• Title/Summary/Keyword: Lambert function

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A comparison of inverse transform and composition methods of data simulation from the Lindley distribution

  • Okwuokenye, Macaulay;Peace, Karl E.
    • Communications for Statistical Applications and Methods
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    • v.23 no.6
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    • pp.517-529
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    • 2016
  • This study compares the inverse transform and the composition methods for generating data from the Lindley distribution. The expression for the inverse of the distribution function for the Lindley distribution does not exist in closed form. Hence, authors of many empirical studies on the Lindley distribution used methods for generating Lindley variates other than the inverse transform. We generated data from the Lindley distribution using the inverse transform approach by obtaining the Lindley variates numerically; we also generated data from this distribution using the composition approach. Following the generation of the Lindley variates using these two methods, we compare some statistical properties of the estimates of the Lindley model parameters based on the generated data. We conclude that the two methods produce similar results.

Determination of Air-dry Density of Wood with Polychromatic X-ray and Digital Detector

  • Kim, Chul-Ki;Kim, Kwang-Mo;Lee, Sang-Joon;Lee, Jun-Jae
    • Journal of the Korean Wood Science and Technology
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    • v.45 no.6
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    • pp.836-845
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    • 2017
  • Gravimetric method is usually used to evaluate air-dry density, which is governing physical or mechanical properties of wood. Although it had high evaluation accuracy, the method is time consuming process. Thus, this study was conducted to estimate air-dry density of wood with high accuracy by using polychromatic X-ray and digital detector as alternative of gravimetric method. To quantify polychromatic X-ray projection for evaluating air-dry density, Lambert-Beer's law with the integral value of probability function was used. The integral value was used as weighting factor in the law, and it was determined by conducting simple test at various penetration depths and tube voltage. Mass attenuation coefficient (MAC) of wood also calculated by investigating polychromatic X-ray projection according to species, penetration depth and tube voltage. The species had not an effect on change of MAC. Finally, an air-dry density of wood was estimated by applying the integral value, MAC and Lambert-Beer's law to polychromatic X-ray projection. As an example, the relation of the integral value (${\alpha}$) according to penetration depth (t, cm) at tube voltage of 35 kV was ${\alpha}=-0.00091t{\times}0.0184$ while the regression of the MAC (${\mu}$, $cm^2/g$) was ${\mu}=0.5414{\exp}(-0.0734t)$. When calculation of root mean squared error (RMSE) was performed to check the estimation accuracy, RMSE at 35, 45 and 55 kV was 0.010, 0.013 and $0.009g/cm^3$, respectively. However, partial RMSE in relation to air-dry density was varied according to tube voltage. The partial RMSE below air-dry density of $0.41g/cm^3$ was $0.008g/cm^3$ when tube voltage of 35 kV was used. Meanwhile, the partial RMSE above air-dry density of $0.41g/cm^3$ decreased as tube voltage increased. It was conclude that the accuracy of estimation with polychromatic X-ray and digital detector was quite high if the integral value and MAC of wood were determined precisely or a condition of examination was chosen properly. It was seemed that the estimation of air-dry density by using polychromatic X-ray system can supplant the gravimetric method.

Measurements of Monostatic Bottom Backscattering Strengths in Shallow Water of the Yellow Sea (서해 천해환경에서 단상태 해저면 후방산란강도 측정)

  • Son, Wuju;Son, Su-Uk;Choi, Jee Woong;Cho, Sungho;Jung, Seom-Kyu
    • The Journal of the Acoustical Society of Korea
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    • v.34 no.6
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    • pp.444-454
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    • 2015
  • Measurements of bottom backscattering strengths in a frequency range of 6-14 kHz were made on the shallow water off the southern Gyeonggi Bay in Yellow Sea in May 2013, as part of the KIOST-HYU joint acoustics experiment. Geological surveys for the experimental area were performed using multi-beam echo sounder, sparker system, and grab sampling to investigate the bottom topography, sub-bottom profile and composition of surficial sediment, respectively. In this paper, the backscattering strengths as a function of grazing angle (in range of $28^{\circ}{\sim}69^{\circ}$) were estimated and compared to the predictions obtained by Lambert's law and APL-UW scattering model. Finally, the effects of geoacoustic parameters corresponding to the experimental area on the backscattering strengths are discussed.

Symmetric and Asymmetric Double Gate MOSFET Modeling

  • Abebe, H.;Cumberbatch, E.;Morris, H.;Tyree, V.;Numata, T.; Uno, S.
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.9 no.4
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    • pp.225-232
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    • 2009
  • An analytical compact model for the asymmetric lightly doped Double Gate (DG) MOSFET is presented. The model is developed using the Lambert Function and a 2-dimensional (2-D) parabolic electrostatic potential approximation. Compact models of the net charge and channel current of the DG-MOSFET are derived in section 2. Results for the channel potential and current are compared with 2-D numerical data for a lightly doped DG MOSFET in section 3, showing very good agreement.

