• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2002년도 Proceedings of International Symposium on Remote Sensing
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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.

• 한국정밀공학회지
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• 제24권11호
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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.

• 대한수학회보
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• 제29권1호
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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.

• 대한수학회보
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• 제54권1호
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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]).

• 대한수학회지
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• 제57권2호
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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.

• 대한수학회지
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• 제48권5호
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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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• 제53권2호
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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.

• 대한수학회지
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• 제56권3호
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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.

• 대한수학회보
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• 제61권4호
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• pp.1067-1086
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• 2024

For a foliation 𝓕 of degree r over ℙ², we can regard it as a maximal invertible sheaf N^∨_𝓕 of Ω_ℙ², which is represented by a section s ∈ H⁰(Ω_ℙ² (r+2)). The singular locus Sing𝓕 of 𝓕 is the zero dimensional subscheme Z(s) of ℙ² defined by s. Campillo and Olivares have given some characterizations of the singular locus by using some cohomology groups. In this paper, we will give some different characterizations. For example, the singular locus of a foliation over ℙ² can be characterized as the residual subscheme of r collinear points in a complete intersection of two curves of degree r + 1.

• 자원환경지질
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• 제54권4호
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• pp.465-473
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• 2021

본 연구에서는 수치모델링을 통해 단열의 교차각과 같은 기하학적 특징이 교차점에서의 유동특성과 용질의 혼합·분배에 미치는 영향을 연구하였다. Pe(Peclect number; 이류와 확산의 상대적인 비)뿐만이 아니라 단열의 교차각이 교차점에서의 용질의 혼합·분배모델을 결정하는데 있어 중요한 역할을 하는 것으로 나타났다. 교차각이 90°미만인 경우, 주입된 유동방향과 동일한 방향의 유출구로 진행하기 때문에 교차점에서 양쪽 주입구에서 온 유선들의 접촉을 용이하게 한다. 반면, 교차각이 90°보다 큰 경우 유체가 주입된 유동방향과 유출구의 방향이 반대이기 때문에, 교차점에 두 주입구에서 온 유선들 간의 접촉은 최소화 되었다. 그러므로 전자의 경우에서는 높은 Pe에서도 용질의 혼합이, 후자에서는 낮은 Pe에서도 유선경로에 따른 용질의 이동이 나타났다. 따라서 Pe < 1의 경우, 완전혼합모델이 지배적인 것으로 알려졌지만, 교차각이 150°인 경우 교차점에서 혼합뿐만이 아니라 일부는 유선의 경로를 따라 유출구로 유출되었다. 전반적으로 Pe가 0.1 - 100에서 완전혼합모델에서 유선경로모델로의 전이가 나타났지만, 이는 교차각에 따라 크게 달라진다. 교차각이 클수록(≧ 150°) Pe가 0.1 - 10에서, 교차각이 작을수록(≦ 30°) Pe가 10 - 100에서 전이가 발생하였다. Pe > 100에서는 교차각과 상관없이 유선경로모델이 더 지배적인 것으로 나타났다. Pe > 1,000에서는 교차각이 150°이상인 경우에만 100% 유선경로모델이 나타나며, 교차각이 150°미만인 경우 유선경로모델이 지배적이지만 여전히 교차점에서 용질의 혼합이 발생하였다.