• Honam Mathematical Journal
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• v.38 no.4
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• pp.849-856
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• 2016

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.9A
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• pp.758-766
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• 2011

Cooperative communications are adopted as a promising solution to achieve high data rate over large areas in the future 40 wireless system and the relay station (RS) is the key concept in cooperative communications. However, most existing works in this area focus only on optimal RS selections. In addition, there are only few works consider another crucial issue: how many relay stations we need to place. Only when the number of relay stations is defined, the relay station selection can be performed well. In this paper we derive a formula which describes the impact of varying number of RS on end-to-end link throughput assuming a clustering scheme which is based on Voronoi tessellation. In addition to mathematical analysis on the feasibility of the formula, we also examine its performance through a set of simulations under the Erceg path loss model. Simulation results verify that the link throughput gain of our proposed scheme is promising.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.7
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• pp.693-699
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• 2006

An accurate and compact map is essential to an autonomous mobile robot system. For navigation, it is efficient to use an occupancy grid map because the environment is represented by probability distribution. But it is difficult to apply it to the large environment since it needs a large amount of memory proportional to the environment size. As an alternative, a topological map can be used to represent it in terms of the discrete nodes with edges connecting them. It is usually constructed by the Voronoi-like graphs, but in this paper the topological map is incrementally built based on the local grid map using the thinning algorithm. This algorithm can extract only meaningful topological information by using the C-obstacle concept in real-time and is robust to the environment change, because its underlying local grid map is constructed based on the Bayesian update formula. In this paper, the position probability is defined to evaluate the quantitative reliability of the end nodes of this thinning-based topological map (TTM). The global TTM can be constructed by merging each local TTM by matching the reliable end nodes determined by the position probability. It is shown that the proposed TTM can represent the environment accurately in real-time and it is readily extended to the global TTM.