The paper describes recent experimental results on the development of Digital Magnetic Compass (DMC), which can provide smart automatic correction functions to the magnetic interferences. The design methodology of magnetic sensing circuit with ring-core fluxgate sensor is represented. The performance results of the sensing circuits are discussed with error analysis by polynomial regressions. As test results, the sensing circuit filtered only the second harmonic signal that is proportional to the direction of earth's magnetic field, and it leads to the obtainment of bearing information. In addition, the total residual errors of DMC can be analyzed by the adoption of polynomial regressions. It shown that the possibility of high precise DMC, in the future.