• Title/Summary/Keyword: symbolic powers

Search Result 14, Processing Time 0.021 seconds

A GRADED MINIMAL FREE RESOLUTION OF THE m-TH ORDER SYMBOLIC POWER OF A STAR CONFIGURATION IN ℙn

  • Park, Jung Pil;Shin, Yong-Su
    • Journal of the Korean Mathematical Society
    • /
    • v.58 no.2
    • /
    • pp.283-308
    • /
    • 2021
  • In [30] the author finds a graded minimal free resolution of the 2-nd order symbolic power of a star configuration in ℙn of any codimension r. In this paper, we find that of any m-th order symbolic power of a star configuration in ℙn of codimension 2, which generalizes the result of Galetto, Geramita, Shin, and Van Tuyl in [15, Theorem 5.3]. Furthermore, we extend it to the m-th order symbolic power of a star configuration in ℙn of any codimension r for m = 3, 4, which also generalizes the result of Biermann et al. in [1, Corollaries 4.6 and 5.7]. We also suggest how to find a graded minimal free resolution of the m-th order symbolic power of a star configuration in ℙn of any codimension r for m ≥ 5.

A GRADED MINIMAL FREE RESOLUTION OF THE 2ND ORDER SYMBOLIC POWER OF THE IDEAL OF A STAR CONFIGURATION IN ℙn

  • Shin, Yong-Su
    • Journal of the Korean Mathematical Society
    • /
    • v.56 no.1
    • /
    • pp.169-181
    • /
    • 2019
  • In [9], Geramita, Harbourne, and Migliore find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a linear star configuration in ${\mathbb{P}}^n$ n of any codimension r. In [8], Geramita, Galetto, Shin, and Van Tuyl extend the result on a general star configuration in ${\mathbb{P}}^n$ but for codimension 2. In this paper, we find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a general star configuration in ${\mathbb{P}}^n$ of any codimension r using a matroid configuration in [10]. This generalizes both the result on a linear star configuration in ${\mathbb{P}}^n$ of codimension r in [9] and the result on a general star configuration in ${\mathbb{P}}^n$ of codimension 2 in [8].

A Study on the Symbolic Significance of the Shaman`s Costume(II) -With Special Reference to the Religious Life of Korean Residents in Japan- (巫俗服飾의 象徵的 意味에 관한 硏究(II) -在日 韓國人의 宗敎生活을 中心으로-)

  • 이자연
    • The Research Journal of the Costume Culture
    • /
    • v.7 no.1
    • /
    • pp.68-81
    • /
    • 1999
  • This paper makes a report of Shaman\`s ritual performed among Korean resiednts in Japan as socio-historical facts, and this also examines the symbolic meanings of Shamans\` costumes. The results are as follows ; 1) At the ritual of Jungsip-Wang Maji, Shamans wear Gwandae, Kunbok, Jangsam, Durumaki, and Chima-jugori. These costumes show that their wearers are priests and gods at the same time. 2) The reason why Simbang performs the ritual in different costumes at different Jaechas is that each object-god needs different costumes to represent its different character. 3) Shamans\` instruments consist of musical instruments and other instruments. Among the musical instruments are such percussions as Buk, Jing, Janggo and Sulsae. Among other insttruments are Sindo, Sanban and Yoryung. 4)Shamans think that the musical instruments have magic powers to drive out minor demons and invite gods. Sindo, Sanban and Yoryung are thought to be the symbolic instruments representing god\`s will.

  • PDF

A SYMBOLIC POWER OF THE IDEAL OF A STANDARD 𝕜-CONFIGURATION IN 𝕡2

  • Shin, Yong-Su
    • The Pure and Applied Mathematics
    • /
    • v.25 no.1
    • /
    • pp.31-38
    • /
    • 2018
  • In [4], the authors show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type ($d_1$, ${\ldots}$, $d_s$) with $d_s$ > $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(md_s-1)$ is the number of lines containing exactly $d_s-points$ of ${\mathbb{X}}$ for $m{\geq}2$. They also show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)$ is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}s+1$. In this paper, we explore a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ and find that if ${\mathbb{X}}$ is a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)=3$, which is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}2$ instead of $m{\geq}s+1$.

A Study on the Use of Animal Symbols for Healing of the Korean Traditional Medicine - Focusing on "Donguibogam(東醫寶鑑)"

  • Nang Ye Kim
    • CELLMED
    • /
    • v.13 no.10
    • /
    • pp.11.1-11.5
    • /
    • 2023
  • Animal symbols exert a profound influence on humans. This can be likened to homeopathic magic, with its source tied to the symbol. It has been believed that consuming an animal or crafting items from its parts would imbue humans with the creature's powers, thereby enhancing its symbolic significance over time. An animal can have various symbolic meanings, and among them, those related to healing have been adopted as folk remedies. Therefore, in this study, we would like to examine an example in which animals were used in folk therapy as a symbol of healing in traditional Korean medicine through "Donguibogam(東醫寶鑑)". In this context, 'healing' not only pertains to direct cures but also encompasses the use of amulets to fend off afflictions and bolster one's immunity. By looking at animals that have traditionally been used in folk remedies, it is possible to reaffirm the role of animals as healing symbols and to find ways to effectively use animal symbols to enhance the healing effect in the future by recognizing their value.

