• 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 ${\underline{Coh}}_X^{\underline{\alpha}}$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.139-165
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• 2020

Mirror symmetry for del Pezzo surfaces was studied in [3] where they suggested that the mirror should take the form of a Landau-Ginzburg model with a particular type of elliptic fibration. This argument came from symplectic considerations of the derived categories involved. This problem was then considered again but from an algebro-geometric perspective by Gross, Hacking and Keel in [8]. Their construction allows one to construct a formal mirror family to a pair (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. In the case where the self intersection matrix for D is not negative semi-definite it was shown in [8] that this family may be lifted to an algebraic family over an affine base. In this paper we perform this construction for all smooth del Pezzo surfaces of degree at least two and obtain explicit equations for the mirror families and present the mirror to dP₂ as a double cover of ℙ².

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.131-144
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• 2020

Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫₁, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.

• Journal for History of Mathematics
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• v.30 no.3
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

• Proceedings of the Korean Information Science Society Conference
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• 2007.10c
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• pp.443-446
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• 2007

원영상과 목적영상 사이의 원근 변환(projective transform)에 의해서 생성되는 조강도 영상은 영상의 확대와 축소가 동시에 일어나는 특징을 가지고 있다. 조감도 영상을 구성하는 과정은 원영상의 위치에 따라서 원영상을 확대하거나 축소하여 목적영상을 만들어 내기 때문에, 원영상의 확대와 축소영역을 목적영상에 적합하게 나타내기 위한 보간법이 필요하다. 이중선형 보간법(bilinear interpolation)은 낮은 연산량 때문에 영상변환에 많이 사용되는 보간법이다. 하지만 영상의 확대와 축소 영역에서는 흐려지거나 에일리어싱(aliasing) 효과에 의한 아티팩트(artifact)가 일어나는 문제점을 가지고 있다. 이러한 문제점을 개선하기 위해서 고주파성분을 유지하는 에지(edge)정보 기반의 변형된 EWA를 사용 한다. 그리고 엔티 에일리어싱(anti-aliasing)을 수행하는 MIP-mapping을 이용한 보간법을 통해서 축소 영역에서 발생하는 에일리어싱 문제를 해결하여 조감도 영상의 화질을 개선한다.

• Journal of Digital Contents Society
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• v.8 no.3
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• pp.365-370
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• 2007

This paper proposes a new algorithm that generates a panorama image for reconstruction of image-based virtual environment. Proposed algorithm can generate panorama image from input images using the projective transform based on the feature model and a fully immersive image-based virtual environment according to the user's view point by the sphere mapping. Especially, proposed algorithm supports robust methods of camera rotation and is applied to various images to estimate ist performance.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.999-1007
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• 2013

This research shows several types of moving pictures from the data: 1) the word cloud of Korean texts, 2) the heat map of n ${\times}$ p matrices, 3) the moving image of p ${\times}$ p scatterplot matrix, 4) the local projective display of k clusters (Huh and Lee, 2012). Moving pictures may reveal the hidden information and beauty of the datasets and ignite the curiosity of information consumers. Video files are attached.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.7
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• pp.127-137
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• 1996

The 3-dimensional measurement using stereo vision system must achieve a camera calibration. So far, the 3-dimensional calibration technique that uses two-dimensional grid papar and a non-linear least square method has been developed and tested. But, this method is inefficient because it has many calculation procedure and a non-linear analysis. Therefore, this paper proposed the projective geometric method which produced the calibration parameter by vanishing point. The vanishing point is producted by a cross ratio and a parallel line pairs. The results of the computer simulation show utility of the proposed method.

• Journal of the Korea Computer Graphics Society
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• v.11 no.4
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• pp.34-38
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• 2005

본 논문에서는 대형 스크린 기반 디스플레이 환경에서 시각 커뮤니케이션 증진을 위한 비디오 아바타 생성 기법에 대하여 소개한다. 일반적으로 대형 스크린 기반 가상 환경에서는 스크린으로 투사되는 빛의 변화 때문에 정적 배경을 보장할 수 없다. 뿐만 아니라 카메라 위치 설정이 자유롭지 못하기 때문에 디스플레이 환경 내에 있는 사용자를 대상으로 비디오 아바타를 생성하기 쉽지 않다. 본 논문에서는 적외선 및 필터를 이용하여 가시광선을 차단함으로써 사용자 영역을 쉽게 정의할 수 있도록 하였고, 나란히 배치된 컬러 영상에 실루엣 마스크를 적합하여 배경이 제거된 사용자 컬러 영상을 추출할 수 있도록 하였다. 또한 생성된 스테레오 비디오 아바타 영상은 투영 텍스처를 이용하여 보정된 후 가상세계에 투사되어 입체 디스플레이 된다. 제안된 기법은 일반적인 카메라를 이용하고 있으며, 간단한 조명 조건만 설정해주면 기존의 대형 스크린 기반 프로젝션 환경을 변형하지 않고도 쉽게 설치하여 사용할 수 있기 때문에 많은 활용도가 있을 것이라 기대된다.

• Journal of Korean Home Economics Education Association
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• v.6 no.2
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• pp.133-145
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• 1994

The purposes of this study are to investigate the relationship between the Piaget’s cognitive developmental theory and the practical course subject in elementary school which have the characteristics of skillful subject and living subject, and to discriminate the suitability of contents of the practical course subject for the childrens’level of cognitive development. This work could serve the theoretical background that the practical course subject presents practical experiences which lead the development of logicomathematical thinking abilities. The results of the content analysis shows that create activities develop the logicomathematical thinking abilities such as projective geometry, topology geometry, area conservation, length & distance conservation, and volume & mass conservation. And the most contents of the practical course subject are suitable for the childrens’level of cognitive development.