• East Asian mathematical journal
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• 제40권3호
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• pp.329-339
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• 2024

In the work we generate arithmetic matrix P^(c,b,a) of (cx² + bx+a)ⁿ from a Pascal matrix P^(1,1). We extend an identity P^(1,1))O^(1,1) = P^(1,1,1) with an obtuse matrix O^(1,1) to k degree polynomials. For the purpose we study P^(1,1)kO^(1,1) and find generating polynomials of O^(1,1)k.

• Communications for Statistical Applications and Methods
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• 제19권2호
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• pp.267-276
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• 2012

Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

• 대한수학회보
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• 제53권4호
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• pp.1149-1156
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• 2016

In this paper, we introduce the degenerate Carlitz q-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and p-adic integral equations.

• East Asian mathematical journal
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• 제30권2호
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• pp.93-121
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• 2014

In this paper we study generating and proving methods of symmetric inequalities. We analyze various literatures related with proofs of symmetric inequalities. As a result, we can describe generating method of symmetric inequalities, and suggest some symmetric inequalities that are generated by using parameterization to elementary symmetric polynomials. And we are able to classify some proving methods, and show proofs of symmetric inequalities.

• 융합신호처리학회논문지
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• 제15권2호
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• pp.48-54
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• 2014

원소 ${\in}F(p)$에 대하여 두 종류의 기저함수가 알려져 있다. 통상적인 다항식 기저(polynomial bases)는 $\{1,{\alpha},{\alpha}^2,{\cdots},{\alpha}^{n-1}\}$로 이루어지고 이와 다르게 정규 기저(normal bases)는 $\{{\alpha},{\alpha}^p,{\alpha}^{p^2},{\cdots},{\alpha}^{p^{n-1}}\}$의 형태를 갖는다. 본 논문에서는 소수 p의 원소로 이루어지는 유한장 GF(p)상에서 n차원 벡터공간인 확대장 $GF(p^n)$을 이룰 수 있는 정규기저의 발생과 생성에 대하여 검토하고 정규기저를 기반으로 부호계열 발생알고리즘을 분석하여 발생기구성함수를 도출하였다. 차수 n=5와 n=7인 두 종류의 정규기저를 생성할 수 있는 정규다항식을 발견하고 부호계열 발생기를 설계 구성하였다. 마지막으로 Simulink를 이용하여 두 종류(n=5, n=7)의 부호계열 그룹을 발생시키고 발생된 부호계열간의 자기상관함수, $R_{i,i}(\tau)$와 상호상관함수, $R_{i,j}(\tau)$, $i{\neq}j$ 특성을 분석하였다. 이 결과로부터 정규기저를 이용한 부호계열 발생알고리즘의 분석, 그리고 부호계열 발생기 설계와 구성이 타당함을 확인하였다.

• 전기학회논문지
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• 제66권12호
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• pp.1772-1781
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• 2017

In this study, the design methodology for alleviating the overfitting problem of Polynomial Neural Networks(PNN) is realized with the aid of two kinds techniques such as L2 regularization and Sum of Squared Coefficients (SSC). The PNN is widely used as a kind of mathematical modeling methods such as the identification of linear system by input/output data and the regression analysis modeling method for prediction problem. PNN is an algorithm that obtains preferred network structure by generating consecutive layers as well as nodes by using a multivariate polynomial subexpression. It has much fewer nodes and more flexible adaptability than existing neural network algorithms. However, such algorithms lead to overfitting problems due to noise sensitivity as well as excessive trainning while generation of successive network layers. To alleviate such overfitting problem and also effectively design its ensuing deep network structure, two techniques are introduced. That is we use the two techniques of both SSC(Sum of Squared Coefficients) and $L_2$ regularization for consecutive generation of each layer's nodes as well as each layer in order to construct the deep PNN structure. The technique of $L_2$ regularization is used for the minimum coefficient estimation by adding penalty term to cost function. $L_2$ regularization is a kind of representative methods of reducing the influence of noise by flattening the solution space and also lessening coefficient size. The technique for the SSC is implemented for the minimization of Sum of Squared Coefficients of polynomial instead of using the square of errors. In the sequel, the overfitting problem of the deep PNN structure is stabilized by the proposed method. This study leads to the possibility of deep network structure design as well as big data processing and also the superiority of the network performance through experiments is shown.

• 한국측량학회:학술대회논문집
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• 한국측량학회 2003년도 추계학술발표회 논문집
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• pp.417-422
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• 2003

The KOMPSAT-2 MSC(Multi-Spectral Camera), with high spatial resolution, is currently under development and will be launched in the end of 2004. A sensor model relates a 3-D ground position to the corresponding 2-D image position and describes the imaging geometry that is necessary to reconstruct the physical imaging process. The Rational Function Model (RFM) has been considered as a generic sensor model. form. The RFM is technically applicable to all types of sensors such as frame, pushbroom, whiskbroom and SAR etc. With the increasing availability of the new generation imaging sensors, accurate and fast rectification of digital imagery using a generic sensor model becomes of great interest to the user community. This paper describes the procedure to generation of the RPC (Rational Polynomial Coefficients) for KOMPSAT-2 MSC.

• 대한수학회지
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• 제54권4호
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• pp.1243-1264
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• 2017

In this paper, we introduce w-Catalan polynomials as a generalization of Catalan polynomials and derive fourteen basic identities of symmetry in three variables related to w-Catalan polynomials and analogues of alternating power sums. In addition, specializations of one of the variables as one give us new and interesting identities of symmetry even for two variables. The derivations of identities are based on the p-adic integral expression for the generating function of the w-Catalan polynomials and the quotient of p-adic integrals for that of the analogues of the alternating power sums.

• 한국통신학회논문지
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• 제18권1호
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• pp.150-156
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• 1993

본 논문에서는 정보통신에 있어서 수신자가 송신자 및 송신문을 인증하는 방법으로써Galois Field에서의 다항식을 이용한 암호가 기법을 적용하여 인증에 걸리는 처리속도를 향상시켰으며, 또한 송신자에 대한 인증정보를 대화방식으로 영지식증명 절차를 이용하여 생성하고, 이를 송신문에대한 인증정보에 포함하여 전송하므로써 비밀정보 교환의 안전성을 강화하였다.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.973-981
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• 2008

In this paper we focus on a type of Unimodular polynomial pair used for digital systems and present some new properties of them which lead us to estimation of their autocorrelation coefficients and the moments of a Rudin-Shapiro polynomial product. Some new results on the Rudin-shapiro sequences will be presented in the last section. Main Facts: For positive integers M and n with $M\;<\;2^n$ - 1, consider the $2^n$ - M numbers ${\epsilon}_k$ ($M\;{\leq}\;k\;{\leq}\;2^n$ - 1) which form a collection of Rudin-Shapiro coefficients. We verify that $|{\sum}_{k=M}^{2^{n-1}}\;{{\epsilon}_k}e^{ikt}|$ is dominated by $(2+\sqrt{2})\;\sqrt {2^n-M}-{\sqrt{2}}$.