• Korean Journal of Mathematics
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• 제17권2호
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• pp.189-196
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• 2009

Let D be an integral domain, and let U be a group of units of D. Let $D^*=D-\{0\}$ and ${\Gamma}=D^*/U$ be the commutative cancellative semigroup under aU+bU=abU. We prove that $Cl(D)=Cl({\Gamma})$ and that D is a PvMD (resp., GCD-domain, Mori domain, Krull domain, factorial domain) if and only if ${\Gamma}$ is a PvMS(resp., GCD-semigroup, Mori semigroup, Krull semigroup, factorial semigroup). Let U=U(D) be the group of units of D. We also show that if D is integrally closed, then $D[{\Gamma}]$, the semigroup ring of ${\Gamma}$ over D, is an integrally closed domain with $Cl(D[{\Gamma}])=Cl(D){\oplus}Cl(D)$; hence D is a PvMD (resp., GCD-domain, Krull domain, factorial domain) if and only if $D[{\Gamma}]$ is.

• Communications of the Korean Mathematical Society
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• 제25권3호
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• pp.327-333
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• 2010

Let R be a 2-torsion free prime ring, U a nonzero Lie ideal of R such that $u^2\;{\in}\;U$ for all $u\;{\in}\;U$. In the present paper, it is proved that if d is a nonzero derivation and [[d(u), u], u] = 0 for all $u\;{\in}\;U$, then $U\;{\subseteq}\;Z(R)$. Moreover, suppose that $d_1$, $d_2$, $d_3$ are nonzero derivations of R such that $d_3(y)d_1(x)\;=\;d_2(x)d_3(y)$ for all x, $y\;{\in}\;U$, then $U\;{\subseteq}\;Z(R)$. Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the above results are not superfluous.

• Communications of the Korean Mathematical Society
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• 제27권3호
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• pp.441-448
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• 2012

Let R be a prime ring with center Z and characteristic different from two, U a nonzero Lie ideal of R such that $u^2{\in}U$ for all $u{\in}U$ and $d$ be a nonzero (${\sigma}$, ${\tau}$)-derivation of R. We prove the following results: (i) If $[d(u),u]_{{\sigma},{\tau}}$ = 0 or $[d(u),u]_{{\sigma},{\tau}}{\in}C_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$. (ii) If $a{\in}R$ and $[d(u),a]_{{\sigma},{\tau}}$ = 0 for all $u{\in}U$, then $U{\subseteq}Z$ or $a{\in}Z$. (iii) If $d([u,v])={\pm}[u,v]_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$.

• Journal of the Korean Mathematical Society
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• 제31권3호
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• Bulletin of the Korean Mathematical Society
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• 제31권1호
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• pp.55-60
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• 1994

It is well known that if P(x,D) is an elliptic differential operator, with real analytic coefficients, and P(x,D)u = 0 in an open, connected subset .ohm..mem.R$^{n}$ , then u is real analytic in .ohm. Hence, if there exists x$_{0}$ .mem..ohm. such that u vanishes of .inf. order at x$_{0}$ , u must be identically 0. If a differential operator P(x, D) has the above property, we say that p(x,D) has the strong unique continuation property (s.u.c.p.). If, on the other hand, P(x,D)u = 0 in .ohm., and u = 0 in .ohm.', an open subset of .ohm., implies that u = 0 in .ohm. we say that P(x,D)u = 0 in .ohm., and suppu .contnd. K .contnd. .ohm implies that u = 0 in .ohm. we sat that P(x,D) has the weak unique continuation property (m.u.c.p.).

• 한국디지털정책학회:학술대회논문집
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• 한국디지털정책학회 2006년도 추계학술대회
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• pp.409-418
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• 2006

The purpose of this paper is to present a low cost u-City portal development idea and to propose an exclusive system architecture using 3-D interface layers. 3-D interface layers consist of reused ideas of data from existed public data produced from GIS in order to reduce Produce Processes. 3-D interface layers implement a u-City portal systems that tags from physical spaces 1 ink to mobiles from ubiquitous networks between electronic spaces and physical spaces. Primary produce of this study exhibits an exclusive architecture of a u-City portal for speedy and low cost web 3-D interface layers and GIS data, and for implementation interface of 3-D types on USN of physical spaces. Secondary produce of this study represents that a 3-D u-City portal system has visualized speedy implementation characteristics for implementation of the application systems to execute an ubiquitous concept by returning electronic space to physical space, and to present the low cost 3-D u-City portal than an existed 3-D u-city development strategy. Therefore continuous expansion and study of the 3-D interface physical space under a 상황인지(Context Awareness)ubiquitous will appear the innovated u-City portal systems.

• Nuclear industry
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• 제29권7호
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• pp.58-60
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• 2009

시험 검사 인증 기술 컨설팅 분야의 세계적인 서비스 기업인 T$\ddot{U}$V S$\ddot{U}$D 그룹의 한국 법인인 T$\ddot{U}$V S$\ddot{U}$D Korea가 최근 원자력 기기 및 시스템 설계 엔지니어링 기업인 (주)GNEC를 인수, 합병하면서 국내 원자력 시장에 성큼 진출하는 한편 우리나라 원자력사업의 해외 시장 진출을 적극적으로 도울 계획을 세우고 있다. 라이너 블록 사장은 GNEC 인수 후 기자회견을 통해 "원자력 기기 및 설계, 교육 및 엔지니어링 서비스 등 관련 기술 지원에 앞장서 국내 에너지 산업의 활성화에 앞장서는 것을 물론 국내 원자력 산업의 해외 진출을 지원하면서 중국, 인도 및 중국 등 아시아 시장에 적극 진출할 것" 이라고 말하고 "원전 관련 기술을 갖고 있는 다른 기업에 대해서도 향후 인수 합병(M&A)에 나설 계획"이라고 밝혔다. T$\ddot{U}$V S$\ddot{U}$D Korea가 GNEC 인수를 마무리한 시점인 지난 10월 19일, 한강이 내려다보이는 여의도 대한생명 63빌딩 12층 T$\ddot{U}$V S$\ddot{U}$D Korea 사장실에서 라이너 블록 사장을 만났다. 인터뷰 자리에는 이번 GNEC 합병에 큰 역할을 한 김두일 T$\ddot{U}$V S$\ddot{U}$D 고문이 배석하여 인터뷰를 도왔다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.525-532
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• 2004

For two vertices u and v of an oriented graph D, the set I(u, v) consists of all vertices lying on a u-v geodesic or v-u geodesic in D. If S is a set of vertices of D, then I(S) is the union of all sets 1(u, v) for vertices u and v in S. The geodetic number g(D) is the minimum cardinality among the subsets S of V(D) with I(S) = V(D). In this paper, we give a partial answer for the conjecture by G. Chartrand and P. Zhang and present some results on orient able geodetic number.

• Bulletin of the Korean Mathematical Society
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• 제20권1호
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• pp.31-36
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• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).