• Title/Summary/Keyword: Gaussian distribution theory

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Dual-phase-lag model on microstretch thermoelastic medium with diffusion under the influence of gravity and laser pulse

  • Othman, Mohamed I.A.;Abd-Elaziz, Elsayed M.;Mohamed, Ibrahim E.A.
    • Structural Engineering and Mechanics
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    • v.75 no.2
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    • pp.133-144
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    • 2020
  • This investigation is to study the effect of gravitational field and diffusion on a microstretch thermoelastic medium heating by a non-Gaussian laser beam. The problem was studied in the context of the dual-phase-lag model. The normal mode analysis is used to solve the problem to obtain the exact expressions for the non-dimensional displacement components, the micro-rotation, the stresses, and the temperature distribution. The effect of time parameter, heat flux parameter and gravity response of three theories of thermoelasticity i.e. dual-phase-lag model (DPL), Lord and Shulman theory (L-S) and coupled theory (CT) on these quantities have been depicted graphically for a particular model.

Analysis of Threshold Voltage Characteristics for Double Gate MOSFET Based on Scaling Theory (스켈링이론에 따른 DGMOSFET의 문턱전압 특성분석)

  • Jung, Hak-Kee;Han, Ji-Hyung;Jeong, Dong-Soo
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2012.05a
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    • pp.683-685
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    • 2012
  • This paper have presented the analysis of the change for threshold voltage and drain induced barrier lowering among short channel effects occurred in subthreshold region for double gate(DG) MOSFET with two gates to be next-generation devices, based on scaling theory. To obtain the analytical solution of Poisson's equation, Gaussian function been used as carrier distribution to analyze closely for experimental results, and the threshold characteristics have been analyzed for device parameters such as channel thickness and doping concentration and projected range and standard projected deviation of Gaussian function. Since this potential model has been verified in the previous papers, we have used this model to analyze the threshold chatacteristics. As a result to apply scaling theory, we know the threshold voltage and drain induced barrier lowering is changed, and the deviation rate is changed for device parameters for DGMOSFET.

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Structural Analysis and Magnctic Propcrics of Amorphous $Fe_{78}Si_{9}B_{13}$ Alloy (비정질 $Fe_{78}Si_{9}B_{13}$ 합금의 구조와 자성 연구)

  • 이희복;송인명;유성초;임우영
    • Journal of the Korean Magnetics Society
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    • v.3 no.3
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    • pp.179-184
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    • 1993
  • The X-ray diffraction pattern of amorphous $Fe_{78}Si_{9}B_{13}$ alloy was analyzed to obtain the radial distribution function (RDF) where the first peak was in the form of Gaussian function. The calculated coordination number of the form of Gaussian functiono The calculated coordination number of the sample is 13.5, the mean distance betweeon near-neighbor atoms $r_{0}$ is $2.595{\AA}$ and a Gaussian parametet ${\delta}r$ indicating near-neighbor atomic distri-bution is $0.27{\AA}$. The temperature dependence of saturated magnetization at low temperature could be explained by spin wave excitations theory yielding the spin wave stiffness constant as $117.8\;meV\;{\AA}^2$. Also, we tried to fit the observed temperature dependence of saturated magnetization with the Handrich's equation of the modified molecular field theory for the amorphous ferromagnet. Nice fittings are obtained when we used the parameters ${\Delta}=0.32$(S=1/2) and ${\Delta}=0.23$(S=1), respectively. Finally, the calculated spin wave stiffness constant using the parameters and the structural data are $149\;meV\;{\AA}^2$ for S=1/2 and $138\;meV\;{\AA}^2$ for S=1, respectively. The mean exchange coupling integral between near-neighbor atoms was estimated to be 17.9 meV for S=1/2 and 6.7 meV for S=1.

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Statistical Inference in Non-Identifiable and Singular Statistical Models

  • Amari, Shun-ichi;Amari, Shun-ichi;Tomoko Ozeki
    • Journal of the Korean Statistical Society
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    • v.30 no.2
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    • pp.179-192
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    • 2001
  • When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

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Finite Element Analysis of Large-Electron-Beam Polishing-Induced Temperature Distribution (대면적 전자빔 폴리싱 공정 시 발생하는 온도 분포 유한요소해석 연구)

  • Kim, J.S.;Kim, J.S.;Kang, E.G.;Lee, S.W.;Park, H.W.
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.22 no.6
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    • pp.931-936
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    • 2013
  • Recently, the use of large-electron-beam polishing for polishing complex metal surfaces has been proposed. In this study, the temperature induced by a large electron beam was predicted using the heat transfer theory. A finite element (FE) model of a continuous wave (CW) electron beam was constructed assuming Gaussian distribution. The temperature distribution and melting depth of an SUS304 sample were predicted by changing electron-beam polishing process parameters such as energy density and beam velocity. The results obtained using the developed FE model were compared with experimental results for verifying the melting depth prediction capability of the developed FE model.

A joint probability distribution model of directional extreme wind speeds based on the t-Copula function

  • Quan, Yong;Wang, Jingcheng;Gu, Ming
    • Wind and Structures
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    • v.25 no.3
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    • pp.261-282
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    • 2017
  • The probabilistic information of directional extreme wind speeds is important for precisely estimating the design wind loads on structures. A new joint probability distribution model of directional extreme wind speeds is established based on observed wind-speed data using multivariate extreme value theory with the t-Copula function in the present study. At first, the theoretical deficiencies of the Gaussian-Copula and Gumbel-Copula models proposed by previous researchers for the joint probability distribution of directional extreme wind speeds are analysed. Then, the t-Copula model is adopted to solve this deficiency. Next, these three types of Copula models are discussed and evaluated with Spearman's rho, the parametric bootstrap test and the selection criteria based on the empirical Copula. Finally, the extreme wind speeds for a given return period are predicted by the t-Copula model with observed wind-speed records from several areas and the influence of dependence among directional extreme wind speeds on the predicted results is discussed.

