• Title/Summary/Keyword: $W^{1,p}$ error estimates

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Lp and W1,p Error Estimates for First Order GDM on One-Dimensional Elliptic and Parabolic Problems

  • Gong, Jing;Li, Qian
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.2
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    • pp.41-57
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    • 2000
  • In this paper, we consider first order generalized difference scheme for the two-point boundary value problem and one-dimensional second order parabolic type problem. The optimal error estimates in $L_p$ and $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) as well as some superconvergence estimates in $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) are obtained. The main results in this paper perfect the theory of GDM.

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[ $L_p$ ] ERROR ESTIMATES AND SUPERCONVERGENCE FOR FINITE ELEMENT APPROXIMATIONS FOR NONLINEAR HYPERBOLIC INTEGRO-DIFFERENTIAL PROBLEMS

  • Li, Qian;Jian, Jinfeng;Shen, Wanfang
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.9 no.1
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    • pp.17-29
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    • 2005
  • In this paper we consider finite element methods for nonlinear hyperbolic integro-differential problems defined in ${\Omega}\;{\subset}\;R^d(d\;{\leq}\;4)$. A new initial approximation of $u_t(0)$ is taken. Optimal order error estimates in $L_p$ for $2\;{\leq}\;p\;{\leq}\;{\infty}$ are established for arbitrary order finite element. One order superconvergence in $W^{1,p}$ for $2\;{\leq}\;p\;{\leq}\;{\infty}$ are demonstrated as well.

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GENERALIZED DIFFERENCE METHODS FOR ONE-DIMENSIONAL VISCOELASTIC PROBLEMS

  • Li, Huanrong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.9 no.2
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    • pp.55-64
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    • 2005
  • In this paper, generalized difference methods(GDM) for one-dimensional viscoelastic problems are proposed and analyzed. The new initial values are given in the generalized difference scheme, so we obtain optimal error estimates in $L^p$ and $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.

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FINITE VOLUME ELEMENT METHODS FOR NONLINEAR PARABOLIC INTEGRODIFFERENTIAL PROBLEMS

  • Li, Huanrong;Li, Qian
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.7 no.2
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    • pp.35-49
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    • 2003
  • In this paper, finite volume element methods for nonlinear parabolic integrodifferential problems are proposed and analyzed. The optimal error estimates in $L^p\;and\;W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ are obtained. The main results in this paper perfect the theory of FVE methods.

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Lp error estimates and superconvergence for finite element approximations for nonlinear parabolic problems

  • LI, QIAN;DU, HONGWEI
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.1
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    • pp.67-77
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    • 2000
  • In this paper we consider finite element mathods for nonlinear parabolic problems defined in ${\Omega}{\subset}R^d$ ($d{\leq}4$). A new initial approximation is taken. Optimal order error estimates in $L_p$ for $2{\leq}p{\leq}{\infty}$ are established for arbitrary order finite element. One order superconvergence in $W^{1,p}$ for $2{\leq}q{\leq}{\infty}$ are demonstrated as well.

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FINITE VOLUME ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

  • LI, QIAN;LIU, ZHONGYAN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.2
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    • pp.85-97
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    • 2002
  • In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.

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PSNR Evaluation of P Company DSA System between Server Display Monitor and Client Display Monitor (P사 DSA 시스템의 Server Display Monitor와 Client Display Monitor의 PSNR 평가)

  • Lee, Junhaeng
    • Journal of the Korean Society of Radiology
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    • v.8 no.1
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    • pp.43-49
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    • 2014
  • PACS is needed medical imaging with large-capacity storage device. Slower transmission degrades the performance of the PACS. Thus, the image read by the reading of the long-term stored image without compromising the quality of the video, which does not affect future readings in the range will be compressed and stored. Compression and video storage, and video transport Noise generated during storage and transmission of medical images and the resulting loss of information that occurs when the monitor output from many problems. The study estimates server display monitor and client display monitor of philips DSA system, and suggests that the evaluation and improvement about PSNR, process from server display signal obtaining to client display monitor. P company DSA is used in the test. Two monitors that are $1280{\times}1024$ pixel monitor of P company and 1536x2048 pixel monitor of Wide are used displaying angiography picture. MARO-view is taken in PACS program, and Visual $C^{++}$ is taken as accomplishing PSNR measurement program. As a result of experiment, no change in No 1, 3 of PSNR appear that there is no error in telephotograph and display. In terms of compressibility, low compressibility has small change of definition, and there was not remarkable drawback of compressibility which has little change in definition.

