• Kyungpook Mathematical Journal
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• 제4권1호
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• pp.23-47
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• 1961

• 대한수학회보
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• 제53권6호
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• pp.1697-1705
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• 2016

In this article, we consider the problem on finding non-degenerate nary m-ic forms having an $n{\times}n$ matrix A as a linear isomorphism. We show that it is equivalent to solve a linear diophantine equation. In particular, we find all integral ternary cubic forms having A as a linear isomorphism, for any $A{\in}GL_3({\mathbb{Z}})$. We also give a family of non-degenerate cubic forms F such that F(x) = N always has infinitely many integer solutions if exists.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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• pp.285-293
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• 2009

By using the notion of fuzzy functions introduced by Dib and Youssef, we obtain fuzzy analogues of some results concerning ordinary functions. In particular, we give the denition dierent from one of invertible fuzzy function introduced by Dib and Youssef. And we show that the two denitions are equivalent. Furthermore, we introduce the concepts of fuzzy increasing functions and fuzzy isomorphisms, and we obtain fuzzy analogues of many results concerning ordinary increasing functions and isomorphisms.

• 대한수학회지
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• 제60권6호
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• pp.1137-1169
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• 2023

Let C be a curve and V → C an orthogonal vector bundle of rank r. For r ≤ 6, the structure of V can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between Spin(r, ℂ) and other groups for these r. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Furthermore, the locus of isotropic vectors in V defines a quadric subfibration Q_V ⊂ ℙV . Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of V and certain ordinary Quot schemes of line subbundles. In particular, for r ≤ 6 this gives a method for enumerating the isotropic subbundles of maximal degree of a general V , when there are finitely many.

• 대한수학회지
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• 제30권2호
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• pp.457-464
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• 1993

• 대한수학회지
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• 제59권2호
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• pp.421-438
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• 2022

We investigate how closed string mirror symmetry is related to homological mirror symmetry, under the presence of an explicit geometric mirror functor.

• 대한수학회지
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• 제42권2호
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• pp.243-254
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• 2005

The Alaway's theorem on orthogonality preserving maps [1] is revisited and we provide a new proof of this result, through an original separation property involving regular forms. In fact, we show a light more general result concerning weakly orthogonal sequences(see section 3).

• 대한수학회논문집
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• 제10권4호
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• pp.831-837
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• 1995

In this paper, we introduce a permutation graph over a graph G as a generalization of both a graph bundle over G and a standard permutation graph, and study a characterization of a natural isomorphism and an automorphism of permutation graphs over a graph.

• 대한수학회논문집
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• 제14권1호
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• pp.135-146
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• 1999

In this paper, we introduce the (4k-1)-diagonal algebra $Alg{\iota}(\array{4k-1\\\infty}\)$ and investigate the necessary and sufficient condition that isomorphisms of $Alg{\iota}(\array{4k-1\\\infty}\)$ are quasi-spatial.

• 대한수학회보
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• 제43권4호
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• pp.821-829
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• 2006

We determine reducibility points of degenerate principal series for exceptional p-adic groups of type $G_2$ via Jacquet module techniques and Hecke algebra isomorphisms.