• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.233-242
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• 2004

The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $\Gamma$-ring and Q a quotient $\Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $W\Gamma$W $\neq 0. Furthermore Q is a semi-prime $\Gamma$-ring. (2) Let M be a semi-prime $\Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{\Gamma}$ is a regular $\Gamma$-ring. (3) Let M be a semi-prime $\Gamma$-ring and $C_{\gamma}$ the extended centroid of M. If $C_{\gamma}$ is a $\Gamma$-field, then the $\Gamma$-ring M is a prime $\Gamma$-ring.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.609-622
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• 2006

In this paper, we established the monotony properties of generalized projection bodies $II_{\imath}K$, intersection bodies $I_{\imath}K$ and centroid bodies ${\Gamma}_{\imath}K$.

• Steel and Composite Structures
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• v.22 no.5
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• pp.1073-1084
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• 2016

Rectangular concrete-filled steel tubular columns with unequal wall thickness were investigated in the paper. The physical centroid, the centroidal principal axes of inertia, and the section core were given. The generalized bending formula and the generalized eccentric compression formula were deduced, and the equation of the neutral axis was also provided. The two rectangular concrete-filled steel tubular stub specimens subjected to the compression load on the physical centroid and the geometric centroid respectively were tested to verify the theoretical formulas.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.203-213
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• 2007

The aim of this paper is to introduce modules over the generalized of a semi-prime ${\Gamma}$-ring

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.709-737
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• 2020

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x₁, …, x_n) be a non central multilinear polynomial over C. If F(f(r₁, …, r_n))G(f(r₁, …, r_n)) - f(r₁, …, r_n)T(f(r₁, …, r_n)) = H(f(r₁, …, r_n)²) for all r₁, …, r_n ∈ R, then we describe all possible forms of F, G, H and T.

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

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.917-922
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• 2011

Let R be a prime ring, H a generalized derivation of R, L a noncentral Lie ideal of R, and 0 ${\neq}$ a ${\in}$ R. Suppose that $au^sH(u)u^t$ = 0 for all u ${\in}$ L, where s; t ${\geq}$ 0 are fixed integers. Then H = 0 unless satisfies $S_4$, the standard identity in four variables.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.599-605
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• 2009

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that $u^sH(u)u^t$ = 0 for all u $\in$ L, where s $\geq$ 0, t $\geq$ 0 are fixed integers. Then H(x) = 0 for all x $\in$ R unless char R = 2 and R satisfies $S_4$, the standard identity in four variables.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.568-570
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• 2001

fiducial mark는 PCB 정밀조립/검사 장비에서 위치보정을 위해 필수적으로 사용되는데, 실제 생산현장에서의 fiducial mark의 품질은 완전하지 않고, 손상된 상태인 경우가 많이 발생한다. 기존에 주로 사용되는 blob centroid 방법에 의한 mark의 위치추출은 mark의 상태가 손상되었을 경우, 큰 오차를 수반하게 된다. 본 논문에서는 Generalized Hough Transform을 이용한 fiducial mark의 중심위치 기법을 개발하여, 적용한 결과 손상된 mark에 대해서도 매우 강건한 결과를 보여주었다.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.761-768
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• 2021

Let I be a nonzero ideal of a prime ring R and m, n are positive integers. If R admits a generalized derivation F satisfying F(x)ⁿF(y)^m - xⁿy^m = 0 for any y, x ∈ I, then F(x) = ax for any x ∈ R and a^m+n = 1, where a ∈ C, the extended centroid of R.