• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.161-170
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• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.173-184
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• 1997

An n-dimensional complex space form $M_n(c)$ is a Kaehlerian manifold of constant holomorphic sectional curvature c. As is well known, complete and simply connected complex space forms are a complex projective space $P_n C$, a complex Euclidean space $C_n$ or a complex hyperbolic space $H_n C$ according as c > 0, c = 0 or c < 0.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.835-848
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• 1995

Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.369-383
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• 1994

A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of a complex projective space $P_{n}$ C, a complex Euclidean space $C^{n}$ or a complex hyperbolic space $H_{n}$ C, according as c > 0, c = 0 or c < 0.(omitted)

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.749-763
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• 2022

Let C[0, T] denote an analogue of Weiner space, the space of real-valued continuous on [0, T]. In this paper, we investigate the translation of time interval [0, T] defining the analogue of Winer space C[0, T]. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on C[0, T] as the analogue of Wiener measures on C[0, s] and C[s, T] with 0 < s < T.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.11
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• pp.970-975
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• 2002

We suggests an effective method to construct time-varying C-obstacles in the 3-dimensional configuration space (C-space) using free arc. The concept of free arc was defined mathematically and the procedure to find free arc in the case off-dimensional C-space was derived in [1]. We showed that time-varying C-obstacles can be constructed efficiently using this concept, and presented simulation results for two SCARA robot manipulators to verify the efficacy of the proposed approach. In this paper, extensions of this approach to the 3-dimensional C-space is introduced since nearly all industrial manipulators are reasonably treated ill the too or three dimensional C-space f3r collision avoidance problem The free arc concept is summarized briefly and the method to find lice arc in the 3-dimensional f-space is explained. To show that this approach enables us to solve a practical collision avoidance problem simulation results f3r two PUMA robot manipulators are presented.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1009-1018
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• 1997

Observing that for any $\beta_c$-Wallman functor $A$ and any Tychonoff space X, there is a cover $(C_1(A(X), X), c_1)$ of X such that X is $A$-disconnected if and only if $c_1 : C_1(A(X), X) \longrightarrow X$ is a homeomorphism, we show that every Tychonoff space has the minimal $A$-disconnected cover. We also show that if X is weakly Lindelof or locally compact zero-dimensional space, then the minimal G-disconnected (equivalently, cloz)-cover is given by the space $C_1(A(X), X)$ which is a dense subspace of $E_cc(\betaX)$.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.297-303
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• 2007

In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is $Fr\acute{e}chet$-Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits ${\equiv}KC{\equiv}C-closed{\equiv}SC-closed$, and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.461-468
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• 2004

Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in C(z). The overlapping space $L(\varphi)$ of H(W) in C(z) is a Herglotz space with Herglotz function $\varphi(z)$ which satisfies $\varphi(z)+\varphi^＊(z^{-1})=2[1-W^{*}(z^{-1})W(z)]$. The identity ${}_{L(\varphi)}={-}_{H(W)}$ holds for every f(z) in $L(\varphi)$ and for every vector c.