• 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.

• The Journal of Engineering Geology
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• v.4 no.2
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• pp.127-138
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• 1994

The stationary dual-porosity model is not sufficient to describe the hydraulic characteristics of fractured aquifers as the groundwater flow in fractured aquifers is often controlled by the fractal geometry of fractures. This study deals with new stationary dual-porosity fractal model. This model simulates pseudo-steady state flow from matrix block to fissure in the fractal aquifer. Furthermore, it considers storage capacity and well loss effect at the production well. Type curves for different flow dimensions with different drainage factors are plotted. This new model has been applied to experimental data. The result of the interpretation shows a good accordance between the theoretical model and the observed data.

• Economic and Environmental Geology
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• v.30 no.5
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• pp.433-442
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• 1997

A dual-permeability fractal model of fluid flow is proposed. The model simulates groundwater flow in fissured dual aquifer system composed of Aquifer 1 and Aquifer 2. For this model. groundwater flow originates only from Aquifer 1 on the pumping well. The model considers wellbore storage and skin effects at the pumping well and then shows exact drawdown at the early time of pumping. Type curves for different flow dimensions and for two cases are presented and analyzed. The case 1 represents the aquifer system which consists of Aquifer 1 with low permeability and high specific storage and Aquifer 2 with high permeability and low specific storage. The case 2 is inverse to the case 1. Dimensionless drawdown curves in Aquifer 1 and Aquifer 2 shows characteristic trend each other. Consequently, the model will be useful to analyze pumping test data of different draw down patterns on the pumping well and observation wells.

• The Journal of Engineering Geology
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• v.4 no.3
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• pp.283-295
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• 1994

A new nonstationary dual-porosity fractal model is presented which simulates a nonsteady state block-to-fissure flow with or without fracture skin between the block and the fissure in a fractal aquifer. The model includes weilbore storage and well loss effects on the production well. Type curves for different flow dimensions with different values of hydraulic parameters are created. The application of the model to experimental data in fractured aquifer is described.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.11
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• pp.1216-1224
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• 2003

In this paper Dual Band Log-Periodic Dipole Antenna(DLPDA), which can be used at the Cellular/IMT-2000 band, is proposed. The proposed antenna is composed of 2 of Log-Periodic Dipole Antenna(LPDA) and parasitic elements. To investigate the reliability of the proposed antenna, DLPDA is designed at the cellular/IMT-2000 band and analyzed by using the method of moment, Numerical results are compared with measured results. It is shown that although the antenna length is 70 cm, its radiation characteristics satisfied the design goals of gain, VSWR and beamwidth at the Cellular/IMT-2000 band. From these results, the proposed DLPDA is confirmed as the dual band antenna which can be used at the cellular/IMT-2000 band.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.61-78
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• 2008

In this paper, we discuss about De Morgan's view on the development of algebra according to following distinctions: arithmetic, universal arithmetic, symbolic algebra, significant algebra. De Morgan thought that the differences between arithmetic and universal arithmetic lie in the usage of letters and the immediate performance of computation. In his viewpoint, universal arithmetic is a transitional phase, in which absurd phenomena occur, from arithmetic to algebra and these absurd phenomena call for algebra. The feature of De Morgan's view on the development of algebra is that symbolic calculus which consist of symbol system without symbol's meaning is acquired, then as extended meanings are furnished to symbols, symbolic calculus become logical so significant calculus is developed. For example, Single algebra is developed, as an extended meaning is furnished to a symbol -1, and double algebra is developed, as an extended meaning is furnished to a symbol $\sqrt{-1}$. According to De Morgan, a symbol system is derived from the incompleteness of a prior symbol system.

• 한국상하수도협회지
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• s.6
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• pp.96-100
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• 2004

• Journal of the Korean Society of Groundwater Environment
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• v.4 no.2
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• pp.95-102
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• 1997

So far, several fractal models of fluid flow in a fractured aquifer have been developed. In this study, a new fractal model is derived that considers transient flow in the dual-porosity aquifer with the fracture skin between the fissure and the block, and the storage capacity and the wellbore skin on the pumping well. Constant-head upper boundary is specified in the block. This model is a generalized one which comprises both modified Hantush equation (1960) and Boulton-Streltsova equation (1978). Type curves are plotted for different flow dimensions (0.5, 1, 1.5, 2, 2.5 and 3) with various values of the leakage factor and the fracture skin. They show dimensionless drawdown in the pumping well and observation wells located either in the fissure system or in the matrix block.

• The Journal of Engineering Geology
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• v.29 no.4
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• pp.509-529
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• 2019

This study performs to evaluate the role of filter material at alluvial well for intake of riverbank filtration and the applicability and improvement effect of dual filter well. To achieve this objective, dual filter intake well and single filter intake well were installed with different filter conditions at riverbank free surface aquifer in soil layer then we evaluated filter material condition, permeability, optimum yield and well efficiency according to yield in drawdown test. As a results, we assumed forming dual filter layer minimizes sudden speed changes at boundary between aquifer and filter layer by cushioning of groundwater flow. This suppresses warm current then intake groundwater efficiently, therefore it seems decreasing peripheral groundwater level changes in spite of higher intake water amount than single filter intake well. Furthermore, we confirmed by test, installing dual filter improves permeability, optimum yield and well efficiency. The result will be used by combining with former study to set up standard of design/construction of dual filter intake well at alluvial aquifer layer. Furthermore, we expect this result will be used to prove application effect of dual filter intake well compared to single filter one and radial collector well which are mainly applied on riverbank filtration.

• The Journal of Engineering Geology
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• v.15 no.4 s.42
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• pp.407-421
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• 2005

This study aims to investigate hydrogeological properties of the central area from Yangjeong-Dong to Sujeong-Dong in Busan Metropolitan City. For this study, pumping tests were carried out in the bedrock aquifer of Yangjeong-Dong and the unconsolidated aquifer near Busanjin railway station. The pumping test in the bedrock aquifer containing the Dongrae fault revealed specific hydraulic characteristics with respect to the fault. The pumping test in the unconsolidated aquifer revealed the hydrogeologic properties of both coastal landfill and fine sediments. It was found that the Moench's sphere-shaped dual-porosity model fits the bedrock aquifer, whereas the Neuman's uncofined aquifer model accords with the unconsolidated aquifer. The average transmissivity and storage coefficient of the bedrock aquifer are $2.75{\times}10^{-5}m^2/s\;and\;6.41{\times}10^{-5}$ and those of the unconsolidated aquifer are $8.24{\times}10^{-4}m^2/s\;and\;3.70{\times}10^{-3}$, respectively. On the other hand, slug tests gave average transmissivity and storage coefficient values of $9.84{\times}10^{-4}m^2/s\;and\;1.21{\times}10^{-2}$, respectively.