• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.543-558
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• 2002

We investigate the fragmentation process developed by Kolmogorov and Filippov, which has been studied extensively by many physicists (independently for some time). One of the most interesting phenomena is the shattering (or disintegration of mass) transition which is considered a counterpart of the well known gelation phenomenon in the coagulation process. Though no masses are subtracted from the system during the break-up process, the total mass decreases in finite time. The occurrence of shattering transition is explained as due to the decomposition of the mass into an infinite number of particles of zero mass. It is known only that shattering phenomena occur for some special types of break-up rates. In this paper, by considering the n-particle system of stochastic fragmentation processes, we find general conditions of the rates which guarantee the occurrence of the shattering transition.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.855-867
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• 2005

Shattering or disintegration of mass is a well known phenomenon in fragmentation processes first introduced by Kol­mogorov and Filippop and extensively studied by many physicists. Though the mass is conserved in each break-up, the total mass decreases in finite time. We investigate this phenomenon in the n particle system. In this system, shattering can be interpreted such that, in uniformly bounded time on n, order n of mass is located in order o(n) of clusters. It turns out that the tagged particle processes associated with the systems are useful tools to analyze the phenomenon. For the newly defined stochastic shattering based on the above ideas, we derive far sharper conditions of fragmentation kernels which guarantee the occurrence of such a phenomenon than our previous work [9].

• KOREAN JOURNAL OF CROP SCIENCE
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• v.36 no.4
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• pp.370-381
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• 1991

In Nongsajiksul, rice varieties were not appeared but varieties groups were introduced and divided according to growth periods, or 'Sun, Gang, Na'or introduced names of some of local varieties. However, the weather conditions for rice culture in Korea were characterized by 'early drought and late flooding', and winds and rains in summer, so that rice safe harvest by avoiding these disasters was the most important. Thus, development of rice varieties after the 15th century has gradually been adapted for ‘early-seeding and early-harvesting’, and for disaster tolerance. With time, rice varieties, which were early maturing, had awned, had color on panicles, had tolerance for grain shattering, had tolerance for winds, and had good responses to fertilizers, were grown in large areas.rown in large areas.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.37 no.3
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• pp.299-303
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• 1992

Methods for harvesting and storage of rice were also originally introduced from the ancient China like other practices of agricultural techniques. Thus, optimum time or rice harvesting was adopted by appropriate draining to prevent the losses, and efficient tools were utilized for harvesting and manufacturing. In addition, our unique and original techniques for rice storage were learned and handed down, which prevented winds and rains, and allowed good ventilation. In the 15th and 16th centuries, treatment of smartweed extracts as emphasized to prevent insect damage for stored barley and rice cutting immediately at harvest was encouraged to prevent shattering of rice grains. In the 18th and 19th centuries, means for prevention of damages by water, insects and rats when grains stored in the field were suggested. Also, studies for ecology of various rice cultivars and storage techniques for a long period of time were necessarily emphasized to assume the optimum time of harvest regionally and to cooperatively work timely.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.37 no.1
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• pp.104-115
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• 1992

The rice culture techniques included 'Jodosukyungbeob'(旱稻水耕法 : culture techniques of early-ripening paddy rice), 'Mandosukyungbeob' (晩稻水耕法) : culture techniques of late-Ripening paddy rice 'Handobeob'(旱稻＆lt;山稻＆gt;法 : culture techniques of upland rice), 'Myojongbeob'(苗種法 : culture techniques of paddy rice by transplanting), 'Kunangbeob'(乾秧法 : culture techniques of rice by transplanting which rears seeding in dry paddy) and 'Sudogunpanongbeob'(水稻乾播農法 : culture techniques of paddy rice seeding in dry field). Especially, 'Kunangbeob' and 'Sudogunpanongbeob' were originally developed in Korea as seen in 1600s(Kyoungje : 經濟) and early 1800s (Yoji : 要旨). In 'Jodosukyungbeob' it took 9 days for seed dipping, water-sprouting and prevent damage by birds, each for 3 days in China, but in Korea seed dipping in water took 3 days and the rest of the procedures were flexibly established. In matured soils, practices were fall plowing right after harvest, recognition of effective tillering and additional fertilization use of human manure, and stimulation of sprouting by lime application. The unique culture techniques adequate for Korean situations were practiced, which included weed control after draining accurately for 3 to 4 times, draining at mid season for improving wind and drought tolerance, rice harvesting at appropriate time for preventing grain shattering, and seeding in rows. 'Mandosukyungbeob' was improved techniques contrast to those of China, and the major contents were selection of proper varieties, good stand establishment by seeding high rates, induction of vigorous tillers, and adoption of 'Jokjongbeob'(足種法 : seeding method by foot). Also, one of the most prominent rice cultures by our ancestors was 'Kunpanongbeob' that was systemized form habitual practice of Pyongan Province. The unique technique actualized was 'Hando [旱稻(山稻)]' culture technique which was the combinations of 'Jokjongbeob', root stimulation method, and disaster-tolerant mixture cropping with adoptation of variety theory, although it was originated from China. The transplanting techniques has come before 'Jikseol'($\ulcorner$直說$\lrcorner$) and its merits were sufficiently realized. However, this method was basically prohibited from the early Chosun dynasty because extremely bad harvest was expected under drought conditions and insufficient conditions of water storage. But, it was permitted in the areas that contained water all the times and in case of large-scale farming especially. Most of rice culture was transplanted in the end of the Chosun dynasty because transplanting was continuously spreaded in the three southern provinces of Korea. Under these circumstances, transplanting technique was improved from the early to the end of the Chosun dynasty by weed control, fertilizing, water management, and quadratic transplanting. Based on these techniques, agricultural productivity was improved 5 times by that time. 'Kunpanongbeob' was created and developed properly for Korean conditions that is dry in early season and flooding in late season. This was successively developed and established into transplanting technique of nursery seedling.