• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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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.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.147-168
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• 2002

In this paper, we introduce the arrangement of hyperplanes and the graph theory. In particular, we explain how to study the 4-color problem by using characteristic polynomials of the arrangement of hyperplanes. The 4-color problem was appeared in 1852 at first and Appel and Haken proved it by using computer in 1976. The arrangement of hyperplanes induced from a graph is called a graphic arrangement. Graphic arrangement is a subarrangement of Braid arrangement. Thus the chromatic function of a graph is equal to the characteristic polynomial of a graphic arrangement. If we use this result, we can apply the theory of the arrangement of hyperplanes to the study for the chromatic functions.

• Journal of Industrial Technology
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• v.11
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• pp.27-31
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• 1991

Consider a problem to keep half of the poles unchanged when some of the coefficients of stable characteristic polynomials are perturbed. A procedure was proposed for the problem. However, the pole assignment procedure has not been addressed. A simple algorithm for the procedure is proposed in this paper.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5C
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• pp.443-451
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• 2003

We propose an appropriate approach of defining the linear complexities (LC) of sequences over unknown symbol set. We are able to characterize those p-ary sequences whose R-tuple versions now eve. GF($p^{R}$ ) have the same characteristic polynomial as the original with respect to any basis. This leads to a construction of $p^{R}$ -ary sequences whose characteristic polynomial is essentially over GF(p). In addition, we can characterize those $p^{R}$ -ary sequences whose characteristic polynomials are uniquely determined when symbols are represented as R-tuples over GF(p) with respect to any basis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.137-145
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• 1999

In this paper, We consider two-dimensional Maximum Length Cellular Automata (2-D MLCA) as an extension of the 1-D MLCA. 2-D MLCA can display much better random patterns than those generated by 1-D CA and LFSR. To generate random pattern, a CA should have a maximum length cycle. So, it is necessary to find MLCA that the characteristic polynomial of the transition matrix is primitive. New boundary conditions of 3 types are proposed and some rules having primitive polynomials of 2-D MLCA are found.

• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.53-67
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• 1999

The natural frequencies and modes of free vibration of specially orthotropic elliptic and circular plates are analysed using the Rayleigh-Ritz method. The assumed functions used are two-dimensional boundary characteristic orthogonal polynomials which are generated using the Gram-Schmidt orthogonalization procedure. The first five natural frequencies are reported here for various values of aspect ratio of the ellipse. Results are given for various boundary conditions at the edges i.e., the boundary may be any of clamped, simply-supported or fret. Numerical results are presented here for several orthotropic material properties. For rectilinear orthotropic circular plates, a few results are available in the existing literature, which are compared with the present results and are found to be in good agreement.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.623-628
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• 2004

In this study, the assumed-mode method using characteristic polynomials of Timoshenko beam is applied for the free vibration analysis of rectangular stiffened plates. The polynomial is derived considering the rotational constraint along the boundary edges of plate and the orthogonal relation of Timoshenko beam functions, which enables to simplify the free vibration analysis of plate structure having various boundary conditions. To verify the validity and effectiveness of the adopted method, numerical analysis for cross-stiffened plates were carried out and its results were compared with those obtained by the general purpose FEA software.

• ETRI Journal
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• v.28 no.6
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• pp.745-760
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• 2006

In this paper, we particularly deal with no $F_p$-rational two-torsion elliptic curves, where $F_p$ is the prime field of the characteristic p. First we introduce a shift product-based polynomial transform. Then, we show that the parities of (#E - 1)/2 and (#E' - 1)/2 are reciprocal to each other, where #E and #E' are the orders of the two candidate curves obtained at the last step of complex multiplication (CM)-based algorithm. Based on this property, we propose a method to check the parity by using the shift product-based polynomial transform. For a 160 bits prime number as the characteristic, the proposed method carries out the parity check 25 or more times faster than the conventional checking method when 4 divides the characteristic minus 1. Finally, this paper shows that the proposed method can make CM-based algorithm that looks up a table of precomputed class polynomials more than 10 percent faster.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.10
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• pp.1259-1268
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• 1995

This note presents the robust root clustering problem of interval systems whose characteristic equation might be given as either a family of interval polynomials or a family of polytopes. Corresponding to damping ratio and robustness margin approximately, we consider a certain class of D-region such as parabola, left-hyperbola, and ellipse in complex plane. Then a simpler D-stability criteria using rational function mapping is presented and prove. Without .lambda. or .omega. sweeping calculation, the absolute criteria for robust D-stability can be determined.