A NEW STOCHASTIC EVALUATION THEORY OF ARBITRARY ACOUSTIC SYSTEM RESPONSE AND ITS APPLICATION TO VARIOUS TYPE SOUND INSULATION SYSTEMS -EQUIVALENCE TRANSFORMATION TOWARD THE STANDARD HERMITE AND/OR LAGUERRE EXPANSION TYPE PROBABILITY EXPRESSIONS

  • Ohta, Mitsuo;Ogawa, Hitoshi
    • Proceedings of the Acoustical Society of Korea Conference
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    • 1994.06a
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    • pp.692-697
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    • 1994
  • In the actual sound environmental systems, it seems to be essentially difficult to exactly evaluate a whole probability distribution form of its response fluctuation, owing to various types of natural, social and human factors. Up to now, we very often reported two kinds of unified probability density expressions in the standard expansion from of Hermite and Laguerre type orthonormal series to generally evaluate non-Gaussian, non-linear correlation and/or non-stationary properties of the fluctuation phenomenon. However, in the real sound environment, there still remain many actual problems on the necessity of improving the above two standard type probability expressions for practical use. In this paper, first, a central point is focused on how to find a new probabilistic theory of practically evaluating the variety and complexity of the actual random fluctuations, especially through introducing some equivalence transformation toward two standard probability density expressions mentioned above in the expansion from of Hermite and Laguerre type orthonormal series. Then, the effectiveness of the proposed theory has been confirmed experimentally too by applying it to the actual problems on the response probability evaluation of various sound insulation systems in an acoustic room.

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Fundamental Theory on the Zeros Distribution of Multizeros Optical Beam for Longrange Optical Measurement Applications (광학식 장거리 계측을 위한 다중영점 광빔의 영점 배치에 관한 기초 이론)

  • Fujimoto, Ikumatsu;Sato, Seichi;Kurihara, Toru;Ando, Sigeru;Kim, Min-Young
    • Journal of the Korean Society for Precision Engineering
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    • v.27 no.3
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    • pp.33-40
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    • 2010
  • Multizeros(multiple order zeros) optical beams which belong to the Laguerre-Gaussian beams, have rotational phase and conically-shaped amplitude structures around multizeros points in their phase and amplitude profiles, respectively. Especially, they have their own characteristics that the multizero points do not vanish over free-space propagation. Therefore, they are expected to be adequate for the applications of long-range optical measurement by using their multizero points as optical markers for the deformation sensing. In this paper, fundamental properties of multizeros optical beams for long-range optical measurement applications are investigated and clarified. In particular, the mathematical investigations are described on the characteristics of multizeoros optical beams such as (1) separation of a multizero into isolated single order zeros, (2) topological charge of zeros distribution which are induced by superposing them. And also the outline of a fundamental experiment and its result are explained briefly.

Value at Risk with Peaks over Threshold: Comparison Study of Parameter Estimation (Peacks over threshold를 이용한 Value at Risk: 모수추정 방법론의 비교)

  • Kang, Minjung;Kim, Jiyeon;Song, Jongwoo;Song, Seongjoo
    • The Korean Journal of Applied Statistics
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    • v.26 no.3
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    • pp.483-494
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    • 2013
  • The importance of financial risk management has been highlighted after several recent incidences of global financial crisis. One of the issues in financial risk management is how to measure the risk; currently, the most widely used risk measure is the Value at Risk(VaR). We can consider to estimate VaR using extreme value theory if the financial data have heavy tails as the recent market trend. In this paper, we study estimations of VaR using Peaks over Threshold(POT), which is a common method of modeling fat-tailed data using extreme value theory. To use POT, we first estimate parameters of the Generalized Pareto Distribution(GPD). Here, we compare three different methods of estimating parameters of GPD by comparing the performance of the estimated VaR based on KOSPI 5 minute-data. In addition, we simulate data from normal inverse Gaussian distributions and examine two parameter estimation methods of GPD. We find that the recent methods of parameter estimation of GPD work better than the maximum likelihood estimation when the kurtosis of the return distribution of KOSPI is very high and the simulation experiment shows similar results.

Analysis of Subthreshold Characteristics for Double Gate MOSFET using Impact Factor based on Scaling Theory (스켈링이론에 가중치를 적용한 DGMOSFET의 문턱전압이하 특성 분석)

  • Jung, Hak-Kee
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.16 no.9
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    • pp.2015-2020
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    • 2012
  • The subthreshold characteristics has been analyzed to investigate the effect of two gate in Double Gate MOSFET using impact factor based on scaling theory. The charge distribution of Gaussian function validated in previous researches has been used to obtain potential distribution in Poisson equation. The potential distribution was used to investigate the short channel effects such as threshold voltage roll-off, subthreshold swings and drain induced barrier lowering by varying impact factor for scaling factor. The impact factor of 0.1~1.0 for channel length and 1.0~2.0 for channel thickness are used to fit structural feature of DGMOSFET. The simulation result showed that the subthreshold swings are mostly effected by impact factor but are nearly constant for scaling factors. And threshold voltage roll-off and drain induced barrier lowering are also effected by both impact factor and scaling factor.