• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.427-436
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• 2011

In this paper, we first show that the pull-back morphism between two K-groups of the Steinberg varieties, obtained respectively from partial flag varieties and quiver varieties of type A, is a ring homomorphism with respect to the convolution product. Then, we prove that this ring homomorphism yields a property of compatibility between two certain convolution actions.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1109-1133
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• 2023

We prove that the two-step flag variety 𝓕ℓ(1, n; n+1) carries a non-displaceable and non-monotone Lagrangian Gelfand-Zeitlin fiber diffeomorphic to S³ × T^2n-4 and a continuum family of non-displaceable Lagrangian Gelfand-Zeitlin torus fibers when n > 2.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.347-353
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• 2011

In [1], Maffei proved a certain relationship between quiver varieties of type A and the geometry of partial flag varieties over the nilpotent cone. This relation was conjectured by Naka-jima, and Nakajima proved his conjecture for a simple case. In the Maffei's proof, the key step was a reduction of the general case of the conjecture to the simple case treated by Nakajima through a certain isomorphism. In this paper, we study properties of this isomorphism.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1527-1575
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• 2017

In a spirit of Givental's constructions Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested Landau-Ginzburg models for smooth Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau-Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.15
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• pp.1-31
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• 1974

Introducing genes for earliness of wheat varieties is important to develop early varieties in winter wheat. In oder to obtain basic informations on the response of heading to the different day length and temperature treatments and on the inheritance of heading dates, experiments were conducted at the field and greenhouse of the Crop Experiment Station, Suwon. Varieties used in this experiments were, early variety Yecora F70, medium varieties Suke #169, Parker and Yukseung #3, and late varieties Changkwang, Bezostaia, Sturdy and Blueboy. The parents and F$_1$s of partial diallel crosses of above eight varieties were subjected the following four different treatments; 1. high temperature and long day, 2. high temperature and short day, 3. low temperature and long day, and 4. low temperature and short day. The same materials were grown also in field condition. Parents, F$_1$ and F$_2$ generation were grown also in both greenhouse under high temperature and short day and in field. The results obtained were summarized as follow: 1. No effects of temperature and daylength on the number of leaves on the main stem were found when -varieties were vernalized. The number of main stem leaves were fewer for spring type of varieties than for winter type of varieties. 2. The effects of temperature and daylength on the days to flag leaf opening were dependent on the speed of leaf emergence. The speed of leaf emergence were faster for lower leaves than for upper leaves. 3. The response to short day and long day (earliness of narrow sense) of varieties were found to be direct factor responsible to physiology of heading dates in vernalized varieties. Great difference of varieties to heading date was found in high temperature and short day treatment, but less differences were found in high temperature and long day, low temperature and long day and low temperature and short day treatments respectively. The least varietal difference for heading dates was found in the field condition. 4. Changkwang and Parker were found to be the most sensitive to short day treatment (photosensitive) and the heading of these varieties were delayed by short day treatment. No great varietal differences were found among other varieties. 5. Varietal differences of heading dates due to daylength were greater in high temperature than in low temperature. 6. Varietal differences of heading dates due to temperature were not great. but in general the heading dates of varieties were faster under high temperature than under low temperature. 7. Earliness of heading dates was due to partial dominance effect of genes involved in any condition. The degree of dominance was greater under short day than under long day treatment. 8. The varietal differences of heading date under high temperature and long day were due to earliness or narrow sense (response to long day) of varieties. The degree of dominance was greater for Yecora F70, spring type than for other winter type of varieties. No differences or less differences of degree of dominance was found among winter type of varieties. The estimated number of effective factor concerned in the earliness of narrow sense was one pair of allele with minor genes. 9. The insensitivity of varieties to short day treatment in heading dates was due to single dominant gene effect. Under the low temperature the sensitivity of varieties to short day treatment was less apparent. 10. The earliness of short day and long day (earliness of narrow sense) sensitivities of varieties appearea to be due to partial dominance of earliness over lateness. In strict sense, the degree of the dominance should be distinguished. 11. Dominant gene effects were found for the thermo-sensitivity of varieties, and the effect was less, significant than the earliness in narrow sense. 12. One pair of allele, ee and EE, for photosensitivity was responsible for the difference in the heading dates between Changkwang and Suke #169. Two pairs of alleles, ee, enen and EE, EnEn. appeared to be responsible for the difference between Changkwang and Yecora F70. The effects of EE and EnEn were, additive to the earliness and the effects of EE were greater than EnEn under short day. However, the effects of EE were not evident in long day but the effects of EnEn were observed in long day. 13. Two pairs of dominant alleles for the earliness were estimated from the analysis of F$_1$ diallels in the field but the effects of these alleles in F$_2$ were not apparent due to low temperature and short day treatment in early part of growth and high temperature and long day treatment in later part of growth. The F$_2$ population shows continuous variation due to environmental effects and due to other minor gene effects. 14. The heritabilities for heading dates were ranged from 0.51 to 0.72, indicating that the selection in early generation might be effective. The extent of heritability for heading dates varied with environments; higher magnitude of heritability was obtained in short day treatment and high temperature compared with long day and low temperature treatments. The heritabilities of heading date due to response to short day were 0.86 in high temperature and 0.76 in low temperature. The heritabilities of heading date due to temperature were not significantly high. 15. The correlation coefficients of heading dates to the number of grains per spike, weight of 1, 000 grains. and grain yield were positive and high, indicating the difficulties of selections of high yielding lines from early population. But no significant correlation coefficient was obtained between the earliness and the number of spikes, indicating the effective selection for high tillering from early varieties for high yielding.

• Korean Journal of Agricultural Science
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• v.4 no.2
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• pp.254-282
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• 1977

To obtain information on the inheritance of the quantitative characters related with the vegetative and reproductive growth of rice, the $F_1$ seeds were obtained in 1974 from the all possible combinations of the diallel crosses among five leading rice varieties : Nongbaek, Tongil, Palgueng, Mangyeong and Gimmaze. The $F_1$'s including reciprocals and parents were grown under the standard cultivation method at Chungnam Provincial Office of Rural Development in 1975. The arrangement of experimental plots was randomized block design with 3 replications and 12 characters were used for the analysis. Analytical procedure for genetic components was followed the Griffing's and Hayman's methods and the results obtained are summarized as follows. 1. In all $F_1$'s of Tongil crosses, the longer duration to heading was due to dominant effect of Tongil and each $F_1$ showed high heterosis in delaying the heading time. It was assumed that non-allelic gene action besides dominant gene effect might be involed in days to heading character. However, in all $F_1$'s from the crosses among parents excluding Tongil the shorter duration was due to dominant gene action and the degree of dominance was partial, since dominance effects were not greater than the additive effect. The non-allelic gene interaction was not significant. Considering the results mentioned above, it was regarded that there were two kinds of Significantly different genetic systems in the days to heading. 2. The rate of heterosis was significantly different depending upon the parents used in the crosses. For instance, the $F_1$'s from Togil cross showed high rate of heterosis in longer culm. Compared to short culm, longer culm was due to recesive gene action and short culm was due to recesive gene action. The dominant gene effect was greater than the additive gene effect in culm length. The narrow sense of heretability was very low and the maternal effects as well as reciprocal effects were significantly recognized. 3. The lenght of the of the uppermost internode of each $F_1$ plant was a little lorger than these of respective parental means or same as those of parents having long internodes, indicating partial dominance in the direction of lengthening the uppermost internodes. The additive gene effects on the uppermost internode was greater than the dominance gene effect. The narrow as well as broad sense of heritabilities for the character of the uppermost internode were very high. There were significant maternal and reciprocal effect in the uppermost internode. 4. The gene action for the flag leaf angle was rather dominance in a way of getting narrower angle. However, in the Palgueng combinations, heterosis of $F_1$ was observed in both narrow and wide angles of the flag leaf. The dominant effects were greater than the additive effects on the flag leaf angle. There were observed also a great deal of non-allelic gene interacticn on the inheritance of the flag leaf angle. 5. Even though the dominant gene action on the length and width of flag leaf was effective in increasing the length or width of the flag leaf, there were found various degrees of hetercsis depending upon the cross combination. Over-dominant gene effect were observed in the inheritance of length of the flag leaf, while additive gene effects was found in the inheritance of the width of the flag leaf. High degree of heretabilities, either narrow or broad sense, were found in both length and width of the flag leaf. No maternal and reciprocal effect were found in both characters. 