• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.943-956
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• 2023

Let p(z) be a polynomial of degree n and for any complex number 𝛽, let D_𝛽p(z) = np(z) + (𝛽 - z)p'(z) denote the polar derivative of the polynomial with respect to 𝛽. In this paper, we consider the class of polynomial $$p(z)=(z-z_0)^s \left(a_0+\sum\limits_{{\nu}=0}^{n-s}a_{\nu}z^{\nu}\right)$$ of degree n having a zero of order s at z₀, |z₀| < 1 and the remaining n - s zeros are outside |z| < k, k ≥ 1 and establish upper bound estimates for the maximum of |D_𝛽p(z)| as well as |p(Rz) - p(rz)|, R ≥ r ≥ 1 on the unit disk.

• Journal of Positioning, Navigation, and Timing
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• 제11권4호
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• pp.297-304
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• 2022

The models used for ionosphere error correction in positioning using Global Navigation Satellite System (GNSS) are representatively Klobuchar model and NeQuick model. Although these models can correct the ionosphere error in real time, the disadvantage is that the accuracy is only 50-60%. In this study, a method for polynomial modeling of Global Ionosphere Map (GIM) which provides Vertical Total Electron Content (VTEC) in grid type was studied. In consideration of Ionosphere Pierce Points (IPP) of satellites with a receivable elevation angle of 15 degrees or higher on the Korean Peninsula, the target area for model generation and provision was selected, and the VTEC at 88 GIM grid points was modeled as a polynomial. The developed VTEC polynomial model shows a data reduction rate of 72.7% compared to GIM regardless of the number of visible satellites, and a data reduction rate of more than 90% compared to the Slant Total Electron Content (STEC) polynomial model when there are more than 10 visible satellites. This VTEC polynomial model has a maximum absolute error of 2.4 Total Electron Content Unit (TECU) and a maximum relative error of 9.9% with the actual GIM. Therefore, it is expected that the amount of data can be drastically reduced by providing the predicted GIM or real-time grid type VTEC model as the parameters of the polynomial model.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.23-35
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• 2019

Self-reciprocal polynomials are important because it is possible to specify only half of the coefficients. The special case of the self-reciprocal polynomial, the maximum weight polynomial, is particularly important. In this paper, we analyze even cell 90/150 cellular automata with linear rule blocks of the form < $a_1,{\cdots},a_n,d_1,d_2,b_n,{\cdots},b_1$ >. Also we show that there is no 90/150 CA of the form < $U_n{\mid}R_2{\mid}U^*_n$ > or < $\bar{U_n}{\mid}R_2{\mid}\bar{U^*_n}$ > whose characteristic polynomial is $f_{2n+2}(x)=x^{2n+2}+{\cdots}+x+1$ where $R_2$ =< $d_1,d_2$ > and $U_n$ =< $0,{\cdots},0$ >, and $\bar{U_n}$ =< $1,{\cdots},1$ >.

• Journal of the Korean Statistical Society
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• 제33권3호
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• 정보보호학회논문지
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• 제14권6호
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• pp.25-30
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• 2004

최대길이를 갖는 선형 90/150 셀룰라 오토마타(CA)가 패턴생성, 신호분석, 암호, 오류정정 부호에 응용되면서 n차 원시다항식을 특성다항식으로 갖는 선형 CA에 관한 연구가 활발하게 이루어지고 있다. 본 논문은 최대길이를 갖는 다양한 셀룰라 오토마타의 효과적인 생성방법을 제안한다. 특성다항식이 n차 원시다항식인 선형이며 최대길이를 갖는 CA(MLCA)로부터 유도된 여원 CA가 MLCA임을 밝히며 여원 MLCA의 여러 가지 성질들을 분석한다 또한 n-셀 MLCA를 ${\phi}(2^{n}-1)2^{n+1}$/n.개 생성할 수 있음을 보인다.

• 디지털산업정보학회논문지
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• 제7권4호
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• pp.7-14
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• 2011

Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rate per fault (hazard function). This infinite non-homogeneous Poisson process is model which reflects the possibility of introducing new faults when correcting or modifying the software. In this paper, polynomial hazard function have been proposed, which can efficiency application for software reliability. Algorithm for estimating the parameters used to maximum likelihood estimator and bisection method. Model selection based on mean square error and the coefficient of determination for the sake of efficient model were employed. In numerical example, log power time model of the existing model in this area and the polynomial hazard function model were compared using failure interval time. Because polynomial hazard function model is more efficient in terms of reliability, polynomial hazard function model as an alternative to the existing model also were able to confirm that can use in this area.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.813-830
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• 2023

Let p(z) be a polynomial of degree n having no zero in |z| < 1. In this paper, by involving some coefficients of the polynomial, we prove an inequality that not only improves as well as generalizes the well-known result proved by Rivlin but also has some interesting consequences.

• 한국전자통신학회논문지
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• 제14권1호
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• pp.235-242
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• 2019

유한체 상에서 자기상반다항식은 역방향읽기 성질을 갖는 가역 부호를 설계하는 데 유용하다. 본 논문은 자기상반다항식 중 하나인 최대무게 다항식을 특성다항식으로 갖는 90/150 CA에 관한 연구이다. 전이규칙이 <$100{\cdots}0$>인 n-셀 90/150 CA를 이용하여 2n차 최대무게 다항식에 대응하는 90/150 MWCA가 존재하는지에 대한 판정법을 제안한다. 제안하는 방법은 실험을 통하여 검증한다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 하계종합학술대회 논문집(2)
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• pp.129-132
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• 2001

This paper presents an efficient method to estimate the maximum SSN (simultaneous switching noise) for ground interconnection networks in CMOS systems using Taylor's series and analyzes the truncation error that has occurred in Taylor's series approximation. We assume that the curve form of noise voltage on ground interconnection networks is linear and derive a polynomial expression to estimate the maximum value of SSN using $\alpha$-power MOS model. The maximum relative error due to the truncation is shown to be under 1.87% through simulations when we approximate the noise expression in the 3rd-order polynomial.

• 한국식품과학회지
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• 제37권2호
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• pp.194-198
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• 2005

게맛살의 HACCP system에 있어서 critical control point중의 하나인 L. monocytogenes가 오염된 제품에서 균의 성장변화를 정량적으로 예측할 수 있는 수학적 모델의 개발을 위한 기초 자료를 제공하고자 게맛살 성분조성을 고려한 modified imitation crab(MIC) broth에서 온도와 초기균수에 따른 L. monocytogenes의 성장 실험 결과를 데이터베이스화하여 이를 바탕으로 균의 성장을 정량적으로 평가할 수 있는 수학적 모델을 개발하였다. 균의 증식 지표인 최대증식속도상수(k), 유도기(LT), 세대시간(GT)은 온도에 지배적인 영향을 받았으며, 초기균수에 따른 유의적인 차이는 없었다(p>0.05). 최대증식속도상수(k)와 온도 및 초기균수의 상관관계를 나타내는 수학적 정량평가모델인 polynomial model과 square root model을 이용하여 L. monocytogenes 성장을 정량적으로 예측할 수 있는 모델인 $polynomial\;mode(k=0.71{\cdot}exp(-0.5(\;((T-36.05)/11.84)^{2}+((A_{0}+8.12)/21.59)^{2})))$과 square root model($\sqrt{k}$ =0.02(T-(-3.42)) [1-exp(0.36(T-44.51))])을 개발하였으며 실험치와 예측치의 상관관계는 각각 0.92. 0.95로 polynomial model보다 square root model 예측치가 실험치와 상관관계가 더 높은 것으로 나타났다.