• Title/Summary/Keyword: Strong law of large number

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Weak convergence for weighted sums of level-continuous fuzzy random variables (수준 연속인 퍼지 랜덤 변수의 가중 합에 대한 약 수렴성)

  • Kim, Yun-Kyong
    • Journal of the Korean Institute of Intelligent Systems
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    • v.14 no.7
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    • pp.852-856
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    • 2004
  • The present paper establishes a necessary and sufficient condition for weak convergence for weighted sums of compactly uniformly integrable level-continuous fuzzy random variables as a generalization of weak laws of large numbers for sums of fuzzy random variables.

ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF FUZZY RANDOM SETS

  • Joo, Sang-Yeol;Kim, Yun-Kyong;Kwon, Joong-Sung
    • Proceedings of the Korean Reliability Society Conference
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    • 2004.07a
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    • pp.177-182
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    • 2004
  • In this paper, we establish some results on almost sure convergence for sums and weighted sums of uniformly integrable fuzzy random sets taking values in the space of upper-semicontinuous fuzzy sets in $R^{p}$.

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ON LIMIT BEHAVIOURS FOR FELLER'S UNFAIR-FAIR-GAME AND ITS RELATED MODEL

  • An, Jun
    • Journal of the Korean Mathematical Society
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    • v.59 no.6
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    • pp.1185-1201
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    • 2022
  • Feller introduced an unfair-fair-game in his famous book [3]. In this game, at each trial, player will win 2k yuan with probability pk = 1/2kk(k + 1), k ∈ ℕ, and zero yuan with probability p0 = 1 - Σk=1 pk. Because the expected gain is 1, player must pay one yuan as the entrance fee for each trial. Although this game seemed "fair", Feller [2] proved that when the total trial number n is large enough, player will loss n yuan with its probability approximate 1. So it's an "unfair" game. In this paper, we study in depth its convergence in probability, almost sure convergence and convergence in distribution. Furthermore, we try to take 2k = m to reduce the values of random variables and their corresponding probabilities at the same time, thus a new probability model is introduced, which is called as the related model of Feller's unfair-fair-game. We find out that this new model follows a long-tailed distribution. We obtain its weak law of large numbers, strong law of large numbers and central limit theorem. These results show that their probability limit behaviours of these two models are quite different.

J-integral and fatigue life computations in the incremental plasticity analysis of large scale yielding by p-version of F.E.M.

  • Woo, Kwang S.;Hong, Chong H.;Basu, Prodyot K.
    • Structural Engineering and Mechanics
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    • v.17 no.1
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    • pp.51-68
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    • 2004
  • Since the linear elastic fracture analysis has been proved to be insufficient in predicting the failure of strain hardening materials, a number of fracture concepts have been studied which remain applicable in the presence of plasticity near a crack tip. This work thereby presents a new finite element model to predict the elastic-plastic crack-tip field and fatigue life of center-cracked panels(CCP) with ductile fracture under large-scale yielding conditions. Also, this study has been carried out to investigate the path-dependence of J-integral within the plastic zone for elastic-perfectly plastic, bilinear elastic-plastic, and nonlinear elastic-plastic materials. Based on the incremental theory of plasticity, the p-version finite element is employed to account for the accurate values of J-integral, the most dominant fracture parameter, and the shape of plastic zone near a crack tip by using the J-integral method. To predict the fatigue life, the conventional Paris law has been modified by substituting the range of J-value denoted by ${\Delta}J$ for ${\Delta}K$. The experimental fatigue test is conducted with five CCP specimens to validate the accuracy of the proposed model. It is noted that the relationship between the crack length a and ${\Delta}K$ in LEFM analysis shows a strong linearity, on the other hand, the nonlinear relationship between a and ${\Delta}J$ is detected in EPFM analysis. Therefore, this trend will be depended especially in the case of large scale yielding. The numerical results by the proposed model are compared with the theoretical solutions in literatures, experimental results, and the numerical solutions by the conventional h-version of the finite element method.

