• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.35-54
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• 2007

Let $M_c$ = M(2, 0, c) be the moduli space of O(l)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0\;and\;c_2=c$ on a K3 surface X, where O(1) is a generic ample line bundle on X. When $c=2n\geq4$ is even, $M_c$ is a singular projective variety equipped with a holomorphic symplectic structure on the smooth locus. In particular, $M_c$ has trivial canonical divisor. In [22], O'Grady asks if there is any symplectic desingularization of $M_{2n}$ for $n\geq3$. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\geq3$. This obviously implies that there is no symplectic desingularization.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.359-369
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• 2000

Let X be an integral Gorenstein projective curve with g:=pa(X) $\geq$ 3. Call $G^r_d$ (X,**) the set of all pairs (L,V) with L$\epsilon$Pic(X), deg(L) = d, V $\subseteq$ H^0$(X,L), dim(V) =r+1 and V spanning L. Assume the existence of integers d, r with 1 $\leq$ r$\leq$ d $\leq$ g-1 such that there exists an irreducible component, , of $G^r_d$(X,**) with dim($\Gamma$) $\geq$ d - 2r and such that the general L$\geq$$\Gamma$ is spanned at every point of Sing(X). Here we prove that dim( ) = d-2r and X is hyperelliptic.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.279-291
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• 2024

In this paper, we investigate a few strategies to construct Ulrich bundles of small ranks over smooth fourfolds in ℙ⁵, with a focus on the case of special quartic fourfolds. First, we give a necessary condition for Ulrich bundles over a very general quartic fourfold in terms of the rank and the Chern classes. Second, we give an equivalent condition for Pfaffian fourfolds in every degree in terms of arithmetically Gorenstein surfaces therein. Finally, we design a computer-based experiment to look for Ulrich bundles of small rank over special quartic fourfolds via deformation theory. This experiment gives a construction of numerically Ulrich sheaf of rank 4 over a random quartic fourfold containing a del Pezzo surface of degree 5.

• Journal of Biosystems Engineering
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• v.15 no.2
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• pp.110-122
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• 1990

This study was undertaken to develop the feed rate control system for the head feed thresher by making use of the microprocessor and to evaluate the response of the system to a various threshing conditions. The control unit was composed of one-board microcomputer. The speed of the wet-paddy feeding chain was controlled by dc moter with PI controller. It was used the adaptive control method to maintain the constant feed rate regardless of the fed rice varieties. The sliding type potentiometer was used as the feed rate sensor, which was attached on the sheaf-holding apparatus. The mathematical models of the system components were derived and computer simulation was developed for investigating the parameters affecting on control performance and for estimating the response of the system. A one-board microcomputer-based feed rate control system developed in this study was properly functioned and assessed as adequate for the feed rate control system of the head feed thresher. Based on the simulation for the bundle feed, it was anticipated that the lower setting value of the cylinder speed(RL) is to be set higher than the limiting operational speed. In addition, the higher setting value of the cylinder speed(RH) is to be set lower than the limiting cylinder speed for threshing. The computer simulation for the continuous spread feed showed that the lower the setting value of straw layer thickness(LL) was set, the shorter the correction time. However, if too low LL may be established, the feed rate could not reach to its desired rate.

• Korean Journal of Medicinal Crop Science
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• v.12 no.6
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• pp.519-522
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• 2004

'Sanggang' was a new adlay cultivar which was developed from the three way crosses of $(Hukuhane\;{\times}\;Suwon-6)\;{\times}$ Suwon-6 at the Northern Agricultural Research Station, Gyunggido ARES. This cultivar had green sheaf, dark-green leaf, green culm, milky white silk and darkbrown seedcoat. Sanggang shortened 10 days of heading date and 12 days of ripening time compared with Yulmoo 1. In the yield's conponent of Sanggang, the number of grains was by 56 grains less but ripening rate and 1,000 grain weight were higher by 6.5% and 20.1 g compared with Yulmoo 1, respectively. This cultivar showed moderate resistance to leaf blight. The yield of Sanggang was about 313 kg/10a of unpolished grain at ordinary cultivation. This cutivar showed about 17% and 27% higher yield in Yonchon Gyeonggi province and Cheongju Chungbuk province compared with the check variety respectively. This cultivar was adaptable to mono cropping in central and northern region of Korea.