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Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods

  • Qin, Xiaolong;Su, Yongfu;Shang, Meijuan
    • Kyungpook Mathematical Journal
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    • v.48 no.1
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    • pp.133-142
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    • 2008
  • In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

Effect of Glutaminase on the Production of L-Glutamic Acid in Soybean Fermentation Products during Aging (Glutaminase첨가에 의한 장류 발효물의 숙성 중 L-Glutamic acid 함량 변화)

  • Kim, Nam-Dae;Kim, Hyun-Jin;Jang, Duck-Kyu;Ahn, Byung-Kwoun;Joo, Hyun-Kyu;Lee, Si-Kyung
    • Applied Biological Chemistry
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    • v.43 no.1
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    • pp.29-33
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    • 2000
  • This study was carried out to investigate the effect of glutaminase added to Doenjang, Kochujang and Kanjang in manufacturing. The consequential changes of L-glutamic acid and amino nitrogen contents were periodically analysed during aging. L-Glutamic acid contents in Kochujang, Doenjang and Kanjang aged for 45 days increased to 671.8%, 298.1% and 193.4% with glutaminase and also increased to 363.1%, 159.2% and 35.7% as compared with those without glutaminase. The 0.01% addition of glutaminase to Kochujang made L-glutamic acid content increased more than 3 times. The increase ratio of amino nitrogen was 216%, 120.8% and 84.5% in Kochujang, Kanjang and Doenjang with glutaminase which aged for 45 days, respectively. The effect of glutaminase added was the greatest in Kochujang. It increased to 35.7%, 8.4% and 40.3% as compared with those without glutaminase. The results of sensory evaluation showed that the products were favorably affected in taste, flavor and acceptability by glutaminase added.

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The Optical Properties of B2O3-Bi2O3-PbO-SiO2 Glass System (B2O3-Bi2O3-PbO-SiO2계 유리의 광학적인 특성)

  • Joung, Maeng Sig;Kim, Hong Seon;Lee, Su Dae
    • Journal of Korean Ophthalmic Optics Society
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    • v.5 no.2
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    • pp.167-173
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    • 2000
  • Four glasses of $B_2O_3-Bi_2O_3-PbO-SiO_2$ (BBPS) system were prepared by melting the appropriate amounts of reagent grade oxides of $B_2O_3$, $Bi_2O_3$, PbO, and $SiO_2$ in an open crucible. The differential thermal analysis showed crystallization temperature decreased with increasing $Bi_2O_3$ or PbO content in the sample. The structures of glasses system were studied using scanning electron microscopy and Fourier transform-Infra red (FT-IR) spectroscopy. The UV cut-off and refractive index were found to be sensitive to the $Pb^{+2}$ and $Bi^{+3}$ content in the glasses. The behavior of the IR spectra of the glasses in the BP series was consistent with a role of $Bi_2O_3$ as a network former. In the BP series of glasses, the result of IR spectrum indicated that PbO behaved as a network former.

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STRONG CONVERGENCE THEOREMS BY VISCOSITY APPROXIMATION METHODS FOR ACCRETIVE MAPPINGS AND NONEXPANSIVE MAPPINGS

  • Chang, Shih-Sen;Lee, H.W. Joseph;Chan, Chi Kin
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.59-68
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    • 2009
  • In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.

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APPROXIMATION OF SOLUTIONS FOR GENERALIZED WIENER-HOPF EQUATIONS AND GENERALIZED VARIATIONAL INEQUALITIES

  • Gu, Guanghui;Su, Yongfu
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.465-472
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    • 2010
  • The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].

Application of Polymer Brush to Enzyme-Multilayered Porous Hollow-Fiber Membrane

  • Kawakita Hidetaka;Uezu Kazuya;Tsuneda Satoshi;Saito Kyoichi;Tamada Masao;Sugo Takanobu
    • Proceedings of the Membrane Society of Korea Conference
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    • 2004.11a
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    • pp.142-145
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    • 2004
  • Anion-exchange porous hollow-fiber membranes with a thickness of about 1.2 mm and a pore size of about $0.30{\mu}m$ were used as a supporting matrix to immobilize cycloisomaltooligosaccharide glucanotransferase (CITase). CITase was immobilized to the membrane via anion-exchange adsorption and by subsequent enzymatic cross-linking with transglutaminase, the amount of which ranged from 3 to 110 mg per g of the membrane. The degree of enzyme multilayer binding was equivalent to 0.3 to 9.8. Dextran, as the substrate, was converted into seven- to nine-glucose-membered cycloisomaltooligosaccharides (CI-7, -8, and -9) at a maxi mum yield of $28\%$ in weight at a space velocity of 10 per hour during the permeation of $2.0(w/w)\%$ dextran solution across the CITase-immobilized porous hollow-fiber membrane.

