• Korean Journal of Mathematics
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• v.17 no.3
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• pp.315-330
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1759-1776
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• 2015

We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.491-502
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• 2010

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x + y) + f(2x - y) = 4(f(x + y) + f(x - y)) - $\frac{3}{7}$(f(2y) - 2f(y)) + 2f(2x) - 8f(x).

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.387-397
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• 1996

Let G be a finite group and F be a field of characteristic $p \geq 0$. Let $\Gamma = F^f G$ be a twisted group algebra corresponding to a 2-cocycle $f \in Z^2(G,F^*), where F^* = F - {0}$ is the multiplicative subgroup of F.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.16
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• pp.7053-7060
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• 2015

In the present work, novel orange peel was extracted with 100%EtOH (ethanol) and fractionated into four fractions namely F1, F2, F3, F4 which were eluted from paper chromatographs using 100%EtOH, 80%EtOH, 50%EtOH and pure water respectively. The crude extract and its four fractions were evaluated for their total polyphenol content (TPC), total flavonoid content (TFC) and radical scavenging activity using DPPH (1,1-diphenyl-2-picrylhydrazyl) assay. Their cytotoxic activity using WST assay and DNA damage by agarose gel electrophoresis were also evaluated in a human leukemia HL-60 cell line. The findings revealed that F4 had the highest TPC followed by crude extract, F2, F3 and F1. However, the crude extract had the highest TFC followed by F4, F3, F2, and F1. Depending on the values of $EC_{50}$ and trolox equivalent antioxidant capacity, F4 possessed the strongest antioxidant activity while F1 and F2 displayed weak antioxidant activity. Further, incubation HL-60 cells with extract/fractions for 24h caused an inhibition of cell viability in a concentration-dependent manner. F3 and F4 exhibited a high antiproliferative activity with a narrow range of $IC_{50}$ values ($45.9-48.9{\mu}g/ml$). Crude extract exhibited the weakest antiproliferative activity with an $IC_{50}$ value of $314.89{\mu}g/ml$. Analysis of DNA fragmentation displayed DNA degradation in the form of a smear-type pattern upon agarose gel after incubation of HL-60 cells with F3 and F4 for 6 h. Overall, F3 and F4 appear to be good sources of phytochemicals with antioxidant and potential anticancer activities.

• Asian-Australasian Journal of Animal Sciences
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• v.20 no.12
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• pp.1805-1811
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• 2007

A simulation study was conducted to evaluate the effect of reciprocal cross on the detection and characterization of parent-of-origin (POE) QTL in $F_2$ QTL populations. Data were simulated under two different mating designs. In the one-way cross design, six $F_0$ grand sires of one breed and 30 $F_0$ grand dams of another breed generated 10 $F_1$ offspring per dam. Sixteen $F_1$ sires and 64 $F_1$ dams were randomly chosen to produce a total of 640 $F_2$ offspring. In the reciprocal design, three $F_0$ grand sires of A breed and 15 $F_0$ grand dams of B breed were mated to generate 10 $F_1$ offspring per dam. Eight $F_1$ sires and 32 $F_1$ dams were randomly chosen to produce 10 $F_2$ offspring per $F_1$ dam, totaling 320 $F_2$ offspring. Another mating set comprised three $F_0$ grand sires of B breed and 15 $F_0$ grand dams of A breed to produce the same number of $F_1$ and $F_2$ offspring. A chromosome of 100 cM was simulated with large, medium or small QTL with fixed or different allele frequencies in parental breeds. A series of tests between Mendelian and POE models were applied to characterize QTL as Mendelian, paternal, maternal or partial expression QTL. The overall detection powers were similar between the two mating designs. However, the proportions of paternally expressed QTL that were declared as paternal QTL type were greater in the reciprocal cross design than in the one-way cross, and vice versa for Mendelian QTL. When QTL alleles were segregating in parental breeds, a significant proportion of Mendelian QTL were spuriously declared POE QTL, suggesting that care must be taken to characterize imprinting QTL in a QTL mapping population with a small number of $F_1$ parents.

