• East Asian mathematical journal
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• v.21 no.1
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• pp.77-103
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• 2005

The theory of multiple Gamma functions was studied in about 1900 and has, recently, been revived in the study of determinants of Laplacians. There is a class of mathematical constants involved naturally in the multiple Gamma functions. Here we summarize those mathematical constants associated with the Gamma and multiple Gamma functions and will show how they are involved, if possible.

• East Asian mathematical journal
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• v.18 no.2
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• pp.219-224
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• 2002

Recently the theory of the multiple Gamma functions, which were studied by Barnes and others a century ago, has been revived in the study of determinants of Laplacians. Here we are aiming at evaluating the values of the multiple Gamma functions ${\Gamma}_n(\frac{1}{2})$ in terms of the Hurwitz or Riemann Zeta functions.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.523-550
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• 2009

In the paper two-weight inequalities of various type for strong fractional maximal functions and potentials with multiple kernels defined on $\mathbb{R}^2$ are established.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.631-640
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• 2007

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions with small functions in the whole complex plane. We obtain a more general theorem which improves and extends strongly the results of R. Nevanlinna, Li-Qiao, Yao, Yi, and Thai-Tan.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.11
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• pp.2365-2374
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• 1997

This paper describes two algorithms for technology mapping of multiple output functions into interesting and pupular FPGAs(Field Programmable Gate Array) that use look-yp table memories. For improvement of technology mapping for FPGA, we use the functional decompoition method for multiple output functions. Two algorithms are proposed. The one is the Roth-Karpalgorithm extended for multiple output functions. The other is the efficient algorithm which looks for common decomposition functions through the decomposition procedure. The cost function is used to minimize the number of CLBs and nets and to improve performance of the network. Finally we compare our new algorithm with previous logic design technique. Experimental resutls show sigificant reduction in the number of CLBs and nets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.380-383
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• 2003

In this paper, we propose a fuzzy group decision making method for multiple decision maker-multiple objective programming problems to obtain the agreeable solution. In the proposed method, considering the vague nature of human subjective judgement it is assumed that each of multiple decision makers has a fuzzy goal for each of his/her own objective functions. After eliciting the membership functions from the decision makers for their fuzzy goals, total M-Pareto optimal solution concept is defined in membership spaces in order to deal with multiple decision maker-multiple objective programming problems. For generating a candidate of the agreeable solution which is total M-Pareto optimal, the extended weighted minimax problem is formulated and solved for some weighting vector which is specified by the decision makers in their subjective manner, Given the total M-Pareto optimal solution, each of the derision makers must either be satisfied with the current values of the membership functions, or update his/her weighting vector, However, in general, it seems to be very difficult to find the agreeable solution with which all of the decision makers are satisfied perfectly because of the conflicts between their membership functions. In the proposed method, each of the decision makers is requested to estimate the degree of satisfaction for the candidate of the agreeable solution. Using the estimated values or satisfaction of each of the decision makers, the core concept is desnfied, which is a set of undominated candidates. The interactive algorithm is developed to obtain the agreeable solution which satisfies core conditions.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.3
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• pp.191-200
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• 2002

In this paper, we present the method transforming the interval functions into the truncated difference functions for multi-variable multi-valued functions and implementing the truncated difference functions to the multiple valued logic circuits with uniform patterns using the current mirror circuits and the inhibit circuits by current-mode CMOS. Also, we apply the presented methods to the implementation of circuits for additive truth table of 2-variable 4-valued MOD(4) and multiplicative truth table of 2-variable 4-valued finite fields GF(4). These circuits are simulated under 2${\mu}{\textrm}{m}$ CMOS standard technology, 15$mutextrm{A}$ unit current, and 3.3V power supply voltage using PSpice. The simulation results have shown the satisfying current characteristics. Both implemented circuits using current-mode CMOS have the uniform Patterns and the regularity of interconnection. Also, it is expansible for the variables of multiple valued logic functions and are suitable for VLSI implementation.

• The Transactions of the Korea Information Processing Society
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• v.4 no.11
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• pp.2923-2930
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• 1997

This paper describes two algorithms for technology mapping of multiple output functions into interesting and popular FPGAs (Field Programmable Gate Arrays) that lise look-up table memories. For improvement of technology mapping for FPGA, we use the functional decomposition method for multiple output functions. Two algorithms are proposed. The one is the Roth-Karp algorithm extended for multiple output functions. The other is the novel and efficient algorithm which looks for common decomposition functions through the decomposition procedure. The cost function is used to minimize the number of CLBs and nets and to improve performance of the network. Finally we compare our new algorithm with previous logic design technique. Experimental results show significant reduction in the number of CLBs and nets.

• 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.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1239-1248
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• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.