• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.401-411
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• 2021

A Diophantine m-tuple is a set {a₁, a₂, …, a_m} of positive integers such that a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E_k be the elliptic curve induced by Diophantine triple {F_2k, 5F_2k+2, 3F_2k + 7F_2k+2}. In this paper, we find the structure of a torsion group of E_k, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1 and some further conditions.

• Journal of the Korea Institute of Military Science and Technology
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• v.2 no.1
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• pp.139-149
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• 1999

In this paper, we estimate the scale factor error and random walk characteristics of the ring laser gyro which has the body dither for Lock-in compensation. And then, we compared those results with the static test results for 28cm square ring laser gyro which has about 0.5 deg/sec static Lock-in. In the case of sinusoidal body dither, dynamic Lock-in occurs periodically at the points where the gyro output pulse becomes the integer multiples of body dither frequency. The width of dynamic Lock-in is changed by variation of dither amplitude, and, between the width of dynamic Lock-in which occurs at the even multiple points of body dither frequency and that at the odd muliple points of body dither frequency, it has 180o phase difference. Generally random body dither is adopted to compensate for dynamic Lock-in. Then if the irregularity is not large enough, the scale factor error by dynamic Lock-in is not vanished. And if the irregularity is large enough, the scale factor error decreases, but random walk becomes larger relatively. And we confirmed that the larger body dither amplitude, the smaller random walk.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2601-2610
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• 2013

The main limiting factors of Precise Point Positioning(PPP) accuracy are errors in broadcast satellite orbits, clock errors, and the others, which are receiver-dependent errors(ionospheric, tropospheric refraction, multipath, and tides, etc.). Therefore, to facilitate high precision PPP, precise orbits/clocks corrections, the receiver-dependent errors corrections have to apply to multi frequency GNSS measurements for an ionosphere free combination and integer ambiguity resolution in real-time. Currently, there are many Analysis Centers, which offer the precise corrections stream computed in real-time using the global or regional GNSS tracking network. The goles of this research considered performances of the real-time static PPP with using RTCM corrections from NTRIP casters. For this, the corrections streams of Analysis Centers received via NTRIP does apply to GNSS data of check points individually, as well as jointly, in accordance with various session lengths. After that, have compared the PPP results from the corrections streams with each other, and with Standard Point Positioning(SPP) results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37B no.12
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• pp.1102-1112
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• 2012

We propose a cell selection and resource allocation scheme that assigns users to nearby accessible cells in heterogeneous wireless networks consisting of macrocell, femtocells, and Wi-Fi access points, under overload situation. Given the current power level of all accessible cells nearby users, the proposed scheme finds all possible cell assignment mappings of which user should connect to which cell to maximize the number of users that the network can accommodate at the same time. We formulate the cell selection problem with heterogeneous cells into an optimization problem of binary integer programming, and compute the optimal solution. We evaluate the proposed algorithm in terms of network access failure compared to a local ad-hoc based cell selection scheme used in practical systems using network level simulations. We demonstrate that our cell selection algorithm dramatically reduces network access failure in overload situation by fully leveraging network resources evenly across heterogeneous networks. We also validate the practical feasibility in terms of computational complexity of our binary integer program by measuring the computation time with respect to the number of users.

• KIISE Transactions on Computing Practices
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• v.21 no.1
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• pp.94-99
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• 2015

With the recent machine learning paradigm of using nonparametric Bayesian statistics and statistical inference based on random sampling, the Dirichlet distribution finds many uses in a variety of graphical models. It is a multivariate generalization of the gamma distribution and is defined on a continuous (K-1)-simplex. This paper presents a sampling method for a Dirichlet distribution for the problem of dividing an integer X into a sequence of K integers which sum to X. The target samples in our problem are all positive integer vectors when multiplied by a given X. They must be sampled from the correspondingly gridded simplex. In this paper we develop a Markov Chain Monte Carlo (MCMC) proposal distribution for the neighborhood grid points on the simplex and then present the complete algorithm based on the Metropolis-Hastings algorithm. The proposed algorithm can be used for the Markov model, HMM, and Semi-Markov model for accurate state-duration modeling. It can also be used for the Gamma-Dirichlet HMM to model q the global-local duration distributions.

