• Journal of Biosystems Engineering
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• v.6 no.1
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• pp.60-72
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• 1981

This study was carried out to find out the effects of the sheaf size of paddy harvested by the binders on the threshing performance, load characteristics and power requirement of an auto-feed thresher. The results of the study are summarized as follows: 1. The seperating performance of the thresher appeared to be satisfactory for all the sheaf sizes although the amount of rubbishes and empty grains slightly increased with the sheaf size of paddy. 2. There was no significant difference in grain output quality of the thresher among the three sheaf sizes. However, the amount of grains left unthreshed increased with the sheaf size. In the case of the largest sheaf size with the feed rate of 780kg/h, it exceeded the limit set by the national inspection regulations. 3. The position of the feed-chain rail gave a significant effect on the power requirement of the thresher. At the feed rate of 780kg/h, the net power required to convey sheafs through the feed chain was in the range of 0.37 to 0.50 PS for the middle and lowest position of feed-chain rail, and there was no significant difference among the sheaf sizes. At the highest position, however, it appeared that the smallest sheaf required more power than the others. The net power requirements at this position were 1.03, 0.59. 0.65 PS for the smallest, medium and largest sheafs respectively. 4. The torques of both the thresher and the engine shaft increased with the feed rate and were not affected by the sheaf size for the lower two feed rates of 520 and 780kg/h. At the highest feed rate of 1,040 kg/h, however, they were affected by the sheaf size. In this case, the medium sheaf size gave lower values than the others. 5. The variations in the thresher and the engine torque increased with the feed rate and were not affected by the sheaf size for the feed rate of 520kg/h. At the feed rate of 780kg/h, however, they increased with sheaf size. And at the feed rate of 1,040 kg/h, the torque variations increased greatly for all the sheaf sizes due to an over-load operating condition. 6. It appeared that the average and maximum power requirements of the thresher increased with the feed rate. But, there was no significant difference in power requirement among the sheaf sizes for the lower two feed rates. 7. The threshing efficiency of the thresher was in the range of 214-249 kg/ps.h with the feed rates of 520 and 780 kg/h, and it was not affected by both the sheaf size and the feed rate. At the feed rate of 1,040 kg/h, however, it decreased to as low as 171-174 kg/ps.h because of a sudden increase in power requirement. 8. The average power requirements of the engine were slightly higher than those of the thresher due to the slippage of flat belt between the thresher and engine. It appeared that power transmission from the engine to the thresher was maintained properly since slippages were moderately low with the range of 2.78 to 6.51% throughout the tests. 9. The specific fuel consumption of the engine (diesel 8PS) decreased as the feed rate increased. However, there was no significant reduction in specific fuel consumption as the feed rate increased above 780 kg/h.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.1-15
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• 2013

In this paper, we study a sheaf-theoretic analysis of the convolution algebra on quiver varieties. As by-products, we reinterpret the results of H. Nakajima. We also produce a refined form of the BBD decomposition theorem for quiver varieties. Finally, we study a construction of highest weight modules through constructible functions.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.593-609
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• 2002

The order of speciality of an ample invertible Sheaf L on a curve is the least integer m so that $L^{ m}$ is nonspecial. There is a reasonable upper bound of the order of speciality for a simple invertible sheaf in terms of its degree and projective dimension. We study the case where it reaches the upper bound. Moreover we for mulate Castelnuovo's genus bound involving the order of speciality.ality.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.13-18
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• 1980

모든 기호(記號)는 G.E Bredon의 저(著) Sheaf Theory의 기호(記號)를 따른다. A가 torsion free이며 elementary sheaf이라 하자. 그리고 L을 injective L-module이라 하자 $dim_{\varphi}X<{\infty}$이라면 support의 $family{\varphi}$와 locally subset z에 대하여 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{\varphi}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-p}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ 이며 support의 family c와 compact subset z에 대하여도 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{c}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-y}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ A가 elementary이면 locally closed z와 z에서 closed인 $z^{\prime}$ 그리고 $z^{\prime\prime}=z-z^{\prime}$에 대하여 exact sequence ⋯⋯${\rightarrow}H^{z^{\prime}}_{p}\;(X:A){\rightarrow}H^{z}_{p}(X:A){\rightarrow}H^{z^{\prime\prime}}_{p}\;(X:A){\rightarrow}$⋯⋯ 가 존재(存在)한다.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.187-198
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• 2021

This work presents an exposition of both the internal structure of derived category of an abelian category D^*(𝓐) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D^*(𝓐) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D^*(𝓐) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.

• East Asian mathematical journal
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• v.16 no.1
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• pp.27-31
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• 2000

• East Asian mathematical journal
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• v.17 no.2
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• pp.339-348
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• 2001

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.623-669
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• 2018

In Donaldson-Thomas theory, moduli spaces are locally the critical locus of a holomorphic function defined on a complex manifold. In this paper, we develop a theory of critical virtual manifolds which are the gluing of critical loci of holomorphic functions. We show that a critical virtual manifold X admits a natural semi-perfect obstruction theory and a virtual fundamental class $[X]^{vir}$ whose degree $DT(X)=deg[X]^{vir}$ is the Euler characteristic ${\chi}_{\nu}$(X) weighted by the Behrend function ${\nu}$. We prove that when the critical virtual manifold is orientable, the local perverse sheaves of vanishing cycles glue to a perverse sheaf P whose hypercohomology has Euler characteristic equal to the Donaldson-Thomas type invariant DT(X). In the companion paper, we proved that a moduli space X of simple sheaves on a Calabi-Yau 3-fold Y is a critical virtual manifold whose perverse sheaf categorifies the Donaldson-Thomas invariant of Y and also gives us a mathematical theory of Gopakumar-Vafa invariants.

• Journal of the Mineralogical Society of Korea
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• v.9 no.2
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• pp.64-70
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• 1996

Early weathering products of anorthosite were investigated by using scanning electron microscopy in order to trace the development of halloysite particles and aggregates. Tiny short tubes or spheres precipitate on the plagioclase surface in the initial stage of weathering and form the compact globular aggregates. With continued growth, several globules are coalesced into wrinkled halloysite aggregates, and short tubes or spheres in globules grow into long tubes forming sheaf-like aggregates. Particle shape of halloysite varies with changing supersaturation degree of weathering solution, and determines the morphology of halloysite aggregates.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1147-1165
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• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.