• 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.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1147-1165
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• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.

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

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

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1329-1339
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• 2011

For a manifold with a linear connection, we find an obstruction class to have a volume form parallel with respect to its connection which corresponds to the Chern-Simons secondary invariant in the frame bundle of the manifold.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.461-486
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• 2003

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.949-966
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• 2009

In this paper we introduce in study a new class of complex Finsler spaces, namely the complex Randers spaces, for which the fundamental metric tensor and the Chern-Finsler connection are determined. A special approach is devoted to $K{\ddot{a}}ahler$-Randers metrics. Using the length arc parametrization for the extremal curves of the Euler-Lagrange equations we obtain a complex nonlinear connections of Lorentz type in a complex Randers space.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.591-593
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• 2003

The study demonstrates the data extraction capabilities from the simulated ROCSAT-2 image by manual delineation. The GIS data are able to identify as fifteen categories of the classes I & II for the simulated ROCSAT-2 and SPOT image data. The areas of the paddy are identified almost the same results for both cases, but the arid farmland are identified differently about 30%. The ROCSAT-2 case can be also identified as seven more categories of the class III, but SPOT-4 case cannot.

• Journal of Digital Convergence
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• v.14 no.5
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• pp.57-66
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• 2016

In this paper, we describe capstone-related courses in the Computer information department of Dongyang-Mirae University and propose a capstone design model for computer engineering discipline based on operating experiences during the last year. Class schedules and contents, etc are presented from the case studies of two courses on system analysis and design and graduation work(capstone design) opened in 2015. Towards the successful operation of capstone design targeted to training practical and talented professionals with creative problem-solving skills, we propose six execution steps along with principal activities and outputs: Course plan, Project plan, Development, Reporting, Evaluation of students and coursework, and Course feedback. The capstone design model of this study is characterized by presenting the necessity and importance of pre and post steps such as 'Course Plan' and 'Course reflux' from a macroscopic view and by applying software engineering techniques such as prototyping, configuration managements, etc to it.