• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.83-93
• /
• 2019

Let R be a noncommutative prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R and f($x_1,{\ldots},x_n$) a noncentral multilinear polynomial over C in n noncommuting variables. Denote by f(R) the set of all the evaluations of f($x_1,{\ldots},x_n$) on R. If d is a nonzero derivation of R and G a nonzero generalized derivation of R such that $$d(G(u)u){\in}Z(R)$$ for all $u{\in}f(R)$, then $f(x_1,{\ldots},x_n)^2$ is central-valued on R and there exists $b{\in}U$ such that G(x) = bx for all $x{\in}R$ with $d(b){\in}C$. As an application of this result, we investigate the commutator $[F(u)u,G(v)v]{\in}Z(R)$ for all $u,v{\in}f(R)$, where F and G are two nonzero generalized derivations of R.

• Journal of the Korean Society for Precision Engineering
• /
• v.18 no.11
• /
• pp.58-66
• /
• 2001

GPC has been reported as a useful self-tuning control algorithm for systems with unknown time-delay and parameters. GPC is easy to understand and implement, and thus has won popularity among many practicing engineers. Despite its success, GPC does not guarantee is nominal stability. So, in this paper, GPC is rederived in frequency domain instead of in the time domain to guarantee its nominal stability. Derivation of GPC in frequency domain involves spectral factorization and Diophantine equation. Frequency domain GPC control law is stable because the zeros of characteristic polynomial are strictly Schur. Recursive least square algorithm is used to identify unknown parameters. To see the effectiveness of the proposed controller, the controller is simulated for a numerical problem that changes in dead-time, in order and in parameters.

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

• Proceedings of the KIEE Conference
• /
• 2003.11b
• /
• pp.127-130
• /
• 2003

In this paper, a hypothesis in order that the impulse response of a stable linear system does not change sign is suggested. For fixed zeros of the systems, the problem of synthesizing such a system is reduced to the problem of finding a proper denominator polynomial so that the step response of the overall system will not overshoot. The hypothesis is associated with the generalized time constant by Kim[5]. Under the hypothesis, we propose several methods that allow to compose a continuous time LTI systems achieving non-negative impulse response.

• ETRI Journal
• /
• v.21 no.1
• /
• pp.28-39
• /
• 1999

Koblitz has suggested to use "anomalous" elliptic curves defined over ${\mathbb{F}}_2$, which are non-supersingular and allow or efficient multiplication of a point by and integer, For these curves, Meier and Staffelbach gave a method to find a polynomial of the Frobenius map corresponding to a given multiplier. Muller generalized their method to arbitrary non-supersingular elliptic curves defined over a small field of characteristic 2. in this paper, we propose an algorithm to speed up scalar multiplication on an elliptic curve defined over a small field. The proposed algorithm uses the same field. The proposed algorithm uses the same technique as Muller's to get an expansion by the Frobenius map, but its expansion length is half of Muller's due to the reduction step (Algorithm 1). Also, it uses a more efficient algorithm (Algorithm 3) to perform multiplication using the Frobenius expansion. Consequently, the proposed algorithm is two times faster than Muller's. Moreover, it can be applied to an elliptic curve defined over a finite field with odd characteristic and does not require any precomputation or additional memory.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.13 no.4
• /
• pp.819-826
• /
• 2018

The generalized Hamming weight is one of the important parameters of the linear code. It determines the performance of the code when the linear codes are applied to a cryptographic system. In addition, when the block code is decoded by soft decision using the lattice diagram, it becomes a measure for evaluating the state complexity required for the implementation. In particular, a bit-parallel multiplier on finite fields based on trinomials have been studied. Cellular automata(CA) has superior randomness over LFSR due to its ability to update its state simultaneously by local interaction. In this paper, we deal with the efficient synthesis of the pseudo random number generator, which is one of the important factors in the design of effective cryptosystem. We analyze the property of the characteristic polynomial of the simple 90/150 transition rule block, and propose a synthesis algorithm of the reversible 90/150 CA corresponding to the trinomials $x^2^n+x^{2^n-1}+1$($n{\geq}2$) and the 90/150 reversible CA(RCA) corresponding to the maximum weight polynomial with $2^n$ degree by using this rule block.