• Journal for History of Mathematics
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• v.25 no.4
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• pp.69-82
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• 2012

The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.

• Journal of Biomedical Engineering Research
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• v.32 no.1
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• pp.15-24
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• 2011

While Compton imaging is recognized as a valuable 3-D technique in nuclear medicine, reconstructing an image from Compton scattered data has been of a difficult problem due to its computational complexity. The most complex and time-consuming computation in Compton camera reconstruction is to perform the conical projection and backprojection operations. To alleviate the computational burden imposed by these operations, we investigate a rebinning method which can convert conical projections into parallel projections. The use of parallel projections allows to directly apply the existing deterministic reconstruction methods, which have been useful for conventional emission tomography, to Compton camera reconstruction. To convert conical projections into parallel projections, a cone surface is sampled with a number of lines. Each line is projected onto an imaginary plane that is mostly perpendicular to the line. The projection data rebinned in each imaginary plane can then be treated as the standard parallel projection data. To validate the rebinning method, we tested with the representative deterministic algorithms, such as the filtered backprojection method and the algebraic reconstruction technique. Our experimental results indicate that the rebinning method can be useful when the direct application of existing deterministic methods is needed for Compton camera reconstruction.

• Journal of the Korea Fashion and Costume Design Association
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• v.5 no.1
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• pp.47-57
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• 2003

Today there are increasing number of internet users. Internet is wide use of banking, shopping, school and studding. Also, internet is used in everyday living and its use is getting larger. Korea has the one of the most use of internet in the world. Most of houses have computer with internet, and there are alot of PC rooms in the streets. anyone can enjoy the internet anytime anywhere. Now, in internet there are group formed by community purpose. The 'dot com' companies was not making much of profit from their goods. However, they came out with an idea "avata" Soon, the avata became a hit and its known for its success. Avata is used for E-mail, name card, post stamp, and chatting. Also, Avata is very popular among chatting service, icon chatting, and 3D graphic chatting. Avata represent the user himself in internet and computer created imaginary space, and it connects between imaginary space and reality, also it exist between real name and nick name. Past years, the internet users were satisfied with their nick name, however resent year users wants to express them more. For the result the "Avata" is created to fulfill the need to express user themselves. There are three different ways to see how Korean react to fashion industry. first, Korea's land structure makes the density of population high, the transmission of information is very fast. Next, collectively is high among Koreans. Finally wide use to internet made the transmission of the fashion information much faster. The User wants to keep up with the fashion at the sametime they want to express themselves, and "avata" is the one that fulfill their needs. New technology and the desire to express themselves made the new term "avata industry". which was never existed before. In addition, the internet markets have potential power. Although, it is in start stage of avata industry. However, the experts say that its possibility of its development is not predictable. In conclusion, watch the development of a situation to analyze the avata industry and develop new avata fashion market.

• Journal of the Korean Geotechnical Society
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• v.21 no.2
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• pp.93-103
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• 2005

This study was performed to identify the presence of measurement distortions such as electrode polarization and to investigate the influence of soil water content on complex permittivity at low frequency. In low frequency measurement using two-terminal electrode system, electrode polarization effect was observed at frequencies less than approximately 100 HBz. The analysis for real permittivity should be performed at frequencies above 100 kHz in order to exclude electrode polarization effect in the analysis of real permittivity at low frequency measurements. For a given soil, both of real and effective imaginary permittivity of wet soil increased continuously with volumetric water content. This is evidenced by the facts that the real permittivity is proportional to the number of dipole moments per unit volume and effective imaginary permittivity is effected by the conduction due to water. However, proportional relation between real permittivity and volumetric water content is valid at upper MHz frequencies.

• Journal of Industrial Convergence
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• v.21 no.9
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• pp.49-56
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• 2023

ID is used as identifying information and password as user authentication for ID-based authentication. In order to have a secure user authentication, the password is generated as a hash value on the client and sent to the server, where it is compared with the stored information and authentication is performed. However, if even one character is incorrect, the different hash value is generated, authentication will be failed and cannot be performed and various functions cannot be applied to the password. In this study, we generate several hash value including imaginary number of entered password and transmit to server and perform authentcation. we propose a technique can grants the right differentially to give various rights to the user who have many rights by one account. This can defend shoulder surfing attack by imaginary password and provide convenience to users who have various rights by granting right based on password.

