• East Asian mathematical journal
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• v.14 no.1
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• pp.99-106
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• 1998

We establish a version of Fernique lemma for Gaussian processes which plays an important role in studying their moduli of continuity properties and related limit theorems.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.33-42
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• 2000

We generalize LePage-type representation of infinitely divisible processes and survey type G processes. Finally, we get integral representation and some inequality of processes of type G.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.831-839
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• 1996

In the last years there has been growing interest in concepts of positive (negative) dependence of stochastic processes such that concepts are considerable us in deriving inequalities in probability and statistics. Lehmann [7] introduced various concepts of positive(negative) dependence in the bivariate case. Stronger notions of bivariate positive(negative) dependence were later developed by Esary and Proschan [6]. Ahmed et al.[2], and Ebrahimi and Ghosh[5] obtained multivariate versions of various positive(negative) dependence as described by Lehmann[7] and Esary and Proschan[6]. Concepts of positive(negative) dependence for random variables have subsequently been extended to stochastic processes in different directions by many authors.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.311-319
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• 2001

We show that it is possible to associate diffusion processes to second order perturbations of the Ornstein-Uhlenbeck operator L on the Wiener space of the form L = L + 1/2∑L$^2$(sub)ξ(sub)$\kappa$ where the ξ(sub)$\kappa$ are "tangent processes" (i.e., semimartingales with antisymmetric diffusion coefficients).

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.309-323
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• 2000

The purposes of this paper are to revise the definitions of Ishikawa and Mann type iterative processes with errors, to study the unique solution of the m-accretive operator equation x+Tx=f and the convergence problem of Ishikawa and Mann type iterative processes with errors for m-accretive mappings without the Lipschitz condition. The results presented in this paper improve, extend, and unify the corresponding results in [4, 7, 8, 12, 16] in more general setting.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1009-1031
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• 2013

In this paper, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided pointwise estimates for Poisson kernels for subordinate Brownian motions. In particular, by combining the recent result of Kim and Mimica [5], our result provides the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes.

• Journal of Korean Society on Water Environment
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• v.40 no.4
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• pp.179-194
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• 2024

Biophysicochemical processes in water environments and treatment systems have been great concerns of engineers and scientists for controlling the fate and transport of contaminants. These processes are practically formulated as mathematical models written in coupled differential equations. However, because these process-based mathematical models consist of a large number of model parameters, they are complicated in analytical or numerical computation. Users need to perform substantial trials and errors to achieve the best-fit simulation to measurements, relying on arbitrary selection of fitting parameters. Therefore, this study adopted a Bayesian calibration method to estimate best-fit model parameters in a systematic way and evaluated the applicability of the calibration method to biophysicochemical processes of water environments and treatment systems. The Bayesian calibration method was applied to the microbial growth-decay kinetics and flocculation kinetics, of which experimental data were obtained with batch kinetic experiments. The Bayesian calibration method was proven to be a reasonable, effective way for best-fit parameter estimation, demonstrating not only high-quality fitness, but also sensitivity of each parameter and correlation between different parameters. This state-of-the-art method will eventually help scientists and engineers to use complex process-based mathematical models consisting of various biophysicochemical processes.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.35-53
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• 2005

The purpose of this study is to analyze and confirm the effectiveness of two teacher-centered instruction methods in the context of linear functions: one with emphasis on mathematical thinking processes as an alternative to the more traditional method without such emphasis. The level of achievement of students under the teacher-centered instruction with explicit emphasis on mathematical thinking processes is consistently higher than that of students receiving the more traditional teacher-centered instruction. The alternative instruction method in the current study is expected to encourage and prompt students to better grasp and understand mathematical concepts, principles, as well as problem solving strategies. In contrast to other alternatives, the method offers the advantage of being readily incorporated into the actual teaching practices in the classroom, as the traditional frame of teacher-centered pedagogy familiar to teachers remains in tact.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.565-584
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• 2009

This study is aimed at providing the theoretical framework of characteristics of mathematical thinking processes and structuring the thinking process patterns of the mathematical gifted students through the analysis of their cognitive thinking processes. For this purpose, this study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using think-aloud method. For comparative study, the analysis framework with the use of the thinking characteristic code as a content-oriented method and the problem-solving processes code as a process-oriented method was developed, and the differences of thinking characteristics between the two groups chosen by the coding system which represented the subjects' thinking processes in the form of the language protocol through thinking-aloud method were compared and analyzed.

• Journal of the Korean Society of Tobacco Science
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• v.17 no.2
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• pp.160-169
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• 1995

A mathematical model for the pyrolysis processes during unforced smoldering of cigarette was proposed in this study by analyzing the physical model of the smoldering cigarette (including the establishment of burning front between burning zone and pyrolysis zone, and analyzing the involvement of main factors such as pyrolysis of virgin tobacco, evaporation of water, and internal heat transport in the processes). Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered via the thermal resistance law for the competitive heat transfer mechanisms. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed, or linear burn rate, as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to be close to the experimental data in the literature (Muramatsu, 1981). The model provides a relatively fast and efficient way to simulate the pyrolysis processes and offers a practical tool for exploring important parameters for a smoldering cigarette, such as blended tobacco composition, properties of cigarette paper, and heat flux from the burning zone to the pyrolysis zone.