• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.963-965
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• 1999

A linear chromosome combined with a grid-based representation of the network and a new crossover operator allow the evolution of the architecture and the weights simultaneously. In our approach there is no need for a separate weight optimization procedure and networks with more than one type of activation function can be evolved. In this paper one evolutionary' strategy of a given dual neural controller was introduced and the simulation results were described in detail through applications to a stabilization control of an Inverted Pendulum System.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.183-200
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• 2012

A two-strain epidemic model with an age structure mutation and varying population is studied. By means of the spectrum theory of bounded linear operator in functional analysis, the reproductive numbers according to the strains, which associates with the growth rate ${\lambda}^*$ of total population size are obtained. The asymptotic stability of the steady states are obtained under some sufficient conditions.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.207-215
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• 2004

Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in extC(z). The overlapping space $\varepsilon$(W) of D(W) in C(z) is a Herglotz space with Herglotz function $\varphi$(z) which satisfies $\varphi$(z) + ${\varphi}^*(z^{-1})$ = 2[1-W$^*(z^{-1})W(z)]$.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.261-269
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• 2020

For any Banach spaces X and Y, let L(X, Y) denote the set of all bounded linear operators from X to Y. Let A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA. In this paper, we prove that AC and BA share the local spectral properties such as a finite ascent, a finite descent, property (K), localizable spectrum and invariant subspace.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.333-341
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• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.231-244
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• 2005

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.29-40
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• 2010

In this paper, we study a generalization of the Banach space B($l_2$) of all bounded linear operators on $l_2$. Over this space, we present some reasonable ways to define Schatten-type classes which are generalizations of the classical Schatten classes of compact operators on $l_2$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1469-1484
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• 2014

In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.661-676
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• 2020

To understand the interaction of a fluid and a rigid body, we use the concept of B-evolution. Then in a similar way to the usual Navier-Stokes system, we obtain a Helmholtz type decomposition. Using B-evolution theory and the decomposition, we work on the semigroup to analyze the linear part of the system.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.317-325
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• 1994

Suppose X is a complex Banach space and write B(X) for the Banach algebra of bounded linear operators on X, X＊ for the dual space of X, and T＊$\in$ B(X＊) for the dual operator of T. For T $\in$ B(X) write a(T) = dim T$^{-1}$ (0) and $\beta$(T) = codim T(X).(omitted)