• Title/Summary/Keyword: ${\Delta}$-convergence

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EMPIRICAL BAYES TESTING FOR MEAN LIFE TIME OF RAYLEIGH DISTRIBUTION

  • Liang, TaChen
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.1-15
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    • 2007
  • Consider a Rayleigh distribution with $$pdf\;p(x/{\theta})\;=\;2x{\theta}^{-1}\;{\exp}\;({-x^2}/{\theta})$$ and mean lifetime ${\mu}\;=\;\sqrt{\pi\theta}/2$. We study the two-action problem of testing the hypotheses $H_{0}\;:\;{\mu}{\leq}{\mu}_{0}$ against $H_{1}\;:\;{\mu}\;>\;{\mu}_{0}$ using a linear error loss of ${\mid}{\mu}\;-\;{\mu}_{0}{\mid}$ via the empirical Bayes approach. We construct a monotone empirical Bayes test ${\delta}^{*}_{n}$ and study its associated asymptotic optimality. It is shown that the regret of ${\delta}^{*}_{n}$ converges to zero at a rate $\frac{{\ln}^{2}n}{n}$, where n is the number of past data available when the present testing problem is considered.

Adaptive Digital Background Gain Mismatch Calibration for Multi-lane High-speed Serial Links

  • Lim, Hyun-Wook;Kong, Bai-Sun;Jun, Young-Hyun
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.15 no.1
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    • pp.96-100
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    • 2015
  • Adaptive background gain calibration loop for multi-lane serial links is proposed. In order to detect and cancel gain mismatches between lanes, a single digital loop using a ${\sum}{\Delta}$ ADC is employed, which provides a real-time adaptation of gain variations and is shared among all lanes to reduce power and area. Evaluation result showed that gain mismatches between lanes were well calibrated and tracked, resulting in timing budget at $10^{-6}$ BER increased from 0.261 UI to 0.363 UI with stable loop convergence.

Treatment of Essential Boundary Conditions using Modified Weight Functions in Meshless Method (무요소법에서 가중함수를 수정한 필수경계조건 처리법)

  • 강명석;윤성기
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.11
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    • pp.2705-2712
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    • 2000
  • In meshless methods some techniques to impose essential boundary conditions have been developed since the approximations do not satisfy Kronecker delta properties at nodal points. In this study, new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta property on the bound ary nodes. In addition, the resulting shape functions possess and interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore the essential boundary conditions can be exactly satisfied with the new method. More importantly, the impositions of essential boundary conditions using the present method is relatively easy as in finite element method. Numerical examples show that the method also retains high convergence rate comparable to Lagrange multiplier method.

On an improved numerical method to solve the equilibrium problems of solids with bounded tensile strength that are subjected to thermal strain

  • Pimpinelli, Giovanni
    • Structural Engineering and Mechanics
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    • v.15 no.4
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    • pp.395-414
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    • 2003
  • In this paper we recall briefly the constitutive equations for solids subjected to thermal strain taking in account the bounded tensile stress of the material. In view to solve the equilibrium problem via the finite element method using the Newton Raphson procedure, we show that the tangent elasticity tensor is semi-definite positive. Therefore, in order to obtain a convergent numerical method, the constitutive equation needs to be modified. Specifically, the dependency of the stress by the anelastic deformation is made explicit by means of a parameter ${\delta}$, varying from 0 to 1, that factorizes the elastic tensor. This parameterization, for ${\delta}$ near to 0, assures the positiveness of the tangent elasticity tensor and enforces the convergence of the numerical method. Some numerical examples are illustrated.

CA/C Ratio of Adults in Their Early Twenties with Normal Binocular Vision (양안시가 정상인 20대 초반 성인의 CA/C비)

  • Lee, Mu-Hyuk;Yu, Dong-Sik
    • Journal of Korean Ophthalmic Optics Society
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    • v.17 no.2
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    • pp.153-158
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    • 2012
  • Purpose: The purpose of this study was to evaluate the convergence accommodation to convergence (CA/C) ratio and to investigate relationships among age, accommodative amplitude and PD (interpupillary distance) of adults in their early twenties with normal binocular vision. Methods: 44 subjects (mean age, $21.75{\pm}1.16$ years) with healthy eyes were examined. The CA/C ratios were measured by using the difference of Gaussian (DOG) target with retinoscopy. Results: The mean CA/C ratio was $0.052{\pm}0.017$ D/$\Delta$. A moderate negative correction was present between CA/C ratio and age (r = -0.50, p = 0.0005), and a highly positive correction was found between CA/C ratio and accommodative amplitude (r = 0.79, p<0.0001). There was no relation between PD and CA/C ratio. Conclusions: The CA/C ratio presented was mean value for adults in their early twenties with healthy eye between 19 and 25 years of age. There was a high correlation between accommodative amplitude and CA/C ratio. Therefore, the CA/C ratio will be useful basic information for comparison in age, gender and binocular anomalies with similar data from other countries.

