• Current Optics and Photonics
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• v.2 no.2
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• pp.119-124
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• 2018

The errors in retrieved aerosol backscattering coefficients due to different lidar ratios are analyzed quantitatively in this paper. The actual calculation shows that the inversion error of the aerosol backscattering coefficients using the Fernald backward-integration method increases with increasing inversion distance. The greater the error in the lidar ratio, the faster the error in the aerosol backscattering coefficient increases. For the same error in lidar ratio, the smaller actual aerosol backscattering coefficient will get the larger relative error of the retrieved aerosol backscattering coefficient. The errors in the lidar ratios for dust or the cirrus layer have great impact on the retrievals of backscattering coefficients. The interval between the retrieved height and the reference range is one of the important factors for the derived error in the aerosol backscattering coefficient, which is revealed quantitatively for the first time in this paper. The conclusions of this article can provide a basis for error estimation in retrieved backscattering coefficients of background aerosols, dust and cirrus layer. The errors in the lidar ratio of an aerosol layer influence the retrievals of backscattering coefficients for the aerosol layer below it.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.479-490
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• 2013

In this paper, we investigate a priori error estimates and superconvergence of varitional discretization for nonlinear parabolic optimal control problems with control constraints. The time discretization is based on the backward Euler method. The state and the adjoint state are approximated by piecewise linear functions and the control is not directly discretized. We derive a priori error estimates for the control and superconvergence between the numerical solution and elliptic projection for the state and the adjoint state and present a numerical example for illustrating our theoretical results.

• Atmosphere
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• v.23 no.1
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• pp.33-37
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• 2013

In meteorology, exploitation of Kalman filter as a data assimilation system is virtually impossible due to simultaneous requirements of adjoint model and large computer resource. The other substitute of utilizing ensemble Kalman filter is only affordable by compensating an enormous usage of computing resource. Furthermore, the latter employs ensemble integration sets for evolving the background error covariance matrix by compensating the dynamical feature of the temporal evolution of weather conditions. We propose a new implementation method that works without the adjoint model by utilizing the explicit expression of the background error covariance matrix in backward evolution. It will also break a barrier in the evolution of the covariance matrix. The method may be applied with a slight modification to the real time assimilation or the retrospective analysis.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.12
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• pp.34-41
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• 2003

This paper suggests a methodology fur improving the machining accuracy by compensating for the machining errors based on on-machine measurement process. Probing errors and machine tool errors included in the measurement data were calibrated or compensated to obtain the actual machining errors. Machine tool errors were modeled in forward and backward directions according to the axis movement direction to consider the effects of backlash errors on the measurement data, and model parameters were determined by measuring a cube array artifact. A rectangular workpiece was machined and then measured with a touch probe as a verification experiment. Machining experiments showed that the machining errors were reduced to within the designated tolerance after compensating for the actual machining errors by modifying the original footpath for the next-step machining.

• Proceedings of the SAREK Conference
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• 2009.06a
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• pp.386-391
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• 2009

In this study, the numerical study has carried out to analyze the factors of the efficiency decrease at backward flow situation in an axial fan with adjustable blades. The analysis is carried out the pitch angle $36^{\circ}$ on the forward flow and the pitch angle $-26^{\circ}$ on the backward flow. The numerical results show that the air flow rates of the pitch angle $36^{\circ}$ and $-26^{\circ}$ are respectively calculated to 285 CMM and 212 CMM. The results are similar to the experimental results carried out by Chang, and have made the maximum error of 10.6% when compared with the experimental results. The important reason of the fan efficiency decrease is that axial fan used for this study was designed to use for the forward flow. As the results, the pitch angle $-26^{\circ}$ has occurred the recirculation around the impeller blade, impeller cover and stator.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.9
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• pp.3672-3684
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• 2015

Recently, the standardization of backward compatible JPEG image coding for high dynamic range (HDR) image has been undertaken to establish an international standard called "JPEG XT." The JPEG XT consists of two layers: the base layer and the residual layer. The base layer contains tone mapped low dynamic range (LDR) image data and the residual layer contains the error signal used to reconstruct the HDR image. This paper gives the result of a study to evaluate the overall performance of tone mapping operators (TMOs) for this standard. The evaluation is performed using five HDR image datasets and six TMOs for profiles A, B, and C of the proposed JPEG XT standard. The Tone Mapped image Quality Index (TMQI) and no reference image quality assessment (NR IQA) are used for measuring the LDR image quality. The peak signal to noise ratio (PSNR) is used to evaluate the overall compression performance of JPEG XT profiles A, B, and C. In TMQI and NR IQA measurements, TMOs using display adaptive tone mapping and adaptive logarithmic mapping each gave good results. A TMO using adaptive logarithmic mapping gave good PSNRs.

• The Pure and Applied Mathematics
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• v.12 no.4 s.30
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• pp.275-287
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• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.69-75
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• 2010

Advanced T-DMB(Terrestial DMB )system which is a new portable mobile broadcasting system has been developed to increase data rate up to double of conventional T-DMB in same bandwidth while maintaining backward compatibility, using hierarchical modulation method. The Advanced T-DMB system realize high qualification of conventional T-DMB system by adding BPSK signal or QPSK signal as enhanced layer to existing DQPSK signal. The enhanced layer signal should be small enough to maintain backward compatibility and to minimize the coverage loss of existing T-DMB service area. But this causes the enhanced layer signal of Advanced T-DMB susceptible to fading effect in transmission channel. In this paper we applied the duo-binary turbo code which has powerful error correction capability to the enhanced layer signal for compensating channel distortion. And the computer simulation results about the performance of the duo-binary turbo code in Advanced T-DMB system are presented along with analysis comments.