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IRREDUCIBILITY OF POLYNOMIALS AND DIOPHANTINE EQUATIONS
우성식 대한수학회 2010 대한수학회지 Vol.47 No.1
In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coefficients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over Q which are not of Eisenstein type.
The group of units of some finite local rings III
우성식 대한수학회 2009 대한수학회지 Vol.46 No.4
As a sequel to the papers [2, 3], we will complete our identification of the groups of units of the finite local rings Z_4[X]/(X^k+2t(X),2X^r) which is the most general type of finite local rings with a single nilpotent generator over Z_4.
Free cyclic codes over finite local rings
우성식 대한수학회 2006 대한수학회보 Vol.43 No.4
In [2] it was shown that a 1-generator quasi-cyclic codeC of length n = ml of index l over Z4 is free ifC is generated bya polynomial which divides X m 1. In this paper, we prove thata necessary and sucient condition for a cyclic code over Zpk oflength m to be free is that it is generated by a polynomial whichdivides X m 1. We also show that this can be extended to nitelocal rings with a principal maximal ideal.
Algebras with a nilpotent generator over $\mathbb{Z}_p^2$
우성식 대한수학회 2006 대한수학회보 Vol.43 No.3
The purpose of this paper is to describe the structureof the rings Zp2 [X ]=((X )) with (X ) a monic polynomial andX k = 0 for some nonnegative integer k. Especially we will see thatany ideal of such rings can be generated by at most two elementsof the special form and we will nd the `minimal' set of generatorsof the ideals. We indicate how to identify the isomorphism types ofthe ideals as Zp2 -modules by nding the isomorphism types of theideals of some particular ring. Also we will nd the annihilators ofthe ideals by nding the most `economical' way of annihilating thegenerators of the ideal.
우성식,이상현,최기영,정란,박태원,Woo, Sung-Sik,Lee, Sang-Hyun,Choi, Ki-Young,Chung, Lan,Park, Tae-Won 한국전산구조공학회 2008 한국전산구조공학회논문집 Vol.21 No.2
In this study, it was investigated for dynamic nonlinear characteristics using dynamic data obtained by shaking table test. The design of Tuned Liquid Damper(TLD) has limitation to plan based on Tuned Mass Damper(TMD) analogy and linear wave theory. Also, while there are many studies regarding properties of TLD under harmonic load, there are not estimated for dynamic non-linear characteristics of TLD under the load that is not governed by particular frequency like a white noise. This paper investigated dynamic non-linear characteristics of TLD varied with load amplitude using a white noise and suggested equations that can estimate damping ratio, natural frequency ratio and effective mass ratio of TLD. 본 연구에서는 진동대 실험을 통해 얻은 동적 데이터를 이용하여 TDL의 동적 비선형 특성에 대한 연구를 수행하였다. 현재까지 TDL의 설계는 액체의 비선형 거동이 나타남에도 불구하고 TMD 근사이론이나 선형파동이론과 같은 선형 거동을 가정으로 설계되어 지는 한계를 가지고 있다. 또한 조화하중과 같은 특정진동수에 지배되는 하중형태에 대한 TDL의 동적 비선형 특성이 규명되었지만 백색잡음과 같은 특정진동수 성분에 지배되지 않은 하중형태에 대한 TDL의 동적 비선형 특성은 아직까지 검증된 바가 없다. 본 논문은 백색잡음을 이용하여 가진 하중 크기에 따른 TDL의 동적 비선형 특성을 검토하여 설계 시 필요한 동조액체감쇠기의 감쇠비, 고유진동수비 및 유효질량비를 평가할 수 있는 산정식을 제안하였다.