6. When Tongil was used as one parent in the cross, the length of panicle of $F_1$'s was remarkedly longer than that of parents. In other cross comination, the length of panicle of $F_1$'s was close to the parental mean values. Rather greater dominent gene effect than additive gene effect was observed in the inheritance of panicle length and the dominant gene was effective in increasing the panicle length. 7. The effect of dominant genes was effective in increasing the number of panicles. The degree of heterosis was largely dependent on the cross combination. The effect of dominant gene in the inheritance of panicle number was a little greater than that of additive genes, and the inheritance of panicle number was assumed to be due to complete dominant gene effects. Significantly high maternal and reciprocal effects were found in the character studied. 8. There were minus and plus values of heterosis in the kernel number per panicle depending upon the cross combination. The mean dominant effect was effective in increasing the kernel number per panicle, the degree of dominant effect varied with cross combination. The dominant gene effect and non-allelic gene interaction were found in the inheritance of the kernel number per panicle. 9. Genetic studies were impossible for the maturing ratio, because of environmental effects such as hazards delaying heads. The dominant gene effect was responsible for improving the maturing ratio in all the cross combinations excluding Tongil 10. The heavier 1000 grain weight was due to dominant gene effects. The additive gene effects were greater than the dominant gene effect in the 1000 grain weight, indicating that partial dominance was responsible for increasing the 1000 grain weight. The heritabilites, either narrow or broad sense of, were high for the grain weight and maternal or reciprocal effects were not recognized. 11. When Tongil was used as parent, the straw weight was showing high heterosis in the direction of increasing the weight. But in other crosses, the straw weight of $F_1$'s was lower than those of parental mean values. The direction of dominant gene effect was plus or minus depending upon the cross combinations. The degree of dominance was also depending on the cross combination, and apparently high nonallelic gene interaction was observed.

• Korean Journal of Soil Science and Fertilizer
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• v.18 no.4
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• pp.359-365
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• 1985

The four rice varieties, Kwanak, Nongbaek, Pungsan and Nampung-byo were cultivated to examine the growth conditions and grain yield in a Gyuam SiL paddy field irrigated with cold water around $17^{\circ}C$. Water temperatures for various distances from the inlet were measured. The results were summerized as follows. 1. Culm length, panicle exertion, diameter of the 3rd internode stem, heading date, fertilization rate, ripeness rate, no. of grains per panicle and grain yield were sensitive to water temperature. Panicle length, flag-leaf length, diameter of spike-neck and no. of panicles, however, were negligibly sensitive and there were no differences among varieties. 2. Elongations of the 2nd and 3rd internode steam were unsensitive to water temperature. 1st internode elongation and 4th internode development, however, were sensitive which was major factor in the culm length. 3. Ratios of partial dry weight to total dry weight were closely correlated with water temperature, Therefore, dry weight of grain was increased with water temperature while that of plant and root decreased. 4. Chlorophyll contents were decreased with the increment of water temperature and the highest at $20^{\circ}C$. 5. There was no grain yield at $17^{\circ}C$, Increases of grain yield to water temperature per unit were order at Pungsan > Kwanak > Nongbaek > Nampung. 6. The critical temperature in grain yield was $21^{\circ}C$. Optimum temperatures of Japonica ${\times}$ Indica types were higher than those of Japonica types.