• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.311-315
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• 2008

We introduce nonnegative interval-valued set functions and nonnegative measurable interval-valued Junctions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [17]. We also obtained absolutely continuity of them in [9]. In this paper, we investigate some characterizations of the monotone interval-valued set function defined by the interval-valued Choquet integral, and such as subadditivity, superadditivity, null-additivity, converse-null-additivity.

• Biomolecules & Therapeutics
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• v.30 no.1
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• pp.98-116
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• 2022

The small GTPase RhoA has been studied extensively for its role in actin dynamics. In this study, multiple bioinformatics tools were applied cooperatively to the microarray dataset GSE64714 to explore previously unidentified functions of RhoA. Comparative gene expression analysis revealed 545 differentially expressed genes in RhoA-null cells versus controls. Gene set enrichment analysis (GSEA) was conducted with three gene set collections: (1) the hallmark, (2) the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway, and (3) the Gene Ontology Biological Process. GSEA results showed that RhoA is related strongly to diverse pathways: cell cycle/growth, DNA repair, metabolism, keratinization, response to fungus, and vesicular transport. These functions were verified by heatmap analysis, KEGG pathway diagramming, and direct acyclic graphing. The use of multiple gene set collections restricted the leakage of information extracted. However, gene sets from individual collections are heterogenous in gene element composition, number, and the contextual meaning embraced in names. Indeed, there was a limit to deriving functions with high accuracy and reliability simply from gene set names. The comparison of multiple gene set collections showed that although the gene sets had similar names, the gene elements were extremely heterogeneous. Thus, the type of collection chosen and the analytical context influence the interpretation of GSEA results. Nonetheless, the analyses of multiple collections made it possible to derive robust and consistent function identifications. This study confirmed several well-described roles of RhoA and revealed less explored functions, suggesting future research directions.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.365-371
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• 2003

In this paper, some limit functions of the iteration of the skew product in the stable sets are investigated, which is associated with finitely generated semigroup for the class M, under some additional conditions.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.315-321
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• 2010

Waring's problem deals with representing any nonconstant function in a set of functions as a sum of kth powers of nonconstant functions in the same set. Consider ${\sum}_{i=1}^p\;f_i(z)^k=z$. Suppose that $k{\geq}2$. Let p be the smallest number of functions that give the above identity. We consider Waring's problem for the set of linear fractional transformations and obtain p = k.

• Journal of Korea Game Society
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• v.14 no.6
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• pp.109-118
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• 2014

We studied the creation of fractal images with polygonal rotation symmetry. As in Loocke's method[13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped. Also we can improve fractal images by modifying probabilistic IFS algorithm, and we suggest a method of deforming Julia set by changing exponent value.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.588-592
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• 2005

We note that Jang et al. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions instead of interval valued, we investigate characterization of compact set-valued Choquet integrals.

• The Journal of the Acoustical Society of Korea
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• v.24 no.5
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• pp.255-261
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• 2005

In this paper. experiments are conducted to extract a set of non-Parametric warping functions to examine the characteristics of the warping among speakers' utterances. For this Purpose. we made use of MFCC and LP spectra of vowels in choosing reference spectrum of each vowel as well as representative spectra of each speaker. These spectra are compared by DTW to give the warping functions of each speaker. The set of warping functions are then defined by clustering the warping functions of all the speakers. Noting that male and female warping functions have shapes similar to Piecewise linear function and Power function respectively, a new hybrid set of warping functions is defined. The effectiveness of the extracted warping functions are evaluated by conducting phone level recognition experiments, and improvements in accuracy rate are observed in both warping functions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.170-173
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• 2005

We note that Jang et at. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions, instead of interval valued we investigate characterization of compact set-valued Choquet integrals.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.57-68
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• 2007

In this article, we investigate the problem of uniqueness of meromorphic functions sharing one set and having deficient values, and obtain a result which improves some earlier results.