• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.489-496
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• 2006

The aim of this paper is to use the Stein-Chen method to obtain a non-uniform bound on Poisson approximation in matching problem.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.301-311
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• 2015

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1].

• The Journal of the Korea Contents Association
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• v.9 no.12
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• pp.52-63
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• 2009

The problem of scheduling simply periodic task systems upon a uniform multiprocessor is considered. Partitioning of periodic task systems requires solving the bin-packing problem, which is known to be intractable (NP-hard in the strong sense). This paper presents a global scheduling algorithm which transforms a given simply periodic task system into another using a "task-splitting" technique. Each transformed simply periodic task system is guaranteed to be successfully scheduled upon any uniform multiprocessor using a partitioned scheduling algorithm. It is proven that the proposed algorithm achieves the theoretical maximum utilization bound upon any uniform multiprocessor platform.

• Journal of Communications and Networks
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• v.10 no.1
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.

• Journal of Communications and Networks
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• v.6 no.1
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• pp.1-8
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• 2004

In this paper, we investigate the properties and performance of space-time bit-interleaved coded modulation (STBICM) systems in fast Rayleigh fading channels. We first show that ST-BICM with QPSK signaling in fast fading channels possesses the uniform distance property, which makes performance analysis tractable. We also derive the probability distribution of the squared Euclidean distance between space-time symbols assuming uniform bit-interleaving. Based on the distribution, we show that the diversity order for each codeword pair becomes maximized as the frame length becomes sufficiently long. This maximum diversity order property implies that the bit-interleaver transforms an ST-BICM system over transmit diversity channels into an equivalent coded BPSK system over independent fading channels. We analyze the performance of ST-BICM in fast fading channels by deriving an FER upper bound. The derived bound turns out very accurate, requiring only the distance spectrum of the binary channel codes of ST-BICM. Numerical results demonstrate that the bound is tight enough to render an accurate estimate of performance of ST-BICM systems.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.933-944
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• 2004

Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper Renyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.6 s.261
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• pp.694-700
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• 2007

Recently, a new cellular metal, WBK(Wire woven Bulk Kagome) has been introduced. WBK is fabricated by assembling metal wires in six directions into a Kagome-like truss structure and by brazing it at all the crossings. Wires as the raw material are easy to handle and to attain high strength with minimum defect. And the strength and energy absorption are superior to previous cellular metals. Therefore, WBK seems to be promising once the fabrication process for mass production is developed. In this paper, an upper bound solution for the mechanical properties of the bulk WBK under compression is presented. In order to simulate uniform behavior of WBK consisted of perfectly uniform cells, a unit cell of WBK with periodic boundary conditions is analyzed by the finite element method. In comparison with experimental test results, it is found that the solution provides a good approximation of the mechanical properties of bulk WBK cellular metals except for Young's modulus. And also, the brazing joint size does not have any significant effect on the properties with an exception of an idealized thin joint.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.344-346
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• 1992

In this paper a robust hybrid control algorithm for n-link nonredundant robot manipulators is proposed. This scheme includes an estimation law for the upper bound on the uncertainty such that robust control input is updated as a function of the estimated upper bound. The uniform ultimate boundedness of the tracking error is generated by the Lyapunov based theory.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.4
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• pp.361-371
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• 2012

In order to improve the efficiency of the branch-and-bound method for mixed-discrete nonlinear programming, a nonuniform convergence tolerance scheme is proposed for the continuous subproblem optimizations. The suggested scheme assigns the convergence tolerances for each continuous subproblem optimization according to the maximum constraint violation obtained from the first iteration of each subproblem optimization in order to reduce the total number of function evaluations needed to reach the discrete optimal solution. The proposed tolerance scheme is integrated with five branching order options. The comparative performance test results using the ten combinations of the five branching orders and two convergence tolerance schemes show that the suggested non-uniform convergence tolerance scheme is obviously superior to the uniform one. The results also show that the branching order option using the minimum clearance difference method performed best among the five branching order options. Therefore, we recommend using the "minimum clearance difference method" for branching and the "non-uniform convergence tolerance scheme" for solving discrete optimization problems.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.517-529
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• 2009

In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.