• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.81-93
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• 2008

In [3, 9], using the theory of noncommutative Dirichlet forms in the sense of Cipriani [6] and the symmetric embedding map, authors constructed the KMS-symmetric Markovian semigroup $\{S_t\}_{t{\geq}0}$ on a von Neumann algebra $\cal{M}$ with an admissible function f and an operator $x\;{\in}\;{\cal{M}}$. We give a sufficient and necessary condition for x so that the semigroup $\{S_t\}_{t{\geq}0}$ acts separately on diagonal and off-diagonal operators with respect to a basis and study some results.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.451-459
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• 2019

Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be two operator ${\ast}$-rings such that ${\mathcal{A}}$ is prime. In this paper, we show that if the map ${\Phi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves Jordan or ${\ast}$-Jordan triple product, then it is additive. Moreover, if ${\Phi}$ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of ${\Phi}$. Finally, we show that if ${\mathcal{A}}$ and ${\mathcal{B}}$ are two prime operator ${\ast}$-algebras, ${\Psi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves ${\ast}$-Jordan triple product, then ${\Psi}$ is a ${\mathbb{C}}$-linear or conjugate ${\mathbb{C}}$-linear ${\ast}$-isomorphism.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.259-267
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• 2022

We use L_∞ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion i_n,k : ℂPⁿ ↪ ℂP^n+k between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping aut₁ ℂPⁿ → map(ℂPⁿ, ℂP^n+k; i_n,k) and the resulting G-sequence.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.115-141
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• 2023

We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup {exp tX} is a normal nilpotent subgroup commuting with {exp tX}, and X is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-Kähler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension 5 and those of dimension 7 whose Kähler reduction in the above sense is abelian.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-170
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• 1986

Let M be a von Neumann algebra and .alpha., .betha. be *-automorphisms of M satisfying the operator equation .alpha.+.alpha.$^{-1}$ =.betha.+.betha.$^{-1}$ This operator equation has been extensively studied and many important decomposition theorems have been obtained by several authors (for instance see [4], [5], [2], [1]). Originally, this operator equation arose in the paper of Van Daele on the new approach of the Tomita-Takesaki theory in the case of modular operators ([7]). In the case of one-parameter automorphism groups, this equation has produced a bounded and completely positive map which can play a role similar to the infinitesimal generator (for details see [6] and [1]). A recent and one of the most important applications of this equation has been in developing an anglogue of the Tomita-Takesaki theory for Jordan algebras by Haagerup [3]. One general result of this theory is the following.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.2
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• pp.177-187
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• 1999

Up to date, in many application fields of GSIS, we usually have used vector-based spatial overlay or grid-based spatial algebra for extraction and analysis of spatial data. But, because these methods are based on traditional crisp set, concept which is used these methods. shows that many kinds of spatial data are partitioned with sharp boundary. That is not agree with spatial distribution pattern of data in the real world. Therefore, it has a error that a region or object is restricted within only one attribution (One-Entity-one-value). In this study, for improving previous methods that deal with spatial data based on crisp set, we are suggested to apply into spatial overlay process the concept of fuzzy set which is good for expressing the boundary vagueness or ambiguity of spatial data. two methods be given. First method is a fuzzy interval partition by fuzzy subsets in case of spatially continuous data, and second method is fuzzy boundary set applied on categorical data. with a case study to get a land suitability map for the development site selection of new town, we compared results between Boolean analysis method and fuzzy spatial overlay method. And as a result, we could find out that suitability map using fuzzy spatial overlay method provide more reasonable information about development site of new town, and is more adequate type in the aspect of presentation.

• Journal of the Korean association of regional geographers
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• v.13 no.2
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• pp.143-155
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• 2007

There are many conflicts or interests among various stakeholders on the development of the coastal area. The integrated methodology, which is reflective of physical conditions, socio-economic circumstances, and people's sense of values, is thus needed to solve the problems. In this study, geographical information systems(GIS) and analytic hierarchy process(AHP) that arc one of multi-criteria analysis methodologies are loosely coupled to develop better analytic procedures for coastal assessment. Socio-economic and environmental parameters of the study area, Hampyung Bay area, are converted to a GIS system-applicable format, while AHP is used to assess the relative importance level of each parameter by calculating weighting factors. After standardizing and rasterizing spatial data from various sources. the weighting factors are applied to produce the layers for each parameter. Map algebra and overlay analyses are used to create the final layer according to the decision making logic or model proposed here. Cell values of that layer could be considered as spatial alternatives. In addition to this finding, the flexibility with the weighing factors enable decision-makers to understand the procedures and alternatives in relevance with selective strategies for coastal management.

• Journal of Korean Society of Forest Science
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• v.90 no.4
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• pp.535-542
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• 2001

The objective of this study is to develop a spatial analysis modeling technique to evaluate the functional suitability of forest lands for land slide prevention. The functional suitability is classified into 3 categories of high, medium and low according to the potential of land slide on forest lands. The potential of land slide hazards is estimated using the measurements of 7 major site factors : slope, bed rock, soil depth, shape of slope, forest type and D.B.H. class of trees. The analytic hierarchical process is applied to determining the relative weight of site factors in estimating the potential of land slides. The spatial analysis modeling starts building base layers for the 7 major site factors by $25m{\times}25m$ grid analysis or TIN analysis, reclassifies them and produces new layers containing standardized attribute values, needed in estimating land slide potential. To these attributes, applied is the weight for the corresponding site factor to build the suitability classification map by map algebra analysis. Then, finally, cell-grouping operations convert the suitability classification map to the land unit function map. The whole procedures of the spatial analysis modeling are presented in this paper.

• Journal of the Korean Association of Geographic Information Studies
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• v.14 no.3
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• pp.126-135
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• 2011

In this study, the algorithm for priority area of forest fire surveillance was developed to enhance the effectiveness of fire detection. The high priority surveillance area for forest fire detection was defined as the area with not only low value of viewshed analysis of the lookouts and detection cameras but also high fire occurrence probability. To build the priority map, fuzzy function and map algebra were used. The analysis results of Bonghwa-gun, Gyeongbuk Province, showed that the surveillance priority of central and southern area is higher than north area. This algorithm could be used in the allocation of fire prevention resources and selection of suitable point for new fire detection system.

• Journal of the Korean association of regional geographers
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• v.10 no.3
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• pp.606-623
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• 2004

Emergency medical service pertains highly to the public service sector which has to be provided equally in a society and evenly in a spatial dimension by the government. However, emergency medical centers in Korea are inequally distributed in a space and also human capital, facility, and equipment for emergency medical centers show clear disparity among regions. This research analyzed the spatial balance of the demand supply level for emergency medical service in Seoul by constructing the potential demand surface map and supply surface map for this service. The surface map of demand-supply balance for emergency medical service was constructed by GIS based map algebra algorism. The results by this analysis very clearly reveal the spatial disparity of emergency medical service. The places where are over-represented by demand level compared to their supply level are estimated to require an additional establishment of emergency medical centers in the near future. While, the places where are over-represented by supply level compared to their potential demand for emergency medical services indicate the possibility of problems in the management of emergency medical centers because of a surplus in the supply of emergency medical services. The results of this research can be utilized in providing valuable information for the adequate provision of emergency medical centers and for the estimation of range on the service area of emergency medical services.