• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.159-166
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• 1987

A new family of sinusoidal orthogoal trnasform is introduced. For a derivation, a parametric sinusoidal matrix whose transform might be implemented by a suitable FFT algorithm is modeled basically on the analogy of well-known sinusoidal transform such as DCT,SCT, etc., and its orthogonality condition is calculated. The parameters satisfying orthogonality condition are determined, in a sense, by particular solution after trial and error. However more than then transform matrices not yet known are obtained. It is also shown that these transforms can be computed by a DFT. of an image.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.493-505
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• 2004

We introduce certain local Thomsen condition in a 3-web and prove that it is equivalent to the equation a－(a－b)＝b in its corresponding loop, where we denote the loop operation additively for convenience and simplicity, even though the loop is neither associative nor commutative. Also we interpret such local Thomsen condition using orthogonality of chains in a web.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.1
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• pp.64-71
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• 1994

In this paper, we propose orthogonal integer transform(OIT) with general form. Considering the orthogonality and magnitude value order of the DCT Matrix whose performance is found to be close to that of the KLT, known to be optimal. The proposed OIT matrix is composed of values minimizing Hibert-Schmidt norm among integer values which satisfy the condition of orthogonality and the relative magnitudes of the DCT matrix. Comparing the OIT with the DCT, CMT, and ICT in error characteristics, transform efficiency, and maximum reducible bit, it is shown that the performance of the OIT compares more closely to that of the KLT relative to the performances of the DCT, CMT, and ICT when N=8.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.4
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• pp.80-90
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• 1994

Basic constraint equations derived from orthogonality conditions between a pair of body-fixed vectors and a body-fixed vector or a vector between two bodies are reformulated by using relative coordinate kinematics between two adjacent reference frames. Arithmetic numbers of operations required to compute derivatives of the constraint equations are drastically reduced. A mixed formulation of relative and cartesian coordinates is developed to further simplify derivatives of the constraints. Advantages and disadvantages of the new formulation are discussed. Possible singularity problem of para llelism constraints is resolved by introducing an extra generalized coordinate. Kinematic analysis of a McPherson strut suspension system are carried out to illustrate use and efficiency of the new formulation.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2003.11a
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• pp.126-130
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• 2003

The optical power transfer of TM modes in grating-assisted directional couplers (GADCs) with three-guiding channels is rigorously evaluated by defining a novel coupling efficiency amenable to the rigorous analytical solutions of modal transmission-line theory (MTLT). The results reveal that the incident power is sensitively partitioned through three output channels in terms of such grating parameters as the period, the duty cycle, and wavelength.

• Journal of the Korean Statistical Society
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• v.21 no.1
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• pp.80-86
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• 1992

The concept of Balanced Factorial Experiment (BFE) was introduced by Shah (1958). The conditions for BFE were set up by Kurkjian and Zelen (1963) and Kshirsagar (1966). Generalized Cyclic Factorial Experiment (GCFE), which is more wide class of designs than BFE, do not satisfy the condition of BFE. So all contrasts belonging to the same interaction are not estimated with equal variance. The main purpose of this paper is to show that GCFE have orthogonal factorial structure and the scheme of the size of variances for all normalized contrasts in GCFE is similar to the original intra-block association scheme.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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• pp.1784-1792
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• 2003

A hybrid method with supercompact multiwavelets is suggested as an efficient and practical method to compress CFD dataset. Supercompact multiwavelets provide various advantages such as compact support and orthogonality in CFD data compression. The compactness is a crucial condition for approximated representation of CFD data to avoid unnecessary interaction between remotely spaced data across various singularities such as shock and vortices. But the supercompact multiwavelet method has to fit the CFD grid size to a product of integer and power of two, m${\times}$2$^n$. To resolve this problem, the hybrid method with combination of 3, 2 and 1 dimensional version of wavelets is studied. With the hybrid method, any arbitrary size can be handled without any shrinkage or expansion of the original problem. The presented method allows high data compression ratio for fluid simulation data. Several numerical tests substantiate large data compression ratios for flow field simulation successfully.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.7 s.112
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• pp.769-776
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• 2006

A measured frequency response function can be represented as a ratio of two polynomials. A curve-fitting of frequency responses with Legendre polynomialis suggested in the paper. And the suggested curve-fitting algorithm is based on the least-square error method. Since the Legendre polynomials satisfy the orthogonality condition, the curve-fitting with the polynomials results to more reliable curve-fitting than ordinary polynomial method. Though the proposed curve-fitting with Legendre polynomials cannot cover all frequency range of interest, example shows that the suggested method is quite applicable in a limited frequency band.

• Structural Engineering and Mechanics
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• v.6 no.8
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• pp.857-870
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• 1998

This paper deals with a special class of inverse problems in discrete structural plasticity involving the identification of elastic limits and hardening moduli on the basis of information on displacements. The governing equations lead naturally to a special and challenging optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the orthogonality of two sign-constrained vectors or so-called "complementarity" condition. We investigate numerically the application of two simple algorithms, both based on the use of the general purpose nonlinear programming code CONOPT accessed via the GAMS modeling language, for solving the suitably reformulated problem. Application is illustrated by means of two numerical examples.