A study on the Regulatory Environment of the French Distribution Industry and the Intermarche's Management strategies

  • Choi, In-Sik;Lee, Sang-Youn
    • The Journal of Industrial Distribution & Business
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    • v.3 no.1
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    • pp.7-16
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    • 2012
  • Despite the enforcement of SSM control laws such as 'the Law of Developing the Distribution Industry (LDDI)' and 'the Law of Promoting Mutual Cooperation between Large and Small/medium Enterprises (LPMC)' stipulating the business adjustment system, the number of super-supermarkets (SSMs) has ever been expanding in Korea. In France, however, Super Centers are being regulated most strongly and directly in the whole Europe viewing that there is not a single SSM in Paris, which is emphasized to be the outcome from French government's regulation exerted on the opening of large scale retail stores. In France, the authority to approve store opening is deeply centralized and the store opening regulation is a socio-economic regulation driven by economic laws whereas EU strongly regulates the distribution industry. To control the French distribution industry, such seven laws and regulations as Commission départementale d'urbanisme commercial guidelines (CDLIC) (1969), the Royer Law (1973), the Doubin Law (1990), the Sapin Law (1993), the Raffarin Law (1996), solidarite et renouvellement urbains (SRU) (2000), and Loi de modernisation de l'économie (LME) (2009) have been promulgated one by one since the amendment of the Fontanet guidelines, through which commercial adjustment laws and regulations have been complemented and reinforced while regulatory measures have been taken. Even in the course of forming such strong regulatory laws, InterMarche, the largest supermarket chain in France, has been in existence as a global enterprise specialized in retail distribution with over 4,000 stores in Europe. InterMarche's business can be divided largely into two segments of food and non-food. As a supermarket chain, InterMarche's food segment has 2,300 stores in Europe and as a hard-discounter store chain in France, Netto has 420 stores. Restaumarch is a chain of traditional family restaurants and the steak house restaurant chain of Poivre Rouge has 4 restaurants currently. In addition, there are others like Ecomarche which is a supermarket chain for small and medium cities. In the non-food segment, the DIY and gardening chain of Bricomarche has a total of 620 stores in Europe. And the car-related chain of Roady has a total of 158 stores in Europe. There is the clothing chain of Veti as well. In view of InterMarche's management strategies, since its distribution strategy is to sell goods at cheap prices, buying goods cheap only is not enough. In other words, in order to sell goods cheap, it is all important to buy goods cheap, manage them cheap, systemize them cheap, and transport them cheap. In quality assurance, InterMarche has guaranteed the purchase safety for consumers by providing its own private brand products. InterMarche has 90 private brands of its own, thus being the retailer with the largest number of distributor brands in France. In view of its IT service strategy, InterMarche is utilizing a high performance IT system so as to obtainas much of the market information as possible and also to find out the best locations for opening stores. In its global expansion strategy of international alliance, InterMarche has established the ALDIS group together with the distribution enterprises of both Spain and Germany in order to expand its food purchase, whereas in the non-food segment, it has established the ARENA group in alliance with 11 international distribution enterprises. Such strategies of InterMarche have been intended to find out the consumer needs for both price and quality of goods and to secure the purchase and supply networks which are closely localized. It is necessary to cope promptly with the constantly changing circumstances through being unified with relevant regions and by providing diversified customer services as well. In view of the InterMarche's positive policy for promoting local partnerships as well as the assistance for enhancing the local economic structure, implications are existing for those retail distributors of our country.

