• Honam Mathematical Journal
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• v.34 no.4
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• pp.603-614
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• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. In this sequel, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to present two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, we show that many formulas regarding the Gottlieb polynomials in m variables and their reducible cases can easily be obtained by using one of two generating functions for Choi's generalization of the Gottlieb polynomials in m variables expressed in terms of well-developed Lauricella series $F^{(m)}_D[{\cdot}]$.

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.53-64
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• 2016

In this paper, we give generalization of the $Fej\acute{e}r$-Hadamard inequality by using definition of convex functions on n-coordinates. Results given in [8, 12] are particular cases of results given here.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.529-537
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• 2009

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no. 1-2, 31-37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.225-237
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• 2012

This study proposes a quantification algorithm for a PLS method with several sets of variables. We called the quantification method for PLS with more than 2 sets of data a generalization. The basis of the quantification for PLS method is singular value decomposition. To derive the form of singular value decomposition in the data with more than 2 sets more easily, we used the constraint, $a^ta+b^tb+c^tc=3$ not $a^ta=1$, $b^tb=1$, and $c^tc=1$, for instance, in the case of 3 data sets. However, to prove that there is no difference, we showed it by the use of 2 data sets case because it is very complicate to prove with 3 data sets. The keys of the study are how to form the singular value decomposition and how to get the coordinates for the plots of variables and observations.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.221-234
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• 2010

So far, around 370 various verification of Pythagorean Theorem have been introduced and many studies for the analysis of the method of verification are being conducted based on these now. However, we are in short of the research for the study of the generalization for Pythagorean Theorem. Therefore, by abstracting mathematical materials that is, data(lengths of sides, areas, degree of an angle, etc) which is based on Euclid's elements Vol 1 proposition 47, various methods for the generalization for Pythagorean Theorem have been found in this study through scrutinizing the school mathematics and documentations previously studied.

• Journal of the Korean association of regional geographers
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• v.15 no.2
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• pp.307-315
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• 2009

The purpose of map generalization is a method of map making to transmit the concise cartographic representation and geographic meaning. New generalization algorithm has been developed to be applied in the digital environments by the development of computer cartography. This study aims to look into possibilities of the multiscale mapping by generalization in application with the coordinate transformation and LoD(level of detail) in the web cartography. A method of the coordinate transformation is to improve a transmission of spatial data. Lod is a method which is making web map with selection spatial data by zoom level of users. Layers for test constructed contour line, stream network, the name of a place, a summit of mountain, and administrative office. The generalization was applied to zoom levels by scale for the linear and polygonal features using XML-Based scalable vector graphics(SVG). Resultantly, storage capacity of data was minimized 41% from 9.76mb to 4.08mb in SVG. Generalization of LoD was applied to map elements by stages of the zoom level. In the first stages of zoom level, the main name of places and administrative office, higher order of stream channels, main summit of mountain was represented, and become increase numbers of map elements in the higher levels. Results of this study can help to improve esthetic map and data minimization in web cartography, and also need to make an efforts to research an algorithm on the map generalization over the web.

• Communications of the Korean Mathematical Society
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• v.8 no.4
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• pp.717-722
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• 1993

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.125-132
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• 1998

In this paper we obtain a generalization of Chung's strong law of large numbers to the case of independent fuzzy random variables.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.635-639
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• 1999

We provide a generalization of Whipple's Whipple's quadratic transformation formula for $_3$F$_2$.