• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.527-534
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• 2007

This paper deals with the BK-AK property of the integrated rate space ${\int}{\ell}_{\pi}$. Importance of ${\delta}^{(k)}$ in this content is pointed out. We investigate a determining set for the integrated rate space ${\int}{\ell}_{\pi}$. The set of all infinite matrices transforming ${\int}{\ell}_{\pi}$, into BK-AK space Y is denoted $({\int}{\ell}_{\pi}:\;Y)$. We characterize the classes $({\int}{\ell}_{\pi}:\;Y)$. When $Y={\ell}_{\infty},\;c_0,\;c,\;{\ell}^p,\;bv,\;bv_0,\;bs,\;cs,\;{\ell}_p,\;{\ell}_{\pi}$. In summary we have the following table:

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.689-700
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• 1998

We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.197-201
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• 2014

In this paper, we study some properties of finite or infinite poset P determined by properties of the ideal based zero-divisor graph properties $G_J(P)$, for an ideal J of P.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.569-576
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• 2007

Let $\cal{H}$ be a separable, infinite dimensional, complex Hilbert space. We call "an operator $\cal{T}$ acting on $\cal{H}$ has a star moment sequence supported on a set K" when there exist nonzero vectors u and v in $\cal{H}$ and a positive Borel measure ${\mu}$ such that <$T^{*j}T^ku$, v> = ${^\int\limits_{K}}\;{{\bar{z}}^j}\;{{\bar{z}}^k}\;d\mu$ for all j, $k\;\geq\;0$. We obtain a characterization to find a representing star moment measure and discuss some related properties.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.68.5-68
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• 2001

This paper investigates the problem of linear parameter-dependent output feedback controllers design for interconnected linear parameter-varying(LPV) plant. By using a parameter-independent common Lyapunov function, sucient conditions for solving the problems are established, which allow us to design linear parameter dependent decentralized controllers in terms of scaled H-infinite control problems for related linear systems without interconnections. The solvability conditions are expressed in terms of finite-dimensional linear matrix inequalities(LMI´s) evaluated at the extreme points of the admissible parameter set.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.401-408
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• 2019

A ring R is called right (resp., left) nilpotent-duo if N(R)a ⊆ aN(R) (resp., aN(R) ⊆ N(R)a) for every a ∈ R, where N(R) is the set of all nilpotents in R. In this article we provide other proofs of known results and other computations for known examples in relation with right nilpotent-duo property. Furthermore we show that the left nilpotent-duo property does not go up to a kind of matrix ring.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-257
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• 1999

In this article, we give an example of local derivation, that is not derivation, on the algebra F(x1,…, xn) of rational functions in x1, …, xn over an infinite field F, and show that if X is a set of symbols and {x1,…, xn} is a finite subset of X, n$\geq$1, then each local derivation of F[x1,…, xn] into F[X] is a F-derivation and each local derivation of F[X] into itself is also a F-derivation.

• Bulletin of the Korean Chemical Society
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• v.13 no.6
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• pp.665-669
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• 1992

We consider the problem of a random walker on a one-dimensional lattice (N sites) confronting a centrally-located deep trap (trapping probability, T=1) and N-1 adjacent sites at each of which there is a nonzero probability s(0 < s < 1) of the walker being trapped. Exact analytic expressions for < n > and the average number of steps required for trapping for arbitrary s are obtained for two types of finite boundary conditions (confining and reflecting) and for the infinite periodic chain. For the latter case of boundary condition, Montroll's exact result is recovered when s is set to zero.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.261-275
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• 2011

We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) singulr function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than 0 and the packing dimension of the infinite derivative points of the RNT singular function is less than 1. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the ($\tau$, $\tau$ - 1)-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.955-964
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• 2015

Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let ${\alpha}_0{\in}{\mathbb{A}}^1(K){\subset}{\mathbb{P}}^1(K)$ and let ${\Gamma}_0$ be the set of the images of ${\alpha}_0$ under especially all Chebyshev morphisms. Then for any ${\alpha}{\in}{\mathbb{A}}^1(K)$, we show that there are only a finite number of elements in ${\Gamma}_0$ which are S-integral on ${\mathbb{P}}^1$ relative to (${\alpha}$). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on ${\mathbb{P}}^1$, which generalizes the above finiteness result for Chebyshev morphisms.