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A probabilistic study of the sex ratio at birth related to son preference (남아선호사상에 기반한 출생 성비에 관한 확률론적 고찰)

  • Kim, Yun-Soo;Choi, Eun-Sun;Cha, Kyung-Joon
    • Journal for History of Mathematics
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    • v.21 no.4
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    • pp.79-86
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    • 2008
  • The sex ratio at birth of South Korea is exceeding the natural sex ratio at birth, which is estimated to be about 105. One of the reasons of high sex ratio at birth is due to sex-selective abortion which is caused by strong son preference. The main objective of this study is to identify whether the families which are trying to bear children only until they acquire one son contribute to high sex ratio at birth. As a result, we obtain the theorem that if the number of such families diverge, the sex ratio at birth converges to the natural sex ratio almost surely. Therefore, we conclude that the existence of the families which are trying to bear children only until they receive one son does not affect the sex ratio at birth.

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An Analysis of the Relationship between Climacteric Symptoms and Management of Menopause in Middle-aged Women (일 지역 중년여성의 폐경증상과 폐경관리와의 관계에 대한 연구)

  • Song, Ae-Ri
    • The Journal of Korean Academic Society of Nursing Education
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    • v.7 no.2
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    • pp.308-322
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    • 2001
  • The purpose of this study was to investigate the relationship between climacteric symptoms and management of menopause of middle -aged women. The subjects of this study were 261 women(40 to 60 years old). Data were collected from Jun. 1 to Jul. 15, 2001 by a structured questionnaire. The instruments employed were : 1) The Climacteric Symptoms Scale developed by Aeri Song and Eun soon Chung(1998). 2) The Management of Menopause Scale developed by Aeri Song(1997). The data were analyzed by the SPSS p.c. program using t-test, ANOVA and Pearson correlation coefficient. The results of the study were as follows : 1. Mean score of climacteric symptoms was $2.18{\pm}0.39$(Maximum 4, Minimum 1). The mean scores among the categories of climacteric symptoms, in descending order, were : a) physical and physiological reactions ($2.62{\pm}0.53$), b) social and family relationships ($2.23{\pm}0.50$), c) psychiatric and psychological reactions ($2.08{\pm}0.49$), d) relationship with sexual partner($1.73{\pm}0.54$), e) genitourinary reactions ($1.72{\pm}0.55$). 2. Mean score of management of menopause was $1.79{\pm}0.45$ (Maximum 4, Minimum 1). The mean scores among the categories of management of menopause, in descending order, were : a) dietary management($2.57{\pm}0.52$), b) self control ($2.24{\pm}0.57$), c) management of exercise and physical activity($2.14{\pm}0.75$), d) management of sex life($1.71{\pm}0.47$), e) management of professional health maintenance($1.61{\pm}0.59$). 3. There were statistically significant differences in the score of middle-aged women's self reported climacteric symptoms according to : a) occupation (t=-2.79, p<0.001) b) marriage state (t=-2.29, p<0.05) c) age of menarche (F=4.66, p<0.001) d) method of Sanhujori (post natal care & treatment) (F=4.22, p<0.001) e) hormone replacement therapy (t=-3.09, p<0.05). From the above statistics, several significant findings were noted : a) There were more climacteric symptoms from those who were unemployed, those who had no partner or were divorced and those who started a menarche earlier. b) There were less climacteric symptoms reported from those on hormone replacement therapy and those who followed their parents or parents-in-law advice regarding Sanhujori (postnatal care) 4. There were statistically significant differences in the score of middle-aged women's self reported management of menopause according to : The educational background (F=7.63, p<0.001), religion (F=3.74, p<0.001), income (F=3.65, p<0.001), number of parity (F=4.87, p<0.001), method of Sanhujori(postnatal care) (F=5.73, p<0.001), period of Sanhujori (postnatal care) (F=2.81, p<0.05), hormone replacement therapy (t=3.81, p<0.001). Women with higher educational background, strong religion, higher income, large number of parity, managed their post natal care well, were on HRT, managed their menopause significantly better than the others who took part in the survey. 5. It will be noted from the above that women's degree of climacteric symptoms showed a negative correlation to the management of menopause(r=-0.2146, p<0.001). The findings shown above suggest the need to develop a variable management of menopause, in order to improve climacteric symptoms of middle-aged women. It is hoped that the above findings will stimulate more detailed research into this matter, and thereby enable guidance to be given to women going through the menopause to cope with it in a less stressful way.

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A Study on the Forest Land System in the YI Dynasty (이조시대(李朝時代)의 임지제도(林地制度)에 관(關)한 연구(硏究))

  • Lee, Mahn Woo
    • Journal of Korean Society of Forest Science
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    • v.22 no.1
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    • pp.19-48
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    • 1974
  • Land was originally communized by a community in the primitive society of Korea, and in the age of the ancient society SAM KUK-SILLA, KOKURYOE and PAEK JE-it was distributed under the principle of land-nationalization. But by the occupation of the lands which were permitted to transmit from generation to generation as Royal Grant Lands and newly cleared lands, the private occupation had already begun to be formed. Thus the private ownership of land originated by chiefs of the tribes had a trend to be gradually pervaded to the communal members. After the, SILLA Kingdom unified SAM KUK in 668 A.D., JEONG JEON System and KWAN RYO JEON System, which were the distribution systems of farmlands originated from the TANG Dynasty in China, were enforced to established the basis of an absolute monarchy. Even in this age the forest area was jointly controlled and commonly used by village communities because of the abundance of area and stocked volume, and the private ownership of the forest land was prohibited by law under the influence of the TANG Dynasty system. Toward the end of the SILLA Dynasty, however, as its centralism become weak, the tendency of the private occupancy of farmland by influential persons was expanded, and at the same time the occupancy of the forest land by the aristocrats and Buddhist temples began to come out. In the ensuing KORYO Dynasty (519 to 1391 A.D.) JEON SI KWA System under the principle of land-nationalization was strengthened and the privilege of tax collection was transferred to the bureaucrats and the aristocrats as a means of material compensation for them. Taking this opportunity the influential persons began to expand their lands for the tax collection on a large scale. Therefore, about in the middle of 11th century the farmlands and the forest lands were annexed not only around the vicinity of the capital but also in the border area by influential persons. Toward the end of the KORYO Dynasty the royal families, the bureaucrats and the local lords all possessed manors and occupied the forest lands on a large scale as a part of their farmlands. In the KORYO Dynasty, where national economic foundation was based upon the lands, the disorder of the land system threatened the fall of the Dynasty and so the land reform carried out by General YI SEONG-GYE had led to the creation of ensuing YI Dynasty. All systems of the YI Dynasty were substantially adopted from those of the KORYO Dynasty and thereby KWA JEON System was enforced under the principle of land-nationalization, while the occupancy or the forest land was strictly prohibited, except the national or royal uses, by the forbidden item in KYEONG JE YUK JEON SOK JEON, one of codes provided by the successive kings in the YI Dynasty. Thus the basis of the forest land system through the YI Dynasty had been established, while the private forest area possessed by influential persons since the previous KORYO Dynasty was preserved continuously under the influence of their authorities. Therefore, this principle of the prohibition was nothing but a legal fiction for the security of sovereign powers. Consequently the private occupancy of the forest area was gradually enlarged and finally toward the end of YI Dynasty the privately possessed forest lands were to be officially authorized. The forest administration systems in the YI Dynasty are summarized as follows: a) KEUM SAN and BONG SAN. Under the principle of land-nationalization by a powerful centralism KWA JEON System was established at the beginning of the YI Dynasty and its government expropriated all the forests and prohibited strictly the private occupation. In order to maintain the dignity of the royal capital, the forests surounding capital areas were instituted as KEUM SAN (the reserved forests) and the well-stocked natural forest lands were chosen throughout the nation by the government as BONG SAN(national forests for timber production), where the government nominated SAN JIK(forest rangers) and gave them duties to protect and afforest the forests. This forest reservation system exacted statute labors from the people of mountainious districts and yet their commons of the forest were restricted rigidly. This consequently aroused their strong aversion against such forest reservation, therefore those forest lands were radically spoiled by them. To settle this difficult problem successive kings emphasized the preservation of the forests repeatedly, and in KYEONG KUK DAI JOEN, the written constitution of the YI Dynasty, a