• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.860-879
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• 2002

Traditionally, Geographical Information Systems can only process spatial data in a procedure-oriented way, and the data can't be treated integrally. This method limits the development of spatial data applications. A new and promising method to solve this problem is the spatial structural query language, which extends SQL and provides integrated accessing to spatial data. In this paper, the theory of spatial structural query language is discussed, and a new geographical data model based on the concepts and data model in OGIS is introduced. According to this model, we implemented a spatial structural query language G/SQL. Through the studies of the 9-Intersection Model, G/SQL provides a set of topological relational predicates and spatial functions for GIS application development. We have successfully developed a Web-based GIS system-WebGIS-using G/SQL. Experiences show that the spatial operators G/SQL offered are complete and easy-to-use. The BNF representation of G/SQL syntax is included in this paper.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.144-153
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• 2007

In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.137-143
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• 1992

The purpose of this paper is to provide the affirmative solution of the following conjecture due to Davis and Geramita. Conjecture; Let A=R[T] be a polynomial ring in one variable, where R is a regular local ring of dimension d. Then maximal ideals in A are complete intersection. Geramita has proved that the conjecture is true when R is a regular local ring of dimension 2. Whatwadekar has rpoved that conjecture is true when R is a formal power series ring over a field and also when R is a localization of an affine algebra over an infinite perfect field. Nashier also proved that conjecture is true when R is a local ring of D[ $X_{1}$,.., $X_{d-1}$] at the maximal ideal (.pi., $X_{1}$,.., $X_{d-1}$) where (D,(.pi.)) is a discrete valuation ring with infinite residue field. The methods to establish our results are following from Nashier's method. We divide this paper into three sections. In section 1 we state Theorems without proofs which are used in section 2 and 3. In section 2 we prove some lemmas and propositions which are used in proving our results. In section 3 we prove our main theorem.eorem.rem.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.319-329
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• 2017

Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.283-312
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• 2020

A sufficient condition for an Artinian complete intersection quotient S = 𝕜[x, y]/(x^m, yⁿ), where 𝕜 is an algebraically closed field of a prime characteristic, to have the strong Lefschetz property (SLP) was proved by S. B. Glasby, C. E. Praezer, and B. Xia in [3]. In contrast, we find a necessary and sufficient condition on m, n satisfying 3 ≤ m ≤ n and p > 2m-3 for S to fail to have the SLP. Moreover we find the Jordan types for S failing to have SLP for m ≤ n and m = 3, 4.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.953-967
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• 2011

We show that the characteristic function $1S_{\underline{\alpha}}$ of any Harder-Narasimhan strata $S{\underline{\alpha}}\;{\subset}\;Coh_X^{\alpha}$ belongs to the spherical Hall algebra $H_X^{sph}$ of a smooth projective curve X (defined over a finite field $\mathbb{F}_q$). We prove a similar result in the geometric setting: the intersection cohomology complex IC(${\underline{S}_{\underline{\alpha}}$) of any Harder-Narasimhan strata ${\underline{S}}{\underline{\alpha}}\;{\subset}\;{\underline{Coh}}_X^{\underline{\alpha}}$ belongs to the category $Q_X$ of spherical Eisenstein sheaves of X. We show by a simple example how a complete description of all spherical Eisenstein sheaves would necessarily involve the Brill-Noether stratas of ${\underline{Coh}}_X^{\underline{\alpha}}$.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.149-174
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• 2013

In a previous paper, we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety $\mathcal{X}$ that is the complete intersection of four quadrics in $\mathbb{P}^7(\mathbb{C})$. This is biholomorphic equivalent to the Satake compactification of $\mathcal{H}_2/{\Gamma}^{\prime}$ for a certain subgroup ${\Gamma}^{\prime}{\subset}Sp(2,\mathbb{Z})$ and it will be the starting point of our investigation. It has been pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold $\tilde{\mathcal{X}}$. Then we will consider the action of quotients of modular groups on $\mathcal{X}$ and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.751-766
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• 2019

In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in ${\mathbb{P}}^1{\times}{\mathbb{P}}^1$. A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in ${\mathbb{P}}^2$ and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.

• Economic and Environmental Geology
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• v.54 no.4
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• pp.465-473
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• 2021

This numerical study aims at analyzing the effect of flow characteristics, caused by geometrical features such as intersecting angles, on solute mixing at fracture junctions. It showed that not only Pe, the ratio of advection to diffusion, but also the intersecting angles played an important role in solute mixing at the junction. For the intersection angles less than 90°, the fluid flowed to the outlet in the same direction as the injected flow direction, which increased the contact at the junction with the streamlines coming from the different inlets. On the other hand, for the intersecting angles greater than 90°, the fluid flowed out to the outlet opposite to the flow direction in the inlet, leading to minimizing the contact at the junction. Therefore, in the former case, solute mixing occurred even at high Pe, and in the latter case, solutes transport along the streamlines even at low Pe. For Pe < 1, the complete mixing model was known to occur, but for the intersecting angle greater than 150°, no complete solute mixing occurred. Overall, the transition from the complete mixing model to the streamline-routing model occurred for Pe = 0.1 - 100, but it highly depended on the intersecting angles. Specifically, the transition occurred at Pe = 0.1 - 10 for intersecting angles ≧ 150° and at Pe = 10 - 100 for intersecting angles ≦ 30°. For Pe > 100, the streamline-routing model was dominant regardless of intersecting angles. For Pe > 1,000, the complete streamline-routing model appeared only for the intersecting angles greater than 150°. For the intersecting angles less than 150°, the streamline-routing model dominated over the complete solute mixing, but solute mixing still occurred at the fracture junction.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.155-167
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• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.