• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.715-731
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• 2005

There are five contexts of division algorithm of fractions such as measurement division, determination of a unit rate, reduction of the quantities in the same measure, division as the inverse of multiplication and analogy with multiplication algorithm of fractions. The division algorithm, however, should be taught by 'dividing by using reciprocals' via 'measurement division' because dividing a fraction by a fraction results in 'multiplying the dividend by the reciprocal of the divisor'. If a fraction is divided by a large fraction, then we can teach the division algorithm of fractions by analogy with 'dividing by using reciprocals'. To achieve the teaching-learning methods above in elementary school, it is essential for children to use the maniplatives. As Piaget has suggested, Cuisenaire color rods is the most efficient maniplative for teaching fractions. The instruction, therefore, of division algorithm of fractions should be focused on 'dividing by using reciprocals' via 'measurement division' using Cuisenaire color rods through analogy if necessary.

• Korean Journal of Animal Reproduction
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• v.19 no.4
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• pp.251-258
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• 1996

These studies were carried out to investigate the effect of gonadotropins (GTH), fetal calf serum (FCS), porcine follicular fluid (pFF) and FCS and pFF fractions obtained by the gel filtration on in vitro maturation of porcine follicular fluid. When the oocytes were cultured in TCM-199, the maturation rate was higher in pFF than in FCS in both with or without GTH and in pFF the maturation rate was higher in with GTH than in without GTH. In case of without GTH, pFF increased maturation rates in TCM-199, but not in Whitten's medium (WM). When the oocytes were cultured in WM supplemented with FCS fractions, the maturation rate(51.6%) of oocytes was significantly (P<0.05) higher in fraction B (about 30∼70 kDa) than in control, FCS and other fractions. When oocytes were cultured in WM supplemented with pFF fractions, fractions B (about 30∼70 kDa) and D (about 1∼10 kDa) were significantly (P<0.05) higher than in control, pFF and other fractions. In conclusiion, the addition of gonadotropins into the maturation media was effective for oocyte maturation. The addition of pFF was more effective than addition of FCS for maturation of porcine oocytes in vitro. And fraction B from FCS and fractions B and D from pFF was effective for oocyte maturation.

• The Mathematical Education
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• v.50 no.3
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• pp.337-354
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• 2011

The purpose of the study was to investigate how students understand multiplication and division of fractions and how their understanding influences the solutions of fractional word problems. Thirteen students from 5th to 6th grades were involved in the study. Students' understanding of operations with fractions was categorized into "a part of the parts", "multiplicative comparison", "equal groups", "area of a rectangular", and "computational procedures of fractional multiplication (e.g., multiply the numerators and denominators separately)" for multiplications, and "sharing", "measuring", "multiplicative inverse", and "computational procedures of fractional division (e.g., multiply by the reciprocal)" for divisions. Most students understood multiplications as a situation of multiplicative comparison, and divisions as a situation of measuring. In addition, some students understood operations of fractions as computational procedures without associating these operations with the particular situations (e.g., equal groups, sharing). Most students tended to solve the word problems based on their semantic structure of these operations. Students with the same understanding of multiplication and division of fractions showed some commonalities during solving word problems. Particularly, some students who understood operations on fractions as computational procedures without assigning meanings could not solve word problems with fractions successfully compared to other students.

• Journal of Ginseng Research
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• v.9 no.1
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• pp.86-94
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• 1985

Attempts were made if diol and triol fractions of ginseng saponin affect on glutamine transport into rat renal cortical mitochondria, swelling, phosphate dependent glutaminase activity, and consumption of oxygen. The following results were obtained. When mitochondrial preparation from rat renal cortex was incubated in medium containing 14C-glutamine and either triol or diol fractions, radioactivity was shown to increase at both 10-6% and 10-5% triol fractions of ginseng saponin, but reduce in case of diol fraction. The remarkable acceleration of the rate of swelling of renal cortical mitochondria was observed in the presence of 10-1% trios and diol fractions but no accerelation at lower concentrations. The activity of phosphate dependent glutaminase from renal cortical mitochondria was slightly activated at 10-2% of triol fraction. However, there was no effect in case of diol fraction. Oxygen consumption by mitochondria from renal cortex was remarkably increased at concentrations of 10-5% and 10-6% triol fractions, but reduced in the case of diol fractions. On the basis of these observations it was concluded that triol fraction of ginseng saponin might increase the transport of glutamine into mitochondria by accelerating the respiratory chain and supplying additional energy to mitochondria, and physiological role of triol fraction was entirely different from that of diol fraction of ginseng saponin.

