• Korean Journal of Mathematics
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• v.7 no.1
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• pp.79-84
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• 1999

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.341-371
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• 2003

This article discusses in detail how the study of proper holomorphic rational mappings between balls in different dimensions relates to positivity conditions and to isometric imbedding of holomorphic bundles. The first chapter discusses rational proper mappings between balls; the second chapter discusses seven distinct positivity conditions for real-valued polynomials in several complex variables; the third chapter reveals how these issues relate to an isometric imbedding theorem for holomorphic vector bundles proved by the author and Catlin.

• East Asian mathematical journal
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• v.9 no.2
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• pp.295-311
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• 1993

• East Asian mathematical journal
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• v.6 no.2
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• pp.155-158
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• 1990

• The Journal of Natural Sciences
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• v.10 no.1
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• pp.13-16
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• 1998

Every complex vector bundle over $S^1$ splits sum of line bundle and the first Chern class classify complex line bundle. This implies every complex vector bundle over $S^1$ is trivial. In this paper, we show the existence of some nontrivial complex vector bundle over $S^1$ in the equivariant case.

• East Asian mathematical journal
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• v.14 no.2
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• pp.371-375
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• 1998

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.91-107
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• 2024

We determine the N → ∞ asymptotics of the expected value of entanglement entropy for pure states in H_1,N ⊗ H_2,N, where H_1,N and H_2,N are the spaces of holomorphic sections of the N-th tensor powers of hermitian ample line bundles on compact complex manifolds.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.1-57
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• 2003

Vector fields in three-space admit bundles of internal variables such as a Heisenberg algebra bundle. Information transmission along field lines of vector fields is described by a wave linked to the Schrodinger representation in the realm of time-frequency analysis. The preservation of local information causes geometric optics and a quantization scheme. A natural circle bundle models quantum information visualized by holographic methods. Features of this setting are applied to magnetic resonance imaging.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.403-414
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• 2019

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin's result on bosonic operators, and the author's previous result on fermionic operators.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.6 no.6
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• pp.478-485
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• 2005

This paper analysed the ionized fields around HVDC transmission line by the use of the charge simulation method. As this is very complex and expressed by a non-linear partial differential equations, it is hard to solve problems analytically. So, we developed a computer program which can apply in multi-polar HVDC transmission line with conductor bundles and calculated conductor surface gradient, corona current density and ion charge density to prove validity of a proposed algorithm in this paper.