Multivariate Decision Tree for High -dimensional Response Vector with Its Application

  • Lee, Seong-Keon
    • Communications for Statistical Applications and Methods
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    • v.11 no.3
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    • pp.539-551
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    • 2004
  • Multiple responses are often observed in many application fields, such as customer's time-of-day pattern for using internet. Some decision trees for multiple responses have been constructed by many researchers. However, if the response is a high-dimensional vector that can be thought of as a discretized function, then fitting a multivariate decision tree may be unsuccessful. Yu and Lambert (1999) suggested spline tree and principal component tree to analyze high dimensional response vector by using dimension reduction techniques. In this paper, we shall propose factor tree which would be more interpretable and competitive. Furthermore, using Korean internet company data, we will analyze time-of-day patterns for internet user.

Steady-State and Transient Response Analysis of DSSC Based on Electron Diffusion Coefficient and Chemical Capacitance

  • J. C. Gallegos;J. Manriquez;R. Rodriguez;S. Vargas;D. Rangel
    • Journal of Electrochemical Science and Technology
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    • v.15 no.2
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    • pp.276-290
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    • 2024
  • A study of the transition from transitory state to steady state in DSSCs based on natural dyes is presented; cochineal was used as dye and Li+, Na+, and K+ were the ions added to the electrolyte. The photocurrent profiles were obtained as a function of time. Several DSSCs were prepared with different cations and their role and the transitory-to-steady transition was determined. A novel hybrid charge carrier source model based on the Heaviside function H(t) and the Lambert-Beer law, was developed and applied to analysis of the transient response of the output photocurrent. Additionally, the maximum effective light absorption coefficient α and the electronic extraction rate κ for each ion were determined: ${\alpha}_{Li^+,Na^+,K^+}\,=\,(0.486,\,0.00085,\,0.1126)\,cm^{-1}$, and also the electronic extraction rate ${\kappa}^{Li^+,Na^+,K^+}_{ext.}\,=\,(1410,\,19.07,\,19.69)\,cm\,s^{-1}$. The impedance model using Fick's second law was developed for carrier recombination to characterize the photocurrent.

Mid Frequency Band Reverberation Model Development Using Ray Theory and Comparison with Experimental Data (음선 기반 중주파수 대역 잔향음 모델 개발 및 실측 데이터 비교)

  • Chu, Young-Min;Seong, Woo-Jae;Yang, In-Sik;Oh, Won-Tchon
    • The Journal of the Acoustical Society of Korea
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    • v.28 no.8
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    • pp.740-754
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    • 2009
  • Sound in the ocean is scattered by inhomogeneities of many different kinds, such as the sea surface, the sea bottom, or the randomly distributed bubble layer and school of fish. The total sum of the scattered signals from these scatterers is called reverberation. In order to simulate the reverberation signal precisely, combination of a propagation model with proper scattering models, corresponding to each scattering mechanism, is required. In this article, we develop a reverberation model based on the ray theory easily combined with the existing scattering models. Developed reverberation model uses (1) Chapman-Harris empirical formula and APL-UW model/SSA model for the sea surface scattering. For the sea bottom scattering, it uses (2) Lambert's law and APL-UW model/SSA model. To verify our developed reverberation model, we compare our results with those in Ellis' article and 2006 reverberation workshop. This verified reverberation model SNURM is used to simulate reverberation signal for the neighboring seas of South Korea at mid frequency and the results from model are compared with experimental data in time domain. Through comparison between experiment data and model results, the features of reverberation signal dependent on environment of each sea is investigated and this analysis leads us to select an appropriate scattering function for each area of interest.

Numerical Analysis of Si-based Photovoltaic Modules with Different Interconnection Methods

  • Park, Chihong;Yoon, Nari;Min, Yong-Ki;Ko, Jae-Woo;Lim, Jong-Rok;Jang, Dong-Sik;Ahn, Jae-Hyun;Ahn, Hyungkeun
    • Transactions on Electrical and Electronic Materials
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    • v.15 no.2
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    • pp.103-111
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    • 2014
  • This paper investigates the output powers of PV modules by predicting three unknown parameters: reverse saturation current, and series and shunt resistances. A theoretical model using the non-uniform physical parameters of solar cells, including the temperature coefficients, voltage, current, series and shunt resistances, is proposed to obtain the I-V characteristics of PV modules. The solar irradiation effect is included in the model to improve the accuracy of the output power. Analytical and Newton methods are implemented in MATLAB to calculate a module output. Experimental data of the non-uniform solar cells for both serial and parallel connections are used to extend the implementation of the model based on the I-V equation of the equivalent circuit of the cells and to extend the application of the model to m by n modules configuration. Moreover, the theoretical model incorporates, for the first time, the variations of series and shunt resistances, reverse saturation current and irradiation for easy implementation in real power generation. Finally, this model can be useful in predicting the degradation of a PV system because of evaluating the variations of series and shunt resistances, which are critical in the reliability analysis of PV power generation.