• Journal of Ginseng Research
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• v.9 no.2
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• pp.193-203
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• 1985

Lipid and fatty acid compositions of the free lipids in Panax ginseng (Korea, Japan and China), Panax quinquefolium (America, Canada) and Panax notoginseng (China) were studied by means of silicic acid column chromatography, thin-layer chromatography and gas-liquid chromatography. Free lipid contents were 1.13 to 1.24% in panax ginseng and 0.87 to 1.18% in Panax quinquefolium and 0.39% in panax notoginseng. Neutral lipid fractions were 81.2 to 84.4%, while glycolipid fractions 8.01% to 14.47% and phospholipid fractions 3.49 to 5.74% in free lipid contents. The major components were triglycerides, free sterols, diglyceride, free fatty acids and sterol esters in neutral lipid fractions, sterol glucoside, monogalactosyl diglyceride, digalactosyl diglyceride, esterified steryl glucoside in glycolipid fractions and phosphatidyl glycerol, phosphatide, ethanolamine, phosphatidyl choline in phospholipid fractions. The contents and compositions of neutral lipids and glyclipids were some different among various ginsengs, whereas phospholipids showed relatively similar compositions in the contents. Seventeen fatty acids were analyzed in the four free lipid fractions from the various ginsengs and the main fatty acids were linoleic acid, palmitic acid, oleic acid and linolenic acid. It was found that the amounts of some fatty acids were different among the various ginsengs, but the fatty acid patterns of these ginsengs were on the whole similar.

• Preventive Nutrition and Food Science
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• v.2 no.3
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• pp.202-206
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• 1997

To develop mil fat fractions with desirable physico-chemical properties, anhydrous milk fat (AMF) was fractionated by one- and two-stage extractions using supercritical $CO_2$(SC-$CO_2$). Tow-stage extraction of AMF was performed by first producing tow fractions, an extract and a residue at 4$0^{\circ}C$/241bar, which were subsequently used as the feed for an extraction at 6$0^{\circ}C$/241bar and 4$0^{\circ}C$/345bar, and separated into five and four fractions, respectively, based one extraction time. These fractions were quantified and analyzed for fatty acids and physico-chemical properties. SHort-chain (C4~C8) fatty acids in extract fractions from an extract were 200~150% compared with those of the original AF. Long-chain (C14~C18) fatty acids in extract fractions from a residue were 118~141%. The ratio of unsaturated fatty acids in the residue fraction was 131%. Melting point ranged from 22 to 43$^{\circ}C$, iodine value 21.8 to 36.9, and saponification value 255 to 221 in the extract and residue fractions. SC-$CO_2$ fractionation of AMF by two-stage extraction offers the possibility of developing ractions with discrete fatty acid compositions and physico-chemical properties such as melting point, iodine value and saponification value.

• Journal of Veterinary Clinics
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• v.9 no.2
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• pp.433-449
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• 1992

