• Title, Summary, Keyword: Dirichlet space

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CONTRACTION MAPPING PRINCIPLE AND ITS APPLICATION TO UNIQUENESS RESULTS FOR THE SYSTEM OF THE WAVE EQUATIONS

  • Jung, Tack-Sun;Choi, Q-Heung
    • Honam Mathematical Journal
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    • v.30 no.1
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    • pp.197-203
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    • 2008
  • We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

A FINITE ELEMENT SOLUTION FOR THE CONSERVATION FORM OF BBM-BURGERS' EQUATION

  • Ning, Yang;Sun, Mingzhe;Piao, Guangri
    • East Asian mathematical journal
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    • v.33 no.5
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    • pp.495-509
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    • 2017
  • With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.

SVD-LDA: A Combined Model for Text Classification

  • Hai, Nguyen Cao Truong;Kim, Kyung-Im;Park, Hyuk-Ro
    • Journal of Information Processing Systems
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    • v.5 no.1
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    • pp.5-10
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    • 2009
  • Text data has always accounted for a major portion of the world's information. As the volume of information increases exponentially, the portion of text data also increases significantly. Text classification is therefore still an important area of research. LDA is an updated, probabilistic model which has been used in many applications in many other fields. As regards text data, LDA also has many applications, which has been applied various enhancements. However, it seems that no applications take care of the input for LDA. In this paper, we suggest a way to map the input space to a reduced space, which may avoid the unreliability, ambiguity and redundancy of individual terms as descriptors. The purpose of this paper is to show that LDA can be perfectly performed in a "clean and clear" space. Experiments are conducted on 20 News Groups data sets. The results show that the proposed method can boost the classification results when the appropriate choice of rank of the reduced space is determined.

EXISTENCE OF SOLUTIONS FOR GRADIENT TYPE ELLIPTIC SYSTEMS WITH LINKING METHODS

  • Jin, Yinghua;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.65-70
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    • 2007
  • We study the existence of nontrivial solutions of the Gradient type Dirichlet boundary value problem for elliptic systems of the form $-{\Delta}U(x)={\nabla}F(x,U(x)),x{\in}{\Omega}$, where ${\Omega}{\subset}R^N(N{\geq}1)$ is a bounded regular domain and U = (u, v) : ${\Omega}{\rightarrow}R^2$. To study the system we use the liking theorem on product space.

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SOLVABILITY FOR THE PARABOLIC PROBLEM WITH JUMPING NONLINEARITY CROSSING NO EIGENVALUES

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.16 no.4
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    • pp.545-551
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    • 2008
  • We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

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ASYMPTOTICALLY LINEAR BEAM EQUATION AND REDUCTION METHOD

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • v.19 no.4
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    • pp.481-493
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    • 2011
  • We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

Visualization of Affine Invariant Tetrahedrization (Slice-Based Method for Visualizing the Structure of Tetrahedrization) (어파인 불변성 사면체 분할법의 가시화 (절편 법을 이용한 사면체 구조의 가시화))

  • Lee, Kun
    • The Transactions of the Korea Information Processing Society
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    • v.3 no.7
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    • pp.1894-1905
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    • 1996
  • Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

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A Development of LDA Topic Association Systems Based on Spark-Hadoop Framework

  • Park, Kiejin;Peng, Limei
    • Journal of Information Processing Systems
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    • v.14 no.1
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    • pp.140-149
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    • 2018
  • Social data such as users' comments are unstructured in nature and up-to-date technologies for analyzing such data are constrained by the available storage space and processing time when fast storing and processing is required. On the other hand, it is even difficult in using a huge amount of dynamically generated social data to analyze the user features in a high speed. To solve this problem, we design and implement a topic association analysis system based on the latent Dirichlet allocation (LDA) model. The LDA does not require the training process and thus can analyze the social users' hourly interests on different topics in an easy way. The proposed system is constructed based on the Spark framework that is located on top of Hadoop cluster. It is advantageous of high-speed processing owing to that minimized access to hard disk is required and all the intermediately generated data are processed in the main memory. In the performance evaluation, it requires about 5 hours to analyze the topics for about 1 TB test social data (SNS comments). Moreover, through analyzing the association among topics, we can track the hourly change of social users' interests on different topics.

Effects of Space Increment and Time Step to the Accuracy of the Implicit Finite Difference Method in a Two-Dimensional Transient Heat Conduction Problem (이차원과도열전도에 대한 음함수형 유한차분법의 정도에 미치는 공간증분 및 시간간격의 영향)

  • CHO Kwon-Ok;LEE Yong-Sung;OH Hoo-Kyu
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.18 no.1
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    • pp.15-22
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    • 1985
  • The study on computation time, accuracy, and convergency characteristic of the implicit finite difference method is presented with the variation of the space increment and time step in a two-dimensional transient heat conduction problem with a dirichlet boundary condition. Numerical analysis were conducted by the model having the conditions of the solution domain from 0 to 3m, thermal diffusivity of 1.26 $m^2/h$, initial condition of 272 K, and boundary condition of 255.4 K. The results obtained are summarized as follows : 1) The degree of influence with respect to the accuracy of the time step and space increment in the alternating-direction implicit method and Crank-Nicholson implicit method were relatively small, but in case of the fully implicit method showed opposite tendency. 2) To prescribe near the zero for the space increment and tine step in a two dimensional transient problem were good in a accuracy aspect but unreasonable in a computational time aspect. 3) The reasonable condition of the space increment and the time step considering accuracy and computation time could be generalized with the Fourier modulus increment, F, ana dimensionless space increment, X, irrespective of the solution domain.

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Aerodynamic Analysis of an Arbitrary Three-Dimensional Blended Wing Body Aircraft using Panel Method (패널법을 이용한 임의의 3차원 BWB 형상 항공기에 대한 공력해석)

  • Lee, Sea-Wook;Yang, Jin-Yeol;Cho, Jin-Soo
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.37 no.11
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    • pp.1066-1072
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    • 2009
  • A panel method based on potential flow theory is developed for the steady/unsteady aerodynamic analysis of arbitrary three-dimensional Blended Wing Body aircraft. The panel method uses the piecewise constant source and doublet singularities as a solution. This potential based panel method is founded on the Dirichlet boundary condition and coupled with the time-stepping method. The present method uses the time-stepping loop to simulate the unsteady motion of the aircraft. The present method can solve the three-dimensional flow over the complex bodies with less computing time and provide various aerodynamic derivatives to secure the stability of Blended Wing Body aircraft. That will do much for practical applications such as aerodynamic designs and analysis of aircraft configurations and flight simulation.