• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2003.06a
• /
• pp.434-437
• /
• 2003

Evaluation or the patterning accuracy of e-beam lithography machines requires a high precision inspection system that is capable of measuring the true xy-locations of fiducial marks generated by the e-beam machine under test. Fiducial marks are fabricated on a single photo mask over the entire working area in the form of equally spaced two-dimensional grids. In performing the evaluation, the principles of self-calibration enable to determine the deviations of fiducial marks from their nominal xy-locations precisely, not being affected by the motion errors of the inspection system itself. It is. however, the fact that only repeatable motion errors can be eliminated, while random motion errors encountered in probing the locations of fiducial marks are not removed. Even worse, a random error occurring from the measurement of a single mark propagates and affects in determining locations of other marks, which phenomenon in fact limits the ultimate calibration accuracy of e-beam machines. In this paper, we describe an uncertainty analysis that has been made to investigate how random errors affect the final result of self-calibration of e-beam machines when one uses an optical inspection system equipped with high-resolution microscope objectives and a precision xy-stages. The guide of uncertainty analysis recommended by the International Organization for Standardization is faithfully followed along with necessary sensitivity analysis. The uncertainty analysis reveals that among the dominant components of the patterning accuracy of e-beam lithography, the rotationally symmetrical component is most significantly affected by random errors, whose propagation becomes more severe in a cascading manner as the number of fiducial marks increases

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.23-35
• /
• 2011

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

• Communications for Statistical Applications and Methods
• /
• v.8 no.3
• /
• pp.603-613
• /
• 2001

A test based on score statistic is derived for detecting homoscedasticity of errors in unbalanced random effects linear model. A small simulation study is performed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• Journal of Communications and Networks
• /
• v.8 no.1
• /
• pp.21-27
• /
• 2006

We present and analyze a class of limited sensing random access algorithms with powerful properties. The algorithms are implementable in wireless mobile environments and their operational properties are simple. Their throughput in the worst case of the limit Poisson user model is 0.4297, while this throughput degrades gracefully in the presence of channel feedback errors.

• Proceedings of the Korea Institute of Convergence Signal Processing
• /
• 2000.12a
• /
• pp.85-88
• /
• 2000

Signal splitting and perfect reconstruction in subband coding is based on the assumption that quantization errors are negligible. But if subband signal is quantized, 4 types of errors occurs thus it is not impossible to do perfect reconstruction. These errors are QMF design error, aliasing error, signal error and random error. By using the QMF for subband splitting, the QMF error does not present. and by using the Lloyd-Max quantizer for the quantization and by using an appropriate synthesis filter, all signal dependent errors can be cancelled and the remaining error is random error which is uncorrelated with the original image〔1〕. In this thesis, Lenna and Camera-Man image are devided into 10 subbands by using the D4 and D20 wavelet And the subband signals are quantized by using the Lloyd-Max quantizer and the quantization errors are compared. and evaluated.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.15 no.4
• /
• pp.230-236
• /
• 2022

In this paper, we propose an efficient concatenated code for both random and ISI errors on diffusion-based molecular communication channels. The proposed concatenated code was constructed by combining the ISI-mitigating code designed for ISI mitigation and the ISI-Hamming code strong against random errors, and the BER(bit error rate) performance was analyzed through simulation. In the case of the above M=1,200 channel environment, it was found that the error rate performance of the concatenated code follows the error rate performance of the ISI-mitigating code, which is strong against ISI, and follows the error rate performance of the ISI-Hamming code, which is strong against random errors, in the channel environment below M=600. In M=600~1,200, the concatenated code shows the best error rate performance among those of three codes, which is analyzed because it can correct both random errors and errors caused by ISI. In the following cases of below M=800, it can be seen that the error rate of the concatenated code and the ISI-mitigating code shows an error rate difference of about 1.0×10^-1 on average.

• School Mathematics
• /
• v.17 no.2
• /
• pp.241-255
• /
• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

• Proceedings of the KSRS Conference
• /
• v.1
• /
• pp.446-449
• /
• 2006

It is backscattering of solar radiation by water body that makes ocean color observable from above, either by airplanes or satellites. Given the very low direct contribution to backscattering by phytoplankton cells, it is curious why the retrieval of phytoplankton concentration from remotely observed ocean color is evidently successful. From semianalytical bio-optical models, a dataset is created of spectral absorption, scattering and backscattering coefficients as a function of chlorophyll concentration. Four scenarios are considered, 1) only molecular and no particle scattering, 2) random particle backscattering uncorrelated with chlorophyll concentration, 3) constrained random particle scattering with known backscattering ratio, and 4) constrained random scattering with random backscattering ratio. Scenario 1 only introduces moderate errors of -20% - 90%. And for scenarios 3 and 4, the errors are largely within 30% and 100%. Scenario 2 introduces the largest errors, with the retrieved chlorophyll concentration virtually uncorrelated with the true values, implying the backscattering must somehow be related to the trophic state. The results of the study suggested These 3 cases confirmed that while it is the absorption by phytoplankton that in large part decides the accuracy of chlorophyll concentration retrieval, for the success of monitoring of global ocean primary productivity we have to improve our knowledge on particle backscattering.

• Journal of the Korean Statistical Society
• /
• v.28 no.2
• /
• pp.225-234
• /
• 1999

We consider the following semi-parametric non-linear mixed effect regression model : y\ulcorner=f($\chi$\ulcorner;$\beta$)+$\sigma$$\mu$($\chi$\ulcorner)+$\sigma$$\varepsilon$\ulcorner,i=1,…,n,y*=f($\chi$;$\beta$)+$\sigma$$\mu$($\chi$) where y'=(y\ulcorner,…,y\ulcorner) is a vector of n observations, y* is an unobserved new random variable of interest, f($\chi$;$\beta$) represents fixed effect of known functional form containing unknown parameter vector $\beta$\ulcorner=($\beta$$_1$,…,$\beta$\ulcorner), $\mu$($\chi$) is a random function of mean zero and the known covariance function r(.,.), $\varepsilon$'=($\varepsilon$$_1$,…,$\varepsilon$\ulcorner) is the set of uncorrelated measurement errors with zero mean and unit variance and $\sigma$ is an unknown dispersion(scale) parameter. On the basis of finite-sample, small-dispersion asymptotic framework, we derive an absolute lower bound for the asymptotic mean squared errors of prediction(AMSEP) of the regular-consistent non-linear predictors of the new random variable of interest y*. Then we construct an optimal predictor of y* which attains the lower bound irrespective of types of distributions of random effect $\mu$(.) and measurement errors $\varepsilon$.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.22 no.5
• /
• pp.24-28
• /
• 1985

In this paper, the cyclic product codes which are capable of correcting random erros and burst errors simultaneously have been designed and constructed. First, the procedure for product of two cyclic codes is shown and thin the encoder and decoder system using the (7,4) cyclic Hamming code and the (3,1) cyclic code is implemented. The micro-computer is used for experiment and the system consists of encoder, decoder and interface circuits. The encoder of cyclic product code is implemented by interlacing encoders while the decoder is implemented by cascading decoders that interlace error trapping decoders. In conclusion, cyclic product codas are easily decodable and are capable of correcting four random errors and eight-burst errors. Better performance is obtained with low error rate.