Total CPK activities and CPK isoenzymes fractions of the sera and tissues were examined to obtain the physiological basic data of ruminant available in veterinary clinical practice. For the sera total CPK activities and CPK isoenzymes fractions, total 39 clinically healthy Korean native goats (3 to 10 months old, IS of female and 18 of male) and 6 of Korean native goats (1 to 2 years old, 3 of female and 3 of male) were used. Seventeen Korean native cattle (3 to 6 years old, 10 of female and 7 of male) and 27 Holstein-Friesian cattle (2 to 8 months old, 7 of female and 3 to 12 years old, 20 of female) were also examined for the sera total CPK activities and CPK isoenzymes fractions. For the total CPK activities and CPK isoenzyme fractions, 3 of female Korean native goats (7 months old), 3 of female Korean native cattle (2 years old) and 3 of dairy cattle (2 years old, 2 of female and 1 of male) were used. The tissues examined were the cerebrum (2 of Korean native cattle), spinal cord (1 of Korean native cattle), heart, lung, diaphragm, reticulum, liver, spleen, kidney, jejunum. colon and femoral muscle. The results obtained were as follows : 1. In Korean native goats less than 1-year-old. serum total CPK activities were 67.8${\pm}$17.7(39.0~96.5) IU/$\ell$ in female and 63.4${\pm}$19.0(28.7~94.4) IU/$\ell$ in male. Further they were 67.0${\pm}$5.3(59.5~70.7) IU/$\ell$ and 54.5${\pm}$11.1(39.1~69.4) IU/$\ell$ in female and male Korean native goats over 1-year-old, respectively. Serum total CPK activities of female were slightly higher than those of male. Significance between age and sex was not found. 2. Serum total CPK activities were 56.8${\pm}$19.7(27.6~90.5) IU/$\ell$ and 65.6${\pm}$10.8(52.8~78.0) IU/$\ell$ in female and male Korean native adult cattle, respectively, Serum total CPK activities of male were slightly higher than those of female, but they were not significant 3. Serum total CPK activities we,e 72.5${\pm}$8.2(57.2~83.2) IU/$\ell$ and 60.8${\pm}$12.5(42.7~80.6) IU/$\ell$ in calves and adult of dairy acttle, respectively. Serum total CPK activities of calves were significantly higher than those of adult(p<0.05). 4. In Korean native goats less than 1-year-old, serum CPK isoenzymes fractions were high with decreasing order of MM>MB>BB and MM>BB>MB in female and male, respectively. Further they were high with decreasing order of MM>MB>BB and MM>B8>MB in female and male Korean native goats over 1-year-old, respectively. The main fractions of CPK isoenzymes were MM in sera of Korean native goats. 5. Serum CPK Isoenzyme fractions were high with decreasing order of MM>MB>BB In both female and male of Korean native cattle. The main fraction among them was MM. 6. Serum CPK isoenzymes fractions were high with decreasing order of MM>BB>MB in both calves and adult of dairy cattle. The main fraction among them was MM. 7. Total CPK activities were high with decreasing order of the femoral muscle>kidney>reticulum>diaphragm>liver>spleen>heart>colon>lung>jejunum in Korean native goats. 8. Total CPK activities were high with decreasing order of the spinal cord >cerebrum>femoral muscle>reticulum>kidney>liver>spleen>diaphragm>lung>colon>heart>jejunum in Korean native cattle. 9. Total CPK activities were high with decreasing order. of the femoral muscle >liver>retoculum>kidney>heart>colon>lung>spleen>jejunum>diaphrasm in dairy cattle. 10. The pattern of the cardiac CPK isoenzymes fractions was identical in Korean native goats, Korean native cattle and dairy cattle. They were high in the order of MM>MB without BB fractions and the main fraction was MM. 11. The pattern of the pulmonary CPK isoenzymes fractions was the same Korean native goats, Korean native cattle and dairy cattle. They were high with decreasing order of MM>MB>BB and the main fraction among them was MM. 12. The pattern of CPK isoenzymes fractions of the diaphragm was Identical in Korean native goats and Korean native cattle. They were high with decreasing order of MM >BB >MB except dairy cattle (MM>MB>BB) but the main fraction among them was MM. 13. The pattern of the reticular CPK isoenzymes fractions was identical in Korean native cattle and dairy cattle. They were high with decreasing order of BB >MM >MB except Korean native goats(BB>MB>MM) but the main, fraction among them was BB 14. The pattern of the hepatic CPK isoenzymrs fractions was identical in Korean native cattle and dairy cattle. They were high with decreasing order of MB >BB >MM except Korean native goats(MB>MM>BB)but the main fraction was MB. 15. The splenic CPK isoenzymes fractions showed different pattern. They were high with decreasing order of MB>BB>MM, MM>BB>MB and BB>MB>MM in Korean native goats, Korean native cattle and dairy cattle, respectively. The main fraction among them was different from each other. 16. The pattern of the renal CPK isoenzymes fractions was identical in Korean native cattle and dairy cattle. They were high with decreasing order of MM >MB>BB except Korean native goats(BB>MB>MM). 17. The CPK isoenzymes fractions of the Jejunums showed different pattern. They were high with decreasing order MM>MB>BB, MM>BB>MB and BB>MM>MB in Korean native goats, Korean native cattle and dairy cattle, respectively. The main fractions were MM In Korean native goats and Korean native cattle, and BB in dairy cattle. 18. The colonic CPK isoenzymes fractions showed different pattern. They were high with decreasing order of MM>MB>BB, MM>BB>MB and BB>rrfB>MM in Korean native goats, Korean native cattle and dairy cattle, respectively. The main fractions were MM in Korean native goats and Korean . native cattle, and BB in dairy cattle. 19. The cerebral CPK isoenzymes fractions were high with decreasing order of BB >MM without MB detected in Korean native cattle and those of spinal cord were high with decreasing order of BB >MM >MB. The main fractions in both cerebrum and spinal cord were BB.

