• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.201-202
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• 2006

To analyze the dynamic characteristics of the bundle drawing process, we employed a Random Phase Spectrum method to generate stochastic test signals that had a given autocorrelation function. And the spectra of the dynamics of the process outputs were obtained, based on the dynamic model of the bundle drawing process. Results showed that the RPS method was very effective to generate stochastic signals that had an exponential function form. The drawing process had the traits that there existed a special frequency range, incurring the process resonance.

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1281-1291
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• 2001

The hereditary integral form of a quasi-linear viscoelastic law has been employed. Four new concepts have been employed: 1. a reduced relaxation function with a non-linear exponential function of time, 2. an inverse method to determine the scale factor of the elastic response, 3. an instant elastic recovery strain during unloading, and 4. the results of a constitutive model for cyclic tests may be a function of the Heavyside class. These concepts have been supported by agreement between measured and predicted responses of soft connective tissue to three types of multiple cyclic tests which include rest periods of no extension and alternations between different strain levels. Such agreement has not been attained in the previous studies. Chun and Hubbard (2001) is our companion experimental analysis paper.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.861-869
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• 2006

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, the problem of determining optimal burn-in time for a system which performs given mission is considered. It is assumed that the given mission time is not a fixed constant but a random variable which follows an exponential distribution. Assuming that the underlying lifetime distribution of a system has an eventually increasing failure rate function, an upper bound for the optimal burn-in time which maximizes the probability of performing given mission is derived. The obtained result is also applied to an illustrative example.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.933-942
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• 1992

The effects of the folwrate on the dropsize from the two-phase coaxial nozzle are investigated by using the direct photographic method and the empirical equation is obtained. For the photography, the light source which the life time is the order of 100ns is fabricated and the lens is the zoom lens which has the MICRO function with a teleconvertor. The distillated water and the compressed air of the surrounding temperature are injected and atomized. For the purpose of the exact adjustment and measurement of the flowrates, the two rotameters are used. As a result of this study, the sauter mean diameter of droplets has a tendency for a logarithmic function with air flowrate and for a exponential function with water flowrate.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.2
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• pp.127-136
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• 1989

This paper describes the parameter convergence properties of an adaptive system to identify a single-input single-output plant model. It is demonstrated that, by using power spectrum analysis, the persistency of excitation (PE) condition in order to guarantee the exponential stability of the adaptive control system can be transformed into the positive definite behavior for the auto-correlation function matrix of adaptive signal. The existence of parameter nominal values can be analyzed by this condition and the convergence rates of parameter are determined by examining the auto-correlation function. We may use the sufficient richness (SR) of input spectrum instead of the PE condition to analyze the parameter boundedness. It can be shown that the eigen values of the auto-correlation function are always related with adaptive gain, input amplitude and positions or numbers of input spectra. In each case, the variation of parameter convergence rate can be also verified.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.725-742
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• 2021

The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the authors analyze these bounds in the special domains associated with exponential function and sine function. Further we obtain Fekete-Szegö inequalities for the defined subclasses of analytic functions defined through Poisson distribution series and Pascal distribution series.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.583-590
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• 2002

Point collocation method based on the fast derivatives approximation of meshfree shape function is applied to solid mechanics in this study. Enhanced meshfree approximation with approximated derivative of shape function is reviewed, and formulation of linear elastic solid mechanics by point collocation method is presented. It implies that governing equation of solid mechanics with strong form is directly formulated without no numerical integration cells or grid. The regularity of weight function is not required due to a use of approximated derivative, so we propose the exponential type weight function that is discontinuous in first derivative. The convergence and stability of the proposed method is verified by passing the generalized patch test. Also, the efficiency and applicability of the proposed method in solid mechanics is verified by solving types of solid problems. Numerical results show that not only a use of proposed weight function leads lower error and higher convergence rate than that of the conventional weight functions, but also the improved collocation method with derivative approximation enables to compute the derivatives of shape function very fast and accurately enough to replace the classical direct derivative calculation.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.371-383
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• 1997

In recent years M. Pinto introduced the notion of h-stability. He extended the study of exponential stability to a variety of reasonable systems called h-systems. We investigate h-stability for the nonlinear differential systems using the notions of $t_\infty$-similarity and Liapunov functions.

• East Asian mathematical journal
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• v.34 no.1
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• pp.69-84
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• 2018

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Journal for History of Mathematics
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• v.9 no.2
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• pp.15-21
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• 1996

적률법(method of moment)이란 변수 X의 멱승에대한 기대치를 이용하여 분포의 성질을 알아보는 방법이다. 여기서 적률법이 이용되어진 역사적 배경을 소개하고, 3차 적률들의 선형적 성질을 비교하였다. 먼저, Kagan이 입증한 표본평균에 관한 3차 표본적률의 선형적 성질과 Bayesian 경우에 3차 사후적률(posterior moment)과 사후평균(posterior)의 선형성을 소개하였다. 그리고, 자연지수족(natural exponential family)아래서도 표본평균에 관한 3차 표본적률의 선형성을 알아보기 위해 단순함수(simple function)의 형태로 유도하였으며, 정규분포인 경우에 적용시켜 보았다.