The Evaluations of Phoria and AC/A Ratio by Watching 3D TV at Near (3D TV 근거리 시청에 따른 사위도와 조절성폭주비 평가)

  • Son, Jeong-Sik;Kim, Dong-Su;Kim, Jung-Ho;Kim, Jae-Do;Hamacher, Alaric;Yu, Dong-Sik
    • Journal of Korean Ophthalmic Optics Society
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    • v.20 no.3
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    • pp.319-324
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    • 2015
  • Purpose: This study was designed to evaluate the changes of phoria and calculated AC/A ratio, and their recovery time points by watching 3D television (3D TV). Methods: 50 subjects (male 30, female 20) of 20s to 40s ages who can watch 3D, were measured phoria using a Howell phoria card at 3 m for distance and 40 cm for near. The phoria was evaluated before watching 3D TV and every 10 minutes from starting of watching 3D TV for 30 minutes, and every 5 minutes after finishing of watching 3D TV for 30 minutes again. Results: For the distance phoria during and after watching 3D TV, it was increased to more exophoria $-0.98{\pm}1.37{\Delta}$ (prism diopters) after 10 minutes from starting of 3D TV watching (p=0.063) and increased to more exophoria $-1.00{\pm}1.28{\Delta}$ after 30 minutes (p=0.024), and started to decrease after finishing of watching 3D TV and recovered to the level of before 3D TV watching ($-0.78{\pm}1.11{\Delta}$) after 20 minutes (p=0.32) with comparing to phoria of before watching 3D TV ($-0.80{\pm}1.12{\Delta}$). For the near phoria, it was also increased to more exophoria $-5.71{\pm}4.45{\Delta}$ after 10 minutes from starting of watching 3D TV (p=0.000) and $-6.58{\pm}4.36{\Delta}$ after 30 minutes (p=0.000), and started to decrease after finishing of watching 3D TV and recovered to the level of before watching 3D TV after 20 minutes ($-4.34{\pm}3.67{\Delta}$) (p=0.32) with comparing to the phoria of before watching 3D TV ($-4.36{\pm}3.66{\Delta}$). AC/A ratio was decreased from $4.92{\pm}1.17{\Delta}/D$ for before 3D TV watching to $4.11{\pm}1.50{\Delta}/D$ for after 30 minutes from starting of watching 3D TV (p=0.000), and increased after the end of watching 3D TV and recovered to the level of before 3D TV watching ($4.93{\pm}1.18{\Delta}/D$) after 25 minutes (p=0.598). Conclusions: During watching 3D TV at near, it showed a tendency of convergence insufficiency by decrease of calculated AC/A ratio as result that exophoria at near was higher increased than exophoria at distance. However, the increased exophoria at both near and distance was recovered to the level of base line after 25 minutes from the end of watching 3D TV. Through this study, it seems to need rational proposals of advice for watching 3D TV.

A study on the measurement and tendency of heterophoria using Von Graefe test and Maddox rod test (프리즘 분리법과 마독스 로드 검사법을 이용한 사위측정과 경향 연구)

  • Oh, Hyun-Jin;Doo, Ha-Young;Oh, Seung-Jin
    • Journal of Digital Convergence
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    • v.10 no.11
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    • pp.485-491
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    • 2012
  • To investigate the difference in the value of horizontal heterophoria measured in phoria test of about normal 72 college students, using both Von Graefe test and Maddox rod test. We used two different methods which are Von Graefe test and Maddox rod test on full correction condition at the long distance. Using Von Graefe test of horizontal heterophoria Measurement, We measured 21 patients(29%) for orthophoria, 36 patients(50%) for exophoria and 15 patients(21%) for esophoria at distance. Using Maddox rod test of horizontal heterophoria Measurement, We measured 36 patients(50%) for orthophoria, 26 patients(36%) for exophoria and 10 patients(14%) for esophoria at distance. Each test average were $0.93{\Delta}$ BI for Von Graefe test, $0.96{\Delta}$ BI for Maddox rod test. We could not find the definite difference about the value of horizontal heterophoria aby testing method. Furthermore, heterphoria AC/A ratio was found to vary from 1.0 to 8.8 and its relationship to refractive error could not be determined.

