• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1043-1048
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• 2011

W. Choi([1]) identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. We denote by F the homozygosity and by S the average selection intensity. In this note, we define the Fleming-Viot process with generator of limiting diffusion and provide exact result for the relations of F and S.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.378-385
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• 2008

The present paper deals with the accurate and robust limiting procedure for the multi-dimensional flow analysis on unstructured meshes. The multi-dimensional limiting process (MLP) which was successfully proposed on structured grid system is extended to unstructured meshes. Based on MUSCL-type framework on unstructured meshes, the new slope limiter is devised to satisfy the MLP condition, which is quite effective to regulate the unwanted oscillations, especially on multiple dimensions. Considering the neighborhood based on the vertex of the cell, as well as the edge, this limiting strategy captures the multi-dimensional flow features very accurately with the proper stencils. From the various numerical results, these desirable characteristics of the proposed limiting strategy are clearly shown.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년 추계학술대회논문집
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• pp.378-385
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• 2008

The present paper deals with the accurate and robust limiting procedure for the multi-dimensional flow analysis on unstructured meshes. The multi-dimensional limiting process (MLP) which was successfully proposed on structured grid system is extended to unstructured meshes. Based on MUSCL-type framework on unstructured meshes, the new slope limiter is devised to satisfy the MLP condition, which is quite effective to regulate the unwanted oscillations, especially on multiple dimensions. Considering the neighborhood based on the vertex of the cell, as well as the edge, this limiting strategy captures the multi-dimensional flow features very accurately with the proper stencils. From the various numerical results, these desirable characteristics of the proposed limiting strategy are clearly shown.

• Membrane and Water Treatment
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• 제7권2호
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• pp.127-141
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• 2016

Electrodialysis (ED) is known to be a useful membrane process for desalination, concentration, separation, and purification in many fields. In this process, it is desirable to work at high current density in order to achieve fast desalination with the lowest possible effective membrane area. In practice, however, operating currents are restricted by the occurrence of concentration polarization phenomena. Many studies showed the occurrence of a limiting current density (LCD). The limiting current density in the electrodialysis process is an important parameter which determines the electrical resistance and the current utilization. Therefore, its reliable determination is required for designing an efficient electrodialysis plant. The purpose of this study is the development of a predictive model of the limiting current density in an electrodialysis process using response surface methodology (RSM). A two-factor central composite design (CCD) of RSM was used to analyze the effect of operation conditions (the initial salt concentration (C) and the linear flow velocity of solution to be treated (u)) on the limiting current density and to establish a regression model. All experiments were carried out on synthetic brackish water solutions using a laboratory scale electrodialysis cell. The limiting current density for each experiment was determined using the Cowan-Brown method. A suitable regression model for predicting LCD within the ranges of variables used was developed based on experimental results. The proposed mathematical quadratic model was simple. Its quality was evaluated by regression analysis and by the Analysis Of Variance, popularly known as the ANOVA.

• 한국항공우주학회지
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• 제34권7호
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• pp.1-11
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• 2006

본 논문에서는 불연속면이 포함된 다차원 유동에서 흔히 발생하는 수치적 진동현상을 막기 위해 기존의 TVD 제한자를 분석함으로써 새로운 형태의 다차원 제한 함수를 유도하였다. MLP 기법은 유도된 다차원 제한 함수를 기반으로 하며, 다차원 불연속면에서의 수치 진동을 효과적으로 제거하고 동시에 3차 이상의 공간 정확도 내삽기법과 함께 사용할 수 있다는 장점을 갖는다. 또한, 정상 유동의 경우 수치 진동이 제거됨으로써 수렴성이 향상됨을 확인할 수 있었고, 실제 코드에 적용하는 방법도 간단하다. MLP 기법을 적용함으로써 불연속 유동 뿐 만 아니라 연속 유동에서도 정확성, 효율성, 강건성 면에서 향상된 결과를 얻을 수 있음을 여러 가지 수치 실험을 통하여 확인하였다.

• 대한수학회논문집
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• 제25권2호
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• pp.291-301
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• 2010

This paper consists of two main parts. Firstly, we introduce an evolving binomial process from a binomial stock model and consider various types of limiting behavior of the logarithm of the evolving binomial process. Among others we find that the logarithm of the binomial process converges weakly to a Gaussian process. Secondly, we provide new approaches for proving the limit theorems for an integral process motivated by the evolving binomial process. We provide a new proof for the uniform strong LLN for the integral process. We also provide a simple proof of the functional CLT by using a restriction of Bernstein inequality and a restricted chaining argument. We apply the functional CLT to derive the LIL for the IID random variables from that for Gaussian.

• 경영과학
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• 제14권2호
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• pp.63-68
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• 1997

Limiting probability in the steady state of regenerative process is one of the most useful characteristics. The formula for this limiting probability in the steady state of the regenerative process is presented in this paper. Because this formula is for the general model, it can be applied to many special systems including 2-unit redundant system. An example for this formula is also presented.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.404-411
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• 2010

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP), which has been quite successfully proposed on two- and three-dimensional structured grids, onto the unstructured grids. The basic idea of the present limiting strategy is to control the distribution of both cell-centered and cell-vertex physical properties to mimic a multi-dimensional nature of flow physics, which can be formulated as so called the MLP condition. The MLP condition can guarantee a high-order spatial accuracy without yielding spurious oscillations. Recently, MLP slope limiter was proposed based on the MUSCL-type reconstruction in two-dimensional case and it can be readily extended to three-dimensional case. Through various numerical analyses and extensive computations, it is observed that the proposed limiters are quite effective in controlling numerical oscillations and very accurate in capturing both discontinuous and continuous multi-dimensional flow features on 3-D tetrahedral grids.

• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• 대한수학회지
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• 제47권6호
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.