• Journal of Animal Science and Technology
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• v.49 no.3
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• pp.341-350
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• 2007

The present study was conducted to measure diurnal patterns in the flow of soluble non-ammonia nitrogen (SNAN) fractions in the liquid phase of digesta entering the omasum of cows fed grass-red clover silage supplemented with barley and rapeseed meal. Four ruminally cannulated cows were fed, in a 4×4 Latin square design, grass-red clover silage alone (GS) or supplemented with (on a DM basis) 6.0kg/d of barley grain, 2.1kg/d of rapeseed meal or 6.0kg/d of barley and 2.1kg/d rapeseed meal. Omasal digesta was taken using an omasal sampling system at 1.5h intervals during a 12h feeding cycle, and SNAN fractions (free AA, peptide and soluble protein) in the omasal digesta were assessed using ninhydrin assay. Dietary supplementation numerically increased the mean flow of SNAN fractions relative to GS diet despite the lack of statistical significance. Diurnal patterns in the flow of peptide entering the omasum during a 12h feeding cycle appeared to be highest immediately after feeding, declined by 10.0h post-feeding and slightly increased thereafter. In SNAN fractions, the flow of peptide was higher for supplemented diets than for GS diet throughout the feeding cycle. Based on the microbial contribution to total SNAN using 15N, diurnal patterns in the flow of dietary SNAN for dietary supplemented diets appeared to be higher compared with GS diets. Present results may conclude that peptide flow is quantitatively the most important N in SNAN fractions and that dietary supplementation can increase peptide flow entering the omasal canal.

• Korean Journal of Microbiology
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• v.39 no.4
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• pp.223-229
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• 2003

The purpose of this work was to perform the characterization of NAD(P)H-nitroreductase isolated from Stenotrophomonas sp. OK-5 capable of degrading 2,4,6-trinitrotoluene (TNT). Initially, NADP(H)-nitroreductase by a series of purification processes including ammonium sulfate precipitation, DEAE-sepharose, andQ-sepharose was prepared. From samples harvested from fraction collector, three different fractions (I, II & III)having the enzyme activity of NAD(P)H-itroreductase were detected. Specific activities of three fractions I, II,and III of NAD(P)H-nitroreductase were determined to approximately 5.06 unit/mg, 4.95 unit/mg and 4.86 unit/mg, and concentrated to 10.5, 9.8, and 8.9-fold compared to crude extract, respectively. Among these three fractions,the fraction I of NAD(P)H-nitroreductase demonstrated the highest specific activity in this experiment. Several factors affecting on the enzyme activity of NAD(P)H-nitroreductase (fractions I, II & III) were investigated.The optimum temperature of all NAD(P)H-nitroreductase (fractions I, II & III) was 30oC, and the optimal pH was approximately 7.5. Metal ions such as Ag+, Cu2+, Hg2+ inhibited approximately 80% enzyme activity of all NAD(P)H-nitroreductase, and the enzyme activities were decreased about 30-40% inhibition in the presence of Mn2+ or Ca2+. However, Fe3+ showed stimulatory effect on the enzyme activity. The molecular weights of NAD(P)H-nitroreductase (fractions I, II & III) were measured about 27 kDa on the SDS-PAGE.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.101-114
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• 2001

The ancient Egyptians only used fractions of the form 1/n, so any other fraction had to be represented as a sum of such unit fractions and all the unit fractions were different. This study explores some of the history of Egyptian fractions and gives you an algorithm for such representations. There's lots of investigations to do in this area of mathematics suitable for elementary school students and it is also designed as a resource for teachers.