A Meta-analysis of Ambient Air Pollution in Relation to Daily Mortality in Seoul, $1991\sim1995$ (메타분석 방법을 적용한 서울시 대기오염과 조기사망의 상관성 연구 (1991년$\sim$1995년))

  • Dockery, Douglas W.;Kim, Chun-Bae;Jee, Sun-Ha;Chung, Yong;Lee, Jong-Tae
    • Journal of Preventive Medicine and Public Health
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    • v.32 no.2
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    • pp.177-182
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    • 1999
  • Objectives: To reexamine the association between air pollution and daily mortality in Seoul, Korea using a method of meta-analysis with the data filed for 1991 through 1995. Methods: A separate Poisson regression analysis on each district within the metropolitan area of Seoul was conducted to regress daily death counts on levels of each ambient air pollutant, such as total suspended particulates (TSP), sulfur dioxide $(SO_2)$, and ozone $(O_3)$, controlling for variability in the weather condition. We calculated a weighted mean as a meta-analysis summary of the estimates and its standard error. Results: We found that the p value from each pollutant model to test the homogeneity assumption was small (p<0.01) because of the large disparity among district-specific estimates. Therefore, all results reported here were estimated from the random effect model. Using the weighted mean that we calculated, the mortality at a $100{\mu}g/m^3$ increment in a 3-day moving average of TSP levels was 1.034 (95% Cl 1.009-1.059). The mortality was estimated to increase 6% (95% Cl 3-10%) and 3% (95% Cl 0-6%) with each 50 ppb increase for 9-day moving average of SO2 and 1-hr maximum O3, respectively. Conclusions: Like most of air pollution epidemiologic studies, this meta-analysis cannot avoid fleeing from measurement misclassification since no personal measurement was taken. However, we can expect that a measurement bias be reduced in a district-specific estimate since a monitoring station is hefter representative cf air quality of the matched district. The similar results to those from the previous studios indicated existence of health effect of air pollution at current levels in many industrialized countries, including Korea.

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A Study on the Stock Assessment and Management Implications of the Korean Aucha perch (Coreoperca herzi) in Freshwater: (1) Estimation of Population Ecological Characteristics of Coreoperca herzi in the Mid-Upper System of the Seomjin River (담수산 어류 꺽지 (Coreoperca herzi)의 자원 평가 및 관리 방안 연구: 섬진강 중.상류 수계에서 꺽지의 개체군 생태학적 특성치 추정 (1))

  • Jang, Sung-Hyun;Ryu, Hui-Seong;Lee, Jung-Ho
    • Korean Journal of Ecology and Environment
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    • v.43 no.1
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    • pp.82-90
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    • 2010
  • The ecological characteristics of the Korean Aucha perch, Coreoperca herzi, were determined in order to estimate stock of the mid-upper system of the Seomjin River. The age was determined by counting the otolith annuli. The oldest fish observed in this study was 5 years old. Relationships between body length (BL) and body weight (BW) were $BW=0.0195BL^{3.08}$ ($R^2=0.966$) (p<0.01). Relationships between the otolith radius (R) and body length (BL) were BL=3.882R+1.66 ($R^2=0.944$). The von Bertalanffy growth parameters estimated from a non-linear regression method were $L_{\infty}=19.68\;cm$, $W_{\infty}=188.64\;g$, $K=0.17\;year^{-1}$ and $t_0=-1.46$ year. Therefore, growth in length of the fish was expressed by the von Bertalanffy's growth equation as $L_t=19.68$ ($1-e^{-0.17(t+1.46)}$) ($R^2=0.997$). The annual survival rate (S) was estimated to be $0.666\;year^{-1}$. The instantaneous coefficient of natural mortality (M) of estimated from the Zhang and Megrey method was $0.346\;year^{-1}$, and instantaneous coefficient of fishing mortality (F) was calculated $0.061\;year^{-1}$. From the estimates of survival rate (S), the instantaneous coefficient of total mortality(Z) was estimated to be $0.407\;year^{-1}$.