• Title/Summary/Keyword: KMS states

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VARIATIONAL PRINCIPLE FOR QUANTUM UNBOUNDED SPIN SYSTEMS

  • Choi, S.D.;Jo, S.G.;Kim, H.I.;Lee, H.H.;Yoo, H.J.
    • Journal of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.579-592
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    • 2000
  • We study the variational principle for quantum unbounded spin systems interacting via superstable and regular interactions. We show that the (weak) KMS state constructed via the thermodynamic limit of finite volume Green's functions satisfies the Gibbs variational equality.

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GROUND STATES OF A COVARIANT SEMIGROUP C-ALGEBRA

  • Jang, Sun Young;Ahn, Jieun
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.3
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    • pp.339-349
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    • 2020
  • Let P ⋊ ℕx be a semidirect product of an additive semigroup P = {0, 2, 3, ⋯ } by a multiplicative positive natural numbers semigroup ℕx. We consider a covariant semigroup C-algebra 𝓣(P ⋊ ℕx) of the semigroup P ⋊ ℕx. We obtain the condition that a state on 𝓣(P ⋊ ℕx) can be a ground state of the natural C-dynamical system (𝓣(P ⋊ ℕx), ℝ, σ).

9 Provinces and 5 Secondary Capitals, Myeong-ju(Haseo-ju) - Revolve Around Urban Structure - (구주오소경과 명주(하서주) - 그 도시구조를 중심으로 -)

  • Takahumi, Yamada
    • Korean Journal of Heritage: History & Science
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    • v.45 no.2
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    • pp.20-37
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    • 2012
  • After withdrawal of military troops of Chinese Tang dynasty in the 18th year of King Moon-moo's reign(678), the Silla Kingdom had actually unified the Korean peninsula and had divided the territory into 9 states benchmarking the China's local administrations adjustment system. He had established local administrative units by deploying secondary capitals, counties and prefectures in the nine states. The so-called "9 Provinces and 5 Secondary capitals" are what constitutes the local administrations system. The provinces can be compared to current provinces of the Republic of Korea(hereinafter Korea), and secondary capitals to megalopolises. According to a chapter of the Samkuksaki(三?史記) which had recorded the achievements of king Kyoungdeok in December in his 16th year on the throne(757), the local administrative units had amounted to 5 secondary capitals, 117 counties and 293 prefectures. There are still lots of ambiguous points since there have never been any consultation on locations of provinces and secondary capitals' castles, and on structures of cities because the researches for local cities inside the 9 Provinces and 5 Secondary capitals in the Unified Silla Kingdom has been conducted centering on the historic literatures only. The research for restoring structures of cities seen from an archeological perspective are limited to the studies of Taewoo Park("A study on the local cities in the Unified Kingdom Age" 1987) and that of the author("A study on the restoration of planned cities for the Unified Silla Kingdom in terms of the structures and realities of the castles in the 9 Provinces and 5 Secondary capitals" 2009). The Gangneung city of Gangwon province was originally called Haseoryang(河西良) of the Gogureo Kingdom as an ancient nation of Ye(濊). According to "Samkuksaki", it had evolved from Haseoju(河西州) to a secondary capitals in the 8th year of King Seonduk(639). Afterwards, it had been renamed as Myeongju(溟洲) in the 16th year of King Kyoungduk(757), and then several other names were given to it after Goryo dynasty. Taewoo Park claims that it is being defined as a sanctuary remaining in Myoungjudong because of the vestige of bare castle, and this cannot be ascertained due to the on-going urbanization processes. Also, the Kwandong university authority is suggesting an opinion of regarding Myeongju mountain castle located 3 Kms southwest of the center of Gangwon city as commanding post for the pertinent state. The author has restored the pertinent area into a city composed of villages within a lattice framework like Silla Keumkyoung and many other cities. The structure is depicted next. The downtown of Gangneung is situated on a flat terrain at the west bank of Namdaecheon stream flowing southwest to northeast along the inner area of the city. Though there isn't any hill comparatively higher than others in the vicinity, hills are continuously linked east to west along the northern area of the downtown, and the maximum width of flat terrain is about 1 Km and is not so large. Currently, urbanization is being proceeded into the inner portion of Gangneung city, the lands in all directions from the hub of Gangneung station have been readjusted, and thus previous land-zoning program is almost nullified. However, referring to the topographic chart drawn at the time of Japanese colonial rule, it can be validated that land-zoning program to accord the lattice framework with the length of its one side equaling to 190m leaves its vestige about 0.8Km northwest to southeast and about 1.7Km northeast to southwest of the vicinity of Okcheondong, Imdangdong, Geumhakdong, Myeongjudong, and etcetera which comprize the hub of the downtown. The land-zoning vestige within the lattice framework, compared to other cases related with the '9 states and 5 secondary capitals', is very much likely to be that of the Unified Silla Kingdom. That the length of a side of a lattice framework is 190m as opposed to that of Silla Geumkyoung and other cities with their 140m or 160m long sides is a single survey item in the future. The baseline direction for zoning the lands is tilting approximately 37.5 degrees west of northwest to southeast axis in accordance with the topographic features. It seems that this phenomenon takes place because of the direction of Namdaecheon and the geographic constraints of the hills in the north. Reviewing minimally, a rectangular size of zoned land by 4 Pangs(坊) on the northwest to southeast side multiplied by 7 Pangs(坊) on the northeast to southwest side had been restored within a lattice framework. Otherwise, considering the extent of expansion of the existing zoned lands in the lattice framework and one more Pang(坊) being added to each side, it is likely that the size could have been with 5 Pangs(坊) on the northwest to southeast side multiplied by 8 Pangs(坊) on the northeast to southwest side(950 M on the northwest to southeast side multiplied by 1,520m on the northeast to southwest side). The overall shape is rectangle, but land-zoning programs reminiscent of rebuilt roads(red phoenix road) like Jang-an castle(長安城) of Chinese Tang dynasty or Pyoungseong castle(平城城) in Japan is not to be validated. There are some historic items among the roof tiles and earthen wares excavated at local administrative office sites or Gangneung's town castle in Joseon dynasty inside the area assumed to be containing municipal vestiges even though archeological survey for the vestige of Myeongju has not been made yet, and these items deserve dating back to the Unified Silla Kingdom age. Also, all of the construction sites at local administrative authorities of the Joseon dynasty are showing large degrees of slant in the azimuth. This is a circumstantial evidence indicating the fact that the inherited land-zoning programs to be seen in Gangneung in terms of the lattice framework had ever existed in the past. Also, the author does not decline that Myeongju mountain castle had once been the commanding post when reviewing the roof tiles at the edge of eaves in this stronghold. The ancient municipal castles in the Korean peninsula are composed of castles on the flat terrain as well as hilly areas and the cluster of strongholds like Myounghwal, Namhan, Seohyoung mountain castles built around municipal castle of Geumkyoung based on a lattice framework program. Considering that mountain castles are spread in the vicinity of municipal vestiges in other cities other than the 9 states and 5 secondary capitals, it is estimated that Myeongju was assuming the function of commanding post incorporating cities on the flat terrain and castles on the hills.