• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.27-36
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• 2022

An innovation diffusion model is proposed model consists of three classes, namely, a non-adopter class, adopter class innovation-I, and adopter class innovation-II in a partially competitive and cooperative market. The proposed model is analyzed with the help of the qualitative theory of a system of ordinary differential equations. Basic influence numbers associated with first and second innovation $R_{0_1}$ and $R_{0_2}$ respectively in the absence of each other are quantified. Then the overall basic influence number (R₀) of the system is assessed for analyzing stability in the market in different situations. Sensitivity analysis of basic influence numbers associated with first and second innovation in the absence of each other is carried out. Numerical simulation supports our analytical findings.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-67
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• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.93-101
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• 2003

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.263-271
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• 2010

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, such as the Reidemeister set does in Nielsen fixed point theory. In this paper, using Heath and You's methods on Nielsen type numbers, we show that these numbers can be evaluated by the set of essential orbit classes under suitable hypotheses, and obtain some formulas in some special cases.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.22-24
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• 2002

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy Quantities based on the extension principle suggested by Mares (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous f-norm which holds the distributivity under f-norm based fuzzy arithmetic operations.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.675-677
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• 2005

This study proposes a fuzzy classification using EM algorithm. For cluster validation, this approach iteratively estimates the class-parameters in the fuzzy training for the sample classes and continuously computes the log-likelihood ratio of two consecutive class-numbers. The maximum ratio rule is applied to determine the optimal number of classes.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• Journal of Korean Library and Information Science Society
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• v.18
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• pp.193-216
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• 1991

The purpose of this study is to analyze the area table of twenty editions of the DDC in order to identify what major changes have been made chronologically. The summaries about which were discussed according to the edition order about the change processes of the most extensive area table of the DDC auxiliary table are as follows. 1. It is from the 17th edition that area table appeared as a special auxiliary table in DDC for the first time and the method of classifying areas like from 930 to 999 which is regional history in history class was taken before the introduction of independent area table. 2. The entry numbers in which the area table was applied increased continuously until the 18th edition but the applied entry number was rather decreased in the 20th edition especially the number was mainly decreased in history class, this is the result of the fact that the entry was classified by area table without enumerating each regional history in history class except for the basic area since the 17th edition but recently at least the area of over national unit according to the necessity of enumerating the entry in regional history within history class. 3. The relocation or revision of area table was made according to the literary warrant of the relevant area by period political and administrative conditions and the request of related organization or classifiers of the area rather than by the topographical features therefore the revision was made chiefly about the highly interested Europe Northern America especially the United States. 4. The entry numbers which were expanded according to area indicate that gradual improvement for the international feature as the revision of edition is repeated is made but because of the expansion of Northern America, especially the United States, regional disproportion is represented by the occupation of 56% in the entire entry numbers of the United States in case of the 20th edition. Lastly, the reasonable reform plans of area table will have to be groped on the basis of the results of analysis above and the consideration about the problems in the development of area table of DDC and the other main classification systems.