• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.245-248
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• 2007

This paper provides some simple recursive formulas generation transition functions of finite cellular automata with triplet local transition functions under two states (0 and 1) and four different boundary conditions (0-0,0-1,1-0,1-1), and classify transition functions into several classes.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.127-142
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• 2008

In this paper, we introduce four different approaches of proving Cayley formula, which counts the number of trees(acyclic connected simple graphs). The first proof was done by Cayley using recursive formulas. On the other hands the core idea of the other three proofs is the bijective method-find an one to one correspondence between the set of trees and a suitable family of combinatorial objects. Each of the three bijection gives its own generalization of Cayley formula. In particular, the last proof, done by Seo and Shin, has an application to computer science(theoretical computation), which is a typical example that pure mathematics supply powerful tools to other research fields.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.4B
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• pp.394-402
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• 2009

In this paper, we present a new analytical model for estimating the blocking performance of multi-fiber WDM networt:s with sparse and limited wavelength conversion (SLWC). The proposed model is a reduced-load approximation model that can obtain accurate estimates of blocking probability of such networks. Our model employs three new recurrence formulae to obtain the free wavelength distribution on a multi-fiber link, the free wavelength distribution after limited-range wavelength conversion and the end-to-end blocking probability of a multi-hop path, respectively. From the numerical results on the NSFNET, we demonstrate that the blocking performance of two-fiber NSFNET with three wavelength-convertible nodes, each of which translates an input wavelength to its adjacent output wavelengths, closely approximates the blocking performance of full wavelength conversion.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.10
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• pp.188-198
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• 2013

Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.