• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.943-956
• /
• 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
• /
• v.11 no.4
• /
• pp.297-304
• /
• 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
• /
• v.37 no.1_2
• /
• pp.23-35
• /
• 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
• /
• v.33 no.3
• /
• pp.313-321
• /
• 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.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.14 no.6
• /
• pp.25-30
• /
• 2004

Linear cellular automata(CA) which generate maximum-length cycles, have wide applications in generation of pseudo-random patterns, signature analysis, cryptography and error correcting codes etc. Linear CA whose characteristic polynomial is primitive has been studied. In this paper Ive propose a effective method for generation of a variety of maximum-length CA(MLCA). And we show that the complemented CA's derived from a linear MLCA are all MLCA. Also we analyze the Properties of complemented MLCA. And we prove that the number of n-cell MLCA is ${\phi}(2^{n}-1)2^{n+1}$/n.

• Journal of Korea Society of Digital Industry and Information Management
• /
• v.7 no.4
• /
• pp.7-14
• /
• 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
• /
• v.28 no.3
• /
• pp.813-830
• /
• 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.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.14 no.1
• /
• pp.235-242
• /
• 2019

Self-reciprocal polynomials over finite fields are useful in several applications, including reversible codes with read-backward properties. This paper is a study on 90/150 CA with characteristic polynomials of maximal weight polynomials, which is one of the self-reciprocal polynomials. In this paper, we propose a decision method for determining the existence of 90/150 MWCA corresponding to the maximum weight polynomial of degree 2n using n-cell 90/150 CA with transition rule <$100{\cdots}0$>. The proposed method is verified through experiments.

• Proceedings of the IEEK Conference
• /
• 2001.06b
• /
• pp.129-132
• /
• 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.

• Korean Journal of Food Science and Technology
• /
• v.37 no.2
• /
• pp.194-198
• /
• 2005

Growth curves of Listeria monocytogenes in modified surimi-based imitation crab (MIC) broth were obtained by measuring cell concentration in MIC broth at different culture conditions [initial cell numbers, $1.0{\times}10^{2},\;1.0{\times}10^{3}\;and\;1.0{\times}10^{4}$, colony forming unit (CFU)/mL; temperature, 15, 20, 25, 37, and $40^{\circ}C$] and applied to Gompertz model to determine microbial growth indicators, maximum specific growth rate constant (k), lag time (LT), and generation time (GT). Maximum specific growth rate of L. monocytogenes increased rapidly with increasing temperature and reached maximum at $37^{\circ}C$, whereas LT and GT decreased with increasing temperature and reached minimum at $37^{\circ}C$. Initial cell number had no effect on k, LT, and GT (p > 0.05). Polynomial and square root models were developed to express combined effects of temperature and initial cell number using Gauss-Newton Algorism. Relative coefficients of experimental k and predicted k of polynomial and square root models were 0.92 and 0.95, respectively, based on response surface model. Results indicate L. monocytogenes growth was mainly affected by temperature and square root model was more effective than polynomial model for growth prediction.