• 한국통신학회논문지
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• 제37권5A호
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• pp.279-289
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• 2012

Characteristics, such as the support limit and distortions, of minimum mean-squared error (MSE) N-level uniform and nonuniform scalar quantizers are studied for the family of the generalized gamma density functions as N increases. For the study, MSE-optimal scalar quantizers are designed at integer rates from 1 to 16 bits/sample, and their characteristics are compared with corresponding asymptotic formulas. The results show that the support limit formulas are generally accurate. They also show that the distortion of nonuniform quantizers is observed to converge to the Panter-Dite asymptotic constant, whereas the distortion of uniform quantizers exhibits slow or even stagnant convergence to its corresponding Hui-Neuhoff asymptotic constant at the studied rate range, though it may stay at a close proximity to the asymptotic constant for the Rayleigh and Laplacian pdfs. Additional terms in the asymptote result in quite considerable accuracy improvement, making the formulas useful especially when rate is 8 or greater.

• 전기학회논문지
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• 제65권12호
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• pp.2177-2182
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• 2016

Using the existing exact but quite complicated symbol error rate (SER) expressions for M-ary phase shift keying (M-PSK) and M-ary differential phase shift keying (M-DPSK), we derive effective and concise closed-form asymptotic SER formulas especially in Rician-Nakagami fading channels. The derived formulas can be utilized to efficiently verify the achievable error rate performances of M-PSK and M-DPSK systems for the Rician-Nakagami fading environments. In addition, by exploiting the modulation gains directly obtained from the asymptotic SER formulas, we also theoretically demonstrate that M-DPSK suffers an asymptotic SER performance loss of 3.01dB with respect to M-PSK for a given M in Rician-Nakagami fading channels at high signal-to-noise ratio (SNR).

• 한국통신학회논문지
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• 제40권7호
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• pp.1217-1233
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• 2015

The paper studies characteristics of the minimum mean-square error symmetric scalar quantizers for the generalized gamma, Bucklew-Gallagher and Hui-Neuhoff probability density functions. Toward this goal, asymptotic formulas for the inner- and outermost thresholds, and distortion are derived herein for nonuniform quantizers for the Bucklew-Gallagher and Hui-Neuhoff densities, parallelling the previous studies for the generalized gamma density, and optimal uniform and nonuniform quantizers are designed numerically and their characteristics tabulated for integer rates up to 20 and 16 bits, respectively, except for the Hui-Neuhoff density. The assessed asymptotic formulas are found consistently more accurate as the rate increases, essentially making their asymptotic convergence to true values numerically acceptable at the studied bit range, except for the Hui-Neuhoff density, in which case they are still consistent and suggestive of convergence. Also investigated is the uniqueness problem of the differentiation method for finding optimal step sizes of uniform quantizers: it is observed that, for the commonly studied densities, the distortion has a unique local minimizer, hence showing that the differentiation method yields the optimal step size, but also observed that it leads to multiple solutions to numerous generalized gamma densities.

• 대한수학회보
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• 제41권1호
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• pp.27-43
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• 2004

Let he(x) and $h_{o}(x)$ denote the limits of the sequences $\{^{2n}x\}\;and\;\{^{2n+1}x\}$, respectively. Asymptotic formulas for the functions E\$h_e\;and\;h_o$ at the points $e^{-e}$ and 0 are established.

• Journal of electromagnetic engineering and science
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• 제11권1호
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• pp.56-61
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• 2011

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

• 한국기계가공학회지
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• 제20권2호
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• pp.72-79
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• 2021

The present paper aims to set forth a two-dimensional theory for the dynamics of plates that is valid over a large range of excitation. To construct a dynamic plate theory within the long-wavelength approximation, two dimensional-reduction procedures must be used for analyzing the low- and high-frequency behaviors under the dynamic variational-asymptotic method. Moreover, a separate and logically independent step for the short-wavelength regime is introduced into the present approach to avoid violation of the positive definiteness of the derived energy functional and to facilitate qualitative description of the three-dimensional dispersion curve in the short-wavelength regime. Two examples are presented to demonstrate the capabilities and accuracy of all of the formulas derived herein by using various dispersion curves through comparison with the three-dimensional finite element method.