• Journal of the Korean Society of Tobacco Science
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• v.15 no.1
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• pp.34-48
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• 1993

This experiment were conducted to investigate heterosis and combining ability for several mutant characters by analyzing dialled crosses of flue-cured tobacco. In a dialled cross of 3 flue-cured varieties and the mutant line 83H -5, the heterosis was somewhat higher in Fl than in F2. For growth character, the heterosis was 0.28-6.03% in plant height, leaf number, leaf shape index and yield, and was 43.2% for bacterial wilt disease index. The mutant line 83H-5 showed significantly negative GCA effect for plant height, leaf width and bacterial wilt disease index in Fl and F2, leaf length in F2, and positive GCA effect for total alkaloids, total nitrogen in Fl and days to flower in F2, respectively. Specific combining ability(SCA) in 83H-5 x Hicks was significant in negative effect for leaf length(F2), number of leaves(F2), leaf shape(F1, F2), bacterial wilt(F2) and alkaloids(F1), and in 83H-5 x NC 2326 in positive effect for leaf length(F1, F2) and leaf width(F2), and for 83H-5 x NC 82 in positive effect for plant height(F1, F2) and leaf width(F2), and for 83H-5 x NC 82 in Positive effect for Plant height(F1, F2), leaf length(F2) and yield(F1, F2).

• KOREAN JOURNAL OF CROP SCIENCE
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• v.4 no.1
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• pp.31-71
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• 1968

To clarify the breeding behavior of the hybrids between tropical and temperate area rice varieties, investigations were made on heading days and grain sterility. In this study, crosses were made in half way diallel involving 7 varieties: 2 photoperied sensitive Indicas, 2 less sensitive intermediate Indicas, 1 Ponlai Japonica and 2 high temperature sensitive Japonicas. The parents and $F_1$s were grown under 10 hours and 14 hours daylength controlled conditions at both IRRI(International Rice Research Institute, N$14^{\circ}$17') and Suwon(N$37^{\circ}$16'). F2s with their parents were grown at IRRI in the short day season, and at Suwon under natural conditions. Fa lines with their parents were grown at Suwon under natural conditions. Observations were made for heading days and sterility. The results are summarized as follow; 1. Heading days : 1. For the $F_1$s, earliness showed dominance or overdominance to lateness under the 10 hours condition, and dominance or partial dominance under the 14 hours conditions, at both IRRI and Suwon. 2. For the $F_2$s grown at IRRI during the shortday season earliness appeared to be dominant over lateness and segregation was not distinct and continuous. In the early season culture of $F_2$s at Suwon earliness showed partial dominance or was intermediate. In the proper season culture of $F_2$s lateness showed partial dominance or was intermediate. 3. In the combinations between late parental varieties which do not head at Suwon, transgressive segregants bearing effective panicles were obtained. 4. The crosses of parental varieties having long basic vegetative growth duration showed bigger variance in heading days, and significant correlation was found between of parental varieties and the mean coefficient of variance for parental arrays. 5. The means of heading days of F2 populations were significantly correlated with those of $F_1$ or mid-parents. The means of F 8 lines were also highly correlated with the means of $F_2$s, but, the means of $F_3$ lines grown at Suwon and of their parental $F_2$ individual, grown at IRRI were not correlated. 6. A faint heritability was calculated from the regression of $F_3$ lines grown at Suwon on the $F_2$ individuals grown at IRRI for most combinations, especially in the combinations involving shortday sensitive varieties. This implies low efficiency for the selection of heading days of $F_2$ individuals at IRRI to be grown in lines at Suwon. 7. No significant reciprocal effects were measured for $F_1$ and $F_2$ mean heading days. 8. Partitioning the observed photoperiod sensitivity. into two components, parental array mean md the deviation from this array mean, the parental photoperiod sensitivity contributing to the hybrids was measured in terms of general and specific combining ability for photoperiod sensitivity. 9. The photoperiod sensitivity of $F_1$s was higher than that of the parents, and it decreased as the generation progressed in most combinations of tested varieties. 10. The response of heading days to difference of temperature was weaker for $F_1$ hybrids than for the parents. The differences of temperature responses between the longday and shortday treatments were specific for the variety. 2. Sterility : 1. The $F_1$ sterility was specific for the combinations and not correlated to the parental sterility. The sterility of $F_1$s grown under the 10 hours condition was higher than of those grown under 14 hours. These results were the same at both locations, IRRI and Suwon. 2. The high sterile combinations in $F_1$ showed high sterility in $F_2$. The combinations between a high photoperiod sensitive variety and a high temperature sensitive variety showed high sterility and wider variance. 3. The mean sterility of $F_2$s was lower than of $F_1$s and the mean of $F_3$ lines was lower than of $F_2$s. Sterility decreased as the generation progressed, and the differences of $F_3$ sterility of different combinations were not significant. 4. A faint correlation between grain sterility and pollen sterility was observed in $F_2$ populations. 5. No significant reciprocal effects were measured in $F_1$ and $F_2$ sterility. 6. Following Griffing's method, specific combining ability effects were higher than general combining ability effects, especially in the combinations between highly photoperiod sensitive varieties and highly temperature sensitive varieties. 7. No distinct correlations were found between $F_2$ individual sterility grown at IRRI and $F_3$ line sterility grown at Suwon. 8. No distinct correlations were observed between heading days and sterility of $F_2$ individuals.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.23 no.2
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• pp.1-24
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• 1978

