• Wind and Structures
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• v.16 no.5
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• pp.457-476
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• 2013

This paper presents theoretical background for a semi-empirical, mathematical model of critical vortex excitation of slender structures of compact cross-sections. The model can be applied to slender tower-like structures (chimneys, towers), and to slender elements of structures (masts, pylons, cables). Many empirical formulas describing across-wind load at vortex excitation depending on several flow parameters, Reynolds number range, structure geometry and lock-in phenomenon can be found in literature. The aim of this paper is to demonstrate mathematical background of the vortex excitation model for a theoretical case of the structure section. Extrapolation of the mathematical model for the application to real structures is also presented. Considerations are devoted to various cases of wind flow (steady and unsteady), ranges of Reynolds number and lateral vibrations of structures or their absence. Numerical implementation of the model with application to real structures is also proposed.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.239-266
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• 2004

This article presents new perspectives for analysing and diagnosing students' mathematical errors on the basis of Pascaul-Leone's neo-Piagetian theory. Although Pascaul-Leone's theory is a cognitive developmental theory, its psychological mechanism gives us new insights on mathematical errors. We analyze mathematical errors in the domain of proof problem solving comparing Pascaul-Leone's psychological mechanism with mathematical errors and diagnose misleading factors using Schoenfeld's levels of analysis and structure and fuzzy cognitive map(FCM). FCM can present with cause and effect among preconceptions or misconceptions that students have about prerequisite proof knowledge and problem solving. Conclusions could be summarized as follows: 1) Students' mathematical errors on proof problem solving and LC learning structures have the same nature. 2) Structures in items of students' mathematical errors and misleading factor structures in cognitive tasks affect mental processes with the same activation mechanism. 3) LC learning structures were activated preferentially in knowledge structures by F operator. With the same activation mechanism, the process students' mathematical errors were activated firstly among conceptions could be explained.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.733-748
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• 2017

We give Hodge structures on quasitoric orbifolds. We define orbifold Hodge numbers and show a correspondence of orbifold Hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend Hodge structures to a non almost complex setting.

• East Asian mathematical journal
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• v.5 no.2
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• pp.155-165
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• 1989

• East Asian mathematical journal
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• v.1
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• pp.65-70
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• 1985

• East Asian mathematical journal
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• v.14 no.1
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• pp.141-148
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• 1998

• Research in Mathematical Education
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• v.20 no.1
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• pp.11-19
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• 2016

Investigating students' lived mathematical experiences presents dual challenges for the researcher. On the one hand, we must respect that students' experiences are not directly accessible to us and are likely very different from our own experiences. On the other hand, we might not want to rely upon the students' own characterizations of what constitutes mathematics because these characterizations could be limited to the formal products students learn in school. I suggest a characterization of mathematics as objectified action, which would lead the researcher to focus on students' operations-mental actions organized as objects within structures so that they can be acted upon. Teachers' and researchers' models of these operations and structures can be used as a launching point for understanding students' experiences of mathematics. Teaching experiments and clinical interviews provide a means for the teacher-researcher to infer students' available operations and structures on the basis of their physical activity (including verbalizations) and to begin harmonizing with their mathematical experience.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1359-1370
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• 2022

In this paper, we study the Finsler warped product metric which is dually flat or projectively flat. The local structures of these metrics are completely determined. Some examples are presented.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.123-130
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• 2013

It is well known that SuanXue QiMeng has given the greatest contribution to the development of Chosun mathematics and that the topics and their presentation including TianYuanShu in the book have been one of the most important backbones in the developement. The purpose of this paper is to reveal that Zhu ShiJie emphasized decidedly mathematical structures in his SuanXue QiMeng, which in turn had a great influence to Chosun mathematicians' structural approaches to mathematics. Investigating structural approaches in Chinese mathematics books before SuanXue QiMeng, we conclude that Zhu's attitude to mathematical structures is much more developed than his precedent ones and that his mathematical structures are very close to the present ones.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.1-12
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• 1998

We construct exotic symplectic structures on $S^3 \times R$ which is obtained by the symplectic sum of two smooth symplectic four-manifolds with exotic symplectic structures, each of which is diffeomorphic to $R^4$.