• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.557-562
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• 2004

A surface-piercing barrier model is presented for understanding morphological development in the sheltered region and investigating the main factors causing the severe accumulation. Surface-piercing structures like vertical barriers, surface docks and floating breakwaters are recently favored from the point of view of a marine scenario since they do not in general partition the natural sea. The numerical solutions are compared with experimental data on wave profiles and morphological change rates within a rectangular harbor of a constant depth protected by surface-piercing thin breakwaters as a simplified problem. Our numerical study involves several modules: 1) wave dynamics analyzed by a plane-wave approximation, 2) suspended sediment transport combined with sediment erosion-deposition model, and 3) concurrent morphological changes. Scattering waves are solved by using a plane wave method without inclusion of evanescent modes. Evanescent modes are only considered in predicting the reflection ratio against the vertical barrier and energy losses due to vortex shedding from the lower edge of plate are taken into account. A new relationship to relate the near-bed concentration to the depth-mean concentration is presented by analyzing the vertical structure of concentration. The numerical solutions were also compared with experimental data on morphological changes within a rectangular harbor of constant water depth. Through the numerical experiments, the vortex-induced flow appears to be not ignorable in predicting the morphological changes although the immersion depth of a plate is not deep.

• Journal of Communications and Networks
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• v.6 no.3
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• pp.258-268
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• 2004

We demonstrate rotationally invariant space-time (ST) trellis codes with a 4-D rectangular signal constellation for data transmission over fading channels using two transmit antennas. The rotational invariance is a good property to have that may alleviate the task of the carrier phase tracking circuit in the receiver. The transmitted data stream is segmented into eight bit blocks and quadrature amplitude modulated using a 256 point 4-D signal constellation whose 2-D constituent constellation is a 16 point square constellation doubly partitioned. The 4-D signal constellation is simply the Cartesian product of the 2-D signal constellation with it-self and has 32 subsets. The partition is performed on one side into four subsets A, B, C, and D with increased minimum-squared Euclidian distance, and on the other side into four rings, where each ring includes four points of equal energy. We propose both linear and nonlinear ST trellis codes and perform simulations using an appropriate multiple-input multiple-output (MIMO) channel model. The 4-D ST codes constructed here demonstrate about the same frame error rate (FER) performance as their 2-D counterparts, having however the added value of rotational invariance.

• The Journal of the Korea Contents Association
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• v.10 no.4
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• pp.106-114
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• 2010

Mesh parameterization is the process of finding one-to-one mapping between an input mesh and a parametric domain. It has been considered as a fundamental tool for digital geometric processing which is required to develop several applications of digital geometries. In this paper, we propose a novel 3D volume parameterization by means that a harmonic mapping is established between a 3D volume mesh and a unit solid cube. To do that, we firstly partition the boundary of the given 3D volume mesh into the six different rectangular patches whose adjacencies are topologically identical to those of a surface cube. Based on the partitioning result, we compute the boundary condition as a precondition for computing a volume mesh parameterization. Finally, the volume mesh parameterization with a low-distortion can be accomplished by performing a harmonic mapping, which minimizes the harmonic energy, with satisfying the boundary condition. Experimental results show that our method is efficient enough to compute 3D volume mesh parameterization for several models, each of whose topology is identical to a solid sphere.