• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• East Asian mathematical journal
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• v.24 no.4
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• pp.369-375
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• 2008

In this paper, we first introduce inwards set valued maps in hyperconvex metric spaces. Then we present fixed point theory for continuous condensing inward set valued maps.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1183-1197
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• 2006

Let X be a smooth, closed, connected spin 4-manifold with $b_1(X)=0$ and signature ${\sigma}-(X)$. In this paper we use Seiberg-Witten theory to prove that if X admits a spin alternating $A_4$ action, then $b^+_2(X)$ ${\geq}$ |${\sigma}{(X)}$|/8+3 under some non-degeneracy conditions.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.321-338
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• 2011

In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1153-1162
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• 2023

In this paper, for the bounded solution of the non-densely defined non-autonomous evolution equation, we present the condition for asymptotic periodicity by using the circular spectral theory of functions on the half line and the extrapolation theory of non-densely defined evolution equation.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.359-370
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• 1997

In this paper we get the Morava K-theory of the double loop spaces of quarternionic Stiefel manifolds for an odd prime p by computing the Atiyah - Hirzebruch spectral sequence. We also get the homology with Z/(p) coefficients and analyze p torsion in the homology with Z coefficients.

• East Asian mathematical journal
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• v.36 no.5
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• pp.547-554
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• 2020

Synchronization of unidirectional identical FitzHugh-Nagumo systems coupled in a ring structure under ionic and external electrical stimulations is investigated. In this network, each neuron is only connected and transmit signals to its next neuron via synaptic strength called gapjunctions. Adaptive control theory and Lyapunov stability theory are used to propose a unique control scheme with necessary and sufficient conditions which guarantee the synchronization of the neuronal network. Finally, the effectiveness of the proposed scheme is shown through numerical simulations.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1149-1167
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• 2015

We get a theorem which shows the existence of at least four $2{\pi}$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.199-204
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• 1997

To develope the theory of BCI-algebras, the idel theory plays an important role. The first author [4] introduced the notion of T-ideal in BCI-algebras. In this paper, we first construct a special set, called T-part, in a BCI-algebra X. We show that the T-part of X is a subalgebra of X. We give equivalent conditions that the T-part of X is an ideal. By using T-part, we provide an equivalent condition that every ideal is a T-ideal.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.55-72
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• 2000

In this paper, we develop the Grobner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Grobner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite dimensional irreducible representations of the simple tie algebra sl$_3$. Each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux with a given shape.