• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.455-463
• /
• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Journal of the Korean Mathematical Society
• /
• v.40 no.6
• /
• pp.933-942
• /
• 2003

It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T/sup 2*/T/sup 2/ - 2T/sup */T ＋ I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict ontraction.

• Journal of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.929-944
• /
• 2015

We give a quotient of the ring ${\mathbb{Q}}[A^{{\pm}1},\;t^{{\pm}1]$ so that the Miyazawa polynomial is a non-trivial invariant of welded links. Furthermore we show that this is also an invariant under the other forbidden move $F_u$, and so it is a fused isotopy invariant. Also, we give some quotient ring so that the index polynomial can be an invariant for welded links.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.347-355
• /
• 2001

Let ($X, \omega$) be a closed symplectic 4-manifold. Let a finite cyclic group G act semifreely, holomorphically on X as isometries with fixed point set $\Sigma$(may be empty) which is a 2-dimension submanifold. Then there is a smooth structure on the quotient X'=X/G such that the projection $\pi$:X$\rightarrow$X' is a Lipschitz map. Let L$\rightarrow$X be the Spin$^c$ -structure on X pulled back from a Spin$^c$-structure L'$\rightarrow$X' and b_2^$+(X')>1. If the Seiberg-Witten invariant SW(L')$\neq$0 of L' is non-zero and $L=E\bigotimesK^-1\bigotimesE$ then there is a G-invariant pseudo-holomorphic curve u:$C\rightarrowX$,/TEX> such that the image u(C) represents the fundamental class of the Poincare dual $c_1$(E). This is an equivariant version of the Taubes' Theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.327-340
• /
• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• Journal of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.275-306
• /
• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.11 no.1
• /
• pp.66-74
• /
• 2008

This paper presents a new small target detection method using scale invariant feature. Detecting small targets whose sizes are varying is very important to automatic target detection. Scale invariant feature using the Laplacian scale-space can detect different sizes of targets robustly compared to the conventional spatial filtering methods with fixed kernel size. Additionally, scale-reflected adaptive thresholding can reduce many false alarms. Experimental results with real IR images show the robustness of the proposed target detection in real world.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 2001.04a
• /
• pp.131-136
• /
• 2001

The purpose of this paper is to develop image inspection system endows an automatic operating and measuring that the moment values are invariant with respect to variable object size and rotation. In this paper, using these moment feature vector with Hu s 7 invariant moment is also given. The characteristics of section which is applied in the mechanics used moment descriptor of invariant moment detection algorithm for image inspection system. Corresponding rates between 94% and 96% have been achived for all object tested.

• Journal of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.109-128
• /
• 2003

In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP$^{n}$ invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chen's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP$^{n}$ ; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.

• Journal of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.139-151
• /
• 2012

In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [${S_z}^n$, $S_w^*$] = 0 for a positive integer n ${\geq}$ 2. In this case, it holds that ${S_z}^n=cI$ for some $c{\in}\mathbb{C}$. In this paper, it is proved that if [$S_{\varphi}$, $S_w^*$] = 0 and ${\varphi}{\in}H^{\infty}({\Gamma}_z)$, then $S_{\varphi}=cI$ for some $c{\in}\mathbb{C}$.