• Korean Journal of Mathematics
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• v.7 no.1
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• pp.45-51
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• 1999

Let X and Y be topological vector spaces. For a sequence {$T_j$} of bounded operators from X into Y the $c_0$-multiplier convergence of ${\sum}T_j$ is an invariant on topologies which are stronger (need not strictly) than the topology of pointwise convergence on X but are weaker (need not strictly) than the topology of uniform convergence on bounded subsets of X.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.278-282
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• 2014

We define a numerical invariant $row^*_j(A)$ over Cohen-Macaulay local ring A, which is related to the presenting matrices of the j-th syzygy module (with or without free summands). We show that $row_d(A)$=$row_{CM}(A)$ and $row^*_d(A)$=$row^*_{CM}(A)$ for a Cohen-Macaulay local ring A of dimension d.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.507-530
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• 2018

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.81-90
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• 2019

We construct gradient Ricci solitons as n-dimensional submanifolds in $S^n{\times}S^n$ by using solutions of some nonlinear ODE.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.623-669
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• 2018

In Donaldson-Thomas theory, moduli spaces are locally the critical locus of a holomorphic function defined on a complex manifold. In this paper, we develop a theory of critical virtual manifolds which are the gluing of critical loci of holomorphic functions. We show that a critical virtual manifold X admits a natural semi-perfect obstruction theory and a virtual fundamental class $[X]^{vir}$ whose degree $DT(X)=deg[X]^{vir}$ is the Euler characteristic ${\chi}_{\nu}$(X) weighted by the Behrend function ${\nu}$. We prove that when the critical virtual manifold is orientable, the local perverse sheaves of vanishing cycles glue to a perverse sheaf P whose hypercohomology has Euler characteristic equal to the Donaldson-Thomas type invariant DT(X). In the companion paper, we proved that a moduli space X of simple sheaves on a Calabi-Yau 3-fold Y is a critical virtual manifold whose perverse sheaf categorifies the Donaldson-Thomas invariant of Y and also gives us a mathematical theory of Gopakumar-Vafa invariants.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.6-8
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• 2005

Study that uses geometrical information in computer vision is lively. Problem that should be preceded is matching problem before studying. Feature point should be extracted for well matching. There are a lot of methods that extract feature point from former days are studied. Because problem does not exist algorithm that is applied for all images, it is a hot water. Specially, it is not easy to find feature point in endoscope image. The big problem can not decide easily a point that is predicted feature point as can know even if see endoscope image as eyes. Also, accuracy of matching problem can be decided after number of feature points is enough and also distributed on whole image. In this paper studied algorithm that can apply to endoscope image. SIFT method displayed excellent performance when compared with alternative way (Affine invariant point detector etc.) in general image but SIFT parameter that used in general image can't apply to endoscope image. The gual of this paper is abstraction of feature point on endoscope image that controlled by contrast threshold and curvature threshold among the parameters for applying SIFT method on endoscope image. Studied about method that feature points can have good distribution and control number of feature point than traditional alternative way by controlling the parameters on experiment result.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.122-124
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• 2005

In this paper, we propose a switching control method for 2nd order nonlinear systems. The main idea behind the method is changing the control law before the trajectory of the solution arrives at the singularities imposed on the denominator of the control law. We show that the control system is asymptotically stable from the fact that the sector consisting of the singular hyperplanes is an invariant set. Illustrative examples are given.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.3
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• pp.186-195
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• 2003

This paper deals with eigenvalue assignment techniques for linear time-varying systems as a way of achieving feedback stabilization. For this, the novel eigenvalue concepts, which are the time-varying counterparts of the conventional (time-invariant) eigenvalue notions, are introduced. Then, the Ackermann-like formulae for SISO/MIMO linear time-varying systems are proposed. It is believed that these techniques are the generalized versions of the Ackermann formulae for linear time-invariant systems. The advantages of the proposed Ackermann-like formulae are that they neither require the transformation of the original system into the phase-variable form nor compute the eigenvalues of the original system. Two examples are given to demonstrate the capabilities of the proposed techniques.