• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1995.11a
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• pp.200-210
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• 1995

Almost all hash functions suggested up till now provide security by using complicated operations on fixed size blocks, but still the security isn't guaranteed mathematically. The difficulty of making a secure hash function lies in the collision freeness, and this can be obtained from permutation polynomials. If a permutation polynomial has the property of one-wayness, it is suitable for a hash function. We have chosen Dickson polynomial for our hash algorithm, which is a kind of permutation polynomials. When certain conditions are satisfied, a Dickson polynomial has the property of one-wayness, which makes the resulting hash code mathematically secure. In this paper, a message digest algorithm will be designed using Dickson polynomial.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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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.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.247-263
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• 2023

In this article, we investigate the uniqueness problem of q-shift difference polynomial of meromorphic (entire) function with zero-order. Consequently, we prove three results with significantly generalize the results of Goutam Haldar.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.597-600
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• 1997

In this paper, the authors propose a new method for linearizing a nonlinear dynamical system by use of polynomial compensation. In this method, an M-sequence is applied to the nonlinear system and the crosscorrelation function between the input and the output gives us every crosssections of Volterra kernels of the nonlinear system up to 3rd order. We construct a polynomial compensation function from comparison between lst order Volterra kernel and high order kernels. The polynomial compensation function is, in this case, of third order whose coefficients are variable depending on the amplitude of the input signal. Once we can get compensation function of nonlinear system, we can construct a linearization scheme of the nonlinear system. That is. the effect of second and third order Volterra kernels are subtracted from the output, thus we obtain a sort of linearized output. The authors applied this method to a saturation-type nonlinear system by simulation, and the results show good agreement with the theoretical considerations.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.307-313
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• 2006

In this paper, we first establish an interesting new finite integral whose integrand involves the product of a general class of polynomials introduced by Srivastava [13] and the generalized H-function ([9], [10]) having general argument. Next, we present five special cases of our main integral which are also quite general in nature and of interest by themselves. The first three integrals involve the product of $\bar{H}$-function with Jacobi polynomial, the product of two Jacobi polynomials and the product of two general binomial factors respectively. The fourth integral involves product of Jacobi polynomial and well known Fox's H-function and the last integral involves product of a Jacobi polynomial and 'g' function connected with a certain class of Feynman integral which may have practical applications.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.701-712
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• 2009

In this paper, we study the simultaneous approximation to functions in $C^m$[0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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• pp.89-99
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• 2006

In this paper a new shape reconstruction method that allows us to construct surface models from very large sets of points is presented. In this method the global domain of interest is divided into smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together according to weighting coefficients to obtain a global solution using partition of unity function. The suggested approach gives us considerable flexibility in the choice of local shape functions which depend on the local shape complexity and desired accuracy. At each domain, a quadratic polynomial function is created that fits the points in the domain. If the approximation is not accurate enough, other higher order functions including cubic polynomial function and RBF(Radial Basis Function) are used. This adaptive selection of local shape functions offers robust and efficient solution to a great variety of shape reconstruction problems.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.247-260
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• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Proceedings of the IEEK Conference
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• 2009.05a
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• pp.261-263
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• 2009

본 연구에서는 복잡한 비선형 모델링 방법인 RBF 뉴럴 네트워크(Radial Basis Function Neural Network)와 PNN(Polynomial Neural Network)을 접목한 새로운 형태의 Radial Basis Function Polynomial Neural Network(RPNN)를 제안한다. RBF 뉴럴 네트워크는 빠른 학습 시간, 일반화 그리고 단순화의 특징으로 비선형 시스템 모델링 등에 적용되고 있으며, PNN은 생성된 노드들 중에서 우수한 결과값을 가진 노드들을 선택함으로써 모델의 근사화 및 일반화에 탁월한 효과를 가진 비선형 모델링 방법이다. 제안된 RPNN모델의 기본적인 구조는 PNN의 형태를 이루고 있으며, 각각의 노드는 RBF 뉴럴 네트워크로 구성하였다. 사용된 RBF 뉴럴 네트워크에서의 커널 함수로는 FCM 클러스터링을 사용하였으며, 각 노드의 후반부는 다항식 구조로 표현하였다. 또한 각 노드의 후반부 파라미터들은 최소자승법을 이용하여 최적화 하였다. 제안한 모델의 적용 및 유용성을 비교 평가하기 위하여 비선형 데이터를 이용하여 그 우수성을 보인다.

• Journal of Environmental Impact Assessment
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• v.16 no.5
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• pp.341-350
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• 2007

Lake Youngrang is a lagoon whose effluent flows into the East Sea. Because two resort towns and two golf courses are situated at the lake basin, many tourists visit this area. Stormwater runoff surveys were carried out for the eight storm events from 2004 to 2005 in the eutrophic lake watershed to give a basic data for the diffuse pollution control of the lake. Dimensionless mass-volume curves indicating the distribution of pollutant mass vs. volume were used to analyze the first flush phenomenon. The mass-volume curves were fitted with a power function and polynomial equation curves. The regression analysis showed that the polynomial equation curves were better than the power function in representing the tendency of the first flush, and second degree polynomial equation curves indicated the strength of the first flush effectively.