• Journal of the Korean Institute of Navigation
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• v.25 no.4
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• pp.371-379
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• 2001

We have reported the new measurement system which was substituted digital filter for the analog filter in order to develop the optimal system that could find the time delay between each sensors with high accuracy. And also we have confirmed through the experiments that the accuracy of measurements were differentiated by the methods what kind of digital filter had been adopted. This paper suggests two algorithms which approximate the sound source's bearing and distance. One is that sound source's relative bearing can be approximately regarded as the gradient of hyperbolic asymptote, the other is that the source's range can be approximated under the condition of a long range source relative to the sensor's interval. And a series of experiments were carried out with the source's distance 22.42meters and the random bearing interval within the limits of $-90^{\circ}$~$+90^{\circ}$. As a result, we have recognized that the approximation methods could measure the bearing and distance with higher accuracy than the method using trigonometric relation could do.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.3C
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• pp.248-256
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• 2003

Space-time coding was designed for an efficient transmit diversity technique to improve performance of wireless communication. For the transmit diversity using space-time coding, the receiver requires to estimate channel parameters corresponding to each transmit antennas. In this paper, we propose an efficient channel estimation scheme based on trigonometric polynomial approximation in OFDM systems with transmit diversity using space-time coding. The proposed scheme is more efficient than the conventional scheme in terms of the computational complexity. For QAM modulation, when the size of FFH is 128, the conventional scheme with significant tap caching of 7 requires 9852 complex multiplications for TU, HT and BU channels. But the proposed scheme requires 2560, 7680 and 3584 complex multiplications for TU, HT and BU channels, respectively. Especially, for channels with smaller Doppler frequency and delay spreads, the proposed scheme has the improved BER performance and complexity. In addition, we evaluate the performance of maximum delay spread estimation in unknown channel. The performance of the proposed scheme is investigated by computer simulation in various multi-path fading environments.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.185-196
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• 1998

This study is undertaken to clarify the evolution of the mathematics regarding the $\pi$ ratio, square root, trigonometric ration which are dealing by approximate value according to the curriculum of Korean Middle School and its subsequent growth of methods for attaining the approximate value. Furthermore a brief survey has been thought for assessing the significance of the core of approximate value and its utility which will be given a guide line to many young learners. I'd better teach these historical background to the students and it makes clear the approximate value and the content about the approximate value. This research should help to improve the student's ability of solving a problem by making them think it mathematically through the life and the effort of the mathematician.

• Architectural research
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• v.10 no.1
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• pp.25-32
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• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method to study parametrical instability of lattice dome structures, which is subjected to harmonically pulsating load. We consider elastic stiffness and geometrical stiffness simultaneously during the calculation of stiffness matrix, and adopt consistent mass matrix to make the solution more correct. In order to obtain instability regions, we represent displacements and accelerations in dynamic equation by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability regions eventually. Finally, we take 24-bar star dome and 90-bar lamella dome as examples to investigate dynamic instability phenomena.

• Journal of Astronomy and Space Sciences
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• v.32 no.2
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• pp.127-136
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• 2015

We present a by-product of our long term photometric monitoring of cataclysmic variables. 2MASS J18024395 +4003309 = VSX J180243.9 +400331 was discovered in the field of the intermediate polar V1323 Her observed using the Korean 1-m telescope located at Mt. Lemmon, USA. An analysis of the two-color VR CCD observations of this variable covers all the phase intervals for the first time. The light curves show this object can be classified as an Algol-type variable with tidally distorted components, and an asymmetry of the maxima (the O'Connell effect). The periodogram analysis confirms the cycle numbering of Andronov et al. (2012) and for the initial approximation, the ephemeris is used as follows: Min I. BJD = 2456074.4904+0.3348837E. For phenomenological modeling, we used the trigonometric polynomial approximation of statistically optimal degree, and a recent method "NAV" ("New Algol Variable") using local specific shapes for the eclipse. Methodological aspects and estimates of the physical parameters based on analysis of phenomenological parameters are presented. As results of our phenomenological model, we obtained for the inclination $i=90^{\circ}$, $M_1=0.745M_{\odot}$, $M_2=0.854M_{\odot}$, $M=M_1+M_2=1.599M_{\odot}$, the orbital separation $a=1.65{\cdot}10^9m=2.37R_{\odot}$ and relative radii $r_1=R_1/a=0.314$ and $r_2=R_2/a=0.360$. These estimates may be used as preliminary starting values for further modeling using extended physical models based on the Wilson & Devinney (1971) code and it's extensions

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.13-24
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• 1993

The dispersion in the oscillatory flow generated by gravitational waves above the spatially periodic repples is studied. The steady parts of equations describing the orbit of the passive particle in a two dimensional field are assumed to be simply trigonometric functions. From the view point of nonlinear dynamics, the motion of the particle is chaotic under externally time-periodic perturbations which come from the wave motion. Two cases considered here are; (i) shallow water, and (ii) deep water approximation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.4
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• pp.727-736
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• 2009

In this paper, the $arccos(cos^{-1})$ arithmetic unit for mobile graphics accelerator is designed. The mobile vector graphics applications need tight area, execution time, power dissipation, and accuracy constraints compared to desktop PC applications. The designed processor adopts 2nd-order polynomial approximation scheme based on IEEE floating point data format to satisfy speed and accuracy conditions and reduces area via hardware sharing structure. The arccosine processor consists of 15,280 gates and its estimated operating frequency is about 125Mhz at operating condition of $0.35{\mu}m$ CMOS technology. Because the processor can execute arccosine function within 7 clock cycles, it has about 17 MOPS(million arccos operations per second) execution rate and can be applicable to mobile OpenVG processor. And because of its flexible architecture, it can be applicable to the various transcendental functions such as exponential, trigonometric and logarithmic functions via replacement of ROM and minor hardware modification.

• The Mathematical Education
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• v.61 no.1
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• pp.47-62
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• 2022

This study investigated the contents related to the plane figures in the geometry domains of Joseon-Sanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problem-solving process, and the newly emerged mathematical topics. For this purpose, We analyzed , and written in the late 18th century and and written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. Joseon-Sanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics