• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.197-202
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• 2007

Most of seismic reflection prospecting assumes subsurface formation to be homogeneous media. These models are not capable of estimating small scale heterogeneity which is verified by well log data or drilling core. And those synthetic seismograms by homogeneous media are limited to explain various changes at field data. So we developed a inhomogeneous velocity model which can estimate inhomogeneity of background medium to implement numerical modeling from homogeneous medium and inhomogeneous medium on the model. Background medium using three autocorrelation functions in order to generate inhomogeneous velocity media was according to dominant wavelength of background medium and correlation length of random medium. And then we compared shot gathers. The results show that numerical modeling implemented at inhomogeneous medium depicts complex wave propagation of field data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.263-279
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• 2022

This paper presents an automatic inspection of defects in semiconductor images. We devise a statistical method to find defects on homogeneous background from the observation that it has a log-normal distribution. If computer aided design (CAD) data is available, we use it to construct a signed distance function (SDF) and change the pixel values so that the average of pixel values along the level curve of the SDF is zero, so that the image has a homogeneous background. In the absence of CAD data, we devise a hybrid method consisting of a model-based algorithm and two neural networks. The model-based algorithm uses the first right singular vector to determine whether the image has a linear or complex structure. For an image with a linear structure, we remove the structure using the rank 1 approximation so that it has a homogeneous background. An image with a complex structure is inspected by two neural networks. We provide results of numerical experiments for the proposed methods.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.361-370
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• 1998

A condition for a certain maximal operator to be of weak type (p, p) is studied. This operator unifies various maximal operators cited in the literatures.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.4
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• pp.1239-1247
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• 2010

In this paper, we were researched decision problem called an optimal release policies after testing a software system in development phase and transferring it to the user. The applied model of release time exploited infinite failure non-homogeneous Poisson process This infinite failure non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The intensity function used Gompertz, Preto and Log-logstic pattern which has the efficient various property. Thus, optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

• Interaction and multiscale mechanics
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• v.6 no.3
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• pp.287-300
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• 2013

In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1107-1116
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• 2001

In this paper, we study the rationality of the Reidemeister zeta function of an endomorphism of a group extension. As an application, we give sufficient conditions for the rationality of the Reidemeister and the Nielsen zeta functions of selfmaps on an exponential solvmanifold or an infra-nilmanifold or the coset space of a compact connected Lie group by a finite subgroup.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.249-262
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• 2014

In this paper, we have developed a non-homogeneous q-difference equation of first order for the generalized Mock theta function of order eight and besides these established limiting case of Mock theta functions of order eight. We have also established identities for Partial Mock theta function and Mock theta function of order eight and provided a number of cases of the identities.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.309-318
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• 2009

We prove the homogeneous property of the norm of the new space $L\alpha(X)$ which has been developed in [3]. We also present $Poincar\acute{e}^{\prime}s$ inequality that is fitted to the function space $L\alpha(X)$ with an appropriate slope condition.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.435-443
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• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• Earthquakes and Structures
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• v.9 no.2
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• pp.305-320
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• 2015

The present paper is devoted to study SH-wave propagation in heterogeneous layer laying over an inhomogeneous isotropic elastic half-space. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the upper layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-wave increases with the increase of inhomogeneity parameter.