• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.257-262
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• 2010

Let f be a $C^2$-diffeomorphism on a closed surface which satisfies the Axiom A. Then f is in the $C^2$-interior of the set of all diffeomorphisms having the inverse shadowing property with respect to the class of the continuous methods if and only if f satisfies the strong transversality condition.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.243-265
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• 2004

In this paper, we introduce the fundamental concepts of intuitionistic fuzzy Q-neighborhood, intuitionistic Q-first axiom of countability, intuitionistic first axiom of countability, intuitionistic fuzzy closure operator, intuitionistic fuzzy boundary point and intuitionistic fuzzy accumulation point and investigate some of their properties.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.523-535
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• 2010

There are different categorifications of the notion of a ring such as Ann-category due to N. T. Quang, ring category due to M. M. Kapranov and V. A. Voevodsky. The main result of this paper is to prove that every axiom in the definition of a ring category, but the axiom $x_0 = y_0$, can be deduced from the axiomatics of an Ann-category.

• Journal of the Korean Society of Industry Convergence
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• v.17 no.4
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• pp.194-202
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• 2014

Bonding Machine is new concept of semi industry. In this study, bonding machine is designed with aximatic design, then manufactured based on it. Axiomatic design offers a scientific base for design in an efficient way. Many application of the independence axiom have been pulished, however, the information axiom has been mainly applied to FR - DP problems except for few case studies.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.235-239
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• 2012

Let $f$ be an Axiom A difeomorphism of a closed 2- dimensional smooth manifold M: We show that $f$ has the limit shadowing property if and only if $f$ satisfies the $C^0$ transversality condition.

• The Mathematical Education
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• v.22 no.1
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• pp.31-33
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• 1983

In this paper, we investigate the properties of the semi-continuous functions on the first axiom space, n-th product space, pseudo-metric space, and proximity space. Counterexample is used when the converse of the theorem is not hold.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.987-998
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• 2023

It is shown that every continuum-wise expansive C¹ generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C¹ generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C¹ generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1028-1033
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• 2008

The mount type HVAC control system is a type of an HVAC control system which is installed between a ceiling and ceiling boards of a room to control room temperature. Although the device is quite popular, design is conducted by a conventional way where engineering intuition and experiences are utilized. It is found that the design process is fairly inefficient and time-consuming because there are a lot of feedbacks. The axiomatic approach is used to investigate the design characteristics of the mount type HAVC control system and the Independence Axiom is utilized for the investigation. The Overall hierarchy is established up to the level of parts. It is found that the current design has many coupled and redundant aspects. The hierarchy is reorganized based on the Independence Axiom and a new design process is found. To exploit the new design process in practice, a design manual is made.

• Communications of Mathematical Education
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• v.32 no.2
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• pp.207-223
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• 2018

In this study, we studied Bumwoo KIM Chi Young's cogitation on mathematics, and analyzed his typical 3 essays on mathematics by KoNLP. Approximately 80% of Bumwoo's sentences consist of less than 30. His writing became clearer over the years. It is verified from the mean and standard deviation of the number of words in a sentence are decreasing. Bumwoo emphasized the structure in mathematics, and he was a strong advocate of importancy on axiom, topolized and category as the characteristics of modern mathematics. In particular, it can be seen that the relations between 'mathematics', 'axiom', 'structure', 'Euclid', 'axiomatic system' and 'set' were his main topic.