• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.23-31
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• 2002

A scale parameter is the principal parameter to be estimated, since it corresponds to one of the main reliability characteristics, namely the average time to failure. To provide robustness of scale estimators to gross errors in the data, we apply the Huber minimax approach in time to failure models of the statistical reliability theory. The minimax valiance estimator of scale is obtained in the important particular case of the exponential distribution.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1147-1157
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• 1996

Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.31-36
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• 2002

In this paper we first introduce a space of homogeneous type X, and we consider a kind of generalized upper half-space X $\times$ (0, $\infty$). We are mainly concerned with some inequalities in terms of Carleson measures or in terms of certain maximal operators with respect to general approach regions in X $\times$ (0, $\infty$). The main tool of the proof is the Whitney decomposition.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.845-860
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• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.709-715
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• 1994

The aim of of the study is a powerful test for the discrimination and therefore an optimal desin for that purpose. This problem is studied by Chernoff ([5]) and used in Chernoff ([6]) for accelerated life tests using the exponential distribution for life times. The approach used here is similar to that suggested by Lauter ([10]) and used in Chaloner ([3]) and Chaloner and Larntz ([4]) where it is motivated using Bayesian arguments. The approach taken in this paper the loss function $L(\cdot)$ evaluating a test procedure and a design d.

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.709-725
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• 2003

We give an analytic approach to the versal deformation of a resolution of a germ of normal isolated singularities. In this paper, we treat only formal deformation theory and it is applied to complete the CR-description of the simultaneous resolution of a cone eve. a rational curve of degree n in P$^{n}$ (n $\leq$ 4).

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.527-543
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• 2014

The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov's axiomatization of the theory of random variable structures used an early result on the completeness theorem for Lukasiewicz's [0, 1]-valued propositional logic. In this paper, we give an elementary approach to axiomatizing the theory of random variable structures. Only well-known results from probability theory are required here.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.469-481
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• 1997

In this paper we consider TU-cooperative games in the form of characteristic function. We notice that if one uses the necessary and sufficient condition for the core to be not empty in a dual form, it may be used for selecting the final outcome in the core. Using the linear programming approach for constructing the subcore, which is a subset of the core, we represent it in a simple form. We consider reduced games due to Davis-Mashler, Moulin and Funaki and formulate the sufficient conditions for the subcore to be S-consistent.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.307-315
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• 2017

In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.

• East Asian mathematical journal
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• v.21 no.1
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• pp.41-48
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• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.