• The Mathematical Education
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• v.57 no.3
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• pp.311-328
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• 2018

In school mathematics, the concept of an average is not a concept that is limited to a unit of statistics. In particular, high school students will learn about arithmetic mean and geometric mean in the process of learning absolute inequality. In calculus learning, the concept of average is involved when learning the concept of average speed. The arithmetic mean is the same as the procedure used when students mean the test scores. However, the procedure for obtaining the geometric mean differs from the procedure for the arithmetic mean. In addition, if the arithmetic mean and the geometric mean are the discrete quantity, then the mean rate of change or the average speed is different in that it considers continuous quantities. The average concept that students learn in school mathematics differs in the quantitative nature of procedures and objects. Nevertheless, it is not uncommon to find out how students construct various mathematical concepts into mathematical knowledge. This study focuses on this point and conducted the interviews of the students(three) in the second grade of high school. And the expression of students in the process of average concept formation in arithmetic mean, geometric mean, average speed. This study can be meaningful because it suggests practical examples to students about the assertion that various scholars should experience various properties possessed by the average. It is also meaningful that students are able to think about how to construct the mean conceptual properties inherent in terms such as geometric mean and mean speed in arithmetic mean concept through interview data.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1186-1189
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• 2005

Focused Ion Beam machining is an attractive approach to produce nano-scale 3D structures. However, like other beam-based manufacturing processes, the redeposition of the sputtered material during the machining deteriorates the geometric accuracy of ion beam machining. In this research a new approach to reduce the geometric error in FIB machining is introduced. The observed redeposition phenomena have been compared with existing theoretical model. Although the redeposition effect has good repeatability the prediction of exact amount of geometric error in ion beam machining is difficult. Therefore, proposed method utilizes process control approach. Developed algorithm measures the redeposition amount after every production cycle and modifies next process plan. The method has been implemented to a real FIB machine and the experimental results demonstrated considerable improvement of five micrometer-sized pocket machining.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.65-77
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• 2020

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The in-control fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

• Korean Journal of Geomatics
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• v.5 no.1
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• pp.35-42
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• 2005

Precise geometric registration is required in multi-source data fusion process to obtain synergistic results successfully. However, most of the previous studies focus on the assumption of perfect registration or registration in a limited local area with intuitively derived simple geometric model. In this study, therefore, we developed a robust method for geometric registration based on a systematic model that is derived from the geometry associated with the data acquisition processes. The key concept of the proposed approach is to utilize smooth planar patches extracted from LIDAR data as control surfaces to adjust exterior orientation parameters of the aerial images. Registration of the simulated LIDAR data and aerial images was performed. The experimental results show that the RMS value of the geometric discrepancies between two data sets is decreased to less than ${\pm}0.30\;m$ after applying suggested registration method.

• Journal of the Korea Institute of Military Science and Technology
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• v.21 no.1
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• pp.17-24
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• 2018

Polar fomat algorithm (PFA) was derived from medical imaging theory, known as back projection, to process synthetic aperture radar(SAR) data. The difference between the operating condition of SAR and back projection assumption makes two distortions. First, the focusing performance of PFA is degraded in proportion to distances from the scene center. Second, the geometric accuracy in SAR images is distorted. Several methods were introduced to mitigate the distortions, but some disadvantages, such as the geometric discontinuity, are arisen when sub-images are combined. This paper proposes the novel method to compensate the geometric distortion with chirp Z-transform (CZT). This method corrects precisely the geometric errors without any problems, because a whole image can be processed all at once.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.549-551
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• 2003

Satellite images are utilized for various purposes and many people are concerned about them. But it is necessary to process geometric correction for using of satellite images. However, common user regards geometric correction, which is basic preprocessing for satellite image, as laborious job. Therefore we should provide an automatic geometric correction method for Landsat image using GCP chip database. The GCP chip database is the collection of pieces of images with geoinformation and is provided by XML web service. More specifically, XML web service enables common users to easily use our GCP chip database for their own geometric correcting applications.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.3
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• pp.82-91
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• 1995

The purpose of this research is to develop a new real-time process control system. In this paper, a theoretical method for acquiring the control limit of cutting process(cutting surface) according to the required value(geometric tolerance) based on geometrical relations was propsed. In particular, the three following points are amphasized. Firstly, the process control was based on the cutting process, and the control limit was determined from the analysis of geometrical relations. Secondly, AMGD(Actual Measured Geometrical Deviation) was used as a new substitute value in process analysis. Thirdly, fuzzy reasoning was introduced to get the control limit flexibility according to the variations in the required value and general consideration of each measurememnt items.

• 한국HCI학회:학술대회논문집
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• 2008.02a
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• pp.39-44
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• 2008

This paper proposes a real-time geometric correction system based on a projector to project digital images onto deformable surface. Markers use to trace lots of corresponding points would spoil the projected image when the projector projects a digital image onto the surface because they leave marks on the surface. In addition, it is difficult to build a real-time geometric correction system since bottlenecks occur through the process of the geometric correction for projecting images. In this paper, we use invisible infrared markers and a vertex shader of GPU using Cg TookKit of NVIDIA in order to eliminate disadvantage and bottlenecks in the process of markers recognition so that it is possible to project natural correction images in real-time. As a result, this system overlays an interactive virtual texture onto the real paper by using the geometric transformation. Therefore, it is possible to develop variation of AR(Augmented Reality) based on digital contents systems.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.409-417
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• 1995

We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.733-749
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• 2016

We aim to compute discretely monitored geometric Asian option prices under the Heston model. This method involves explicit formula for multivariate generalized Fourier transform of volatility process and their integrals over different time intervals using a recursive method. As numerical results, we illustrate efficiency and accuracy of our method. In addition, we simulate scenarios which show evidently practical importance of our work.