• Journal of Elementary Mathematics Education in Korea
• /
• v.22 no.4
• /
• pp.369-384
• /
• 2018

Multiplication is able to be described by using repeated addition, a Cartesian product, a scalar operation, rectangular array and area in many various context. Multiplication in various problem situations is learned by various of the teaching method and the order of teaching more than any other mathematical concepts and operations in elementary school. Nevertheless, the context of multiplication leaves further room for improvement. The purpose of this study is to examine the similarities and differences between the conceptual aspects of multiplication through the literature and to analyze the appropriateness of the teaching method and the order of teaching through textbook analysis. As a result of the study, it was found that multiplication of a scalar operation was introduced too early and did not properly reflect of meaning of multiplication as a scalar operation. There is also a need to use the concept of the rectangular array or area as a meaning of multiplication two quantities.

• Korean Journal of Materials Research
• /
• v.21 no.12
• /
• pp.697-702
• /
• 2011

Two-dimensional (2D) nano patterns including a two-dimensional Bravais lattice were fabricated by laser interference lithography using a two step exposure process. After the first exposure, the substrate itself was rotated by a certain angle, $90^{\circ}$ for a square or rectangular lattice, $75^{\circ}$ for an oblique lattice, and $60^{\circ}$ for a hexagonal lattice, and the $90^{\circ}$ and laser incident angle changed for rectangular and the $45^{\circ}$ and laser incident angle changed for a centered rectangular; we then carried out a second exposure process to form 2D bravais lattices. The band structure of five different 2D nano patterns was simulated by a beam propagation program. The presence of the band-gap effect was shown in an oblique and hexagonal structure. The oblique latticed ZnO nano-photonic crystal array had a pseudo-bandgap at a frequency of 0.337-0.375, 0.575-0.596 and 0.858-0.870. The hexagonal latticed ZnO nano-crystallite array had a pseudo-bandgap at a frequency of 0.335-0.384 and 0.585-0.645. The ZnO nano structure with an oblique and hexagonal structure was grown through the patterned opening window area by a hydrothermal method. The morphology of 2D nano patterns and ZnO nano structures were investigated by atomic force microscopy and scanning electron microscopy. The diameter of the opening window was approximately 250 nm. The height and width of ZnO nano-photonic crystals were 380 nm and 250 nm, respectively.

• Journal of Advanced Marine Engineering and Technology
• /
• v.37 no.1
• /
• pp.40-46
• /
• 2013

Turbulent flow and heat transfer in a channel with a detached rib array have been simulated. The computations are based on the finite volume method with the SIMPLE algorithm. The forms of ribs considered in this study were rib with rectangular cross section, rib with groove, broken rib, and V-shaped rib. The ribs were deployed transverse or aligned $60^{\circ}$ to the main direction of the flow. Local heat transfer coefficients were obtained at various Reynolds numbers within the turbulent flow regime. Area-averaged data were calculated in order to compare the overall performance of the tested ribbed surfaces and to evaluate the degree of heat transfer enhancement induced by the ribs with respect to the smooth channel. The highest heat transfer occurred for the rib with groove which was aligned $60^{\circ}$ to the main flow direction. Performance factor was decreased with the increase of velocity, and it was found that the best performance factor was obtained in the low velocity region.