regulation for the forest preservation was provided but the desired results could not be obtained. Subsequently the split of bureaucrats with incessant feuds among politicians and scholars weakened the centralism and moreover, the foreign invasions since 1592 made the national land devasted and the rural communities impoverished. It happned that many wandering peasants from rural areas moved into the deep forest lands, where they cultivated burnt fields recklessly in the reserved forest resulting in the severe damage of the national forests. And it was inevitable for the government to increase the number of BONG SAN in order to solve the problem of the timber shortage. The increase of its number accelerated illegal and reckless cutting inevitably by the people living mountainuos districts and so the government issued excessive laws and ordinances to reserve the forests. In the middle of the 18th century the severe feuds among the politicians being brought under control, the excessive laws and ordinances were put in good order and the political situation became temporarily stabilized. But in spite of those endeavors evil habitudes of forest devastation, which had been inveterate since the KORYO Dynasty, continued to become greater in degree. After the conclusion of "the Treaty of KANG WHA with Japan" in 1876 western administration system began to be adopted, and thereafter through the promulgation of the Forest Law in 1908 the Imperial Forests were separated from the National Forests and the modern forest ownership system was fixed. b) KANG MU JANG. After the reorganization of the military system, attaching importance to the Royal Guard Corps, the founder of the YI Dynasty, TAI JO (1392 to 1398 A.D.) instituted the royal preserves-KANG MU JANG-to attain the purposes for military training and royal hunting, prohibiting strictly private hunting, felling and clearing by the rural inhabitants. Moreover, the tyrant, YEON SAN (1495 to 1506 A.D.), expanded widely the preserves at random and strengthened its prohibition, so KANG MU JANG had become the focus of the public antipathy. Since the invasion of Japanese in 1592, however, the innovation of military training methods had to be made because of the changes of arms and tactics, and the royal preserves were laid aside consequently and finally they had become the private forests of influential persons since 17th century. c) Forests for official use. All the forests for official use occupied by government officies since the KORYO Dynasty were expropriated by the YI Dynasty in 1392, and afterwards the forests were allotted on a fixed standard area to the government officies in need of firewoods, and as the forest resources became exhausted due to the depredated forest yield, each office gradually enlarged the allotted area. In the 17th century the national land had been almost devastated by the Japanese invasion and therefore each office was in the difficulty with severe deficit in revenue, thereafter waste lands and forest lands were allotted to government offices inorder to promote the land clearing and the increase in the collections of taxes. And an abuse of wide occupation of the forests by them was derived and there appeared a cause of disorder in the forest land system. So a provision prohibiting to allot the forests newly official use was enacted in 1672, nevertheless the government offices were trying to enlarge their occupied area by encroaching the boundary and this abuse continued up to the end of the YI Dynasty. d) Private forests. The government, at the bigninning of the YI Dynasty, expropriated the forests all over the country under the principle of prohibition of private occupancy of forest lands except for the national uses, while it could not expropriate completely all of the forest lands privately occupied and inherited successively by bureaucrats, and even local governors could not control them because of their strong influences. Accordingly the King, TAI JONG (1401 to 1418 A.D.), legislated the prohibition of private forest occupancy in his code, KYEONG JE YUK JEON (1413), and furthermore he repeatedly emphasized to observe the law. But The private occupancy of forest lands was not yet ceased up at the age of the King, SE JO (1455 to 1468 A.D.), so he prescribed the provision in KYEONG KUK DAI JEON (1474), an immutable law as a written constitution in the YI Dynasty: "Anyone who privately occupy the forest land shall be inflicted 80 floggings" and he prohibited the private possession of forest area even by princes and princesses. But, it seemed to be almost impossible for only one provsion in a code to obstruct the historical growing tendecy of private forest occupancy, for example, the King, SEONG JONG (1470 to 1494 A.D.), himself granted the forests to his royal families in defiance of the prohibition and thereafter such precedents were successively expanded, and besides, taking advantage