To obtain basic information on the breeding of early maturing, short culm naked-barley varieties, the following 10 varieties, Ehime ＃ 1, Shikoku ＃42, Yamate hadaka, Eijo hadaka, Kagawa ＃ 1, Jangjubaeggwa, Baegdong, Cheongmaeg, Seto-hadaka and Mokpo ＃42 were used in diallel crosses in 1974. Heading date, culm length and grain yield per plant for the parents, $F_1's$ and $F_2's$ of the 10X10 partial diallel crosses were measured in 1976 for analysis of their combining ability, heritability and inheritance. The results obtained are summarized below; 1. Heritabilities in broad sense for heading date, culm length and grain yield per plant were 0.7831, 0.7599 and 0.6161, respectively. Narrow sense heritabilities for heading date were 0.3972 in $F_1$ and 0.7789 in $F_2$ and for culm length 0.6567 in $F_1$ and 0.6414 in $F_2.$ These values suggest that earliness and culm length could be successfully selected for in the early generations. Narrow sense heritability for grain yield was 0.3775 in $F_1$ and 0.4170 in $F_2.$ 2. GCA effects of the $F_1$ and $F_2$ generations for days to heading were high in the early direction for early-heading varieties, while for late-heading varieties the GCA effects were high in the late direction. Absolute values for GCA effects in $F_1$ were higher than in $F_2.$ SCA effects of the $F_1$ and $F_2$ generations were high in the early-heading direction for Shikoku ＃ 42 x Mokpo ＃ 42, Ehime ＃ 1 x Yamate hadaka, Shikoku ＃ 42 x Yamate hadaka and Shikoku ＃42 x Eijo hadaka. 3. The GCA effects for culm length in the $F_1$ and $F_2$ generations for tall varieties were high in the tall direction while short varieties were high in the short direction. Absolute values for the GCA effects in $F_1$ were higher than in $F_2.$ SCA effects were high in the short direction for the combinations of Mokpo ＃ 42 with Ehime ＃ 1, Yamate had aka and Eijo hadaka. 4. The GCA effects for grain yields per plant in the $F_1$ and $F_2$ generations for varieties with high yields per plant were high in the high yielding direction, while varieties with low yields per plant were high in the low yielding direction. Absolute values of the $F_1$ GCA effects were higher than the $F_2$ effects. The combinations with high SCA effects were Mokpo ＃ 42 x Shikoku ＃ 42, Mokpo ＃ 42 x Seto hadaka and Mokpo ＃ 42 x Cheongmaeg. 5. Mean heading dates of the $F_1$ and $F_2$ generations were earlier than those of mean mid-parent. Mean heading date of the $F_1$ generation was earlier than the $F_2$ generation. Crosses involving early-heading varieties showed a greater $F_1, $ mid-parent difference than crosses involving late-heading varieties. 6. Heading date was controlled by a partial dominance effect. Nine varieties excluding Mokpo ＃ 42 showed allelic gene action. Ehime ＃ 1, Shikoku ＃ 42, Kagawa ＃ 1 and Mokpo ＃ 42 were recessive to the other tested varieties. 