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EXISTENCE OF TRIPLE POSITIVE SOLUTIONS OF A KIND OF SECOND-ORDER FOUR-POINT BVP

  • Zhao, Junfang;Ge, Weigao
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.183-194
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    • 2009
  • In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

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Physicochemical Characteristics and Functional Components of Mudeungsan Watermelon and the other Cultivars from Korea (일반 수박과 무등산 수박의 이화학적 특성)

  • Kim, Jeong Yeon;Lee, Seong Hee;Hwang, Su Jung;Kim, Gun Hee;Eun, Jong-Bang
    • Korean Journal of Food Science and Technology
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    • v.45 no.3
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    • pp.345-349
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    • 2013
  • Physicochemical characteristics of Citrullus lanatus cv. Mudeungsan and 5 other cultivars of Citrullus lanatus were investigated. The color of watermelon (redness) was not significantly different among the cultivars. Hardness ranged from 38.76 to 52.12 force (g) among cultivars. Soluble solid content in Taeyangggul and Mudeungsan were higher than that in other cultivars. pH ranged from 5.39 to 6.02 among cultivars, and total acidity was the highest in Mudeungsan (0.147 mg/100 g). No significant difference in total carotenoid content was observed among the cultivars. Lycopene content in Mudeungsan cultivar was higher than that in other cultivars. Citrullin contents of watermelon flesh and rind in Mudeungsan and GangryeokSambok were higher than those in other cultivars. The major free sugars of watermelon were sucrose and fructose, and the predominant organic acids were succinic acid and citric acid. In conclusion, Mudeungsan cultivar had better properties as outlined above and contained soluble solids and functional components, compared to the other watermelon cultivars.

Physicochemical and Organoleptic Qualities of Sliced-dried Persimmons as Affected by Drying Methods (건조방법을 달리한 감말랭이의 이화학적 및 관능적 품질 특성)

  • Kim, Yeon-Joo;Lee, Su-Jin;Kim, Mi-Yeung;Kim, Gui-Ran;Chung, Hun-Sik;Park, Hyun-Ju;Kim, Mi-Ok;Kwon, Joong-Ho
    • Korean Journal of Food Science and Technology
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    • v.41 no.1
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    • pp.64-68
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    • 2009
  • The effects of drying methods (hot air, cold air, vacuum, and infrared drying) on physicochemical and organoleptic qualities of sliced-dried persimmons (Diospyros kaki Thumb. cv. Cheungdobansi) were investigated. The weight of the sliceddried persimmons ranged from 9.30 to 12.01 g, the length from 3.55 to 4.06 cm, the width and thickness were from 3.17 to 3.73 cm and 1.82 to 2.04 cm, respectively. Hot air drying resulted in the highest hardness value as well as Hunter's L, a, and b values. Infrared drying showed the lowest L value and vacuum drying revealed the lowest a and b values. Moisture contents of the sliced-dried persimmons ranged from 38.04 to 46.41%, and soluble solid contents were 42.96-$48.44^{\circ}Bx$. The phenolic compounds and DPPH radical scavenging activity were high for infrared and vacuum drying methods, and all the sliced-dried persimmons showed relatively high antioxidant activities. The sensory evaluation results indicated that the organoleptic scores for the overall preference were high in the order of vacuum > infrared > hot air > cold air drying. These results suggest that the drying methods affected the qualities of the sliced-dried persimmons, showing that vacuum drying is the mast effective among the methods tested for manufacturing the high-quality sliced-dried persimmons.

Physicochemical Characteristics of Korean Traditional Wines Prepared by Addition of Sorghum (Sorghum bicolor L. Moench) Using Different Nuruks (수수 첨가량 및 누룩을 달리한 발효주의 이화학적 특성)