• Communications for Statistical Applications and Methods
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• 제24권6호
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• pp.663-671
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• 2017

Some genetic association tests include an unidentifiable nuisance parameter under the null hypothesis of no association. When the mode of inheritance (MOI) is not specified in a case-control design, the Cochran-Armitage (CA) trend test contains an unidentifiable nuisance parameter. The transmission disequilibrium test (TDT) in a family-based association study that includes the unaffected also contains an unidentifiable nuisance parameter. The hypothesis tests that include an unidentifiable nuisance parameter are typically performed by taking a supremum of the CA tests or TDT over reasonable values of the parameter. The p-values of the supremum test statistics cannot be obtained by a normal or chi-square distribution. A common method is to use a Davies's upper bound of the p-value instead of an exact asymptotic p-value. In this paper, we provide a unified sine-cosine process expression of the CA trend test that does not specify the MOI and the TDT that includes the unaffected. We also present a closed form expression of the exact asymptotic formulas to calculate the p-values of the supremum tests when the score function can be written as a linear form in an unidentifiable parameter. We illustrate how to use the derived formulas using a pharmacogenetics case-control dataset and an attention deficit hyperactivity disorder family-based example.

• 한국통신학회논문지
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• 제33권5C호
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• pp.413-421
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• 2008

이 논문은 최소 평균제곱오차 라플라스 양자기가 평균이나 표준편차가 불일치된 신호에 적용될 때 야기되는 평균제곱오차 왜곡과 신호대 양자화 잡음비의 점근식을 유도한다. 이들 식은 양자점의 개수 N, 평균값의 변이량 $\mu$, 양자기 설계 기준으로 사용된 표준편차에 대해 적용되는 신호의 표준편차 비율 $\rho$로써 왜곡과 신호대잡음비의 직접적인 관계를 명확히 표시하고 있다. 수치 결과에 의하면, 논문의 주 근사식은, 요율 R=$log_2N$이 6 이상인 경우에, 상당히 넓은 $\mu$와 $\rho$에 대해 신호대잡음비 참값의 1% 이내의 값을 예측하여 정확도가 아주 높은 것으로 판단된다. 이 논문을 통해 새로 발견된 점은 첫째 ${\rho}>3/2$인 분산 강불일치의 경우에 신호대잡음비는 $9/\rho$ dB/bit 비율로 증가한다는 것과 둘째 최적 균일양자기는, 비록 최적으로 설계되었지만, 분산 임계불일치보다 조금 더 불일치된 것임을 밝힌 점이다. 또 $\mu$에 의한 신호대잡음비 손실은 비교적 크지 않은 것이 관찰되었다. 여기에 유도된 공식들은, 단구간 분산이 변하는 라플라스 분포로 잘 모형되는 음성이나 음악 신호를 하나의 양자기로 양자화하는 경우에 쓰임새가 있을 것으로 사료된다.

• 대한조선학회논문집
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• 제53권2호
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• pp.92-100
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• 2016

A comparative method is applied to evaluate well-known formulas for estimating the size of supercavities of axisymmetric cavitators for the supercavitating underwater vehicle. Basic functional forms of these formulas are derived first for the cavity diameter from a momentum integral estimate and second for the cavity length from an asymptotic analysis of inviscid supercavity flows. The length and the diameter of axisymmetric supercavities estimated by each formula are compared, with available experimental data for a disk and a 45° conical cavitators, and also with computational results obtained by a CFD code, ‘fluent’, for conical cavitators of wide range of cone angles. Results for estimating the length and the diameter of the supercavities show in general a good agreement, which confirms the size of the supercavities for disk and conical cavitators can be estimated accurately by these simple formulas of an elementary function of cavitation number and drag coefficient of the cavitator. These formulas will be useful for from conceptual design of the cavitator to real-time control of the supercavitating underwater vehicle.

• 대한수학회논문집
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• 제35권1호
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• pp.301-319
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• 2020

In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ₀ where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.