• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.545-554
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• 2014

We provide a new Ostrowski-type inequality involving functions of two independent variables, as well as some related results.

• 대한수학회보
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• 제41권3호
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• pp.559-571
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• 2004

The aim of the present paper is to establish some nonlinear integral inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential equations.

• Journal of the Korean Statistical Society
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• 제17권1호
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• pp.46-55
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• 1988

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).

• Korean Journal of Mathematics
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• 제26권4호
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• pp.665-674
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• 2018

A generalization of Ostrowski-type inequality involving functions of two independent variables is given.

• 대한수학회지
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• 제45권1호
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• pp.121-136
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• 2008

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

• 대한수학회보
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• 제45권3호
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• pp.509-522
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• 2008

The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type $X^2_N={\Sigma}^N_{i=1}\;X^2_i$ with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables $X_i$. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.717-737
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• 2020

In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using p-norms. Special cases of our results reduce to the inequalities in earlier study.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 추계학술대회 학술발표 논문집 제15권 제2호
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• pp.276-279
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• 2005

A review of how the functions of two or more independent variables can be approximated by using fuzzy systems is provided in this paper. We start with an exact represention of a linear interpolation function of two independent variables by using a fuzzy system. Next, we describe how this function can be approximated by another fuzzy system with a lesser number or with a desired number of output fuzzy sets. Thus, a reduction of the storage needed is achieved by storing the fuzzy rules or equivalently the output fuzzy set numbers instead of storing the whole discrete function values. A description on how the cubic spl me interpolation function can be represented exactly by using the fuzzy system method is provided, along with a few examples where fuzzy rule tables with a size of 7$\times$7 provide a representation of the functions with relative errors of the order of $10^{2}$ or less.

• 디지털융복합연구
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• 제17권5호
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• pp.217-223
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• 2019

자동차 분야에서 저항 점용접의 결함 및 품질을 실시간으로 예측할 수 있는 연구는 원가절감과 고품질 생산을 위한 필수 불가결한 연구 분야라 할 수 있다. 용접 품질은 전단강도와 너깃의 크기에 의해서 결정되며 여러 가지 독립변수에 따라 결과가 달라진다. 실시간 예측시스템을 개발하기 위하여 다중 회귀분석을 실시하여 3개의 독립변수로 두 가지 종속변수를 충분한 통계적 결과로 구하였으나 회귀식에 의한 품질 예측은 정확도를 보장할 수 없었다. 본 연구에서는 다층 신경망 회로를 구축하였다. 10가지의 동저항 변수에 의한 신경망은 3개의 은닉층을 구축하여 실행 함수와 가중치 행렬을 구하였다. 그러나 이 경우, 입력 변수가 너무 많아 실시간 제어에 어려움이 있을 수 있으므로 회귀분석에 의한 3개의 독립변수로 신경망을 구축하였다. 그 결과 모든 시험데이터를 불량, 부분 불량, 양품으로 구분하는데 성공하였다. 따라서 다중 회귀분석에 의해서 구한 3개의 독립변수에 의한 실시간 용접 품질 판정 시스템을 완성할 수 있었다.

• 가정과삶의질연구
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• 제21권3호
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• pp.61-73
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• 2003

The purpose of this study was to compare the consumption expenditure patterns and the effects of socioeconomic variables on expenditure between single-mother families and two-parent families. From the 2001 Household Income and Expenditure Survey conducted by Korea National Statistical Office (KNSO), 693 single-mother families and 14,439 two-parent families were selected. A t-test was completed to examine how the expenditure patterns of two types of families differ. Total expenditures and expenditures on 11 consumption categories were modeled as functions of permanent income and other socioeconomic variables. Also, dummy variable interaction technique was used to examine whether the independent variables differently affected the expenditures between single-mother families and two-parent families. The results of this study indicated that there were differences between single-mother and two-parent families in the levels and shares of expenditures of each consumption category, and the effects of socioeconomic variables on expenditures. Single-mother families had spent less than did two-parent families in each consumption category. However, single-mother families had significantly higher expenditure shares for food at home, shelter, utilities, apparel and shoes, and education. Income elasticities for food at home, shelter, utilities, and education of single-mother families were significantly larger than those of two- parent families.