A Study on Consistency of Numerical Solutions for Wave Equation (파동방정식 수치해의 일관성에 관한 연구)

  • Pyun, Sukjoon;Park, Yunhui
    • Geophysics and Geophysical Exploration
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    • v.19 no.3
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    • pp.136-144
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    • 2016
  • Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

Polymer $1{\times}2$ Thermo-Optic Digital Optical Switch Based on the Total-Internal-Reflection Effect

  • Han, Young-Tak;Shin, Jang-Uk;Park, Sang-Ho;Han, Sang-Pil;Baek, Yong-Soon;Lee, Chul-Hee;Noh, Young-Ouk;Park, Hyo-Hoon
    • ETRI Journal
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    • v.33 no.2
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    • pp.275-278
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    • 2011
  • This letter presents a polymer $1{\times}2$ thermo-optic totalinternal-reflection digital optical switch (TIR-DOS) with an index contrast of 1.5%-${\delta}$ operating at low power consumption. The structure of our $1{\times}2$ TIR-DOS was created by adding a reflection port to that of a conventional multimode filtering variable optical attenuator. To improve the total-internalr-eflection efficiency, a heater offset was applied to the crossing region of multimode waveguides of the TIR-DOS. The fabricated $1{\times}2$ TIR-DOS shows a low electrical power consumption of 18 mW for an on-off ratio of 35 dB.

Analysis of a.c. Characteristics in Cr-doped ZnO Using Dielectric Functions (Cr을 첨가한 ZnO의 유전함수를 이용한 a.c. 특성 분석)

  • Hong, Youn-Woo;Shin, Hyo-Soon;Yeo, Dong-Hun;Kim, Jong-Hee
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2009.06a
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    • pp.16-16
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    • 2009
  • ZnO($Zn_{1+x}O$)는 n-type 반도성 세라믹스로 우수한 전기적, 광학적, 화학적 특성을 갖고 있어 바리스터, 투명 전도막, 화학 및 바이오 센서, UV light emitter 등 다양한 용도로 사용되고 있다. 또한 ZnO에 각종 천이 금속 산화물을 일정량 첨가함에 따라 발생하는 결함준위와 입계 특성의 변화에 대한 연구가 활발히 진행되고 있다. 다양한 천이 금속 산화물의 첨가에 따른 전기적 광학적 특성의 변화에 대한 결과들이 많이 보고되고 있지만 서로 상충되거나 해석상 다소 어려운 것으로 알려져 있다. 따라서 본 연구에서는 ZnO에 $Cr_2O_3$를 2.0 at% 첨가하여 Cr 첨가에 따른 ZnO의 결함준위와 입계 특성 변화에 대하여 각종 유전함수($Z^*$, $Y^*$, $M^*$, $\varepsilon^*$, and $tan{\delta}$)를 이용하여 고찰하였다 ZnO에 Cr을 첨가할 경우 결함 중 장범위 쿨롱 인력에 의한 결함(0.13~0.18 eV)이 ~100K 영역에서 나타났으며, ZnO 내 결함 중 대표적인 $Zn_j$$V_o$는 서로 겹쳐서 나타났다. 이들 중첩된 결함에 대하여 각종 유전함수를 이용할 경우 서로 분리해 낼 수 있는 강점이 있음을 논하였다. 또한 각 결함준위가 강는 정전용랑(C)과 저항(R)을 impedance-modulus spectroscopy를 이용하여 구한 결과, 소결온도가 높아질수록 정전용량은 증가하였으며, 측정온도가 놓아질수록 높아지는 경향을 나타내었다. 입계의 정전용량은 소결온도가 높아질수록 높아 지지만 측정온도가 높아질수록 낮아지는 경향을 나타내었다. 각 저항값은 소결온도 및 측정온도가 높아질수록 지수적으로 감소하였다. 또한 분포함수를 이용하여 입계 안정성에 대하여 고찰하였다.

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