• Journal of Broadcast Engineering
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• v.13 no.5
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• pp.732-743
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• 2008

In H.264/AVC, 4$\times$4 block transform is used for intra and inter prediction instead of 8$\times$8 block transform. Using small block size coding, H.264/AVC obtains high temporal prediction efficiency, however, it has limitation in utilizing spatial redundancy. Motivated on these points, we propose a multi-dimensional transform which achieves both the accuracy of temporal prediction as well as effective use of spatial redundancy. From preliminary experiments, the proposed multi-dimensional transform achieves higher energy compaction than 2-D DCT used in H.264. We designed an integer-based transform and quantization coder for multi-dimensional coder. Moreover, several additional methods for multi-dimensional coder are proposed, which are cube forming, scan order, mode decision and updating parameters. The Context-based Adaptive Variable-Length Coding (CAVLC) used in H.264 was employed for the entropy coder. Simulation results show that the performance of the multi-dimensional codec appears similar to that of H.264 in lower bit rates although the rate-distortion curves of the multi-dimensional DCT measured by entropy and the number of non-zero coefficients show remarkably higher performance than those of H.264/AVC. This implies that more efficient entropy coder optimized to the statistics of multi-dimensional DCT coefficients and rate-distortion operation are needed to take full advantage of the multi-dimensional DCT. There remains many issues and future works about multi-dimensional coder to improve coding efficiency over H.264/AVC.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.557-569
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• 2010

Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.4
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• pp.67-75
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• 2020

This paper proposes a methodology for gantry route optimization in order to maximize the productivity of a odd-type surface mount device (SMD). A odd-type SMD is a machine that uses a gantry to mount electronic components on the placement point of a printed circuit board (PCB). The gantry needs a nozzle to move its electronic components. There is a suitability between the nozzle and the electronic component, and the mounting speed varies depending on the suitability. When it is difficult for the nozzle to adsorb electronic components, nozzle exchange is performed, and nozzle exchange takes a certain amount of time. The gantry route optimization problem is divided into the mounting order on PCB and the allocation of nozzles and electronic components to the gantry. Nozzle and electronic component allocation minimized the time incurred by nozzle exchange and nozzle-to-electronic component compatibility by using an mixed integer programming method. Sequence of mounting points on PCB minimizes travel time by using the branch-and-price method. Experimental data was made by randomly picking the location of the mounting point on a PCB of 800mm in width and 800mm in length. The number of mounting points is divided into 25, 50, 75, and 100, and experiments are conducted according to the number of types of electronic components, number of nozzle types, and suitability between nozzles and electronic components, respectively. Because the experimental data are random, the calculation time is not constant, but it is confirmed that the gantry route is found within a reasonable time.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.3 s.303
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• pp.39-52
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• 2005

In this paper, a registration method is presented to register partial 3D point clouds, acquired from a multi-view camera, for 3D reconstruction of an indoor environment. In general, conventional registration methods require a high computational complexity and much time for registration. Moreover, these methods are not robust for 3D point cloud which has comparatively low precision. To overcome these drawbacks, a projection-based registration method is proposed. First, depth images are refined based on temporal property by excluding 3D points with a large variation, and spatial property by filling up holes referring neighboring 3D points. Second, 3D point clouds acquired from two views are projected onto the same image plane, and two-step integer mapping is applied to enable modified KLT (Kanade-Lucas-Tomasi) to find correspondences. Then, fine registration is carried out through minimizing distance errors based on adaptive search range. Finally, we calculate a final color referring colors of corresponding points and reconstruct an indoor environment by applying the above procedure to consecutive scenes. The proposed method not only reduces computational complexity by searching for correspondences on a 2D image plane, but also enables effective registration even for 3D points which have low precision. Furthermore, only a few color and depth images are needed to reconstruct an indoor environment.

• 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.