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Numerical Solution of Nonlinear Diffusion in One Dimensional Porous Medium Using Hybrid SOR Method

  • Jackel Vui Lung, Chew;Elayaraja, Aruchunan;Andang, Sunarto;Jumat, Sulaiman
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.699-713
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    • 2022
  • This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

A STUDY ON INVARIANT REGIONS, EXISTENCE AND UNIQUENESS OF THE GLOBAL SOLUTION FOR TRIDIAGONAL REACTION-DIFFUSION SYSTEMS

  • IQBAL M. BATIHA;NABILA BARROUK;ADEL OUANNAS;ABDULKARIM FARAH
    • Journal of applied mathematics & informatics
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    • v.41 no.4
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    • pp.893-906
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    • 2023
  • In this article, we are devoted to study the problem of the existence, uniqueness and positivity of the global solutions of the 3 × 3 reaction-diffusion systems with the total mass of the components with time. We also suppose that the nonlinear reaction term has a critical growth with respect to the gradient. The technique that we used to prove the global existence is the method of the compact semigroup.

Experimental Studies on Extracorporeal Circulation by Sarns Heart-Lung Machine with Total Prime of Hartman's Solution (Sarns 심폐기의 혈희석 체외순환에 관한 실험적 연구)

  • 김근호
    • Journal of Chest Surgery
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    • v.8 no.2
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    • pp.135-142
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    • 1975
  • Total body perfusion using Sarns Heart-Lung-Machine, five head pump motor system with Travenol disposable bubble oxygenator was attempted in the dogs by the hemodilution method with total prime of buffered Hartman`s solution under moderate hypothermia. The first of all, the functions of Sarns Heart-Lung-Machine and effects of the hemodilution perfusion by buffered Hartman`s solution was studied. At the same time the changes of pressure of artery and vein, gas contents of the blood, and influence on the blood pictures were observed before, during, and after perfusion in 1-2 days. Hemodilution rates were the ranges of 85.0ml/kg to 97.3ml/kg and perfusion flow rates were maintained with the average 80. 5ml/kg/min [the ranges of 73.3ml/kg/min to 92.8ml/kg/min]. Hypothermia was employed between $35^{\circ}C$ and $31^{\circ} of the esophageal temperature. The total body perfusion was continued for 50-60 minutes. In the total cardiopulmonary bypass, atriotomy, ventriculotomy, and atrioventriculotomy were performed respectively. Arterial pressure was ranged approximately between 50 mmHg and 140 mmHg, but generally, it was maintained over 75 mmHg. Venous pressure was measured between 3.8 cm$H_2O$ and 16.0 cm$H_2O$. Optimum oxygenation could be achieved when oxygen flow into the oxygenator was maintained approximately at 5. 5L/min. In this way, the $pO_2$, $pCO_2$, and oxygen saturation were measured before, during, and afterperfusion in 1-2 days. The $pCO_2$ ranged approximately between 26.0 mmHg and 38.5 mmHg, but generally, it was maintained in the average 30.9-32.5mmHg. The $pO_2$ was ranged between 73.0mmHg and 332.2 mmHg, but it was maintained in the average 103.0-219.0 mmHg. Oxygen saturation was measured over 95. 0% during and after extracorporeal circulation respectively. Erythrocyte count, hemoglobin, hematocrit, and leucocyte count were decreased to 49.2%, 49.0%, 49.4%, and 21. 1% of the preoperative value during extracorporeal circulation respectively and these reductions were not recovered until 1-2 days after perfusion. These. resulted from relatively high degree of hemodilution rate and operative bleeding during these experimental studies. The platelets count was also decreased about to 71% during perfusion, on the contrary, it was increased progressively after perfusion and in 1-21 days after perfusion, the value was returned to preoperative contro1 level. Three dogs were all recovered after extracorporeal circulation.

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Efficacy of antibacterial treatments of fresh ginseng (Panax ginseng C.A. Meyer) (항균제 처리에 따른 수삼의 미생물 저감화 효과)

  • Choi, Jun-Bong;Cho, Won-Il
    • Korean Journal of Food Science and Technology
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    • v.54 no.1
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    • pp.75-79
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    • 2022
  • Fresh, washed ginseng can be contaminated with microorganism loads as high as 6.5 log CFU/g for total bacteria and 4.3 log CFU/g for mold. The goal of this study was to test eight antibacterial agents on ginseng. Immersing fresh ginseng washed in 1% (w/w) sodium citrate, sodium diacetate, sodium acetate, citric acid, and sodium lactate solution for 1 h resulted in a bactericidal effect of 31.0-97.5% for total bacteria. Among the organic acids, sodium citrate had the best antibacterial effect, with total bacteria reduced from 6.5 log to 4.9 log CFU/g. A 1% (w/w) vitamin B1 lauryl sulfate solution with surfactant function by hydrophilic and hydrophobic sites can reduce 2.7 log CFU/g (99.8% inactivation) on total bacteria. In the 1% (w/w) calcium oxide solution, total bacteria were reduced by 3 log, showing an excellent inactivation effect of 99.9%. Calcium oxide is a highly useful material for inactivation of microorganisms in fresh ginseng.

Comparison of Vitrification and Slow Freezing-thawing Method on 1-cell Zygotes (생쥐 1-세포기 수정란의 동결방법에 있어서 초자화동결과 완만동결의 비교)

  • Lee, Ji-Hyang;Han, Hyuck-Dong;Koo, Hye-Young
    • Clinical and Experimental Reproductive Medicine
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    • v.28 no.3
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    • pp.191-198
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    • 2001
  • Objective : This study was conducted to examine the effect of vitrification on the survival and in vitro development of mice 1-cell zygotes. Method: Effects of exposure to vitrification solution and vitrification, with different concentrations of the cryoprotectant solution, were examined. The 1-cell zygotes were also subjected to a slow freezing-thawing method to compare with vitrification method. Solution composed of ethylene glycol (6.0 M, 5.0 M, 4.0 M) and sucrose (1.0 M) were used as cryopropectant. The experiments employed the method loading the embryos on electron microscope grids. Results: I. The effects of exposure in vitrification solution. 1-cell zygotes were non-toxic at all concentrations of the vitrification solution showing the survival rate between 88.1% and 97.5%. Development into 2-cell was more successful in the higher concentrations of the vitrification solution. Therefore, higher concentrations of the vitirification solution do not seem to cause any problems in vitrification procedure. II. The effects of vitrification method. 1-cell zygotes showed the survival rate between 78.8% and 92.4%. The lowest and the highest survival rate was observed in the 6.0 M and 4.0 M vitrification solution, respectively. 2-cell development rates varied from 77.6% to 91.3%. Blastocyst development rate was shown highest in 5.0 M and the lowest in 4.0 M solution. Therefore, the highest 2-cell and blastocyst development rate was observed in 5.0 M solution. III. Comparison of vitrification and slow freezing-thawing method on 1-cell zygotes. This experiment showed that 1-cell zygotes had the highest survival and development rates in 5.0 M vitrification solution. Vitrified group of 1-cell zygotes, in the 5.0 M vitrification solution, were compared with the group processed in slow freezing-thawing method. The development rate into 2-cell and blastocyst as well as the survival rate were higher in the vitrified group than in the slowly freezed group. Conclusion: 1. The results demonstrate that the best cryoprotectant is a 5.0 M vitrification solution for 1-cell zygotes. 2. Vitrification method significantly increases the survival rate of the 1-cell zygote and its development into 2-cell and blastocyst. Equilibration and exposure time during the vitrification was remarkerbly short in this experiment. Total time, from the exposure to vitirification solution to storage in the liquid nitrogen, was taken only 90 seconds. In contrast, the slow freezing-thawing method have taken more than four hours. Taken together, we presume that the overall time used for the procedure contributes to the results as an important parameter. 3. The loading of 1-cell zygotes on the EM grid is technically more simple and takes less time than the straw or cryo vial method.

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Comprehensive evaluation of structural geometrical nonlinear solution techniques Part II: Comparing efficiencies of the methods

  • Rezaiee-Pajand, M.;Ghalishooyan, M.;Salehi-Ahmadabad, M.
    • Structural Engineering and Mechanics
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    • v.48 no.6
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    • pp.879-914
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    • 2013
  • In part I of the article, formulation and characteristics of the several well-known structural geometrical nonlinear solution techniques were studied. In the present paper, the efficiencies and capabilities of residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control and modified normal flow will be evaluated. To achieve this goal, a comprehensive comparison of these solution methods will be performed. Due to limit page of the article, only the findings of 17 numerical problems, including 2-D and 3-D trusses, 2-D and 3-D frames, and shells, will be presented. Performance of the solution strategies will be considered by doing more than 12500 nonlinear analyses, and conclusions will be drawn based on the outcomes. Most of the mentioned structures have complex nonlinear behavior, including load limit and snap-back points. In this investigation, criteria like number of diverged and complete analyses, the ability of passing load limit and snap-back points, the total number of steps and analysis iterations, the analysis running time and divergence points will be examined. Numerical properties of each problem, like, maximum allowed iteration, divergence tolerance, maximum and minimum size of the load factor, load increment changes and the target point will be selected in such a way that comparison result to be highly reliable. Following this, capabilities and deficiencies of each solution technique will be surveyed in comparison with the other ones, and superior solution schemes will be introduced.

Separation of Lysozyme from Chicken Egg White by Ultrafiltration (1) - Dead-end Filtration of Egg White Solution - (한외여과에 의한 계란 난백으로부터 라이소자임의 분리 (1) - 난백용액의 전량여과 -)

  • Park, Hye-Ri;Youm, Kyung-Ho
    • Membrane Journal
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    • v.26 no.4
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    • pp.266-272
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    • 2016
  • The separation and purification of lysozyme enzyme from chicken egg white (CEW) solution was studied using the dead-end filtration. The optimum operation conditions of the dead-end filtration reveal that the maximum value of permselectivity of lysozyme to the other proteins of ovalbumin and conalbumin in the CEW solution was tested with change of molecular weight cut-off (MWCO) of ultrafitration membrane and pH of the CEW solution. The optimum operation conditions for the efficient permeable separation of lysozyme from the CEW solution are that the membrane MWCO is 30 kD and the pH of CEW solution is 11. At this optimum operation conditions, the maximum value of permselectivity of lysozyme to total proteins in CEW solution is about 83.

The Influence of Temperature on the Surface Electrokinetic Features of Particulate Matters in Aqueous Environment (수중입자의 표면 전기적 특성에 미치는 온도의 영향)

  • O, Sejin;Kim, Dong-Su
    • Journal of Korean Society on Water Environment
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    • v.26 no.3
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    • pp.525-531
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    • 2010
  • To figure out the importance of temperature on electrochemical properties in water environment, calcium carbonate, one of important substances in water chemistry, was chosen to make suspensions. The result of electrokinetic potential of calcium carbonate suspensions revealed that it tended to increase as temperature increased. In addition, electrokinetic potential was negatively increased as suspensions became more basic. Its isoelectric point was ca. 7 regardless of temperature. The adsorption of hydrogen ions on calcium carbonate particles followed endothermic reaction. This result was verified by continuously measuring pH as adding HCl solution in calcium carbonate suspension. It explained that suspensions' potential was determined by DLVO theory which calculated total interaction energy between particles. Suspensions' total interaction energy was proportional to the value of electrokinetic potential. Furthermore, total interaction energy between particles increased as suspensions' temperature was increased.

Effects of Dokwhalgisaentang on the Blood in Rats (독활기생탕(獨活寄生湯)이 백서(白鼠)의 혈액(血液)에 미치는 영향(影響))

  • Kim, Hui-Cheol
    • The Journal of Internal Korean Medicine
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    • v.16 no.2
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    • pp.51-60
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    • 1995
  • In order to study the effect of Dokwhalgisaentang on the blood in normal rats with Dokwhalgisaentang extract solution was adminstrated in rats. The rats carried on every day for 5days, l0days and 15days respecitively on the corresponding blood in rats, and thereafter the contents of serum BUN, creatinine, creatine, total protein, albumin, total bilirubin, cholesterol were measured in rats. The following results have been obtained : 1. Dokwhalgisaentang extract decreased the serum BUN significantly in rats. 2. Dokwhalgisaentang extract decreased the serum creatine significantly in rats. 3. Dokwhalgisaentang extract decreased the serum creatinine significantly in rats. 4. Dokwhalgisaentang extract decreased the serum total protein significantly in rats. 5. Dokwhalgisaentang extract decreased the serum albumin significantly in rats. 6. Dokwhalgisaentang extract increased the serum total bilirubin significantly in rats. 7. Dokwhalgisaentang extract decreased the serum cholresterol significantly in rats.

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Pattern-Analysis of Panax ginseng Polysaccharide (고려인삼 다당류의 패턴-분석)

  • Han, Yong-Nam;Kim, Sun-Young;Lee, Hee-Joo;Hwang, Woo-Ik;Han, Byung-Hoon
    • Journal of Ginseng Research
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    • v.16 no.3
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    • pp.217-221
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    • 1992
  • Total polysaccharide contents in Panax ginseng roots were evaluated by a spectrophotometry, utilizing the complex formation of ginseng polysaccharide with alcian blue dye in 50 mM ammonium biphosphate, pH 4.2. The total polysaccharide content in red ginseng was about three times higher than that in fresh ginseng when both were extracted with water, and was increased about two times when red ginseng was extracted with an alkaline solution. The determination of total polysaccharide in various parts of ginseng revealed that main roots contained the component more than fine roots. Fresh ginseng sections stained by the dye showed polysaccharide mainly found in cortex and cambium but not in epidermis. Pattern-analysis on total and acidic polysaccharides from fresh and red ginsengs exhibited that the chemical compositions of the polysaccharides extracted from both ginsengs quite differed from each other.

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