• Kyungpook Mathematical Journal
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• v.54 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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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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• v.17 no.1
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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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• v.26 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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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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• v.28 no.4
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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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.

• Journal of Digital Convergence
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• v.17 no.5
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• pp.217-223
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• 2019

A study in predicting defects of spot welding in real time in automotive field is essential for cost reduction and high quality production. Welding quality is determined by shear strength and the size of the nugget, and results depend on different independent variables. In order to develop the real-time prediction system, multiple regression analyses were conducted and the two dependent variables were obtained with sufficient statistical results with three independent variables, however, the quality prediction by the regression formula could not ensure accuracy. In this study, a multi-layer neural network circuit was constructed. The neural network by 10 dynamic resistance variables was constructed with three hidden layers to obtain execution functions and weighting matrix. In this case, the neural network was established with three independent variables based on regression analysis, as there could be difficulties in real-time control due to too many input variables. As a result, all test data were divided into poor, partial, and modalities. Therefore, a real-time welding quality determination system by three independent variables obtained by multiple regression analysis was completed.

• Journal of Families and Better Life
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• v.21 no.3
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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.