• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.249-264
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• 2009

Equity-indexed annuities(EIAs) provide their customers with the greater of either the return linked to the underlying index or the minimum guaranteed return. Insurance companies have developed EIAs to attract customers reluctant to buy traditional fixed annuities because of low returns and also reluctant to buy mutual funds for fear of the high volatility in the stock market. This paper proposes a new type of EIA embedded with an outside barrier option with flexible monitoring period in order to increase its participation rate. It also derives an explicit pricing formula for this proposed product, and discusses numerical examples to show relationships among participation rate, barrier level, index volatility and correlation.

• Journal of the Korean earth science society
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• v.30 no.1
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• pp.40-48
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• 2009

The attenuation mechanism of seismic waves in the crust is controlled both by intrinsic absorption and scattering of energy. The amount of scattering and intrinsic energy losses from the total attenuation is separately estimated in this study for the southern Korean Peninsula. The formula to be deduced from the theoretical relationship between single back-scattered coda Q and multiple scattering theory was used to separate the total attenuation into the intrinsic Q and the scattering Q. It was found that the intrinsic Q was considerably lower than that of the scattering Q in the frequency range of 1.5 to 20 Hz. This fact implies that the energy loss caused by the intrinsic absorption is relatively larger than one by the scattering effect within the crust of the southern Korean Peninsula. Both intrinsic and scattering Q values appeared to be comparatively larger than those measured in other seismically active regions except for intrinsic Q in the frequency range of 1.5 to 3 Hz.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2002.11a
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• pp.139-145
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• 2002

The flow zone through propeller jets are used in evaluating the environmental and constructional effects of navigation on the waterway. It relies on the characteristics of ships and water depth. A numerical model using the momentum theory of the propeller and Shield's diagram was developed in a restricted waterway. Equations for discharge are presented based on thrust coefficients and propeller speed and are the most accurate means of defining discharge. Approximate methods for discharge are developed based on applied ship's power. Equations for discharge are as a function of applied power, propeller diameter, and ship speed. Water depth of the waterway and draft of the shop are also necessary for the calculation of the grain size of the initial motion. The velocity distribution of discharge from the propeller was simulated by the Gaussian normal distribution function. The shear velocity and shear stress were from the Sternberg's formula. Case studies to show the influence of significant factors on sediment movement induced by the ship's propeller at the channel bottom are presented.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.101-122
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• 2010

Chinese Taipei won the first place at the mathematics achievement of TIMSS 2007. Especially, there was a significant difference in the percentage of correct answers between Chinese Taipei and Korea, and Chinese Taipei' percentage of correct answers was higher than Korea. This study compared the education system, mathematics instruction environment, and instructional activities of two countries. And for algebra, curriculum and textbooks were compared between two countries based on TIMSS 2007 framework. It was found that Chinese Taipei emphasized homework and test, and MCFL of that was low. Their textbook was formal, and induced the hasty abstraction, Also, some themes were introduced earlier than Korea and repeated across different grades.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.11
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• pp.1123-1129
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• 2010

Angular Deviation(AD) on transparency applied to TA-50 Aircraft deteriorates armament system's accuracy because it makes a difference in between actual and theoretical targets. In order to increase accuracy, therefore, TA-50 Aircraft measures AD on transparency and provide the measured values for the integrated mission display computer as a type of AD coefficients. This makes AD revised so that pilots can accurately see the actual target on their head-up display. In order to implement such mechanism into a real field, we develop a new device and system automatically measuring AD for the first time. We also deal with basic concept including AD induction formula as well as operating systems. As a consequence of testing the accuracy and precision for verifying reliability of the system, we got satisfactory results. In specific, the accuracy was within the resultant criterion of 1%. The precision was also satisfied with respect to the whole criteria. The system developed through this research is qualified as a military standard equipment for transparency of the canopy.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.7C
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• pp.658-666
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• 2007

In general, the earlier linear-phase MAXFLAT(maximally flat) lowpass FIR filters have the main disadvantage of a gain response in the half frequency band $(0{\leq}w{\leq}{\pi}/2)$ by the closed form transfer functions used in design techniques for realizing them. Moreover, most of them has existent problems as follows : ripple error in the stopband, gentle-cutoff attenuation, phase and group delay and inexact cutoff frequency response. It is due to the approximation algorithms such as Chebyshev norm and Remez exchange which are used to approach MAXFLAT and linear-phase characteristics in frequency domain. In this paper, a new mathematically closed-form transfer function is introduced for the design of MAXFLAT lowpass FIR filters which have the zero-phase and wideband-gain response. In addition, we verify that the closed-form transfer function is easily realized due to our generalized formulas derived newly by using MAXFLAT conditions including an arbitrary cutoff point. This method is, therefore, useful for "simple and quick designs". Conclusively, we propose a technique for the design of new zero-phase wideband MAXFLAT lowpass FIR filters which can achieve sharp-cutoff attenuation exceeding 250 dB almost everywhere.

• Korean Journal of Optics and Photonics
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• v.18 no.6
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• pp.410-420
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• 2007

We theoretically derive the set of utilizable paraxial zoom locus equations for all complicated zoom lens systems with infinite object distance, such as a camera zoom lens, by using the Gaussian bracket method and the matrix representation of paraxial ray tracing. And we make the zoom locus program according to these equations in Visual Basic. Since we have applied the paraxial ray tracing equations into Gaussian bracket representation, the resultant program systematically simplifies various constraints of the zoom loci of various N group types. Consequently, the solutions of this method can be consistently used in all types of zoom lens in the step of initial design about zoom loci. Finally, in order to verify the usefulness of this method, we show that one example among 4 groups and that among 5 groups, which are very complex zoom lens systems, can be rapidly and with versatility traced through various interpolations by using this program.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.20 no.5
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• pp.151-156
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• 2020

To analyze the diffraction properties of optical signals and the significant impacts of tapered sidewall profile at periodic trapezoidal 2D diffraction gratings, Toeplitz dielectric tensor is first defined and formulated by 2D spatial Fourier expansions associated with trapezoidal profile. The characteristic modes in each layer is then based on eigenvalue problem, and the complete solution is found rigorously in terms of modal transmission-line theory (MTLT) to address the pertinent boundary-value problems. Based on those one, the numerical analysis is performed on how the tapered side profile of grating structures with trapezoidal refractive index distribution affects the design of a sub-wavelength grating reflector. The numerical results reveal that this tapered sidewall profile plays a critical role in determining the reflection bandwidth, the average reflectance, and the band edge.

• The Transactions of the Korea Information Processing Society
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• v.1 no.4
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• pp.531-540
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• 1994

Spline curve scheme is the most valuable tool for the CAD of industrial products. Hence, the development of a new, effective curve scheme can have immediate impact on the current design industries. This paper develops and implements a new methodology for the implementation of the visually continuous class of splines which can produce a more flexible and diverse curve shapes. This class of splines has advantaged over existing splines in that it can accommodate wider range of shapes while maintaining the interpolators property of the ordinary cardinal splines. Most importantly, we avoid using the previous method of implementing G$^1$ curves, where users must specify scalar values for the control of curve shapes. We derive and implement an easy-to -use transformation between the user-specified graphical tangent vectors and the actual parameters for the resulting curve. Since the resulting curve shape reflects original tangential direction faithfully, CAD users can simply represent approximate curve shapes with proper tangents. Consequently, a simple user interface device such as a mouse can effectively produce a various spline curves using the proposed spline tool.