• International Journal of Knowledge Content Development & Technology
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• v.9 no.3
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• pp.23-41
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• 2019

This study combines the concept of degree centrality in complex network with the Term Frequency $^*$ Proportional Document Frequency ($TF^*PDF$) algorithm; the combined method, called PMCN (PDF-Modified similarity and Complex Network), constructs relationship networks among sentences for writing news summaries. The PMCN method is a multi-document summarization extension of the ideas of Bun and Ishizuka (2002), who first published the $TF^*PDF$ algorithm for detecting hot topics. In their $TF^*PDF$ algorithm, Bun and Ishizuka defined the publisher of a news item as its channel. If the PDF weight of a term is higher than the weights of other terms, then the term is hotter than the other terms. However, this study attempts to develop summaries for news items. Because the $TF^*PDF$ algorithm summarizes daily news, PMCN replaces the concept of "channel" with "the date of the news event", and uses the resulting chronicle ordering for a multi-document summarization algorithm, of which the F-measure scores were 0.042 and 0.051 higher than LexRank for the famous d30001t and d30003t tasks, respectively.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.33-40
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• 1995

A space Y is called finitely dominated if there is a finite complex K such that Y is a retract of K in the homotopy category, i.e., we require maps $i : Y \longrightarrow K and r : K \longrightarrow Y with r \circ i \simeq idy$. The following questions are very classical in topology.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.462-465
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• 2006

This paper is aimed at proposing the sampling method to reduce variance of statistical parameters in uncertainty analysis of concrete structures. The proposed method is a modification of Latin Hypercube sampling method. This uses specially modified tables of random permutations of rank number. Also, the Spearman coefficient is used to make modified tables. Numerical analysis is carried out to predict the uncertainty of axial shortening in prestressed concrete bridge. The numerical results show that the method is efficient for uncertainty analysis of complex structural system such as prestressed concrete bridges.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.85-89
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• 2003

Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $D_1$ R in the same system of lines on X the vector bundles E$\mid$D and E$\mid$R have the same splitting type.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.19-28
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• 1997

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.471-479
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• 2010

For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.3
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• pp.53-62
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• 1994

Complex decision-making problems are often characterized by multicriteria phenomena and fuzziness inherent in the structure of information and therefore suitable scientific solution methods. Especially, when similar dependent criteria are introduced, the problems become more complex. This paper presents a fuzzy intersectional dependence relation model for this kind of multicriteria decision-making problems. The model we propose is based on the fuzzy relation from fuzzy systems theory. In ths case of introducing similar dependent criteria, the rank reversal by distortion of weights is hard to occur by our proposed method. A numerical example is presented to illustrate the use of the model.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-297
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• 2002

It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.137-149
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• 2020

Let γ⁽ⁿ⁾ ≡ {γ_ij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ⁽ⁿ⁾. For an odd number n, it is known that γ⁽ⁿ⁾ has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.411-430
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• 2019

Tumor development is driven by complex combinations of biological elements. Recent advances suggest that molecularly distinct subtypes of breast cancers may respond differently to pathway-targeted therapies. Thus, it is important to dissect pathway disturbances by integrating multiple molecular profiles, such as genetic, genomic and epigenomic data. However, missing data are often present in the -omic profiles of interest. Motivated by genomic data integration and imputation, we present a new statistical framework for pathway significance analysis. Specifically, we develop a new strategy for imputation of missing data in large-scale genomic studies, which adapts low-rank, structured matrix completion. Our iterative strategy enables us to impute missing data in complex configurations across multiple data platforms. In turn, we perform large-scale pathway analysis integrating gene expression, copy number, and methylation data. The advantages of the proposed statistical framework are demonstrated through simulations and real applications to breast cancer subtypes. We demonstrate superior power to identify pathway disturbances, compared with other imputation strategies. We also identify differential pathway activity across different breast tumor subtypes.