• 대한수학회지
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• 제56권1호
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• pp.197-224
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• 2019

Let A be a $JB^*$-triple with Banach dual space $A^*$ and bi-dual the $JBW^*$-triple $A^{**}$. Elements x of $A^*$ of norm one may be regarded as normalised 'Q-measures' defined on the complete ortho-lattice ${\tilde{\mathcal{U}}}(A^{**})$ of tripotents in $A^{**}$. A Q-measure x possesses a support e(x) in ${\tilde{\mathcal{U}}}(A^{**})$ and a compact support $e_c(x)$ in the complete atomic lattice ${\tilde{\mathcal{U}}}_c(A)$ of elements of ${\tilde{\mathcal{U}}}(A^{**})$ compact relative to A. Necessary and sufficient conditions for an element v of ${\tilde{\mathcal{U}}}_c(A)$ to be a compact support tripotent $e_c(x)$ are given, one of which is related to the Q-covering numbers of v by families of elements of ${\tilde{\mathcal{U}}}_c(A)$.

• 한국지리정보학회지
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• 제12권1호
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• pp.64-72
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• 2009

등고선에서 생성된 DEM(digital elevation model)은 고도 간격에 따라 미지형 요소 표현에 절대적인 영향을 받기 때문에 미기복 지형이 잘 표현되지 않는 문제가 발생한다. 이를 보완하기 위해 지표피복에 고도정보를 입력하여 buffering과 지도대수 연산기법을 적용하며 미기복 지형을 복원하는 Landcover burning 기법을 개발하고자 하였다. 미지형복원과정은 등고선에서 일차 DEM 생성, 지표피복도 제작, 지표피복요소 중 미지형요소에 대한 buffering 기법에 의한 고도정보 복원, 피복인자에 대한 지도대수 연산을 통한 고도정보 입력에 의해 DEM을 복원하였다. 미지형복원은 하천지형을 중심으로 적용하였다. buffering에 의한 지형복원은 면적인(polygonal) 요소인 사력퇴, 습지에 대해서 지형형상이 오목 혹은 볼록 지형의 특성에 맞추어 일정간격의 등고선을 생성하여 지형을 복원한 후, 고도 정보를 입력하여 복원하였다. 선형적인 요소인 제방, 도로, 수로, 지류는 지도대수함수를 이용하여 지형을 복원할 수 있었다. 하상, 하안단구, 인공지물(농경지)과 같은 면적인 요소들은 평탄하기 때문에 일정한 고도값을 입력하여 지형면을 복원하였다. 연구결과는 단면도를 제작하여 원래의 DEM과 복원된 DEM의 지형표현 정도를 비교 분석하였다. 분석한 결과, 기존의 방법으로 제작된 DEM은 미지형적인 요소들이 거의 표현되지 않았다. 본 연구에서 개발된 방법은 습지, 사력퇴, 하천주변의 지형, 농경지, 제방, 하안단구, 인공지물 위치가 비교적 잘 표현되었다. 본 연구는 중소규모의 저기복 구릉대나 평야지대의 미지형분류와 분석, 하천 주변 미지형복원이 필요한 생태 및 환경분야 연구에 기여할 것으로 기대된다.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.251-258
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• 2015

Let $\mathcal{A}$ be a unital $C^*$-algebra, a, x and y are elements in $\mathcal{A}$. In this paper, we present the expression of the Moore-Penrose inverse and the group inverse of a-$xy^*$ under the conditions $x=aa^+x,y^*=y^*a^+a$, respectively.

• 충청수학회지
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• 제5권1호
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• pp.75-85
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• 1992

Let R be an associative ring and let G be a finite group of Jordan automorphisms of R. Let $R^G$ be the set of elements in R fixed by all $g{\in}G$. In this paper we will study the relationship between the Levitzki radical of $R^G$ and R as that a Jordan ring. We also show that if R is a P.I. algebra, then the algebraicity of $R^G$ implies the algebraicity of R.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.9-16
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• 2004

This paper deals with the development of computational schemes for the dynamic analysis of flexible and nonlinear multibody systems. Different from the existing method, this paper introduces the quaternion algebra to develop the equation of the conservation of energy. Simultaneously, Rodrigues parameters are used to express the finite rotation for the proposed scheme. The proposed energy scheme is derived such that it provides unconditionally stable conditions for the nonlinear problems. Several examples of dynamic systems are presented which illustrate the efficiency and accuracy of the developed energy schemes.

