• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.1-9
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• 2023

An le-module M over a commutative ring R is a complete lattice ordered additive monoid (M, ⩽, +) having the greatest element e together with a module like action of R. This article characterizes the le-modules _RM such that the pseudo-prime spectrum X_M endowed with the Zariski topology is a Noetherian topological space. If the ring R is Noetherian and the pseudo-prime radical of every submodule elements of _RM coincides with its Zariski radical, then X_M is a Noetherian topological space. Also we prove that if R is Noetherian and for every submodule element n of M there is an ideal I of R such that V (n) = V (Ie), then the topological space X_M is spectral.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.351-366
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• 2007

Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $Supp_{R}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.553-563
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• 2017

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1039-1043
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• 2005

Despite the many significant advances made in robot architecture, the basic approaches are deliberative and reactive methods. They are quite different in recognizing outer environment and inner operating mechanism. For this reason, they have almost opposite characteristics. Later, researchers integrate these two approaches into hybrid architecture. In such architecture, Reactive module also called low-level motion control module have advantage in real-time reacting and sensing outer environment; Deliberative module also called high-level task planning module is good at planning task using world knowledge, reasoning and intelligent computing. This paper presents a framework of the integrated planning and control for mobile robot navigation. Unlike the existing hybrid architecture, it learns topological map from the world map by using MST (Minimum Spanning Tree)-based SOFM (Self-Organizing Feature Map) algorithm. High-level planning module plans simple tasks to low-level control module and low-level control module feedbacks the environment information to high-level planning module. This method allows for a tight integration between high-level and low-level modules, which provide real-time performance and strong adaptability and reactivity to outer environment and its unforeseen changes. This proposed framework is verified by simulation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.100-103
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• 1996

Presented in this study is an algorithmic procedure to obtain polyhedral model from a compound surface. The compound surface in this study denotes a collection of trimmed surfaces without topological relations. The procedure consists of two main modules: CAD data interface, and surface conversion to polyhedral model. The interface module gets geometric information from CAD databases, and makes topological information by scanning the geometric information. We are investigating CATIA system as a data source system. In the surface conversion module, a shell(compound surface with topological information) is approximated to a triangular-faceted polyhedral surface model through node sampling and triangulation steps. The obtained polyhedral model should obey the vertex-to-vertex rule and meet tolerance requirements. Since the polyhedral model has a simple data structure and geometry processing for it is very efficient and robust, the polyhedral model can be used in various applications, such as surface rendering in computer graphics, FEM model for engineering analysis, CAPP for surface machining, data generation for SLA, and NC tool path generation.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2834-2836
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• 2000

This paper introduces the behavior-based learning controller for mobile robot using topological map. When the mobile robot navigates to the goal position, it utilizes given information of topological map and its location. Under navigating in unknown environment, the robot classifies its situation using ultrasonic sensor data, and calculates each motor schema multiplied by respective gain for all behaviors, and then takes an action according to the vector sum of all the motor schemas. After an action, the information of the robot's location in given topological map is incorporated to the learning module to adapt the weights of the neural network for gain learning. As a result of simulation, the robot navigates to the goal position successfully after iterative gain learning with topological information.

• Communications of the Korean Mathematical Society
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• v.9 no.1
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• pp.143-146
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• 1994

• Honam Mathematical Journal
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• v.43 no.3
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• pp.403-416
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• 2021

It is known that the rank 2 stably free syzygy module P⁽²⁾ is not free. This algebraic fact was proved analytically, but this remarkable fact still lacks of a simple algebraic proof. The main purpose of this paper is to give a partially algebraic proof by making use of a theorem whose proof is quite topological, and the further properties of the module will be discussed.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.439-447
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• 2020

Let M be a lattice module over a C-lattice L. Let Spec^s(M) be the collection of all second elements of M. In this paper, we consider a topology on Spec^s(M), called the second classical Zariski topology as a generalization of concepts in modules and investigate the interplay between the algebraic properties of a lattice module M and the topological properties of Spec^s(M). We investigate this topological space from the point of view of spectral spaces. We show that Spec^s(M) is always T₀-space and each finite irreducible closed subset of Spec^s(M) has a generic point.