of these facts, the influential persons openly acquired their private forest lands. After tyrannical rule of the King, YEON SAN (1945 to 1506 A.D.), the political disorder due to the splits to bureaucrats with successional feuds and the usurpations of thrones accelerated the private forest occupancy in all parts of the country, thus the forbidden clause on the private forest occupancy in the law had become merely a legal fiction since the establishment of the Dynasty. As above mentioned, after the invasion of Japanese in 1592, the courts of princes (KUNG BANGG) fell into the financial difficulties, and successive kings transferred the right of tax collection from fisherys and saltfarms to each KUNG BANG and at the same time they allotted the forest areas in attempt to promote the clearing. Availing themselves of this opportunity, royal families and bureaucrats intended to occupy the forests on large scale. Besides a privilege of free selection of grave yard, which had been conventionalized from the era of the KORYO Dynasty, created an abuse of occuping too wide area for grave yards in any forest at their random, so the King, TAI JONG, restricted the area of grave yard and homestead of each family. Under the policy of suppresion of Buddhism in the YI Dynasty a privilege of taxexemption for Buddhist temples was deprived and temple forests had to follow the same course as private forests did. In the middle of 18th century the King, YEONG JO (1725 to 1776 A.D.), took an impartial policy for political parties and promoted the spirit of observing laws by putting royal orders and regulations in good order excessively issued before, thus the confused political situation was saved, meanwhile the government officially permittd the private forest ownership which substantially had already been permitted tacitly and at the same time the private afforestation areas around the grave yards was authorized as private forests at least within YONG HO (a boundary of grave yard). Consequently by the enforcement of above mentioned policies the forbidden clause of private forest ownership which had been a basic principle of forest system in the YI Dynasty entireely remained as only a historical document. Under the rule of the King, SUN JO (1801 to 1834 A.D.), the political situation again got into confusion and as the result of the exploitation from farmers by bureaucrats, the extremely impoverished rural communities created successively wandering peasants who cleared burnt fields and deforested recklessly. In this way the devastation of forests come to the peak regardless of being private forests or national forests, moreover, the influential persons extorted private forests or reserved forests and their expansion of grave yards became also excessive. In 1894 a regulation was issued that the extorted private forests shall be returned to the initial propriators and besides taking wide area of the grave yards was prohibited. And after a reform of the administrative structure following western style, a modern forest possession system was prepared in 1908 by the forest law including a regulation of the return system of forest land ownership. At this point a forbidden clause of private occupancy of forest land got abolished which had been kept even in fictitious state since the foundation of the YI Dynasty. e) Common forests. As above mentioned, the forest system in the YI Dynasty was on the ground of public ownership principle but there was a high restriction to the forest profits of farmers according to the progressive private possession of forest area. And the farmers realized the necessity of possessing common forest. They organized village associations, SONGE or KEUM SONGE, to take the ownerless forests remained around the village as the common forest in opposition to influential persons and on the other hand, they prepared the self-punishment system for the common management of their forests. They made a contribution to the forest protection by preserving the common forests in the late YI Dynasty. It is generally known that the absolute monarchy expr opriates the widespread common forests all over the country in the process of chainging from thefeudal society to the capitalistic one. At this turning point in Korea, Japanese colonialists made public that the ratio of national and private forest lands was 8 to 2 in the late YI Dynasty, but this was merely a distorted statistics with the intention of rationalizing of their dispossession of forests from Korean owners, and they took advantage of dead forbidden clause on the private occupancy of forests for their colonization. They were pretending as if all forests had been in ownerless state, but, in truth, almost all the forest lands in the late YI Dynasty except national forests were in the state of private ownership or private occupancy regardless of their lawfulness.

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