• Journal of Multimedia Information System
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• 제3권3호
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• pp.53-61
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• 2016

This research proposes the index optimization as a classification task and application of the graph based KNN. We need the index optimization as an important task for maximizing the information retrieval performance. And we try to solve the problems in encoding words into numerical vectors, such as huge dimensionality and sparse distribution, by encoding them into graphs as the alternative representations to numerical vectors. In this research, the index optimization is viewed as a classification task, the similarity measure between graphs is defined, and the KNN is modified into the graph based version based on the similarity measure, and it is applied to the index optimization task. As the benefits from this research, by modifying the KNN so, we expect the improvement of classification performance, more graphical representations of words which is inherent in graphs, the ability to trace more easily results from classifying words. In this research, we will validate empirically the proposed version in optimizing index on the two text collections: NewsPage.com and 20NewsGroups.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.271-281
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• 2009

We define injective and projective representations of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\bullet}$. Then we show that a representation $M_1\longrightarrow[50]^{f1}M_2\longrightarrow[50]^{f2}M_3$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\bullet}$ is projective if and only if each $M_1,\;M_2,\;M_3$ is projective left R-module and $f_1(M_1)$ is a summand of $M_2$ and $f_2(M_2)$ is a summand of $M_3$. And we show that a representation $M_1\longrightarrow[50]^{f1}M_2\longrightarrow[50]^{f2}M_3$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\bullet}$ is injective if and only if each $M_1,\;M_2,\;M_3$ is injective left R-module and $ker(f_1)$ is a summand of $M_1$ and $ker(f_2)$ is a summand of $M_2$.

• 대한수학회보
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• 제46권4호
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• pp.771-787
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• 2009

We use an idea of linear representations of the symmetric group to reduce the number of communication rounds in the verification protocol, proposed in Crypto 2005 by Peng et al., of a shuffling. We assume Paillier encryption scheme with which we can apply some known zero-knowledge proofs following the same line of approaches of Peng et al. Incidence matrices of 1-subsets and 2-subsets of a finite set is intensively used for the implementation, and the idea of $\lambda$-designs is employed for the improvement of the computational complexity.

• 대한수학회보
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• 제50권4호
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• 대한수학회보
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• 제54권2호
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• pp.391-397
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• 2017

In this note we extend our previous result about the structure of the dual of a crossed product $C^*$-algebra $A{\rtimes}_{\sigma}G$, when G is a finite group. We consider the space $\tilde{\Gamma}$ which consists of pairs of irreducible representations of A and irreducible projective representations of subgroups of G. Our goal is to endow $\tilde{\Gamma}$ with a topology so that the orbit space e $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to the dual of $A{\rtimes}_{\sigma}G$. In particular, we will show that if $\widehat{A}$ is Hausdorff then $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to $\widehat{A{\rtimes}_{\sigma}G}$.

• 대한수학회논문집
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• 제21권1호
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• pp.37-43
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• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

• 대한수학회지
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• 제34권2호
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• 대한수학회보
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• 제55권1호
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• pp.239-250
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• 2018

A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called w-variables. In this paper, we consider the case when pinched octahedra appear as a boundary parabolic solution in this decomposition. The w-solution with pinched octahedra induces a solution for a new knot obtained by changing the crossing or inserting a tangle at the pinched place. We discuss this phenomenon with corresponding holonomy representations and give some examples including ones obtained from connected sum.

• ETRI Journal
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• 제35권6호
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• pp.1021-1028
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• 2013

Automatic facial expression recognition is a widely studied problem in computer vision and human-robot interaction. There has been a range of studies for representing facial descriptors for facial expression recognition. Some prominent descriptors were presented in the first facial expression recognition and analysis challenge (FERA2011). In that competition, the Local Gabor Binary Pattern Histogram Sequence descriptor showed the most powerful description capability. In this paper, we introduce hybrid facial representations for facial expression recognition, which have more powerful description capability with lower dimensionality. Our descriptors consist of a block-based descriptor and a pixel-based descriptor. The block-based descriptor represents the micro-orientation and micro-geometric structure information. The pixel-based descriptor represents texture information. We validate our descriptors on two public databases, and the results show that our descriptors perform well with a relatively low dimensionality.

• 아동학회지
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• 제22권1호
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• pp.83-96
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• 2001

This study examined the links among parents' interaction styles, their children's representational models of parents and peers, and children's peer acceptance and friendship quality. Forty-seven fourth grade children and their parents (47 mothers and 47 fathers) were observed during discussion interaction, and, one year later, 119 children (63 boys, 56 girls), including the original sample, were interviewed to assess representational models and peer competence. Parents' interaction styles predicted children's representations of parents, moderating the effect of each parent's style, children's representations of peers mediated the relations between the representational models of mothers and their peer acceptance.