• School Mathematics
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• v.9 no.1
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• pp.13-28
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• 2007

Division of fractions can be categorized as measurement division, partitive or sharing division, the inverse of multiplication, and the inverse of Cartesian product. Division algorithm for fractions has been interpreted with manipulative aids or models mainly in the contexts of measurement division and partitive division. On the contrary, there are few interpretations for the context of the inverse of a Cartesian product. In this paper the significance and the limits of existing interpretations of division of fractions in the context of the inverse of a Cartesian product were discussed. And some new easier interpretations of division algorithm in the context of a Cartesian product are developed. The problem to determine the length of a rectangle where the area and the width of it are known can be solved by various approaches: making the width of a rectangle be equal to one, making the width of a rectangle be equal to some natural number, making the area of a rectangle be equal to 1. These approaches may help students to understand the meaning of division of fractions and the meaning of the inverse of the divisor. These approaches make the inverse of a Cartesian product have many merits as an introductory context of division algorithm for fractions.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.721-725
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• 2004

Multiple-count problem is occurred when rectangle objects span across several buckets. The Cumulative Density (CD) histogram is a technique which solves multiple-count problem by keeping four sub-histograms corresponding to the four points of rectangle. Although it provides exact results with constant response time, there is still a considerable issue. Since it is based on a query window which aligns with a given grid, a number of errors may be occurred when it is applied to real applications. In this paper, we proposed selectivity estimation techniques using the generalized cumulative density histogram based on two probabilistic models: (1) probabilistic model which considers the query window area ratio, (2) probabilistic model which considers intersection area between a given grid and objects. In order to evaluate the proposed methods, we experimented with real dataset and experimental results showed that the proposed technique was superior to the existing selectivity estimation techniques. The proposed techniques can be used to accurately quantify the selectivity of the spatial range query on rectangle objects.

• Journal of Advanced Navigation Technology
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• v.10 no.4
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• pp.385-393
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• 2006

In this paper, we proposed a location estimation algorithm considering an extension of searching area in 2.45GHz band RTLS and analyzed its performance in terms of an average estimation error distance. The extendable searching area was assumed to be square of $300m{\times}300m$ and 2 dimensions. The arrangement shape of available readers was considered circle, rectangle, and shrinkage rectangle for extendable searching area. Also, we assumed that propagation path was LOS (Line-Of-Sight) environment, and analyzed the estimation error performance as a function of the number of received sub-blink considering an arrangement shape of available readers in searching area. From the results, compared with rectangle shape, circle shape showed the higher estimation accuracy. Also, we confirmed that the proposed location estimation algorithm provided high estimation accuracy in the shrinkage rectangle shape that was suitable for extension of searching area.

• International Journal of Contents
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• v.9 no.1
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• pp.6-10
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• 2013

Foreground estimation in object segmentation has been an important issue for last few decades. In this paper we propose a GrabCut based automatic foreground estimation method using block clustering. GrabCut is one of popular algorithms for image segmentation in 2D image. However GrabCut is semi-automatic algorithm. So it requires the user input a rough boundary for foreground and background. Typically, the user draws a rectangle around the object of interest manually. The goal of proposed method is to generate an initial rectangle automatically. In order to create initial rectangle, we use Gabor filter and Saliency map and then we use 4 features (amount of area, variance, amount of class with boundary area, amount of class with saliency map) to categorize foreground and background. From the experimental results, our proposed algorithm can achieve satisfactory accuracy in object segmentation without any prior information by the user.

• Journal of the Korea Society of Computer and Information
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• v.15 no.2
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• pp.55-64
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• 2010

This paper proposes a face detection method using Free Rectangle feature which possesses a quick execution time and a high efficiency. The proposed mask of Free Rectangle feature is composed of two separable rectangles with the same area. In order to increase the feature diversity, Haar-like feature generally uses a complex mask composed of two or more rectangles. But the proposed feature mask can get a lot of very efficient features according to any position and scale of two rectangles on the feature window. Moreover, the Free Rectangle feature can largely reduce the execution time since it is defined as the only difference of the sum of pixels of two rectangles irrespective of the mask type. Since it yields a quick detection speed and good detection rates on real world images, the proposed face detection method based on Adaboost algorithm is easily applied to detect another object by changing the training dataset.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.4
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• pp.708-712
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• 1987

