• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.697-705
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• 2023

We studied new notions of analogues of topological rings. Salih [10] acquaints us with the notion of irresolute topological ring in 2018. In this paper, we further studied the space closely and characterized indispensable properties of the space. We prove that every open subset of an irresolute topological ring is irresolute topological ring. We also obtained the equivalent condition of neighborhood of an element in an irresolute topological ring. It is proved that ring homeomorphism of an irresolute topological ring is irresolute if it is irresolute at identity element e in the irresolute topological ring 𝓡.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2022.11a
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• pp.168-169
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• 2022

In this study, we investigates the auto-berthing problem for the underactuated surface vessel in the presence of constraints of dynamic uncertainties, finite time, transmission load, and environmental disturbance. A novel control scheme is proposed by fusing the finite time control technology and the event-triggered input algorithm. In the algorithm, differential homeomorphism coordinate the transformation is used to solve the problem of underactuation. Then, we apply the finite time technology and event triggered to save the time of the berthing vessel and relieve transmission burden between the controller and the vessel respectively. Moreover, a radial basis function network is used to approximate unknown nonlinear functions, and minimum learning parameters are introduced to lessen the computational complexity. A sufficient effort has been made to verify the stability of the closed-loop system based on the Lyapunov stability theory. Finally, simulation results display the effectiveness of the proposed scheme.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.1-28
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• 2024

In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.405-410
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• 1994

The purpose of this paper is to present the details of design procedure of a nonlinear regulator by Riemannian geometric approach and to applied it to the case of a double-effect evaporator. A nonlinear geometric model is proposed on a direct sum space of a state vector and a control vector as well as in the previous parers by the authors. The geometric model is derived by replacing the orthogonal straight coordinate axes of a linear system on the direct sum space with the curvilinear coordinate axes. The integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the geometric model a nonlinear regulator with a performance index is designed renewedly by the procedure of optimization. The construction method of the curvilinear coordinate axes on which the nonlinear system behaves as a linear system is discussed. To apply the above regulator theory to double-effect evaporators especially to the pilot plant at the University of Alberta, a suitable nonlinear model is determined by the plant dynamics. The optimal control law is derived through the calculation of the homeomorphism. As a result it is confirmed that the regulator is effective and superior to that of the conventional control.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.628-633
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• 1994

A new Riemannian geometric model for the controlled plant is proposed by imbedding the control vector space in the state space, so as to reduce the dimension of the model. This geometric model is derived by replacing the orthogonal straight coordinate axes on the state space of a linear system with the curvilinear coordinate axes. Therefore the integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the lower dimensional Riemannian geometric model, a nonlinear optimal regulator with a quadratic form performance index which contains the Riemannian metric tensor is designed. Since the integral manifold of the nonlinear regulator is determined to be homeomorphic to that of the linear regulator, it is expected that the basic properties of the linear regulator such as feedback structure, stability and robustness are to be reflected in those of the nonlinear regulator. To apply the above regulator theory to a real nonlinear plant, it is discussed how to distort the curvilinear coordinate axes on which a nonlinear plant behaves as a linear system. Consequently, a partial differential equation with respect to the homeomorphism is derived. Finally, the computational algorithm for the nonlinear optimal regulator is discussed and a numerical example is shown.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.411-421
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• 2004

A digital $(k_0,\;k_1)$-homotopy is induced from digital $(k_0,\;k_1)$-continuity with the n kinds of $k_i$-adjacency relations in ${\mathbb{Z}}^n$, $i{\in}\{0,\;1\}$. The k-fundamental group, ${\pi}^k_1(X,\;x_0)$, is derived from the pointed digital k-homotopy, $k{\in}\{3^n-1(n{\geq}2),\;3^n-{\sum}^{r-2}_{k=0}C^n_k2^{n-k}-1(2{\leq}r{\leq}n-1(n{\geq}3)),\;2n(n{\geq}1)\}$. In this paper two kinds of digital 8-pseudotori stemmed from the minimal simple closed 4-curve and the minimal simple closed 8-curve with 8-contractibility or without 8-contractibility, e.g., $DT_8$ and $DT^{\prime}_8$, are introduced and their digital topological properties are studied by the calculation of the k-fundamental groups, $k{\in}\{8,\;32,\;64,\;80\}$.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.21-25
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• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• 기호학연구
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• no.54
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• pp.119-145
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• 2018

This paper attempts to divide the narrative into three levels and review the approach methodology to understand Princess Bari as a narrative. If the stratification of the narrative, the analysis of each levels, and the integrated approach to them are made, this can contribute to suggesting new directions and ways to understand and study Princess Bari. The story level of Princess Bari, the surface structure, is shaped by the space movement and the chronological sequential structure of the life task that started from the birth of the main character. This story shows how a woman who was denied her existence by her father as soon as she was born finds an ontological transformation and identities through a process. Especially, the journey of finding identity is mainly formed through the events that occur through the relationship with family members. This structure, which can be found in the narrative level, forms a deep structure with the oppositional paradigm of family members' conflict and reconciliation, life and death. The thought structure revealed in this story is the problem of life is the problem of family composition, and the problem of death is also the same. In response to how to look at the unified world of coexistence of life and death, this tradition group of myths makes a relationship with man and God. This story is mainly communicated in the Korean shamanistic ritual(Gut) that sent the dead to the afterlife. Although the shaman is the sender and the participants in the ritual are the receivers, the story is well known a message that does not have new information repeated in certain situations. In gut, the patrons and participants do not simply accept the narrative as a message, but accept themselves as codes for reconstructing their lives and behavior through autocommunication. By accepting the characters and events of as a homeomorphism relationship with their lives, people accept the everyday life as an integrated view of life and death, disjunction and communication, conflict and reconciliation, and the present viewpoint. It can not change the real world, but it changes the attitude of 'I' about life. And it is a change and transformation that can be achieved through personal communication like the transformation of Princess Bari into god in myth. Thus, Princess Bari shows that each meaning and function in the story level, composition level, and communication level is related to each other. In addition, the structure revealed by this narrative on three levels is also effective in revealing the collective consciousness and cultural system of the transmission group.