WATER AND INTROSPECTION (물과 성찰(省察))

  • Shin, Sung-Woong;Cho, Soo-Churl
    • Journal of the Korean Academy of Child and Adolescent Psychiatry
    • /
    • v.12 no.1
    • /
    • pp.3-24
    • /
    • 2001
  • All human being can't exist by oneself. That is, all human being depend on intimate attachment for their survival. Physical and psychological powers and control functions are prerequisites for one's survival and these serve important functions in interpersonal relationships. There are two kinds of powers and controls. One is positive power which helps one survive effectively. Another one is negative power which disturbs one's effective survival. Introspection is one of the positive power and most important process in understanding oneself and others. Thus, the purpose of this study is to elucidate the physical and psychological meaning of the characteristics of water and based on this meaning, to suggest one way of introspection. The authors reviewed the precept of water which is described in Bible and oriental classical books such as 'the Analects of Confuicus(論語)', 'Tao Te Ching(道德經)', 'Mencius(맹자)', 'Chronicle(史記)', 'The Doctrine of the Mean(中庸)', 'University(大學)'. The author also reviewed 'The History of Three Countries(삼국사기, 삼국유사)', 'The Precept of Religion', and 'the modern poems' which includes the symbolic meaning of water. The results are summarized as follows:1) The flow of water itself is the expression of introspection. Because, water does not flow without filling a puddle. 2) Water is the symbol of 'Immortality'. 3) Water symbolizes 'Modesty and Trust'. 4) Water is the symbol of 'Freedom from Greed'. 5) Water symbolizes 'Goodness and Beauty'. 6) Water symbolizes 'Naturality and Love'. Immortality, Modesty and Trust, Freedom from Greed, Goodness and Beauty, and Naturality and Love are eternal, universal values which all human should seek and achieve. By the process of introspection through the symbolic meaning of water, we can achieve these positive aspects of human mind and spirit.

  • PDF

Daily Life Perspectives on Living Arrangements of the Elderly after the Modernization Era (근대 이후 노인의 생활과 생활공간 변화에 대한 일상사적 고찰)

  • Hong, Hyung-Ock;Jun, Nam-Il;Yang, Se-Hwa;Eun, Nan-Soon
    • Journal of the Korean Home Economics Association
    • /
    • v.44 no.8
    • /
    • pp.47-61
    • /
    • 2006
  • The study analyzed the characteristics of the daily life and the living arrangements use of the elderly with literature review after the modernization period based on the daily life perspectives. The changes in the ideology, social system, and family system, which influenced the society and families, also affected the status of the elderly and their daily lives. Consequently, they had been facing conflicts, acceptance, and internal differentiations. The characteristics of the changes in the daily lives of the elderly in different periods were as follows. The contents were written from three different perspectives, phenomenological, symbolic interaction, and Marxist. During the modernization period, the family system and the hierarchy within a family had been reformed. However, the elderly were still considered as the symbolic leader and the respected figure of the family. From a phenomenological perspective, elderlies teach the next generations and influence the family's lives. On the other hand, from a perspective of symbolic interactions, spatial adjustment behaviors toward the largest room between the elderly and the next generation were detected. The actual authority was given to the next generation. However, the elderly were still treated as the symbolic authority. Yet, as the society became more industrialized, conflicts aroused about the support of the elderly. Those, who were neglected from the family, even spent their daily time at the elderly center or the community center. The daily lives from the Marxist perspectives suggested that modernization caused the young generations, who were well-educated and had financial powers, to have initiatives. The role of the elderly was reduced and they became negligible people, who spend meaningless daily lives. The interested the Third Ages is a new perspective on the elderly, who were neglected from the industrialized society. From a phenomenological perspective, the Third Ages are the generations that seek and demand for new housing.

