• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.1-16
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• 2008

Suanxue qimeng(算學啓蒙) is the introduction to mathematics which greatly influenced Chosun mathematics, Muksa-jipsanbup(默思集算法) imitated the style and the contents of Suanxue qimeng, but contains a lot of problems, secondary solutions and topics which is not in Suanxue qimeng and tried to achieve educational improvement. However Muksa-jipsanbup could not use the method of rectangular arrays(方程術) because it excluded the method of positive and negative(正負術), and has a serious limitation in applying the method of extracting roots by iterated multiplication(增乘開方法) because it avoided the technique of the celestial element(天元術).

• The KSFM Journal of Fluid Machinery
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• v.13 no.5
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• pp.43-53
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• 2010

This study investigates a design optimization of a rotating two-pass rectangular cooling channel with staggered arrays of pin-fins. The radial basis neural network method is used as an optimization technique with Reynolds-averaged Navier-Stokes analysis of fluid flow and heat transfer with shear stress transport turbulent model. The ratio of the diameter to height of the pin-fins and the ratio of the streamwise spacing between the pin-fins to height of the pin-fin are selected as design variables. The optimization problem has been defined as a minimization of the objective function, which is defined as a linear combination of heat transfer related term and friction loss related term with a weighting factor. Results are presented for streamlines, velocity vector fields, and contours of Nusselt numbers, friction coefficients, and turbulent kinetic energy. These results show how fluid flow in a two-pass square cooling channel evolves a converted secondary flows due to Coriolis force, staggered arrays of pin-fins, and a $180^{\circ}$ turn region. These results describe how the fluid flow affects surface heat transfer. The Coriolis force induces heat transfer discrepancy between leading and trailing surfaces, having higher Nusselt number on the leading surface in the second pass while having lower Nusselt number on the trailing surface. Dean vortices generated in $180^{\circ}$ turn region augment heat transfer in the turning region and in the upstream region of the second pass. As the result of optimization, in comparison with the reference geometry, thermal performance of the optimum geometry shows the improvement by 30.5%. Through the optimization, the diameter of pin-fin increased by 14.9% and the streamwise distance between pin-fins increased by 32.1%. And, the value of objective function decreased by 18.1%.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.3C
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• pp.323-330
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• 2007

Performance indicators such as output SNR, SIR, SINR for rectangular smart antennas in CDMA basestations have been derived. Simulations have been carried out to find the rectangular smart antenna performance while varying the input SNR, number of antenna elements, and the interferers' spatial distributions. Simplified Conjugate Gradient Method was chosen as the underlying beam forming algorithm. It has been shown that the performance of a rectangular smart antenna is similar to that of the linear one having the same number of elements when the interferers are randomly distributed over the whole azimuth angle range.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.8
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• pp.973-982
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• 1997

Effect of vortex generator on the heat transfer enhancement of electronic chips is investigated using naphthalene sublimation technique. Experiments are performed for a single chip and chip arrays, and shape of vortex generator, position of vortex generator, stream wise chip spacing and air velocity are varied. Local and average heat transfer coefficients are measured on the top surface of simulated electronic chips, and compared with those obtained without vortex generator. In case of a single chip, heat transfer augmentation is seen only on the upstream portion of chip surface, while heat transfer enhancement is found on the whole surface for chip arrays. Rectangular wing type vortex generator is found to be more effective than delta wing.

• Journal of Communications and Networks
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• v.18 no.5
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• pp.735-743
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• 2016

This paper proposes a direction-of-arrival (DOA)-based beamforming approach for multi-cell massive multiple-input multiple-output systems with uniform rectangular arrays (URAs). The proposed approach utilizes the steering vectors of the URA to form a basis of the spatial space and selects the partial space for beamforming according to the DOA information. As a result, the proposed approach is of lower computational complexity than the existing methods which utilize the channel covariance matrices. Moreover, the analysis demonstrates that the proposed approach can eliminate the interference in the limit of infinite number of the URA antennas. Since the proposed approach utilizes the multipaths to enhance the signal rather than discarding them, the proposed approach is of better performance than the existing low-complexity method, which is verified by the simulation results.

• JSTS:Journal of Semiconductor Technology and Science
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• v.7 no.1
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• pp.56-65
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• 2007

This paper describes physical meanings of various influences of cavity (or pillar) shape and filling factor of dielectric material on band structures in two-dimensional photonic crystals. Influences of circular and rectangular cross-sections of cavity (or pillar) arrays on photonic band structures are considered theoretically, and significant aspects of square and triangular lattices are compared. It is shown that both averaged dielectric constant of the photonic crystal and distribution profile of photon energy play important roles in designing optical properties. For the triangular lattice, especially, it is shown that cavity array with a rectangular cross-section breaks the band structure symmetry. So, we discuss this point from the band structure and address optical properties of lattice with a circular cross-section cavity.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2352-2356
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• 2008

Heat transfer and performance characteristics have been investigated for a rectangular wavy duct with dimple or protrusion arrays. The test duct was 15mm in height and 105mm wide. The print diameter of the dimple/protrusion wall was 12.99mm and the depth/height of the dimple/protrusion was 3.75mm. Local heat transfer coefficients on the dimple/protrusion wall were measured using a transient TLC technique. The Reynolds number was varied from 3,000 to 10,000. For the wavy duct tested in this study, adverse static pressure characteristics occurred at turning region of the wavy duct due to secondary flows. For the wavy duct with protrusion array, higher heat transfer enhancement level of 7.4 times than smooth straight case in maximum was obtained at low Reynolds number due to the high heat transfer enhancement by vortex flows. Also, the protrusion array increased the performance level of 3.0 at low Reynolds number of 3,000.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.6
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• pp.861-870
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• 1999

An experimental study was carried out to investigate the effects of using various shapes of turbulence promoter on the heat-transfer enhancement of 2-D and 3-D arrays of rectangular modules in a rectangular channel for design of noiseless and low-powered cooling fan in the electronic systems. Measurements of heat/mass transfer coefficients were made using a naphthalene sublimation technique, and the friction factors were measured for Reynolds numbers in the range$3.3{\time}10^3$~$1.6{\time}10^4$. Flow visualization was peformed by oil-film method. It was found that heat transfer and pressure drop increased remarkably due to the existence of the promoter. The results of the performance evaluation based on equal pumping power were showed that substantial heat-transfer enhancement was obtained at low Reynolds number range by use of a turbulence promoter.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.2
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• pp.24-32
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• 1992

The impedance matching properties of infinite planar arrays of rectangular waveguides with dielectric plug loading and sheath covering are studied here. The effects of several involved parameters on the impedance matching of the phased array antenna are investigated by calculating the reflection coefficients numerically. The improvement of impedance matching and the appearance of forced surface wave resonances are also discussed.