• Title/Summary/Keyword: $W^{1,{\infty}}$-estimate

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SUPERCONVERGENCE OF FINITE ELEMENT METHODS FOR LINEAR QUASI-PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

  • Li, Qian;Shen, Wanfang;Jian, Jinfeng
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.8 no.2
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    • pp.23-38
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    • 2004
  • We consider finite element methods applied to a class of quasi parabolic integro-differential equations in $R^d$. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in $W^{1,p}(\Omega)\;and\;L_p(\Omega)$, for $2\;{\leq}p\;<\;{\infty}$.

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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 $0.407\;year^{-1}$.

Estimation on Population Ecological Characteristics of Crucian Carp, Carassius auratus in the Mid-Upper System of the Seomjin River (섬진강 중.상류 수계에서 붕어 개체군의 생태학적 특성치 추정)

  • Jang, Sung-Hyun;Ryu, Hui-Seong;Lee, Jung-Ho
    • Korean Journal of Environment and Ecology
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    • v.25 no.3
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    • pp.318-326
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    • 2011
  • The population ecological characteristics of the Crucian carp, Carassius auratus, were determined in order to estimate stock of the mid-upper system of the Seomjin River. The fish ranged in size from 95 to 288mm total length. The age was determined by counting the scale annulus. The scales displayed clear annulus that were used to estimate the age. The oldest fish observed in this study was 5 years old. Age-2 fishes were the most numerous in the sample(n=38), followed in frequency be age-3(n=22). Marginal index analysis validated the formation of a single annulus per year. The relationship between body length and body weight was BW = $0.0038BL^{3.73}$($R^2$=0.96) (p<0.01). The relationship between the scale radius and body length was BL = 2.362R+2.76($R^2$=0.89). The von Bertalanffy growth parameters estimated from a non-linear regression method were $L_{\infty}$=33.2 cm, $W_{\infty}$=1,798.4 g, $K=0.20year^{-1}$ and $t_0$=-0.51year. Therefore, Growth in length of the fish was expressed by the von Bertalanffy's growth equation as $L_t=33.23$($1-e^{-0.20(t+0.51)}$)($R^2$=0.98). The annual survival rate was estimated to be 0.427year$^{-1}$. The instantaneous coefficient of natural mortality of estimated from the Zhang and Megrey method was $0.784year^{-1}$, and instantaneous coefficient of fishing mortality was calculated $0.067year^{-1}$. From the estimates of survival rate, the instantaneous coefficient of total mortality was estimated to be $0.851year^{-1}$.