• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.201-204
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• 1992

After this discovery of lower bounds by Stark and Odlyzko, some people searched for number fields with relatively small discriminants. Also some others studied algorithms which will produce number fields with the smallest absolute value of the discriminant for a fixed degree n. However, this algorithmic approach does not work well if the extension degree n is greater than seven or eight. And it is not clear whether current computers can finish those algorithms in a reasonable amount of time for large n. So we are justified in our approach for this subject. In this paper we will report the results of our computations. Some number fields we found are better than previously known examples. Others are rediscoveries of known examples. However, there is theoretically nothing new in our approach to this subject.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2346-2361
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• 2017

A major challenge in cloud infrastructure is the efficient allocation of virtual network elements on top of substrate network elements. Path algebra is a mathematical framework which allows the validation and convergence analysis of the mono-constraint or multi-constraint routing problems independently of the network topology or size. The present study proposes a new heuristic approach based on mathematical framework "paths algebra" to map virtual nodes and links to substrate nodes and paths in cloud. In this approach, we define a measure criterion to rank the substrate nodes, and map the virtual nodes to substrate nodes according to their ranks by using a greedy algorithm. In addition, considering multi-constraint routing in virtual link mapping stage, the used paths algebra framework allows a more flexible and extendable embedding. Obtained results of simulations show appropriate improvement in acceptance ratio of virtual networks and cost incurred by the infrastructure networks.

• The Mathematical Education
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• v.42 no.2
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• pp.87-109
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• 2003

This paper aims to review the overall development of constructivist approaches in science education research from two different perspectives, that is a summary of the past development in science education in general and a report of the outline of a recent research project on students' physics misconceptions in particular. In the summary of the past development of constructivist science education the introduction of constructivism as well as its psychological and philosophical backgrounds are briefly reported. Then main findings of the researches of constructivist approach are discussed in terms of the features of students' misconceptions, of the ways of effective conceptual change, of the implications toward school science education, and of the criticisms given to the constructivist approach. In the report of a recent development in addition to its background necessity and implications, the research structure and the format of the data analysis of the study on the map of students' physics misconceptions are presented. It is particularly emphasized that the practical informations and suggestions for actual teaching of school science, such as the database(DB) of students' misconceptions and teaching guides, are of most practical and effective values in order to maximize the advantage of the constructivist approach to science education.

• Research in Mathematical Education
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• v.24 no.3
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• pp.175-199
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• 2021

The Science Writing Heuristic (SWH) approach is described as an immersive argument-based science inquiry focusing particularly on learning through epistemic practices. In the literature, several previous studies indicate how academic achievement is positively influenced by the SWH. In addition to these previous studies, several meta-syntheses of qualitative data have been conducted on this particular topic. With these literatures in mind, a quantitative meta-analysis was conducted with ten studies (N = 724) to examine the effectiveness of the SWH on student achievement in Turkey. To present a thoroughly detailed report, this study also examined the following moderators: grade level, subject area, school location, intervention length, and report source. Overall, this study found that in Turkey, the SWH classrooms performed better in academic achievement tests than traditional lecture-based classrooms. Additionally, the SWH is more likely to be effective regardless of grade levels, subject areas, and school locations.

• Research in Mathematical Education
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• v.25 no.3
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• pp.227-244
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• 2022

The concrete-representational-abstract integrated (CRA-I) sequence is an explicit approach for teaching students who struggle in mathematics. This approach is beneficial because it assists students in the development of conceptual understanding. This article describes how the approach is used in general as well as its use with a specific geometry concept, area of a rectangle. The author will describe why one might choose CRA-I and the steps needed for implementation. Finally, the CRA-I steps will be shown with a lesson series related to teaching the concept of area. The article will describe lesson activities, methods, materials, and procedures.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.279-294
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• 2016

Half integer values of harmonic numbers and reciprocal binomial squared coeffients sums are investigated in this paper. Closed form representations and integral expressions are developed for the infiite series.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.103-109
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• 1994

Piezoceramic patches as collocated actuator and sensors are widely used in mechanical control systems. An approximation scheme for computing feedback gains arising in heat flux stabilization problem with such control mechanism is introduced. The scheme is based on a finite element method and a variational approach.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1051-1063
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• 2007

The aim of this note is to advertise a method which turns out to be powerful enough to be used successfully in problems which are apparently unrelated. It is based on a modification of a construction that we first introduced in [2].

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.219-225
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• 2014

I use the dynamic programming approach to study the optimal consumption and investment problem with regime-switching and constant labor income. I derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility and constant disutility.

• East Asian mathematical journal
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• v.34 no.5
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• pp.549-570
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• 2018

We establish existence and bifurcation of global positive solutions for parametrized nonhomogeneous elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms. The main approach to the problem is the variational method.