  • Woo, Koan-Sik;Ko, Jee-Yeon;Song, Seuk-Bo;Lee, Jae-Saeng;Oh, Byeong-Geun;Kang, Jong-Rae;Nam, Min-Hee;Ryu, In-Soo;Jeong, Heon-Sang;Seo, Myung-Chul
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.39 no.4
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    • pp.548-553
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    • 2010
  • This study was carried out to compare the physicochemical characteristics of Korean traditional wines fermented by addition of sorghum (Sorghum bicolor) using different nuruks (SH and BS nuruk). The alcohol contents of the fermented wines ranged from 12.36 to 13.21%. The brix degrees of sorghum wines fermented using SH and BS nuruks were $8.6\sim17.9^{\circ}Bx$ and $7.6\sim20.0^{\circ}Bx$ on addition ratio, respectively. Wine no addedsorghum using SH and BS nuruks showed pH 3.74 and 3.40, total acidity of 1.40 and 1.51%, and 0.441 and 0.149 of turbidity. With increase of sorghum addition, brix degree, pH, turbidity and L-value decreased whereas total acidity and a-value increased. Total color difference (${\Delta}Eab$) parameters of wines fermented in 30, 70 and 100% sorghum addition using SH and BS nuruk were 4.33, 6.63 and 26.13, and 4.08, 5.29 and 10.59. Glucose content decreased with increasing amounts of sorghum. Organic acids such as lactic acid and acetic acid were predominantly detected in the fermented wine. Finally, based on sensory evaluations, the wine fermented by BS nuruk showed the best overall quality at 30% sorghum addition.

Quality Characteristics of Malts and Sikhye Made from Barley and Wheat Varieties Grown in Korea (국내 육성 보리와 밀 품종별 엿기름 및 식혜의 품질 특성)

  • Kim, Namgeol;Lee, Seuk Ki;Park, Hye Young;Choi, Induck;Choi, Hyesun;Park, Ji Young;Shin, Dong-Sun;Park, Chang-Hwan;Jeong, Kwang-Ho;Kim, Hyun-Joo
    • The Korean Journal of Food And Nutrition
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    • v.32 no.5
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    • pp.425-433
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    • 2019
  • Sikhye is a traditional rice beverage, produced from steamed rice, barley or wheat malt and water. Nine varieties of barley and seven varieties of wheat cultivars were investigated and compared quality characteristics, diastatic power, and activities of ${\alpha}$- and ${\beta}$-Amylase. For barley malt, the crude lipid and protein content of malt 1.74~2.42% and 10.71~14.36%, respectively. Also, the crude lipid and protein content for wheat malt 1.57~1.71% and 10.07~13.59%, respectively. The 'Dahyang' barley showed the highest diastatic power with $117.61^{\circ}L$, while for wheat, 'Baegjoong' produced the highest diastatic power with $85.25^{\circ}L$. The enzymatic activities, ${\alpha}$- and ${\beta}$-Amylase for barley cultivar was $110.17{\sim}214.70{\mu}nit/g$ and $869.73{\sim}1,638.43{\mu}nit/g$, respectively. Likewise, ${\alpha}$- and ${\beta}$-Amylase for wheat cultivar was $73.19{\sim}132.23{\mu}nit/g$ and $726.70{\sim}889.30{\mu}nit/g$, respectively. The highest sugar content of Sikhye from barley was $11.10^{\circ}Bx$ ('Hyeda'), while from wheat, was $10.20^{\circ}Bx$ ('Baegjoong'). Among the four free sugar components analyzed from Sikhye, maltose was the highest in all cultivars. The highest maltose content was produced in 'Dahyang' Sikhye at 6.91%. There was significant positive-correlation among the diastatic power and enzymatic activities of malt and free sugar components in Sikhye.

Effects of Ripening and Storage Temperatures on the Quality of Banana (바나나의 후숙 밑 저장 온도가 품질에 미치는 영향)

  • 한광수;고하영
    • Food Science and Preservation
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    • v.6 no.2
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    • pp.148-152
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    • 1999
  • Philippine bananas were ripened at various temperatures(18$^{\circ}C$, 21$^{\circ}C$ and 25$^{\circ}C$) for 5 days and stored at 13$^{\circ}C$ and ambient temperature(13-20$^{\circ}C$) for 16 days. Their quality changes were evaluated during the storage. The color chart number and soluble solids of bananas before storage showed 4.2-5.2 and 18.7-18.8$^{\circ}$ Bx at 18$^{\circ}C$ and 21$^{\circ}C$ ripening and 5.5 and 20.1 $^{\circ}$Bx at 25$^{\circ}C$ ripening, respectively. Weight losses reached about 1% around 10 days in all storage conditions. Soluble solids increased initially for 4-6 days and then decreased slightly. Color chart number changed from 4.2-5.5 after ripening to 7 after 2-4 days storage. Blackening of 18$^{\circ}C$ and 21$^{\circ}C$ ripened bananas occurred after 4 days storage at 13$^{\circ}C$ and after 2 days storage at ambient temperature. Decay of 18$^{\circ}C$ and 21$^{\circ}C$ ripening bananas increased from 2.1% after 6 days at 13$^{\circ}C$ storage and 4.2% after 4 days at ambient temperature storage to 75-100% within 2-4 days after that times. The decay of 25$^{\circ}C$ ripened bananas rapidly increased after 2 days at 13$^{\circ}C$ storage and at the initial at ambient temperature storage.

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Characteristics of New Satsuma Mandarin Cultivar 'Sangdojosaeng' (온주밀감 신품종 '상도조생' 특성)

  • Park, Young Chul;Oh, Hyun Woo;Kang, Jong Hoon;Lee, Joong Seok;Chin, Seok Cheon;Kang, Sang Hoon;Kang, Sung Geun
    • Korean Journal of Plant Resources
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    • v.26 no.1
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    • pp.143-147
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    • 2013
  • 'Sangdojosaeng' is a new cultivar from bud spot of Citrus unshiu 'Sasaki unshiu' which has late maturity habit. It was found in 1996, and primary selected and named as 'JARES108' in 1998. 'JARES108' was grafted on to adult satsuma mandarin trees in Seogwipo-si and Jeju-si in 2000. Four years survey on the characteristics of trees and fruits from 2003 to 2006 was carried and confirmed the superiority. Thus it was finally selected as 'Sangdojosaeng'. 'Sangdojosaeng' is a very early wase type satsuma mandarin. It shows relatively strong tree vigor among the very early wase type varieties and its branches are spreading. Its ripening time is late October, 25 days earlier than 'Sasaki unshiu'. Compared to 'Ueno wase' which has similar characteristics with 'Sangdojosaeng' such as ripening time, tree vigor, fruit type and peel color, its soluble solid content of fruit is $0.6^{\circ}Bx$ higher and acidity was a little lower than 'Ueno wase'. Because this cultivar has good quality and its tree makes vigorous growth among very early wase type varieties in Jeju, we expect to substitute it for some very early wase type varieties such as 'Miyamoto wase', 'Ichifumi wase', 'Yamakawa wase', etc.

Effect of Spermine Treatment on Growth, Yield, and Quality of Strawberry under Low-Temperature Condition (이상 저온 조건에서 Spermine 처리가 딸기의 생육과 수량 및 품질에 미치는 영향)

  • Lee, Gyu-Bin;Lee, Jung-Eun;Choe, Yun-Ui;Park, Young-Hoon;Choi, Young-Whan;Kang, Nam-Jun;Kang, Jum-Soon
    • Journal of Environmental Science International
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    • v.27 no.3
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    • pp.195-202
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    • 2018
  • The present study was carried out to investigate the effects of spermine treatment on the growth, yield and quality in strawberry under low-temperature condition, and thereby develop a chemical method to minimize damages by low temperature in greenhouse cultivation. Spermine treatment significantly improved the growth of strawberry in terms of leaf number, leaf area, leaf length, leaf diameter, plant height and plant weight. The highest effect was observed in the 250 uM spermine treatment and the effect tended to be maintained during the entire growth period of 90 days. Fresh weight and dry weight were significantly different depending on the concentrations of spermine. Strawberry plants treated with 250 uM spermine showed higher fresh weight and dry weight compared to untreated control plants during the growth period. Fruit weight, fruit length and fruit diameter were relatively higher when treated with $100{\mu}M$ spermine compared to other treatments. The fruit yield was the highest with 14 fruits per plant at $250{\mu}M$ spermine treatment and the coloration of the fruit was the best at this treatment with the Hunter a and b values of 46.56 and 28.75, respectively. The hardness of strawberry fruit tended to increase higher than 2N at $250{\mu}M$ and $500{\mu}M$ 250 uM spermine treatment. The sugar content of strawberries treated with $250{\mu}M$ spermine was $9.5^{\circ}$ Bx which was $1.6^{\circ}$ Bx higher compared to that in untreated control. However, spermine treatment did not affect the acidity of fruit and it remained 0.68-0.76% regardless of treatment concentrations. These results suggest that spermine treatment has a positive effect on the growth and productivity of strawberry fruit under abnormal low-temperature condition. The positive effect was the highest at $250{\mu}M$ spermine treatment and gradually decreased in the order of $100{\mu}M$, $500{\mu}M$, and untreated control.

