• 대한수학회논문집
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• 제11권4호
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• pp.1159-1174
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• 1996

The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

• Journal of information and communication convergence engineering
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• 제16권3호
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• pp.166-172
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• 2018

A pseudo-random sequence generated by using a primitive polynomial, trace function, and Legendre symbol has been researched in our previous work. Our previous sequence has some interesting features such as period, autocorrelation, and linear complexity. A pseudo-random sequence widely used in cryptography. However, from the aspect of the practical use in cryptographic systems sequence needs to generate swiftly. Our previous sequence generated by utilizing a primitive polynomial, however, finding a primitive polynomial requires high calculating cost when the degree or the characteristic is large. It’s a shortcoming of our previous work. The main contribution of this work is to find some relation between the generated sequence and irreducible polynomials. The purpose of this relationship is to generate the same sequence without utilizing a primitive polynomial. From the experimental observation, it is found that there are (p - 1)/2 kinds of polynomial, which generates the same sequence. In addition, some of these polynomials are non-primitive polynomial. In this paper, these relationships between the sequence and the polynomials are shown by some examples. Furthermore, these relationships are proven theoretically also.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.286-286
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• 2000

We consider a negative unity feedback control system in which Che PIO, PI, PD or P controller and a transfer function having only poles are in cascade, We define the notion of the structural polynomial which means that there exists a subdomain of the coefficient space in which the polynomial is Hurwitz (left half plane stable) polynomial. We obtain the necessary and sufficient condition of the structure of the transfer function of which the characteristic polynomial is a structural polynomial, In addition, this paper present another necessary and sufficient condition for the existence of a constant gain controller with which the characteristic polynomial is structurally stable, For the structurally stabilizable P controller, it is allowed that the transfer function may not to all pole plants.

• 대한수학회보
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• 제46권5호
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• pp.941-947
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• 2009

Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.11-15
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• 2005

This paper presents a method to determine the characteristic polynomial of a closed loop all-pole system in order to obtain desired transient response in terms of the overshoot and speed (rising/settling time). The method adjusts the overshoot by doing some changes in the characteristic ratios of the Bessel-Thompson filter. The closed loop speediness is then tuned by suitable choice of the generalized time constant. Simulation results are presented to evaluate the achievements and make comparison with those of a similar method.

• 제어로봇시스템학회논문지
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• 제10권4호
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• pp.295-303
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• 2004

Previously it has been shown that the all pole systems resulting good time responses can be characterized by so called K-polynomial. The polynomial is defined in terms of the principal characteristic ratio $\alpha_1$ and the generalized time constant $\tau$ . In this paper, Part II presents several sensitivity analyses of such systems with respect to $\alpha_1$ and $\tau$ changes. We first deal with the root sensitivity to the perturbation of $\alpha_1$ . By way of determining the unnormalized function sensitivity, both time response sensitivity and frequency response sensitivity are derived. Finally, the root sensitivity relative to $\tau$ change is also analyzed. These results provide some useful insight and background theory when we select of and l to compose a reference model of which denominator is a K-polynomial, which is illustrated by examples.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2009년도 추계학술대회
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• pp.160-163
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• 2009

HPA(High Power Amplifier)는 무선통신 시스템에서 필수적으로 요구되는 요소 중의 하나다. 그러나 전력 증폭기는 비선형 특성을 가지고 있으며 신호의 비선형 왜곡을 유발 시키고 인접채널 간섭을 심화시켜 시스템의 효율을 떨어뜨린다. 이러한 문제점을 해결하기 위해 많은 선형화 기법들이 제시되어왔다. 다항식 사전왜곡 기법은 증폭기로 입력되는 신호가 미리 증폭기의 역 특성을 갖도록 하는 기법으로 다항식을 통하여 증폭기를 모델링하기 때문에 수렴 속도가 빠르고 다른 기법들에 비해 좋은 성능을 보인다. 하지만 다항식으로 역 비선형 특성을 구할 경우, 증폭기의 포화영역에서 역 비선형 특성이 거의 무한대가 되어야 하기 때문에 선형화기의 성능이 크게 떨어진다. 본 논문에서는 이러한 문제점을 해결하기 위하여 PAPR(Peak-to-Average Power Ratio) 기법을 적용하여 다항식 사전왜곡 기법의 성능을 향상 시켰다.

• 대한수학회보
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• 제33권1호
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• pp.75-86
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• 1996

Let G be a finite simple connected graph with vertex set V(G) and edge set E(G). Let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial $\Phi(G;\lambda) = det(\lambda I - A(G))$ of A(G). A zero of $\Phi(G;\lambda)$ is called an eigenvalue of G.

• 대한수학회지
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• 제54권5호
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• pp.1595-1604
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• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1289-1295
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• 2008

We find the generalized characteristic polynomial of graphs G($F_{1},F_{2},{\cdots},F_{v}$) the semi-zigzag product of G and ${\{F_{i}\}^{v}_{i=1}$ obtained from G by replacing vertices by circulant graphs of vertices and joining $F_{i}$'s along the edges of G. These graphs contain discrete tori and are key examples in the study of network model.