• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• Journal of the Korean Society for Precision Engineering
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• v.10 no.3
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• pp.87-96
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• 1993

In this study, the peak stress of a fuillet in elastic structure was optimized to have minimum value by using quadratic isoparametric element. The method of auomatic gridding was also developed along with shape algorithm and design element technique was adopted in selecting design variables. The computer program developed was combined with the Hooke-Jeeves direct algorithm of optimization techniques in order to minimize the peak stress of the fillet. The imployment of design element technique significantly cut down computer time by the reduction in design variables, and the opitmum fillet shape with uniform minimum stress was obtained by varying design variables along x and y directions in improving the shape compared to other results. By using automatic gridding, in which Bezier surfaces and Coons surfaces of cubic interpolation were employed, the irregular boundary was removed resulting in smoother anbd more accurate fillet shape possessing uniform minimum stress.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.671-680
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• 2007

The objective of this work is to reduce drag on a bluff body within a viscous flow by applying suction or injection of fluid along the surface of the body. In addition to minimizing drag, the optimal solution tends to reduce boundary layer separation and flow recirculation. When discretized by finite elements, the optimal control problem can be posed as a large-scale nonlinearly-constrained optimization problem. The constraints correspond to the discretized form of the Navier-Stokes equations. Unfortunately, solving such large-scale problems directly is essentially intractable. We developed several Sequential Quadratic Programming methods that are tailored to the structure of the control problem. Example problems of laminar flow around an infinite cylinder in two dimensions are solved to demonstrate the methodology. We use these optimal control techniques to study the influence of number of suction/injection holes and location of holes on the resulting optimized flow. We compare the proposed SQP methods against one another, as well as against available methods from the literature, from the point of view of efficiency and robustness. The most efficient of the proposed methods is two orders of magnitude faster than existing methods.

• Journal of Biomedical Engineering Research
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• v.13 no.1
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• pp.19-24
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• 1992

Lineacgrams are diagnostic films taken using X-ray from the linear accelerator with the patient in the treatment position to assure that the treatment is being delivered in accordance with the treatment prescription. But the image quality of the lineacgram is so bad because of the high X-ray energy. This paper presents a new algorithm that enhances the image of lineacgram. Thls algorithm calculates optimal threshold value which is used for segmentation of lineacgram using co-occurrence matrix and enhances the image Inside and outside treatment area preserving treatments boundary.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.451-460
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• 1996

We propose a new shape of cylindrical shell formed by multiples vaults which gives a self-stiffening against buckling. By an experimental and numerical study of cylindrical shells with a repeated defect, on the circumferential direction made only of outside oriented wave-defects, we show that multiple vault cylindrical shells can have a good behaviour in buckling. An optimal behaviour is obtained by optimization of the vaults number, with conduces to a special multiple vault cylindrical shell named "ASTER shell".

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.05b
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• pp.279-282
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• 2000

We have been designed and fabricated a bi-directional ultrasonic linear motor using piezoelectric ceramics. With the finite element method, we design and verify validity of the structure, and determine its optimal structure, size of design variables, material and boundary conditions for proper generation of the ultrasonic waves. Based on the design, a prototype of the ultrasonic linear motor has been fabricated and characterized, which thereby proves practical applicability of this new motor.

• 한국가스학회:학술대회논문집
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• 2005.10a
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• pp.157-162
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• 2005

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1988.10a
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• pp.1-6
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• 1988

In this study, the current progress in computational structural engineering and research trends are discussed. The development of new finite elements, error analysis and adaptive mesh generation, material constitutive model, boundary element methods, structural optimal design, hardware/software, AI application and expert systems are particularly emphasized. The rapid development in computer technologies provides good environment for the technical advancement in computational structural engineering.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• 전기의세계
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• v.29 no.4
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• pp.256-259
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• 1980

A singular pertubation theory is applied to obtain an approximate solution for suboptimal control of nuclear reactors with spatially distributed parameters. The inverse of the neutron velocity is regarded as a small perturbing parameter, and the model, adopted for simplicity, is a cylindrically symmetrical reactor whose dynamics are described by the one group diffusion equation with one delayed neutron group. The Helmholtz mode expansion is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter systems. An asymptotic expansion of the feedback gain matrix is obtained with construction of the boundary layer correction up to the first order.