• 대한수학회보
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• 제32권2호
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• pp.163-170
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• 1995

Let G be a Lie group with Lie algebra L(G) and let $\Omega$ be a nonempty subset of L(G). If $\Omega$ is interpreted as the set of controls, then the set of elements attainable from the identity for the system $\Omega$ is a subsemigroup of G. A system $\Omega$ is called a non-overlapping control system if any element attainable for $\Omega$ is only attainable at one time.

• 대한수학회지
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• 제49권4호
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• pp.855-865
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• 2012

Recently, we have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x{\wedge}y=1_{G{\wedge}G}$ in the exterior square $G{\wedge}G$ of $G$. This number gives restrictions on the Schur multiplier of $G$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $h^m{\wedge}k$ of $H{\wedge}K$ such that $h^m{\wedge}k=1_{H{\wedge}K}$, where $m{\geq}1$ and $H$ and $K$ are arbitrary subgroups of $G$.

• 대한수학회논문집
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• 제27권1호
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• pp.7-13
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• 2012

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements ($x{\leq}a$ implies x = a) in terms of the binary relation $\leq$ which is reflexive and anti-symmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations $\ast$ and $\circ$ are identical, including the property $0{\circ}(0{\ast}a)$ = a. The condition $0{\ast}(0{\circ}x)=0{\circ}(0{\ast}x)=x$ all $x{\in}X$ defines the class of p-semisimple pseudo-BCK/BCI-algebras($0{\leq}x$ implies x = 0) as an interesting subclass whose further properties are also investigated below.

• 대한수학회지
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• 제43권4호
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• pp.783-801
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• 2006

Let A be the mod p Steenrod algebra for p an arbitrary odd prime and S the sphere spectrum localized at p. In this paper, some useful propositions about the May spectral sequence are first given, and then, two new nontrivial homotopy elements ${\alpha}_1{\jmath}{\xi}_n\;(p{\geq}5,n\;{\geq}\;3)\;and\;{\gamma}_s{\alpha}_1{\jmath}{\xi}_n\;(p\;{\geq}\;7,\;n\;{\geq}\;4)$ are detected in the stable homotopy groups of spheres, where ${\xi}_n\;{\in}\;{\pi}_{p^nq+pq-2}M$ is obtained in [2]. The new ones are of degree 2(p - 1)($p^n+p+1$) - 4 and 2(p - 1)($p^n+sp^2$ + sp + (s - 1)) - 7 and are represented up to nonzero scalar by $b_0h_0h_n,\;b_0h_0h_n\tilde{\gamma}_s\;{\neq}\;0\;{\in}\;Ext^{*,*}_A^(Z_p,\;Z_p)$ in the Adams spectral sequence respectively, where $3\;{\leq}\;s\;<\;p-2$.

• 대한수학회지
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• 제56권2호
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• pp.539-558
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• 2019

An ideal of a commutative ring is called a d-ideal if it contains the annihilator of the annihilator of each of its elements. Denote by DId(A) the lattice of d-ideals of a ring A. We prove that, as in the case of f-rings, DId(A) is an algebraic frame. Call a ring homomorphism "compatible" if it maps equally annihilated elements in its domain to equally annihilated elements in the codomain. Denote by $SdRng_c$ the category whose objects are rings in which the sum of two d-ideals is a d-ideal, and whose morphisms are compatible ring homomorphisms. We show that $DId:\;SdRng_c{\rightarrow}CohFrm$ is a functor (CohFrm is the category of coherent frames with coherent maps), and we construct a natural transformation $RId{\rightarrow}DId$, in a most natural way, where RId is the functor that sends a ring to its frame of radical ideals. We prove that a ring A is a Baer ring if and only if it belongs to the category $SdRng_c$ and DId(A) is isomorphic to the frame of ideals of the Boolean algebra of idempotents of A. We end by showing that the category $SdRng_c$ has finite products.