• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.131-139
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• 1996

Topos is a set-like category. For an axiom of choice in a topos, F. W. Lawvere and A. M. Penk introduced another versions of the axiom of choice. Also it is showed that general axiom of choice and Penk's axiom of choice are weaker than Lawvere's axiom of choice. In this paper we study that weak form of axiom of choice, axiom of choice, Penk's axiom of choice and Lawvere's axiom of choice are all equivalent in a well pointed topos.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.29-34
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• 2004

There are various forms of the axiom of choice and also various weak forms of the axiom of choice in a topos. This paper give equivalent forms of the axiom of choice in a well-pointed topos.

• Journal of the Korean Society of Marine Environment & Safety
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• v.20 no.3
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• pp.296-303
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• 2014

The Axiom propeller is a unique 3 bladed propeller and it enables to generate the same amount of thrust going ahead as it does going astern because of its 's' type skew-symmetric blade section. A earlier variant of the design (Axiom I propeller) performed a low propeller efficiency, maximum 35 % efficiency, and further blade outline design was carried out to achieve a higher efficiency. The optimized new blade outline (Axiom II propeller) has more conventional Kaplan geometry shape than Axiom I propeller. Model tests of open water performance and propeller cavitation for both propellers were conducted at Emerson Cavitation Tunnel in order to compare their performances. Experiment results revealed that Axiom II propeller provides a maximum 53 % efficiency and provides better efficiency and cavitation performance over the Axiom I propeller under similar conditions.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.85-92
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• 2008

In topoi, there are various forms of the axiom of choice such as (ES), (AC) and (WO). And also there are various weak forms of the axiom of choice such as (DES), (IAC) and (ASC). First we investigate the relation between (IAC) and (ASC), and then we study the relation between (AC) and (WO). We get equivalent forms of the axiom of choice in a well-pointed topos.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1727-1735
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• 2002

The usage of beam scanning type laser marker is rapidly increasing in the field of semiconductor equipment. A device called ″beam adjuster″ is employed to adjust the visible diode laser, which points the marking position for various setting. The device is very sensitive to manufacturing tolerance and assembly condition. Axiomatic approach has been applied to the design of the device. An existing design is analyzed based on the Independence Axiom. The existing design is found to violate the axiom. Two new designs are proposed to satisfy the Independence Axiom. The Information Axiom is utilized to evaluate the designs. A design is selected to have the minimum information content. The significance of this research is that a full cycle of axiomatic design is applied to a real engineering product.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.3
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• pp.107-114
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• 1999

Design Axiom proposed by N. P. Such consists of Independence Axiom & Information Axiom. Based on the Independence Axiom, it is very useful specially for early design stage such as conceptual design to generate the design alternatives by considering both functions and structures of product. Since the Information Axiom shows that the design solution should have a least information to be the best one among the many alternatives, this axiom can be used for the best selection purpose during the preliminary design stage. In this paper, the possibility of Design Axiom in marine design application is checked by carrying out three examples of marine design. In the conceptual design of thruster, it is proven to use the Independence Axiom very effective by relating directly functional requirements with design parameters, one by one. In main engine selection example, Information Axiom is used to select best solution among alternatives by choosing the one having the minimum information quantity. For similarity based design in which the selection of changing design variables and the amount of those are important, it is proved that design axiom applied to Barge design case would be very effective and useful. As functional requirements and constrains were not clarified in early design stage, design axiom shows some difficulty for larger system design like ship which is basically carried out by an incremental and iterative process.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.25-29
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• 1995

The topos constructed in [6] is a set-like category that includes among its axioms an axiom of infinity and an axiom of choice. In its final form a topos is free from any such axioms. Set$\^$G/ is a topos whose object are G-set Ψ$\sub$s/:G${\times}$S\longrightarrowS and morphism f:S \longrightarrowT is an equivariants map. We already known that Set$\^$G/ satisfies the weak form of the axiom of choice but it does not satisfies the axiom of the choice.(omitted)

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2000.06a
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• pp.3-10
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• 2000

The undesired situation of development of tribology and its reason is analyzed. The problem comes from insufficient study on the concept system and method system, which can match the name, definition and nature of tribology. The existence of three axioms in tribology is discussed. They are axiom of system dependent, axiom of time dependent and axiom of coupling of behaviors of multi-discipline. A series of lemmas has been deduced from three axioms. It is expected that they can be a foundation to establish the concept system and method system.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.249-254
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• 2006

Category Fuz of fuzzy sets has a similar function to the topos Set. But Category Fuz forms a weak topos. We show that supports split weakly(SSW) and with some properties, implicity axiom of choice(IAC) holds in weak topos Fuz. So weak axiom of choice(WAC) holds in weak topos Fuz. Also we show that weak extensionality principle for arrow holds in weak topos Fuz.

• Journal for History of Mathematics
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• v.30 no.5
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• pp.261-287
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• 2017

De Zolt's axiom which is a precise formulation of Euclid's Common Notion 5, "the whole is greater than the part", for the notion of 'content' holds in any Hilbert plane. In this article, we study the history of de Zolt's axiom which has its origin in Euclid's Common Notions, and introduce an example of a plane geometry in which de Zolt's axiom does not hold. We show that there is no area function in this geometry and every square is equidecomposable with a square which is properly contained in the first one. From this we also show that there are two equidecomposable rectangles which have the same base and do not have the same altitude, and there is a rectangle which is equicomplementable with an emptyset.