• Korean Journal of Computational Design and Engineering
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• v.2 no.2
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• pp.122-129
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• 1997

Ball rolling blending is a popular technique for blending between parametric surfaces. The ball rolling blend surface is conceptually a trajectory of a ball rolling between two base sufaces. It is constructed by sweeping a circular arc along a ball contact curve pair. Since a ball rolling blend surfaces does not have a polynomial form like a Bezier surface patch, it is impossible to apply this method directly to a commercial CAD/CAM system. In this paper an algorithm is developed to approximate a ball rolling blend surface into Bezier surface patches. Least square method is applied to obtain proper Bezier surface patches under a given tolerance. The Bezier surface patches have degree three or more and guarantee VC1-continuity.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.413-416
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• 1998

We investigate the Hurwitz stability condition using the coefficient diagram. The coefficient diagram consists of a plot of logarithmic values of the coefficients of the characteristic polynomial versus the degree of the coresponding coefficients. The logarithmic value of the coefficient of the characteristic polynomials are plotted in the descending order. Using the Bhattacharyya, Chapellat and Keel's algorithm, the sufficient and necessary condition for Hurwitz stability are reconstructed using the coefficient diagram. With the coefficient diagram we also present some necessary or sufficient conditions for Hurwitz stability of polynomials. In addition we obtain a lower bound for the Manabe parameter $\tau$.

• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.36-44
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• 1982

A new design concept, called axis-slope-rotatability, is presented for the design of experiments with mixtures. This is an analogue of the Box-Hunter (1957) rotatability for second order response surface designs. By choice of design, it is possible to make the variance of the estimated slopes along the component axes constant for all axial points equidistant from the center point of the factor space. This property is called axis-slope-rotatability for mixture experiments. When the Scheffe's second degree polynomial is used, it is shown that some symmetry conditions are sufficient for axis-slope-rotatability. Several designs having this property are illustrated.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.255-258
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• 2009

It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

• Journal of KSNVE
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• v.10 no.1
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• pp.123-128
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• 2000

This paper describes the optimization of the hexagonal array transducer using finite element method. The transducer consists of the disc type sensors. Three dimensional beam patterns of each element and the array transducer are analysed using the finite element code ATILA. Beam patterns were analyzed for the disc type transducer. To optimize beam patterns of the array transducer, Chebyshev polynomial weight is applied to each element. In case of applying optimized weight, a 30 degree width beam pattern is presented at 10kHz. This paper also includes the effect of rubber filling material instead of using the water inside the transducer array.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.379-383
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• 2000

This paper describes the design program of duct silencer. Duct silencer is used ventilating system. Variables in the program for predicting transmission loss are width of splitter, airway width, perforate plate, absorption material and frequency. Generally used expression for predicting transmission loss has something that don't think about frequency characteristic. Therefore we propose the new expression that considered frequency characteristic. In the 1/1 octave band center frequency, the expected weighting number(K) is fitted with absorption ratio and airway width. The fitted 2nd degree polynomial expression is based on the test data performed in YOUIL Industrial Corperation. This program's accuracy is about 90 percent.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.75-82
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• 1997

An algorithm for computing the cubic spline interpolation coefficients for polynomials is presented in this paper. The matrix equation involved is solved analytically so that numerical inversion of the coefficient matrix is not required. For $f(t)=t^m$, a set of constants along with the degree of polynomial m are used to compute the coefficients so that they satisfy the interpolation constraints but not necessarily the derivative constraints. Then, another matrix equation is solved analytically to take care of the derivative constraints. The results are combined linearly to obtain the unique solution of the original matrix equation. This algorithm is tested and verified numerically for various examples.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.209-229
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• 2004

Let $\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $$\mid$s_{\alpha}$\mid$\;=\;1$ for all multi indices $\alpha$), and let $R\;{\subset}\;{\mathbb{C}}^n$ be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;$\mid$\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha}$\mid$$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. $s_{\alpha}\;=\;{\pm}1$ for all multi indices $\alpha$). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.913-931
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• 1998

Using invariant theory, new invariant cubature formulas over a unit cube are given by imposing a group structure on the formulas. Cools and Haegemans [Computing 40, 139-146 (1988)] constructed invariant cubature formulas over a unit square. Since there exists a problem in directly extending their ideas over the unit square which were obtained by using a concept of good integrity basis to some constructions of invariant cubature formulas over the unit cube, a Reynold operator will be used to obtain new invariant cubature formulas over the unit cube. In order to practically find integration nodes and weights for the cubature formulas, it is required to solve a system of nonlinear equations. With an IMSL subroutine DUNLSF which is used for solutions of the system of nonlinear equations, we shall give integration nodes for the new invariant cubature formulas over the unit cube depending on each degree of polynomial precision.

• Wind and Structures
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• v.5 no.5
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• pp.423-440
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• 2002

The effects of the nonlinear (quadratic) term in wind pressure have been analyzed in many papers with reference to linear structural models. The present paper addresses the problem of the response of nonlinear structures to stochastic nonlinear wind pressure. Adopting a single-degree-of-freedom structural model with polynomial nonlinearity, the solution is obtained by means of the moment equation approach in the context of It$\hat{o}$'s stochastic differential calculus. To do so, wind turbulence is idealized as the output of a linear filter excited by a Gaussian white noise. Response statistical moments are computed for both the equivalent linear system and the actual nonlinear one. In the second case, since the moment equations form an infinite hierarchy, a suitable iterative procedure is used to close it. The numerical analyses regard a Duffing oscillator, and the results compare well with Monte Carlo simulation.