• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.487-498
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• 2010

For some $\phi$-sequences $\phi_1$, $\phi_2$ and $\phi_3$, and $\kappa$-function $\kappa_1$, $\kappa_2$ and $\kappa_3$ with $\kappa_1^{-1}(x)\kappa_2^{-1}(x)\;{\geq}\;\kappa_3^{-1}(x)$ for $x\;{\geq}\;0$, the Luxemburg norm is lower semi-continuous on ${\kappa}{\phi}BV_0$, and some specialized equivalent conditions are considered.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.547-563
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• 2020

We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-890
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• 2020

In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B*(G)⨶B*(K) is isomorphic to the bounded cohomology Ĥ*(G × K) of G × K, which is the cohomology of B*(G × K) as topological vector spaces, where B*(G) is a complex of bounded cochains of G with real coefficients ℝ. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ*(G × K) to the seminorm in the cohomology of B*(G)⨶B*(K).

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.447-455
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• 2003

For some sequnces of monotone nondecreasing convex $\Phi$-functions $\Phi$$_1$, $\Phi$$_2$ and $\Phi$$_3$and $textsc{k}$-functions $textsc{k}$$_1$, $textsc{k}$$_2$ and $textsc{k}$$_3$, we obtain the most general Holder type inequalities, and some special cases are considered for the functions of $textsc{k}$G$\Phi$-bounded variations.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.609-614
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• 2010

We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schr$\ddot{o}$dinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].

• Journal of the Korea Society for Simulation
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• v.11 no.2
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• pp.67-75
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• 2002

This paper proposes a parallel simulation algorithm for bounded Petri nets in a single processor, which exploits the SIMD(Single Instruction Multiple Data)-type parallelism. The proposed algorithm is based on a data packing scheme which packs multiple bytes data in a single register, thereby being manipulated simultaneously. The parallelism can reduce simulation time of bounded Petri nets in a single processor environment. The effectiveness of the algorithm is demonstrated by presenting speed-up of simulation time for two bounded Petri nets.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.631-650
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• 2019

In this paper, for discrete groups G and K, we show that the bounded cohomology group of $G{\times}K$ is isomorphic to the cohomology group of the complex of the projective tensor product $B^*(G){\hat{\otimes}}B^*(K)$, where $B^*(G)$ and $B^*(G)$ are the complexes of bounded cochains with real coefficients ${\mathbb{R}}$ of G and K, respectively.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.707-720
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• 2000

Conley index is used study bifurcation from equilibria of full bounded solutions to parameter dependent families of ordinary differential equations of the form {{{{ {dx} over {dt} }}}} =$\varepsilon$F(x, t, $\mu$). It is assumed that F(x, t,$\mu$) is uniformly almost periodic in t.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.889-895
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• 1995

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$.