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A Study on the Dynamic Fracture Toughness of Welding Structural Steels by Instrumented Impact Testing (계장화 충격시험법에 의한 구조용강 용접부의 동적 파괴인성에 관한 연구)

  • 김헌주;김경민;윤의박
    • Journal of Welding and Joining
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    • v.11 no.1
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    • pp.42-51
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    • 1993
  • In this study, investigations were conducted in calculating parameters of elastic-plastic fracture mechanics using single specimen. The validity of these testing methods was judged by the confirmation of multiple specimen method of stop block test. The results were as follows: In order to measure a fracture toughness using the instrumented impact test, two general requirement must be considered; One, setting up proper impact velocity considered the effect of loading and the other, the necessity of low blow test for obtaining true energy by the compliance correction. It was possible to detect a crack initiation point by calculating the compliance changing rate from a load-defection curve. Criterion of a stable crack growth, $T_{mat}$ could be estimated by using key-curve method for a base metal. and combining Kaiser's rebound compliance with Paris-Hutchison's $T_{appl}$ equation for the brittled zone of welding heat affected.at affected.d.

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A method for quantitative analysis of DEHP in PVC packing material by Near-Infrared Spectroscopy (근적외선 분광광도법을 이용한 PVC포장재 중 DEHP 정량법에 관한연구)

  • 김재관;윤미혜;박포현;김기철
    • Journal of environmental and Sanitary engineering
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    • v.17 no.4
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    • pp.61-67
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    • 2002
  • NIRS(Near infrared spectroscopy) scanning from 1300nm to 2400nm was appl ied for the DEHP(di-(2 ethylhexyl)phthalate) in PVC(polyvinyl chloride_packing material. All samples were devided into calibration group and validation group. As a result of conduction the multiple regression analysis on the correlation between the NIR spectrum data and chemical assay value obtained by the Korea Food Sanitation Act. The validation model for measuring the DEHP content had R of 0.997, SEC of 0.132, SEP of 0.176 by MLR and R of 0.996, SEC of 0.142, SEP of 0.198 by PLS and the detection limit was 0.1%. The obtained results indicate that the NIR procedure can potentially be used as a nondestructive analysis method for the purpose of rapid and simple measurement of DEHP in PVC packing material.

Note on the Prey Items of Marine Cladocerans (해산지각류의 먹이에 관한 보고)

  • KIM, SE-WHA;YOON, YANG-HO;ONBE, TAKASHI
    • 한국해양학회지
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    • v.28 no.1
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    • pp.69-71
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    • 1993
  • Food items of the five species of marine cladocerans were reported to be largely confined to centric diatoms. Reexamination of the prey items, however, revealed that flagellar organisms were also well fed by cladocerans. This additional finding suggests that marine cladocerans might extend their food items to weakly motile flagellates e.g., Prorocentrum micans, Protoperidinium sp. and unidentified flagellates.

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A Discussion to Dimensions of Spline Spaces Over Unconstricted Triangulations

  • Yi, Na;Liu, Huan-Wen
    • International Journal of CAD/CAM
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    • v.9 no.1
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    • pp.25-29
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    • 2010
  • Let $S_n^r(\Omega)$ be the spline space of degree n and smoothness r with respect to $\Omega$ where $\Omega$ is a triangulation of a planner polygonal domain. Dimensions of $S_n^r(\Omega)$ over the so-called unconstricted triangulation were given by Farin in [J. Comput. Appl. Math. 192(2006), 320-327]. In this paper, a counter example is given to show that the condition used in the main result in Farins paper is not correct, and then an improved necessary and sufficient condition is presented.