• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Asian-Australasian Journal of Animal Sciences
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• v.27 no.4
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• pp.457-463
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• 2014

Ultrasound measurements of backfat thickness (UBF), longissimus muscle area (ULMA) and marbling score (UMS) and carcass measurements of carcass weight (CW), backfat thickness (BF), longissimus muscle area (LMA), and marbling score (MS) on 7,044 Hanwoo steers were analyzed to estimate genetic parameters. Data from Hanwoo steers that were raised, finished in Hoengseong-gun, Gangwon-do (province) and shipped to slaughter houses during the period from October 2010 to April 2013 were evaluated. Ultrasound measurements were taken at approximately three months before slaughter by an experienced operator using a B-mode real-time ultrasound device (HS-2000, FHK Co. Ltd., Tokyo, Japan) with a 3.5 MHz linear probe. Ultrasound scanning was on the left side between 13th rib and the first lumbar vertebrae. All slaughtering processes and carcass evaluations were performed in accordance with the guidelines of beef grading system of Korea. To estimate genetic parameters, multiple trait animal models were applied. Fixed effects included in the models were: the effects of farm, contemporary group effects (year-season at the time of ultrasound scanning in the models for UBF, ULMA, and UMS, and year-season at slaughter in the models for CW, BF, LMA, and MS), the effects of ultrasound technicians as class variables and the effects of the age in days at ultrasound scanning or at slaughtering as linear covariates, respectively for ultrasound and carcass measures. Heritability estimates obtained from our analyses were 0.37 for UBF, 0.13 for ULMA, 0.27 for UMS, 0.44 for CW, 0.33 for BF, 0.36 for LMA and 0.54 MS, respectively. Genetic correlations were strongly positive between corresponding traits of ultrasound and carcass measures. Genetic correlation coefficient between UBF and BF estimate was 0.938, between ULMA and LMA was 0.767 and between UMS and MS was 0.925. These results suggest that ultrasound measurement traits are genetically similar to carcass measurement traits.