• 대한수학회지
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• 제58권2호
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• pp.351-381
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• 2021

In this paper we introduce the notion of strong Galois H-progenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ≅ Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.15-30
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• 2024

In this paper, we focus on partial isometry elements and strongly EP elements on a ring. We construct characterizing equations such that an element which is both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have a solution in a given set. In particular, an element a ∈ R^# ∩ R^† is a partial isometry element if and only if the equation x = x(a^†)^*a^† has at least one solution in {a, a#, a^†, a^*, (a^#)^*, (a^†)^*}. An element a ∈ R^#∩R^† is a strongly EP element if and only if the equation (a^†)^*xa^† = xa^†a has at least one solution in {a, a^#, a^†, a^*, (a^#)^*, (a^†)^*}. These characterizations extend many well-known results.

• 대한수학회보
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• 제32권2호
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• pp.145-152
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• 1995

From now on, we assume that a ring R has an identity 1. We have the following Lemma from Park[2].

• 대한수학회논문집
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• 제10권2호
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• pp.331-335
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• 1995

We prover Fredholm alternatives for AF algebras: If an element have the finite null projection and the confinite range projection then its image in the relative Calkin algebra is invertible.

• 한국정보과학회논문지:소프트웨어및응용
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• 제30권1_2호
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• pp.153-163
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• 2003

본 논문에서는 기하학적인 3차원 모델을 사용하지 않고 정면이 얼굴 영상 및 2차원 메쉬만으로 얼굴의 포즈 변형을 수행하는 영상기반 렌더링(Image Based Rendering; IBR) 기법을 제안한다. 3차원 기하학적 모델을 대신하기 위해, 먼저 표준 인물의 정면, 좌우 반측면, 좌우 측면의 얼굴 영상에 대한 표준 메쉬를 작성한다. 합성하고자 하는 임의의 인물에 대해서는 주어진 정면 얼굴 영상의 메쉬만을 작성하고, 그 밖의 메쉬는 표준 메쉬 집합을 근거로 자동 생성된다. 그런 다음, 메쉬 제어점들의 중첩 및 역전을 허용하도록 개선한 역전가능 메쉬워프 알고리즘(invertible meshwarp algorithm)을 이용하여 얼굴의 입체적인 회전 변형을 수행한다. 또한, 눈이나 입의 개폐 변형도 동일한 워핑 알고리즘으로 구현한다. 얼굴 변형 성능을 평가하기 위해, 총 10명으로부터 머리를 수평으로 회전하면서 동영상을 취득한 후, 실제 영상과 변형 영상마다 양 눈의 중간 위치인 기준점에서 각 특징점까지의 거리를 계산하여 평균 차이를 구하였다. 그 결과, 기준점에서 입의 중간 위치까지의 거리에 비해 약 7.0%의 평균 위치 오차만이 발생하였다.

• 호남수학학술지
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• 제32권4호
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• pp.739-746
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• 2010

In this short paper, we show that properties of an ideal I of a ring R are related to those of the homogeneous ideal I(+)IM of a ring R(+)M.

• 대한수학회논문집
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• 제12권1호
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• pp.1-9
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• 1997

We obtained some class fields associated to an order R of a function field and evaluated the valuation of the invariant $\xi (c)$ for an invertible ideal c of R.

• 대한수학회보
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• 제46권5호
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• pp.873-884
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• 2009

We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

• 대한수학회논문집
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• 제9권3호
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• pp.629-639
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• 1994

Loewner ([13]) showend the semigroup of the real non-singular totally positive matrices is generated by itsinfinitesimal elements, that is,s the set of all Jacobi matrices with non-negative off-diagonal elements. In general, a semigroup is not completely recreated from the set of its infinitesimal elements. We extend Loewner's work and show that the semi-group of all invertible upper (or lower) triangular stochastic matrices is generated by the set of its infinitesimal elements.

• East Asian mathematical journal
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• 제23권2호
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• pp.207-212
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• 2007

We describe the class of invertible matrices T such that $TAT^{-1}$ is EPr, for a given EPr matrix A of order n. Necessary and sufficient condition is determined for $TAT^{-1}$ to be EP for an arbitrary matrix A of order n.