Lee Jun-Yeop

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and

In this paper, we present an efficient numerical method for multiphase imagesegmentation using a multiphase-field model. The method combines the vector-valued Allen–Cahn phase-field equation with initial data fitting terms containing prescribed interface widthand fidelity constants. An efficient numerical solution is achieved using the recently developedhybrid operator splitting method for the vector-valued Allen–Cahn phase-field equation. Wesplit the modified vector-valued Allen–Cahn equation i

The Allen–Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the fr

A goal of Magnetic Resonance Imaging is reproducing a spatial map of the effective spin density from the measured Fourier coefficients of a specimen. The imaging procedure can be done by inverse Fourier transformation or backward fast Fourier transformation if the data are sampled on a regular grid in frequency space; however, it is still a challenging question how to reconstruct an image from a finite set of Fourier data on irregular points in k-space. In this paper, we describe some mathematic

Polynomialsareoneofmostimportantandwidelyusednumericaltoolsindealingwith a smooth function on a bounded domain and trigonometric functions work for smoothperiodic functions. However, they are not the best choice if a function has a bounded supportin space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zerohas been known as a best candidate as a basis for band-limited functions.In this paper, we review some basic properties of PSWFs dened as eigenfunctions ofbounded

In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn–Hilliard (vCH) equation.In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose

멀티미디어 기능을 갖춘 빠른 속도의 컴퓨터의 활용을 뜻하는 정보기술의 교육적 활용은 아직은 초기 단계에 있다고 할 수 있다. 또한 정보기술의 한 형태라고 할 수 있는 인터넷 활용의 경우에 있어서도 컴퓨터의 발전과 더불어 생긴 대화 채널이자 정보 검색의 도구인 인터넷은 교사들로 하여금 그 어느 때보다도 교수-학습 자료를 손쉽게 찾을 수 있게 하고 있으나 인터넷의 교육적 활용 역시 초기 단계라고 할 수 있다. 그리하여 본 연구에서는 이러한 교육정보화 및 교사정보화를 목적으로 교사들(수학교과)의 전반적인 인터넷활용 실태에 관한 조사를 바탕으로 학교교육에서의 인터넷 활용 증진 및 개선 방안에 관하여 알아보았다.

Various graph clustering methods have been introduced to identify communities in social or biological networks. This paper studies the entropy-based and the Markov chain-based methods in clustering the undirected graph. We examine the performance of two clustering methods with conventional methods based on quality measures of clustering. For the real applications, we collect the mathematical subject classification (MSC) codes of research papers from published mathematical databases and construct