• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.571-577
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• 1997

We first show that if $\psi : M_n(B(H)) \to M_n (B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi = S_A$. Secondly, we show that for an operator space $\varepsilon, A \in M_n$, the Schur product map $S_A : M_n(\varepsilon) \to M_n(\varepsilon)$ and $\phi_A : M_n(\varepsilon) \to \varepsilon$, defined by $\phi_A([x_{ij}]) = \sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $\Vert S_A \Vert = \Vert S_A \Vert_{cb} = \Vert A \Vert_S, \Vert \phi_A \Vert = \Vert \phi_A \Vert_{cb} = \Vert A \Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.180-188
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• 1995

A modified Kohonen's self-organizing feature map (SOFM) algorithm which has binary reinforcement function and a constant learning rate is proposed. In contrast to the time-varing adaptaion gain of the original Kohonen's SOFM algorithm, the proposed algorithm uses a constant adaptation gain, and adds a binary reinforcement function in order to compensate for the lowered learning ability of SOFM due to the constant learning rate. Since the proposed algorithm does not have the complicated multiplication, it's digital hardware implementation is much easier than that of the original SOFM.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.25-33
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• 2009

Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.581-591
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• 2015

Let $\mathcal{A}$ be a factor von Neumann algebra with dimension greater than 1. We prove that if a linear map ${\delta}:\mathcal{A}{\rightarrow}\mathcal{A}$ satisfies $${\delta}([[a,b],c])=[[{\delta}(a),b],c]+[[a,{\delta}(b),c]+[[a,b],{\delta}(c)]$$ for any $a,b,c{\in}\mathcal{A}$ with ab = 0 (resp. ab = P, where P is a fixed nontrivial projection of $\mathcal{A}$), then there exist an operator $T{\in}\mathcal{A}$ and a linear map $f:\mathcal{A}{\rightarrow}\mathbb{C}I$ vanishing at every second commutator [[a, b], c] with ab = 0 (resp. ab = P) such that ${\delta}(a)=aT-Ta+f(a)$ for any $a{\in}\mathcal{A}$.

• BMB Reports
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• v.36 no.1
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• pp.66-77
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• 2003

Tea is one of the most popular beverages consumed in the world and has been demonstrated to have anti-cancer activity in animal models. Research findings suggest that the polyphenolic compounds, (-)-epigallocatechin-3-gallate, found primarily in green tea, and theaflavin-3,3'-digallate, a major component of black tea, are the two most effective anti-cancer factors found in tea. Several mechanisms to explain the chemopreventive effects of tea have been presented but others and we suggest that tea components target specific cell-signaling pathways responsible for regulating cellular proliferation or apoptosis. These pathways include signal transduction pathways leading to activator protein-1 (AP-1) and/or nuclear factor kappa B(NF-${\kappa}B$ ). AP-1 and NF-${\kappa}B$ are transcription factors that are known to be extremely important in tumor promoter-induced cell transformation and tumor promotion, and both are influenced differentially by the MAP kinase pathways. The purpose of this brief review is to present recent research data from other and our laboratory focusing on the tea-induced cellular signal transduction events associated with the MAP kinase, AP-1, and NF-${\kappa}B$ pathways.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.1-14
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• 2024

We seek for an invertible map B from L²(Γ) to L²(G), where G is a finite abelian group and Γ is the direct product of finite cyclic groups which is isomorphic to G, so that any Gabor frame in L²(G), is a generalized pseudo B-Gabor frame.

• Journal of Korea Multimedia Society
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• v.15 no.4
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• pp.492-500
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• 2012

In this paper, improved contour region coding method is proposed to accomplish better depth map coding performance. First of all, in order to use correlation between color video and depth map, a structure in SVC is applied to 3DVC. This can reduce bit-rate of the depth map while supporting the video to be transferred via various collection of network. As the depth map is mainly used to synthesize videos from different views, corrupted contour region can damage the overall quality of video. We hereby adapt a new differential quantization method when separating the contour region. The experimental results show that the proposed method can improve video quality by 0.06~0.5dB which translate the bit rate saving by 0.1~1.15%, when compared to the reference software.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.601-609
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• 2011

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.13-27
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• 2024

A regular t-balanced Cayley map on a group Γ is an embedding of a Cayley graph on Γ into a surface with certain special symmetric properties. We completely classify regular t-balanced Cayley maps for a class of split metacyclic 2-groups.

• The KIPS Transactions:PartB
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• v.10B no.6
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• pp.587-592
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• 2003

Many real world control problems have continuous states and actions. When the state space is continuous, the reinforcement learning problems involve very large state space and suffer from memory and time for learning all individual state-action values. These problems need function approximators that reason action about new state from previously experienced states. We introduce Fuzzy Q-Map that is a function approximators for 1 - step Q-learning and is based on fuzzy clustering. Fuzzy Q-Map groups similar states and chooses an action and refers Q value according to membership degree. The centroid and Q value of winner cluster is updated using membership degree and TD(Temporal Difference) error. We applied Fuzzy Q-Map to the mountain car problem and acquired accelerated learning speed.