• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.323-331
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• 2004

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang's fuzzy topology, is presented in the paper. Some basic properties are discussed.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.167-189
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• 2007

In this paper we define a topology (analogous to Chang-type fuzzy topology) and a fuzzy topology (analogous to $H\"{o}hle-type$ fuzzy topology) associated with a lattice and study some of their properties.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.1
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• pp.191-210
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• 2011

Topology management, which includes neighbor discovery, tracking and updating, is a key area that need to be dealt with appropriately to increase network performance. The use of directional antenna in Wireless Mesh Networks is beneficial in constructing backbone networks viewing the properties of directional antenna. The backbone links must be robust to obtain better network performance. In this paper, a simple yet effective topology protocol is presented that performs well compared to its predecessors. Our protocol constructs the topology with the constraints in the number of links per node. The full topology is constructed in two phases. The resultant topology is termed as Web-topology. The topology formed is robust, efficient, and scalable.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.53-69
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• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.2
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• pp.344-358
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• 2011

Wireless tactical network (WTN) is the most important present-day technology enabling modern network centric warfare. It inherits many features from WMNs, since the WTN is based on existing wireless mesh networks (WMNs). However, it also has distinctive characteristics, such as hierarchical structures and tight QoS (Quality-of-Service) requirements. Little research has been conducted on hierarchical protocols to support various QoS in WMN. We require new protocols specifically optimized for WTNs. Control packets are generally required to find paths and reserve resources for QoS requirements, so data throughput is not degraded due to overhead. The fundamental solution is to adopt topology aggregation, in which a low tier node aggregates and simplifies the topology information and delivers it to a high tier node. The overhead from control packet exchange can be reduced greatly due to decreased information size. Although topology aggregation is effective for low overhead, it also causes the inaccuracy of topology information; thus, incurring low QoS support capability. Therefore, we need a new topology aggregation algorithm to achieve high accuracy. In this paper, we propose a new aggregation algorithm based on star topology. Noting the hierarchical characteristics in military and hierarchical networks, star topology aggregation can be used effectively. Our algorithm uses a limited number of bypasses to increase the exactness of the star topology aggregation. It adjusts topology parameters whenever it adds a bypass. Consequently, the result is highly accurate and has low computational complexity.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.127-133
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• 1997

In order to study the limits of sequences appearing in, for example, stochastic process, A. V. Skorokhod has defined new function space topologies. We compare these topologies with the topology of compact convergence, the topology of pointwise convergence and others.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.19-28
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• 2007

Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.5
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• pp.691-697
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• 2010

Reliability-based topology optimization (RBTO) is to get an optimal topology satisfying uncertainties of design variables. In this study, reliability-based topology optimization method is applied to the inner reinforcement of vehicle's hood based on BESO. A multi-objective topology optimization technique was implemented to obtain optimal topology of the inner reinforcement of the hood. considering the static stiffness of bending and torsion as well as natural frequency. Performance measure approach (PMA), which has probabilistic constraints that are formulated in terms of the reliability index, is adopted to evaluate the probabilistic constraints. To evaluate the obtained optimal topology by RBTO, it is compared with that of DTO of the inner reinforcement of the hood. It is found that the more suitable topology is obtained through RBTO than DTO even though the final volume of RBTO is a little bit larger than that of DTO. From the result, multiobjective optimization technique based on the BESO can be applied very effectively in topology optimization for vehicle's hood reinforcement considering the static stiffness of bending and torsion as well as natural frequency.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.6
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• pp.1-1
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• 2002

In this paper, we focus on comparison and analysis of performance for existing Topology Aggregation algorithm. For these, we designed and implemented PNNI routing simulator which contain various TA schemes, and evaluate performance of TA schemes by this simulator. The PNNI 1.0 specification of the ATM Forum is recommended that hierarchical routing protocol and topology information is aggregated in the network constructed hierarchically Aggregating topology information is known as TA(Topology Aggregation) and TA is very important for scalability and security in network. Therefore, the performance of PNNI network would vary with TA schemes and routing algorithm. PNNI routing simulator can be applied to develope Routing algorithm and TA algorithm and can be develope these algorithms in short period.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1299-1307
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• 2023

In this paper, we attempt to study several topological properties for the function space H(X), space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at X compact. Furthermore, we prove that the space H(X) endowed with the regular topology is a topological group when X is a metric, almost P-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on ℝ under regular topology are open subspaces of H(ℝ) and are homeomorphic.