Effect of Chia(Salvia hispanica L.) Seeds on Quality Properties of Yanggang (치아 시드 분말 첨가가 양갱의 품질 특성에 미치는 영향)

  • O, Hyeonbin;Song, Ka-Young;Zhang, Yangyang;Jung, Ki Youeng;Kim, Young-Soon
    • The Korean Journal of Food And Nutrition
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    • v.30 no.2
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    • pp.236-242
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    • 2017
  • Chia (Salvia hispanica L.) seed, originated from Central America, is a nutritious food especially rich in dietary fiber and protein. In this study, we investigated the quality and sensory characteristics of Yanggang with chia seed powder (CSP). Red bean paste was replaced with CSP at 0% (Control), 1% (CSP1), 2% (CSP2), 3% (CSP3) and 4% (CSP4). The pH values of chia seed Yanggang tended to decrease from Control (6.84) to CSP4 (6.67); whereas, the moisture contents of Yanggang samples tended to increase. The soluble solid contents of CSP4 were the highest ($3.33^{\circ}Bx$), as compared to the Control which showed the lowest values ($2.77^{\circ}Bx$). In the CSP-added groups, the L-value (lightness), a-value (redness) and b-value (yellowness) were increased, while the ${\Delta}E$ (total color difference) was decreased, as compared to the control group. Hardness and springiness were both increased from control ($49.77g/cm^2$ and 464.80%, respectively) to CSP4 ($72.21g/cm^2$ and 532.43%, respectively). However, cohesiveness decreased from control (47.41%) to CSP4 (37.34%). Chewiness and adhesiveness showed no significant group-wise difference (p<0.05). Total polyphenol content ranged from 7.23 to 10.73 mg GAE/100 g, with a lower ABTS $IC_{50}$ of the CSP-added groups than that of the control group. Samples from the CSP-added as well as Control groups showed no significant differences among all items on the sensory evaluation test, except flavor. The results indicated that CSP had significant effects on the soluble solid contents and texture of Yanggang. Thus, the addition of 2% of CSP is desirable for making Yanggang.

Criteria of Fruit Quality and Harvest for Production of High Quality Small and Medium-Sized Fruits in 'Hanareum' Pear (Pyrus pyrifolia Nakai) (고품질 중소과 생산을 위한 '한아름' 배의 과실 품질 및 수확 기준)

  • Park, YoSup;Kwon, YongHee
    • Journal of Bio-Environment Control
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    • v.23 no.2
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    • pp.131-138
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    • 2014
  • 'Hanareum' pear is expected to produce the high quality small and medium-sized fruits without any major changes in the current cultivation techniques, inasmuch as its basic characteristics are already included in the range of small and medium-sized fruits. Thus, we tested the possibility of utilization of 'Hanareum' pear for producing small and medium-sized fruits, while establishing the limit of minimum fruit weight for the fruits in high quality. With the results of correlation analysis, it was possible to predict the fruit weight through the observation of soluble solid contents and flesh firmness, because both factors were closely correlated to fruit weight in all treatments. Moreover, these factors were confirmed to be useful indicators of forecasting consumer preference in the sensory evaluation. The fruit marketability was excellent under the conditions that were greater than $11.6^{\circ}Bx$ and less than 25.6 N for soluble solid contents and flesh firmness, respectively. When applying these standards of fruit quality to the results of regression analysis for fruit weight, non-treated fruits fulfilled both standards when the fruit weight was higher than 436 g, and the quality uniformity was also high on this state. Therefore, the production of high quality small and medium-sized fruits was determined to be under this condition. The weight limit for GA treated fruits was 620 g, and both fruit quality and uniformity were below the weight range of small and medium-sized fruits, with 300~500 g. Thus, GA treatment was suggested to be avoided, in order to produce the high quality small and medium-sized fruits.