• 대한수학회보
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• 제35권1호
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• pp.91-97
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• 1998

In this paper we study the Weyl spectrum of weight $\alpha, \omega_\alpha(T)$, of an operator T acting on an infinite dimensional Hilbert space. Main results are as follows. Firstly, we show that the Weyll spectrum of weight $\alpha$ of a polynomially $\alpha$-compact operator is finite, and that similarity preserves polynomial $\alpha$-compactness and the $\alpha$-Weyl's theorem both. Secondly, we give a sufficient condition for an operator to be the sum of an unitary and a $\alpha$-compact operators.

• 한국경영과학회지
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• 제14권2호
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• pp.97-104
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• 1989

This paper extends the existence proofs of a Nash equilibrium to a more general class of differentila game models with constraints on the control spaces. With the assumptions of continuity, convexity, and compactness, the existence is proved using Kakutani Theorem and via a path-following approach. Furthermore, the proof for a period-by-period optimization of multi-period problems provides an insight to a numerical solution algorithm to differential game models with constraints.

• 대한수학회보
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• 제48권4호
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• pp.813-838
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• 2011

In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.

• 대한수학회보
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• 제48권4호
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• pp.779-789
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• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• 대한수학회지
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• 제55권6호
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• pp.1337-1358
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• 2018

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths $$-div\({\mid}{\nabla}u{\mid}^{p_1(x)-2}{\nabla}u\)-\sum\limits^n_{i=1}D_i\({\mid}u{\mid}^{p_0(x)-2}D_iu\)+c(x,u)=h(x),\;{\in}{\Omega}$$ in a bounded domain ${\Omega}{\subset}{\mathbb{R}}^n$. Here, one of the operators in the sum is monotone and the other is weakly compact. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.

• 한국수학사학회지
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• 제27권6호
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• pp.403-408
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• 2014

The interdisciplinary study addresses the G$\ddot{o}$del's ontology from the perspective of the mathematical maximality. We first investigate G$\ddot{o}$del's God having all the positive properties as the intersection of ultrafilters in his own ontological proof(1970). Regarding the axiom of choice and his compactness theorem(1930), the next part discusses the ontological meaning of the maximal rather than the maximum in terms of an episteme space. The results show that G$\ddot{o}$del's ontological arguments imply all the existence of the maximal reality, and all the human's epistemological boundedness as well.

• 한국전산구조공학회논문집
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• 제23권3호
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• pp.283-288
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• 2010

모바일 하버용 크레인은 항만 부두에 설치되어 있는 일반 지상식 크레인과는 달리 소형 경량 구조를 요구한다. RORI 크레인은 이러한 요구조건을 만족시키기 위해 고안된 신개념의 모바일 하버용 크레인 시스템으로서 해상에서 컨테이너 상하역 작업을 고속으로 처리할 수 있을 뿐만 아니라 운항 시에는 완전히 접을 수 있도록 되어 있다. 본 연구는 컨테이너 상하역 작업에 따른 RORI 크레인의 수평붐 끝단 처짐량 분석에 관한 내용으로, 카스틸리아노 정리를 이용한 이론적인 방법과 유한요소법에 의한 수치해석적인 방법을 적용하였다. 두 기법으로 구한 끝단 처짐량을 비교분석함으로써 유한요소해석의 타당성을 입증하고, 케이블의 초기장력에 따른 끝단 처짐량 변화특성을 파라메트릭하게 분석하였다.