• East Asian mathematical journal
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• v.30 no.3
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• Journal of Positioning, Navigation, and Timing
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• v.5 no.4
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• pp.221-233
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• 2016

This paper deals with performance assessment of the kinematic network-based GPS positioning technique with a view to using it for ellipsoidally referenced bathymetric surveys. To this end, two field trials were carried out on a land vehicle and a surveying vessel. Single-frequency GPS data acquired from these tests were processed by an in-house software which equips the network modeling algorithm with instantaneous ambiguity resolution procedure. The results reveals that ambiguity success rate based on the network model is mostly higher than 99.0%, which is superior to that of the single-baseline model. In addition, achievable accuracy of the technique was accessed at ${\pm}1.6cm$ and 2.7 cm with 95% confidence level in horizontal and vertical component respectively. From bathymetric survey at the West Nakdong River in Busan, Korea, 3-D coordinates of 2,011 points on its bed were computed by using GPS-derived coordinates, attitude, measured depth and geoid undulation. Note that their vertical coordinates are aligned to the geoid, the so-called orthometric height which is widely adopted in river engineering. Bathymetry was constructed by interpolating the coordinate set, and some discussion on its benefit was given at the end.

• Journal of Computing Science and Engineering
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• v.4 no.3
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• pp.207-224
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• 2010

This paper presents a compression scheme for mesh geometry, which is suitable for mobile graphics. The main focus is to enable real-time decoding of compressed vertex positions while providing reasonable compression ratios. Our scheme is based on local quantization of vertex positions with mesh partitioning. To prevent visual seams along the partitioning boundaries, we constrain the locally quantized cells of all mesh partitions to have the same size and aligned local axes. We propose a mesh partitioning algorithm to minimize the size of locally quantized cells, which relates to the distortion of a restored mesh. Vertex coordinates are stored in main memory and transmitted to graphics hardware for rendering in the quantized form, saving memory space and system bus bandwidth. Decoding operation is combined with model geometry transformation, and the only overhead to restore vertex positions is one matrix multiplication for each mesh partition. In our experiments, a 32-bit floating point vertex coordinate is quantized into an 8-bit integer, which is the smallest data size supported in a mobile graphics library. With this setting, the distortions of the restored meshes are comparable to 11-bit global quantization of vertex coordinates. We also apply the proposed approach to compression of vertex attributes, such as vertex normals and texture coordinates, and show that gains similar to vertex geometry can be obtained through local quantization with mesh partitioning.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.3
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• pp.271-280
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• 2004

Assessment of image registration for Pressure Sensitive Paint (PSP) was performed. A 16 bit camera and LED lamp were used with Uni-FIB paint (ISSI). Because of model displacement and deformation at 'wind-on' condition, a large error of the intensity ratio was induced between 'wind-on' and' wind-off images. To correct the error, many kinds of image registrations were tested. At first, control points were marked on the model surface to find the coefficients of polynomial transform functions between the 'wind-off' 'wind-on' images. The 2nd-order polynomial function was sufficient for representing the model displacement and deformation. An automatic detection scheme was introduced to find the exact coordinates of the control points. The present automatic detection algorithm showed more accurate and user-friendly than the manual detection algorithm. Since the coordinates of transformed pixel were not integer, five interpolation methods were applied to get the exact pixel intensity after transforming the 'wind-on' image. Among these methods, the cubic convolution interpolation scheme gave the best result.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.1
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• pp.98-104
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• 2016

With the development of modern science and technology, weapon systems such as tanks, submarines, combat planes, radar are also dramatically advanced. Among these weapon systems, the ballistic missile, one of the asymmetric forces, could be considered as a very economical means to attack the core facilities of the other country in order to achieve the strategic goals of the country during the war. Because of the current ballistic missile threat from the North Korea, establishing a missile defense (MD) system becomes one of the major national defense issues. This study focused on the optimization of air defense artillery units' deployment for effective ballistic missile defense. To optimize the deployment of the units, firstly this study examined the possibility of defense, according to the presence of orbital coordinates of ballistic missiles in the limited defense range of air defense artillery units. This constraint on the defense range is originated from the characteristics of anti-ballistic missiles (ABMs) such as PATRIOT. Secondly, this study proposed the optimized mathematical model considering the total covering problem of binary integer programming, as an optimal deployment of air defense artillery units for defending every core defense facility with the least number of such units. Finally, numerical experiments were conducted to show how the suggested approach works. Assuming the current state of the Korean peninsula, the study arbitrarily set ballistic missile bases of the North Korea and core defense facilities of the South Korea. Under these conditions, numerical experiments were executed by utilizing MATLAB R2010a of the MathWorks, Inc.

• Journal of Korean Society for Geospatial Information Science
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• v.13 no.1 s.31
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• pp.37-43
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• 2005

GPS has been increasingly used in high precision positioning thanks to rapid advances of GPS technology. In order to acquire precise coordinates from GPS, it is important to solve accurately integer ambiguity inherent in GPS signals. The previous methods to solve this ambiguity were mostly based on multi-epoch data but recently a method based on single-epoch data has been developed. In this study, we selected three sets of software based on these methods, applied them to GPS baseline processing, and analyzed the experimental results. From these analyses, we have also verified the potential of their uses in real time precision positioning.