7. The $F_2$ segregations of the 45 crosses for days to heading showed that 33 cosses were of such complexity that they could not be explained by simple genetic inheritance. One cross showed a 3 : 1 ratio where earliness was dominant. Another cross showed a 3 : 1 ratio where lateness was dominant. Four other crosses showed a 9 : 7 ratio for earliness while six crosses showed a 9 : 7 ratio for lateness. 8. Many transgressive segregants for earliness were found in the following crosses; Eijo hadaka x Baegdong, Ehime ＃ 1 x Seto hadaka, Yamate had aka x Kagawa ＃ 1, Kagawa ＃ 1 x Sato hadaka, Shikoku ＃ 42 x Kagawa ＃ 1, Ehime ＃ 1 x Kagawa ＃ 1, Ehime ＃ 1 x Shikoku ＃ 42, Ehime ＃ 1 x Eijo hadaka. 9. Mean culm length of the F, and F. generations were usually taller than the mid-parent where tall parent were used. These trends were high in the short varieties, but low in the tall varieties. 10. Culm length was controlled by partial dominace which was gonverned by allelic gene(s). Culm length showed a high degree of control by additive genes. Mokpo ＃ 42 was recessive while Baegdong was dominant. 11. The F_2 frequency for culm length was in large part normally distributed around the midparent value. However, some combinations showed transgressive segregation for either tall or short culm length. From combinations between medium tall varieties, Ehime ＃ 1, Shikoku ＃ 42, Eijo hadaka and Seto hadaka, many short segregants could be found. 12. Mean grain yields per plant of the F_1 and F_2 generations were 6% and 5% higher than those of mid-parents, respectively. The varieties with high yields per plant showed a low rate of yield increase in their F_1's and F_2's while the varieties with low yields per plant showed a high rate of yield increase in their F_1's and F_1's. 13. Grain yields per plant showed over-dominnee effects, governed by non-allelic genes. Mokpo ＃ 42 showed recessive genetic control of grain yield per plant. It remains difficult to clarify the inheritance of grain yields per plant from these data.

• Research in Plant Disease
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• v.25 no.4
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• pp.213-219
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• 2019

A total of 1,159 Fusarium strains were isolated from sorghum grown in Danyang and Youngwol in 2017 and 2018. The isolates were analyzed to reveal genetic, toxigenic and pathogenic characteristics. Phylogenetic analysis using TEF-1α and RPB2 genes showed that the samples were contaminated with at least 17 Fusarium species. Among them, F. graminearum, F. proliferatum, F. thapsinum, F. incarnatum, and F. asiaticum were dominant species. In F. graminearum and F. asiaticum, F. graminearum-15-acetyl deoxynivalenol chemotype and F. asiaticum-nivalenol chemotype were frequent. Six Fusarium species tested produced one or more mycotoxins, except F. thapsinum and FTSC 11. F. proliferatum and F. fujikuroi had FUM1 gene (76.0% and 81.6%, respectively) and some isolates produced high level of fumonisin (over 1,000 ㎍). F. proliferatum and F. thapsinum were more virulent than other species on sorghum. These results indicate that Fusarium species in sorghum might produce multiple mycotoxins.