• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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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.

• Journal for History of Mathematics
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• v.27 no.6
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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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.3
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• pp.283-288
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• 2010

Mobile harbor is characterized by the lightweight compact structure when compared to the conventional above-ground port container crane. A new concept RORI crane system, which was devised for mobile harbor to satisfy the compactness and light weightness, not only can load/unload containers with high speed on sea but can be completely folded at maneuvering mode. This study is concerned with the tip deflection of the horizontal boom of mobile harbor at container loading operation. Both the theoretical method utilizing the Castigliano's theorem and the numerical approach by finite element method are employed, and the reliability of the latter approach is verified through the comparison with the theoretical results. And then, the effect of the initial cable tension on the tip deflection is parametrically examined by the finite element analysis.