• Journal of Communications and Networks
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• v.5 no.2
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• pp.174-183
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• 2003

Space-Time (ST) codes are known to provide high transmission rates, diversity and coding gains. In this paper, a tight upper bound on the error probability of ST codes over rapid fading channels is presented. Moreover, ST codes suitable for rapid fading channels are presented. These codes are designed using the QPSK and 16-QAM signal constellations. The proposed codes are based on two different encoding schemes. The first scheme uses a single trellis encoder, whereas the second scheme uses the I-Q encoding technique. Code design is achieved via partitioning the signal space such that the design criteria are maximized. As a solution for the decoding problem of I-Q ST codes, the paper introduces a low-complexity decoding algorithm. Results show that the I-Q ST codes using the proposed decoding algorithm outperform singleencoder ST codes with equal complexity. The proposed codes are tested over fading channels with different interleaving conditions, where it is shown that the new codes are robust under such imperfect interleaving conditions.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.245-257
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• 2007

We showed in [2] that if $r\leq2$, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to $h^{2r+3}$ using zero mean Gaussian distribution under the assumption that we have subintervals (for simplicity equal length) partitioning and that each subinterval has the length. In this paper, if $r\geq3$, we show that zero mean Gaussian distribution of average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $Ch^8$.

• The Transactions of the Korea Information Processing Society
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• v.1 no.3
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• pp.290-298
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• 1994

In this paper we propose parallel sorting algorithm, taking 0( $n^{n}$ log n) time complexity, 0( $n^{x}$ log n) cost (parallel running time * number of processors) and 0( $n^{1-}$x＋ $n^{x}$ )data movement complexity under the ERWW- PRAM model. The methods for solving these problems similar. Parallel algorithm finds pivot for partitioning the data into ordered subsets of approximately equal size by using encording pointers..

• Honam Mathematical Journal
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• v.30 no.3
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• pp.581-587
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• 2008

In this paper, to have a better a posteriori error bound of the average case error between the true value of I(f) and the Trapezoidal rule on subintervals using zero mean-Gaussian, we prove that a new average error between the difference of the true value of I(f) from the composite Trapezoidal rule and that of the composite Trapezoidal rule from the simple Trapezoidal rule is bounded by $c_rH^{2r+3}$ through direct computation of constants $c_r$ for r ${\leq}$ 2 under the assumption that we have subintervals (for simplicity equal length h) partitioning [0, 1].

• School Mathematics
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• v.8 no.2
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• pp.123-138
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• 2006

The fraction concept consists of various meanings and is one of the more abstract and difficult in elementary school mathematics. This study intends to analyze the fraction concept from historical and psychological viewpoints, to examine the current elementary mathematics textbooks by these viewpoints and to seek the direction for improvement of it. Basic ideas about fraction are the partitioning - the dividing of a quantity into subparts of equal size - and about the part-whole relation. So these ideas are heavily emphasized in current textbooks. However, from the learner's point of view, situations related to different meanings of fraction concept draw qualitatively different response from students. So all the other meanings of fraction concept should be systematically represented in elementary mathematics textbooks. Especially based on historico-genetic principle, the current textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction as a unit.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.2
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• pp.23-32
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• 2004

The query optimizer's important task while a query is invoked is to estimate the fraction of records in the databases that satisfy the given query condition. The query result size estimation in spatial databases, like relational databases, proceeds to partition the whole input into a small number of subsets called “buckets” and then estimate the fraction of the input in the buckets. The accuracy of estimation is determined by the difference between the real data counts and approximations in the buckets, and is dependent on how to partition the buckets. Existing techniques for spatial databases are equi-area and equi-count techniques, which are respectively analogous in relation databases to equi-height histogram that divides the input value range into buckets of equal size and equi-depth histogram that is equal to the number of records within each bucket. In this paper we propose a new partitioning technique that determines buckets according to the maximal difference of area which is defined as the product of data ranges End frequencies of input. In this new technique we consider both data values and frequencies of input data simultaneously, and thus achieve substantial improvements in accuracy over existing approaches. We present a detailed experimental study of the accuracy of query result size estimation comparing the proposed technique and the existing techniques using synthetic as well as real-life datasets. Experiments confirm that our proposed techniques offer better accuracy in query result size estimation than the existing techniques for space query size, bucket number, data number and data size.

• Journal of the Economic Geographical Society of Korea
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• v.15 no.3
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• pp.343-357
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• 2012

The Seoul metropolitan subway system can be represented by a graph which consists of nodes and edges. In this paper, we study classification of subway stations and trip behaviour of subway passengers through partitioning the graph of the subway system into roughly equal groups. A weight of each edge of the graph is set to the number of passengers who pass the edge, where the number of passengers is extracted from the transportation card transaction database. Since the graph partitioning problem is NP-complete, we propose a heuristic algorithm to partition the subway graph. The heuristic algorithm uses one of two alternative objective functions, one of which is to minimize the sum of weights of edges connecting nodes in different groups and the other is to maximize the ratio of passengers who get on the subway train at one subway station and get off at another subway station in the same group to the total subway passengers. In the experimental results, we illustrate the subway stations and edges in each group by color on a map and analyze the trip behaviour of subway passengers by the group origin-destination matrix.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.35T no.2
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• pp.13-19
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• 1998

The Median of a set of number is a number which partitions the given set. The specified numbers of a set partitions in one subset and in another subset. In Image Processing, The Sorting method of numbers of one subset equal to the previous Median Filtering. but The Sorting method of numbers of another subset not equal to in the other. In this paper, a fast two-dimentional Median Filtering Algorithm is proposed. The Algorithm designed in such a during the partitioning of the previous window are used. Test results obtained by running the Algorithm on IBM PC(586) are presented and its filtering. It is shown that the proposed Algorithm's processing time is faster and independent of the number of bits used to represent the data values.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.391-394
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• 2005

In this paper, we study the average case error of the Trapezoidal rule using zero mean-Gaussian. Assume that we have n subintervals (for simplicity equal length) partitioning [0,1] and that each subinterval has the length h. Then, for $r{\leq}2$, we show that the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $h^{2r+3}$ through direct computation of constants $c_r$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.8
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• pp.2003-2012
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• 1996

The 16- and 32-state Trellis-coded M-ary 4-dimensional (4-D) orthogonal modulation scheme with a frequency-reuse technique have been investigated. Here, 5 coded bits form a rate 4/5 convolutional encoder provide 32 possible symbols. Then the signals are mapped by a M-ary 4-D orthogonal modulator, where each signal has equal energy and is PSK modulated. In the M-ary 4-D modulator, we have employed the vectors which is derived by the optimization technique of signal waveforms in a 4-D sphere. This technique is usedin maximizing the minimum Euclidean distance between a set of signal poits on a multidimensional sphere. By combinig trellis coding with M-ary 4-D modulation and proper set-partitioning, we have obtained a considerable impeovement in the free minimum distance of the system over an AWGN channel. The 16-state scheme obtains coding gains up to 5.5 dB over the uncoded two-independent QPSK scheme and 2.5 dB over the two-independent 2-D TCM scheme. And, the 32-state scheme obtains coding gains up to 6.4 dB over the uncoded two-independent QPSK schemeand 3.4 dB over the two-independent 2-D TCM scheme.