• 대한수학회지
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• 제43권2호
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• 충청수학회지
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• 제25권4호
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• pp.609-615
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• 2012

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

• 충청수학회지
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• 제21권3호
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• pp.377-384
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• 2008

In this paper, we prove the stability of the functional equation $$\sum\limits_{i=0}^{3}3Ci(-1)^{3-i}f(ix+y)-3!f(x)=0$$ in the sense of P. $G{\breve{a}}vruta$ on the punctured domain. Also, we investigate the superstability of the functional equation.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1999년도 학회창립 10주년 기념 1999년도 가을 학술발표회 논문집
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• pp.545-548
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• 1999

The purpose of this study is application of strengthening technique of R/C concrete bridge by standardization of repair and rehabilitation. For that, experiment to bridge is necessary, and through the experiment, this study can identify the efficiency o applied method and analysis of design parameters with can't get in the laboratory experiment. This study will prove the structural behavior of R/C type girder bridge which is deteriorated but repaired and rehabilitation from standardized strengthening method with fiber plastic.

• 소음진동
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• 제7권6호
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• pp.945-952
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• 1997

This paper shows the feasibility of the suggestion that the angle distribution of incident sound to panels might be gaussian, instead of the conventional uniform distribution in the analysis of transmission loss of panels. To prove the suggestion, the problems with the diffuse sound field in a reverberation room are examined by case studies and the comparision of the prediction with the measurement of sound transmission loss of walls are performed. The results of the comparision show good agreement between the two values.

• 대한수학회보
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• 제53권6호
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• pp.1741-1751
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• 2016

We prove the boundary Harnack principle and the Carleson type estimate for ratios of solutions u/v of non-divergence second order elliptic equations $Lu=a_{ij}D_{ij}+b_iD_iu=0$ in a bounded domain ${\Omega}{\subset}R_n$. We assume that $b_i{\in}L^n({\Omega})$ and ${\Omega}$ is a $H{\ddot{o}}lder$ domain of order ${\alpha}{\in}$ (0, 1) satisfying a strong regularity condition.

• 대한수학회보
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• 제49권4호
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• pp.761-765
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• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• 대한수학회논문집
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• 제23권3호
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• pp.333-342
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• 2008

We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].

• 대한수학회보
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• 제51권2호
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• 대한수학회지
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• 제47권1호
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• pp.1-15
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• 2010

We introduce, in this article, the quasi-stable exchange ideal for associative rings. If I is a quasi-stable exchange ideal of a ring R, then so is $M_n$(I) as an ideal of $M_n$(R). As an application, we prove that every square regular matrix over quasi-stable exchange ideal admits a diagonal reduction by quasi invertible matrices. Examples of such ideals are given as well.