• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.116-127
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• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• Korean Journal of Computational Design and Engineering
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• v.18 no.1
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• pp.49-57
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• 2013

In this paper, orthogonal projection of a point onto a 2D planar curve is discussed. The problem is formulated as finding a point on a curve where the tangent of the curve is perpendicular to the vector connecting the point on the curve and a point in the space. Existing methods are compared and novel approaches to solve the problem are presented. The proposed methods are tested with examples.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.377-391
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• 2024

Accurate household projections are essential for sectors such as housing supply and tax policy planning, given the rapid social changes like declining birthrates, an aging population, and a rise in single-person households that impact household size and type. Korea introduced its first register-based census in 2015, transitioning from five-year general survey-based approach to an annual administrative data-based census. This change in census allows for more frequent and effective capturing the rapid demographic shifts and trends. However, this change in census has caused challenges in future projection by the existing household projection model due to the rapid dynamics. This paper proposes a new household projection method, the N-point Modified Exponential Model (MEM), that accurately reflects register-based census data and mitigates the impact of rapid demographic changes, in three types: the Weighted N-point MEM, the Regression-based N-point MEM, and the Rolling Weighted N+point MEM. Using register-based census data from 2016 to 2020 to forecast household headship rates by age, household size, and household type to 2051, the N-point modified exponential model outperformed the existing model in both long- and short-term forecast accuracy, suggesting its suitability as a future household projection model for Korea.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.279-296
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• 2012

In this paper, we define a generalized duality mapping, which is a generalization of the normalized duality mapping and using this, we extend the notion of a generalized projection and study their properties. Also we construct an approximating fixed point sequence using the generalized projection with the generalized duality mapping and prove its strong convergence.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.823-832
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• 2013

We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.

• East Asian mathematical journal
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• v.24 no.2
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• pp.191-199
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• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• Journal of the Korean housing association
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• v.14 no.5
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• pp.37-46
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• 2003

The quantitative analysis of view tells how surroundings and sky are showed, and requires understanding of visual perception and three dimensional information of buildings. The visual perception and the existing projection methods for view analysis are examined. The results of this study are as follows: The visual perception on the size is determined by the visual angle, which can be described as a solid angle. The analysis of view by planar projection can be narrow-sighted according to the size of the window and the location of the viewpoint, which will cause the obstacles in the normal direction of the window interfere the view. For the analysis of view by fisheye projection, the area around the focus point is calculated wider than other areas, and so the view ratio depends on the position of the focus point. When analyzing sky view by dividing the sky vault into the differential area, the distortion by projection can be minimized.

• Journal of Internet Computing and Services
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• v.11 no.1
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• pp.117-128
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• 2010

There are many researches related to a simulated shooting training system for replacing the real military and police shooting training. In this paper, we propose the point of impact from a simulated shooting target based on image processing instead of using a sensor based approach. The point of impact is extracted by analyzing the image extracted from the camera on the muzzle of a gun. The final shooting result is calculated by mapping the target and the coordinates of the point of impact. The recognition system is divided into recognizing the projection zone, extracting the point of impact on the projection zone, and calculating the shooting result from the point of impact. We find the vertices of the projection zone after converting the captured image to the binary image and extract the point of impact in it. We present the extracting process step by step and provide experiments to validate the results. The experiments show that exact vertices of the projection area and the point of impact are found and a conversion result for the final result is shown on the interface.

• Korean Journal of Applied Biomechanics
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• v.17 no.2
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• pp.157-166
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• 2007

This study was to compare the major kinematic factors between the success and failure group on performing the back somersault motion in floor exercise. Three gymnasts(height : $167.3{\pm}2.88cm$, age : $22.0{\pm}1.0years$, body weight : $64.4{\pm}2.3kg$) were participated in this study. The kinematic data was recorded at 60Hz with four digital video camera. Two successful motions and failure motions for each subject were selected for three dimensional analysis. 1. Success Trail It was appear that success trail was larger than failure group in projection velocity, but success trail was smaller than failure trail in projection angle. Also it was appear that success trail was longer than failure group in the time required. Hand segment velocity and maximum velocity in success trail were larger than those in failure trail, and this result was increasing the projection velocity and finally increasing the vertical height of center of mass. At the take-off(event 2), flection amount of hip and knee joint angle was contributed to the optimal condition for the take-off and at the peak point, hip and knee joint angle was maximum flexed for reducing the moment of inertia. Also in this point, upper extremities of success trail extended more than those of failure trail. in this base, success trail in upward phase(p3) 2. Failure Trail It was appear that failure trail was smaller than success trail in projection velocity, but failure trail was larger than success trail in projection angle. Also it was appear that failure trail was more short than success trail in the time required. Hand segment velocity and maximum velocity in failure trail were smaller than those in success trail, and this result was reducing the projection velocity and finally reducing the vertical high of center of mass. At the take-off(event 2), flection amount of hip and knee joint angle wasn't contributed to the optimal condition for the take-off and at the peak point, hip and knee joint angle wasn't maximum flexed for reducing the moment of inertia. Also in this point, upper extremities of failure trail didn't extended more than those of success trail.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.617-635
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• 2021

Let X be a smooth hypersurface X of degree d ≥ 4 in a projective space ℙⁿ⁺¹. We consider a projection of X from p ∈ ℙⁿ⁺¹ to a plane H ≅ ℙⁿ. This projection induces an extension of function fields ℂ(X)/ℂ(ℙⁿ). The point p is called a Galois point if the extension is Galois. In this paper, we will give necessary and sufficient conditions for X to have Galois points by using linear automorphisms.