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.48-57
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• 2005

A lot of manufacturing knowledge and method have applied to increase manufacturing efficiency in industry field. DES(Discrete Event Simulation) is one of solution to deal with manufacturing problems in factory. Beginning of research, old maintenance system of KNR ( Korea National Railroad) and its technical problems are basically investigated. KNR has maintained railway vehicle with their own solution based on experience. Very advanced railway vehicles such as KTX (Korea Train Express) and TTX(Tilting Train Express) will be difficult to maintain with their old maintenance method. In order to apply knowledge of DES, maintenance field of railway must be considered. Imaginary maintenance machine are selected to variable of DES. Maintenance capability of each machine will be evaluated base on imaginary data from imaginary machine. The machine could be very expensive as well as difficult to replace. Target of research is minimization of number of machine in railway workshop. So basic knowledge of discrete event simulation is introduced. Then five essential stages of discrete event simulation are provided. Each maintenance case defined as event. Each event is discrete and simulated base on different case such as one maintenance line with one machine and one maintenance line with two machines in railway workshop. simple maintenance method, discrete event simulation, will be come out very powerful in complicate maintenance system and will be helpful to reduce maintenance cost as well as maintenance labor.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.17-24
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• 2002

It will be described the discovery of fundamental algebras such as complex numbers and the quaternions. Cardano(1539) was the first to introduce special types of complex numbers such as 5$\pm$$\sqrt{-15}$. Girald called the number a$\pm$$\sqrt{-b}$ solutions impossible. The term imaginary numbers was introduced by Descartes(1629) in “Discours la methode, La geometrie.” Euler knew the geometrical representation of complex numbers by points in a plane. Geometrical definitions of the addition and multiplication of complex numbers conceiving as directed line segments in a plane were given by Gauss in 1831. The expression “complex numbers” seems to be Gauss. Hamilton(1843) defined the complex numbers as paire of real numbers subject to conventional rules of addition and multiplication. Cauchy(1874) interpreted the complex numbers as residue classes of polynomials in R[x] modulo $x^2$＋1. Sophus Lie(1880) introduced commutators [a, b] by the way expressing infinitesimal transformation as differential operations. In this paper, it will be studied general quaternion algebras to finding of algebraic structure in Algebras.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1241-1245
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• 2009

As FFT(Fast Fourier Transform) processor is used in OFDM(Orthogonal Frequency Division Multiplesing) system. According to increase requirement about mobility and broadband, Research about low power and low area FFT processor is needed. So research concern in reduction of memory size and complex multiplier is in progress. Increasing points of FFT increase memory area of FFT processor. Specially, SRU(Signal Reordering Unit) has the most memory in FFT processor. In this paper, we propose a reduced method of memory size of SRU in FFT processor. SRU of 64, 1024 point FFT processor performed implementation by VerilogHDL coding and it verified by simulation. We select the APEX20KE family EP20k1000EPC672-3 device of Altera Corps. SRU implementation is performed by synthesis of Quartus Tool. The bits of data size decide by 24bits that is 12bits from real, imaginary number respectively. It is shown that, the proposed SRU of 64point and 1024point achieve more than 28%, 24% area reduction respectively.

• Journal of KSNVE
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• v.7 no.3
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• pp.511-519
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• 1997

For a number of years it has been known that flexural vibration in a beam and plate can be damped by the application of layer of damping (viscoelastic) material that is in turn constrained by a backing layer or foil. In this study, a quantitative analysis of damping of the sandwich beam has been performed by using impact test. The damping is characterized by the loss factor .etha. in which the damping is normalized by imaginary part of the complex bending stiffiness of the beam. Results show that the relative thickness of the sandwich beam gives more effect on the riatural-frequencies and loss factor than the variation of width does. It is also shown that the Ross-Kerwin-Ungar equation and impact test can be effectively used to identify the damping characteristic of the sandwich beam and viscoelastic material.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.577-580
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• 1999

Padding is a technique that enables applying conventional discrete cosine transform to encode boundary blocks of arbitrarily shaped objects by assigning imaginary values to the pixels that are not included in the object. Padding prevents the increase of high frequency DCT coefficients. However, in some boundary blocks, too many padded pixels are coded due to a small portion of object pixels. To reduce the number of padded pixels and to improve coding efficiency, we propose a block merging method for texture coding. The proposed mothed searches the shape information of boundary blocks and excludes the 4$\times$4 pixels of 8$\times$8 blocks if all the 4$\times$4 pixels are in the background region, and merges the remained 4$\times$4 pixels into new 8$\times$8 blocks. Experimental results show that our proposed method yields a rate-distortion gain about 0.5~1.6㏈ compared to conventional padding method, LPE