This paper deals with minimizing layout area of VLSI design. A long wire in a VLSI layout causes delay which can be reduced by using a driver. There can be significant area increase when many drivers are introduced in a layout. This paper describes a method to obtain tight bound on the worst-case increase in area when drivers are introduced along many long wires in a layout. The area occupied by minimum-area embedding for a circuit can depend on the aspect ratio of the bounding rectangle of the layout. This paper presents a separator-based area optimal embeddings for VLSI graphs in rectangles of several aspect ratios.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.181-199
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• 2011

The area formula for a plane figure represents the relations between the area and the lengths which determine the area of the figure. Students are supposed to understand the relations in it as well as to be able to find the area of a figure using the formula. This study investigates how 5th grade students understand the formulas for the area of triangle, rectangle and parallelogram, focusing on their understanding of functional relations in the formulas. The results show that students have insufficient understanding of the relations in the area formula, especially in the formula for the area of a triangle. Solving the problems assigned to them, students developed three types of strategies: Substituting numbers in the area formula, drawing and transforming figures, reasoning based on the relations between the variables in the formula. Substituting numbers in the formula and drawing and transforming figures were the preferred strategies of students. Only a few students tried to solve the problems by reasoning based on the relations between the variables in the formula. Only a few students were able to aware of the proportional relations between the area and the base, or the area and the height and no one was aware of the inverse relation between the base and the height.

• Fire Science and Engineering
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• v.24 no.3
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• pp.93-98
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• 2010

Even though the sprinkler system is a essential fire suppression system, the design engineers do not fully understand the concept of design area which sprinklers operate. They frequently made a mistake to form design area and calculate it. The shape of design area is a square or a rectangle which branch side line is a little longer than the cross main side. NFPA demands to lengthen the branch side to 1.2 times than the cross main side and FM demands 1.4 times. The longer the branch side at the same design area is, the bigger the water quantity and pressure is. At the results of hydraulic calculation of design areas, when the branch side is longer 1.2 times, the water quantity became 4.6% bigger than exact square and the pressure came to 4.67% bigger. When it is longer 1.4 times, the water quantity and the pressure are bigger 7.52%, 14.51%. Therefore, the sprinkler design engineers should follow the general rule of design area, exact square or rectangle which length along the branch line is a little longer than length along the cross main, to design more stable system.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.1
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• pp.103-107
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• 2024

This paper is a study on a triangle patch antenna using a rectangle slot and strip conductor. The length and spacing of the slot were adjusted to confirm the characteristics of the triangle patch antenna with rectangle slot, and the area and shape of the radiation patch were changed to triangle, rectangle, and hexagon for impedance matching. The HFSS simulator was used to check the antenna parameter characteristics, and the antenna size was 26 mm ×26 mm. In this proposed antenna, the simulation frequency range with VSWR of 2 or less was 5.27 to 6.24 GHz. The bandwidth was 970 MHz. The frequency range of the fabricated antenna was 5.24 to 6.38 GHz, and the bandwidth 1140 MHz. The maximum radiation gain is 5.01 dBi. It was confirmed that all radiation patterns had directional characteristics.

• KIPS Transactions on Software and Data Engineering
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• v.9 no.3
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• pp.83-90
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• 2020

Prototype selection offers the advantage of ensuring low learning time and storage space by selecting the minimum data representative of in-class partitions from the training data. This paper designs a new training data generation method using hyper-rectangles that can be applied to general classification algorithms. Hyper-rectangular regions do not contain different class data and divide the same class space. The median value of the data within a hyper-rectangle is selected as a prototype to form new training data, and the size of the hyper-rectangle is adjusted to reflect the data distribution in the class area. A set cover optimization algorithm is proposed to select the minimum prototype set that represents the whole training data. The proposed method reduces the time complexity that requires the polynomial time of the set cover optimization algorithm by using the greedy algorithm and the distance equation without multiplication. In experimented comparison with hyper-sphere prototype selections, the proposed method is superior in terms of prototype rate and generalization performance.