A Study on the Heaven-Shaped Patterns of the Ceremonial Flags (의장기(儀仗旗)에 있어서의 천상(天象)의 의미(意味) 고찰(考察))

  • Baik, Young-Ja
    • Journal of the Korean Society of Costume
    • /
    • v.5
    • /
    • pp.141-152
    • /
    • 1981
  • Various ceremonial flags were of great importance to the rulers who wished to have the absolute authorities for governing the people. Perhaps nothing indicated the ideas, thoughts and symbols of a certain period and people than the ceremonial flags. The ceremonial flags used in the old China and Korea took the shapes of the heaven and the earth, representing the social backgrounds and thoughts. This study was limited only to the discussion of the heaven-shaped patterns of the ceremonial flags. The 28 constellations of the heaven, in the Oriental way of thinking, were considered to express the immortal powers of Providence and the political domination of the earth. Hence the Polaris, the center of the heaven, symbolized the whole family of king, prince, child born of a concubine and royal harem. Among the constellation pictures were those of Han period, wall painting of old tombs in Koguryeo kingdom and old Japanese kingdom. Referring to the Emperor's ceremonial flags in Daemyeongjibyei, symbolic meanings changed historically and the complete systems of the ceremonial flags were established in Song period when the divine person was drawn on the flags. Animals concerned properly with the particular star and the shapes of the star were both drawn on the flags in Won period and only the shapes of the particular star in Myeong period. In the Imperial enthronement of Kojong the ceremonial flags might be made by the examples of those of Myeong period and remains are now found at Changdeok Palace, which need a further study because the references in detail are not available.

  • PDF

A Consciousness Change of Yangdong Village's Residents connected with Cultural Asset Protection Law -A Comparative Study of 1994 and 2002- (문화재보호법과 관련된 양동마을 주민의식 변화 -1994년과 2002년의 비교 연구-)

  • 강동진
    • Journal of the Korean Institute of Landscape Architecture
    • /
    • v.31 no.3
    • /
    • pp.46-57
    • /
    • 2003
  • The Yangdong traditional historic village is a representative village having symbolic historic values and unique combinations of natural, cultural, and social characteristics of a Korean historic settlement environment, which has been protected by Cultural Asset Protection Law since 1984. Now, in spite of its potential diverse powers, national strategies concerning Yangdong village do not have satisfactory direction and results. In consideration of this notion, this paper is designed to find and to understand the current state of Yangdong village. This paper aims to analyze The changes in Yangdong village between 1994 and 2002, and through these comparisons, to diagnose and predict future aspects of Yangdong village. Primary data was collected by questionnaire investigation between 1994 and 2002. The living conditions, production, and consciousness of residents of Yangdong village are utilized as standards of analysis. The final analysis results can be summarized as follows: because of the Cultural Asset Protection Law, noticeable changes have occurred in Yangdong village over the last 8 years. These change are different from the ones occurring in general farm villages. Also, most issues related to the changes are interpreted as occurring as a result of the top-down approach, which disregards the opinions and wishes of residents. For this, introduction of renovation concept that emphasizes modernization of life and production space is urgently required. To this end, it is necessary that concern for the traditional historic village should diversity and expand, and not concentrate solely on the cultural properties and architecture-oriented historic elements.

The Implications Representated in Korea's Traditional Sokgasan (한국 전통 석가산에 표상된 함의성)

  • Choi, Woo-Young;Yoon, Young-Jo;Seo, Ok-Ha;Yoon, Young-Hwal
    • Journal of the Korean Institute of Traditional Landscape Architecture
    • /
    • v.31 no.1
    • /
    • pp.1-12
    • /
    • 2013
  • Korea's traditional Sokgasans(a artificial rock mountain) are elements of our excellent rock garden culture that have been inherited from Goryeo Era to Chosun Era. This study is to analyze how the culture of Sokgasans in the Goryeo and the Chosun Eras has been has been representated the implications and inherited in terms of historical aspects. Korea's traditional Sokgasans, which were created in the Goryeo Era by imitating the landscape of mountain ranges, created a small artificial mountain made of oddly shaped stones, imitating a real mountain. People in those days would reproduce mountain landscapes through a miniaturization technique, enjoying the pleasure of deep mountains and valleys as they lay on their gardens at home while having an aesthetic experience of the landscape that supported their emotional stability and healing. The inner side of these Sokgasan was intended to represent the world of the Taoist hermit with miraculous powers in terms of utopia, expressing 5 Ak mountains(Song Shan, Taishan, Huashan, Heng Shan and Hyeong Shan) where the mountain of 3 Gods(Youngju, Bongrae and Bangjang) wishing for 'No aging and living long' and idea of the Taoist hermit with miraculous powers are concentrated beyond the beauty of form in the landscape itself. In addition, people could refine their minds by practicing the Confucianist lesson of loving the mountain and water by watching the Sokgasan and imitating 'Famous mountains and lakes" from China and they had been changed and advanced embracing various implications in inner side of Sokgasans. Korea's traditional Sokgasans not only made it possible for people to experience aesthetic landscapes as a practical element of the scenery but also had deep symbolic implications that go beyond their formal beauty and were sublimated as an ideational space of unlimited imagination.