• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.877-896
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• 2017

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1005-1025
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• 2019

The paper is devoted to study local convergence of a continuation method under the assumption of majorant conditions. The method is used to approximate a zero of an operator in Banach space and is of third order. It is seen that the famous Kantorovich-type and Smale-type conditions are special cases of our majorant conditions. This infers that our result is a generalized one in comparison to results based on Kantorovich-type and Smale-type conditions. Finally a number of numerical examples have been computed to show applicability of the convergence analysis.

• Journal of The Korean Association For Science Education
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• v.33 no.7
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• pp.1486-1509
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• 2013

This study aims to identify the image types of secondary school students' perception about the talented person in convergence and to find the differences in drawing images of the talented person in convergence among the students who have taken STEAM class and the ones who haven't. One hundred and eighty seven students in middle and high schools located in the southern part of South Korea participated in this study and they were asked to draw a picture of the talented person in convergence with a brief explanation. Based on students' pictures, researchers categorized their perception about convergence and talented person in convergence by using an inductive method. The result indicated that secondary school students' perceptions were categorized into convergence as individual cognitive processing and collective cognitive processing and convergence as outcomes. The image of the convergence in a talented person leaning toward individual cognitive processing was divided into the following seven types: idea banker type, various talented celebrity type, multi-tasking master type, multi-talented career type, active problem-solver type, creative developer type, and unrealistic ideal man type. Another image of collective cognitive processing was split into expert group type and interactive-mates group type. The other image was transformer type which is the subcategory of convergence as outcomes. From this study, it can be suggested that secondary school students express the various images of the talented person in convergence depending on experiencing STEAM or not.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.7 no.2
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• pp.19-24
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• 2012

This study clearly defined the idea of convergence of small and medium companies and convergence types and understood convergence case of small and medium companies for each type in order to help enhancement of competitiveness of small and medium companies. The convergence type of small and medium companies accepted two levels including technology and industry and value improvement and creation suggested by Deloitte(2009) and it was classified into technology improvement-market expansion type, technology improvement-market creation type, technology creation-market expansion type, and technology creation-market creation type based on the companies introduced in the excellent casebook of convergence and integration technology development business of small and medium companies(August 2011). As a result, it was shown as 5 cases of technology improvement-market expansion, 4 cases of technology improvement-market creation, 3 cases of technology creation-market expansion, and 1 case of technology creation-market creation among the total 13 cases. Therefore, small and medium companies are focusing on technology improvement than technology creation and market expansion than market creation. What we can understand through cases analysis on convergence types of small and medium company is that it is very difficult for small and medium companies to create new technology or new market through convergence. Thus, small and medium companies consider market expansion through technology improvement as the objective and result of convergence. It is important to create new technology or new industry to cultivate new growth engines of the nation, but policy support that cares about reality of small and medium companies must be considered at the same time.

• International Commerce and Information Review
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• v.17 no.1
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• pp.165-191
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• 2015

The results of this study are the two. First, for convergence technology and convergence technology transfer based on analysis of previous studies I suggested a framework for convergence-type technology transfer conceptualization and measurement. Second, I am compared convergence-type technology transfer to total technology transfer from public research(university and public institute) to SME. Overall, despite the trend to increase technology transfer to SMEs, convergence-type technology transfer is only 4.4%. Both total technology transfer and convergence-type technology transfer to the Industry is active to electronic components, machinery, chemicals, food and beverage, and the medical. The role of universities is emphasized in both total technology transfer and convergence-type technology transfer. There are small transactions of less than 5 million in both total technology transfer and convergence-type technology transfer. Both total technology transfer and convergence-type technology transfer to the region are concentrated in Seoul, Daejeon and Gyeonggi-do.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.787-788
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• 2013

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.219-230
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• 2011

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1155-1175
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• 2014

We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost our semilocal convergence criteria can be weaker; the error bounds more precise and in the local case the convergence balls can be larger and the error bounds tighter than in earlier studies such as [1-3,7-14,16,20,21] at least for the cases of Newton's method and the secant method. Numerical examples are also presented to illustrate the theoretical results obtained in this study.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.701-707
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• 2005

Delta sequences play an important role in convergence and approximation theory. Much of classical approximation theory is based on delta sequence. The rate of convergence of certain types of these sequences in Sobolev spaces has recently been studied. Here we estimate convergence rate of convolution type delta sequence in higher dimension.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.671-681
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• 2014

In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators.