• Title/Summary/Keyword: linear approximation

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Use of Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices and One-range Addition Theorems for Ψα-ETO in Evaluation of Potential of Electric Field Produced by Molecule

  • Guseinov, I.I.
    • Bulletin of the Korean Chemical Society
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    • v.30 no.11
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    • pp.2617-2620
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    • 2009
  • Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${\psi}^{\alpha}$‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $\alpha$ = 1, 0, ‒1, ‒2,${\cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${\psi}^{\alpha}$‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.

CALIBRATION OF VECTOR MAGNETOGRAMS BY SOLAR FLARE TELESCOPE OF BOAO

  • MOON YONG-JAE;PARK YOUNG DEUK;YUN HONG SIK
    • Journal of The Korean Astronomical Society
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    • v.32 no.1
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    • pp.65-73
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    • 1999
  • In this study we present a new improved nonlinear calibration method for vector magnetograms made by the Solar Flare Telescope of BOAO. To identify Fe I 6302.5 line, we have scanned monochromatic images of the line integrated over filter passband, changing the location of the central transmission wavelength of a Lyot filter. Then we obtained a filter-convolved line profile, which is in good agreement with spectral atlas data provided by the Sacramento Peak Solar Observatory. The line profile has been used to derive calibration coefficients of longitudinal and transverse fields, employing the conventional line slope method under the weak field approximation. Our improved nonlinear calibration method has also been used to calculate theoretical Stokes polarization signals with various angles of inclination of magnetic fields. For its numerical test, we have compared input magnetic fields with the calibrated ones, which have been derived from the new improved non-linear method and the conventional method respectively. The numerical test shows that the calibrated fields obtained from the improved method are consistent with the input fields, but not with those from the conventional method. Finally, we applied our new improved method to a dipole model which characterizes a typical field configuration of a single, round sunspot. It is noted that the conventional method remarkably underestimates the transverse field component near the inner penumbra.

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Bi-stability in a vertically excited rectangular tank with finite liquid depth

  • Spandonidis, Christos C.;Spyrou, Kostas J.
    • Ocean Systems Engineering
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    • v.2 no.3
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    • pp.229-238
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    • 2012
  • We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

Hybrid Optimization Algorithm based on the Interface of a Sequential Linear Approximation Method and a Genetic Algorithm (순차적 선형화 기법과 유전자 알고리즘을 접속한 하이브리드형 최적화 알고리즘)

  • Lee, Kyung-Ho;Lee, Kyu-Yeul
    • Journal of the Society of Naval Architects of Korea
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    • v.34 no.1
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    • pp.93-101
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    • 1997
  • Generally the traditional optimization methods have possibilities not only to give a different optimum value according to their starting point, but also to get to local optima. On the other hand, Genetic Algorithm (GA) has an ability of robust global search. In this paper, a new optimization method - the combination of traditional optimization method and genetic algorithm - is presented so as to overcome the above disadvantage of traditional methods. In order to increase the efficiency of the hybrid optimization method, a knowledge-based reasoning is adopted in the part of mathematical modeling, algorithm selection, and process control. The validation of the developed knowledge-based hybrid optimization method was examined and verified applying the method to nonlinear mathematical models.

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A Novel Hybrid MPPT Control for Photovoltaic System (태양광 발전시스템의 새로운 하이브리드 MPPT)

  • Kim, Soo-Bin;Jo, Yeong-Min;Kim, Hyeong-Jin;Song, Seung-Ho;Choi, Ju-Yeop;Choy, Ick;Lee, Young-Kwoun
    • Journal of the Korean Solar Energy Society
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    • v.35 no.2
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    • pp.43-52
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    • 2015
  • The performance of a photovoltaic array is affected by temperature, solar insolation, partial shading effect, and array configuration. Maximum power point tracking(MPPT) techniques are employed in photovoltaic systems to make full utilization of the PV array output power which depends on solar irradiation and ambient temperature. As much as MPPT is important in photovoltaic systems, many MPPT techniques have been developed. In this paper, several major existing MPPT methods are comparatively analyzed and novel hybrid MPPT algorithm is proposed. The proposed hybrid MPPT algorithm is developed in combination with traditional MPPT methods to complement each other for improving performance and mitigating partial shading effects. The proposed algorithm is implemented and validated using MATLAB/Simulink simulation tool.

Saddlepoint approximations for the risk measures of portfolios based on skew-normal risk factors (왜정규 위험요인 기반 포트폴리오 위험측도에 대한 안장점근사)

  • Yu, Hye-Kyung;Na, Jong-Hwa
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.6
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    • pp.1171-1180
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    • 2014
  • We considered saddlepoint approximations to VaR (value at risk) and ES (expected shortfall) which frequently encountered in finance and insurance as the measures of risk management. In this paper we supposed univariate and multivariate skew-normal distributions, instead of traditional normal class distributions, as underlying distribution of linear portfolios. Simulation results are provided and showed the suggested saddlepoint approximations are very accurate than normal approximations.

A New Design Approach for Optimization of GA-based SOPNN (GA 기반 자기구성 다항식 뉴럴 네트워크의 최적화를 위한 새로운 설계 방법)

  • Park, Ho-Sung;Park, Byoung-Jun;Park, Keon-Jun;Oh, Sung-Kwun
    • Proceedings of the KIEE Conference
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    • 2003.07d
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    • pp.2627-2629
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    • 2003
  • In this paper, we propose a new architecture of Genetic Algorithms(GAs)-based Self-Organizing Polynomial Neural Networks(SOPNN). The conventional SOPNN is based on the extended Group Method of Data Handling(GMDH) method and utilized the polynomial order (viz. linear, quadratic, and modified quadratic) as well as the number of node inputs fixed (selected in advance by designer) at Polynomial Neurons (or nodes) located in each layer through a growth process of the network. Moreover it does not guarantee that the SOPNN generated through learning has the optimal network architecture. But the proposed GA-based SOPNN enable the architecture to be a structurally more optimized networks, and to be much more flexible and preferable neural network than the conventional SOPNN. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate the performance of the GA-based SOPNN, the model is experimented with using nonlinear system data.

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A Numerical Model of Irregular Wave Diffraction around a Thin Semi-Infinite Breakwater (반무한 방파제 주위에서의 불규칙파 회절에 대한 수치모형)

  • 정신택;채장원;강관수;전인식
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.5 no.1
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    • pp.45-50
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    • 1993
  • The phenomenon of wave diffraction due to structure is an important factor in the wave climate at the site As an approximation, the propagation characteristics of a regular wave train are usually used. instead of those of irregular waves. However, there are great differences between the diffraction coefficients of the irregular waves and monochromatic waves, as shown by Goda (1985). The spectral calculation method. one of the methods to deal with the transformation of random sea waves essentially consists of decomposing a spectrum of the irregular sea state Into various monochromatic components, and assembling the component results by linear superposition. Monoch romatic wave transformation model developed by Chen(1987) is used to make spectral calculation. These calculations agree closely with Goda et al. (1978)'s diffraction diagram for a thin semi-infinite breakwater.

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Study on Adaptive Higher Harmonic Control Using Neural Networks (신경회로망을 이용한 적응 고차조화제어 기법 연구)

  • Park, Bum-Jin;Park, Hyun-Jun;Hong, Chang-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.3
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    • pp.39-46
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    • 2005
  • In this paper, adaptive higher harmonic control technique using Neural Networks (NN) is proposed. First, linear transfer function is estimated to relate the input harmonics and output harmonics, then NN which has the universal function approximation property is applied to expand application range of the transfer function. Optimal control gain matrix computed from the transfer function is used to train NN weights. Online weight adaptation laws are derived from Lyapunov's direct method to guarantee internal stability. Results of the simulation of 6-input 2-output nonlinear system show that adaptive HHC is applicable to the system with uncertain transfer function.

Maximum Power Point Tracking of Photovoltaic System using Approximation Method (근사기법을 이용한 태양광 발전의 MPPT 제어)

  • Park, Ki-Tae;Choi, Jung-Sik;Ko, Jae-Sub;Park, Byung-Sang;Chung, Dong-Hwa
    • Proceedings of the KIEE Conference
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    • 2007.07a
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    • pp.1215-1217
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    • 2007
  • This paper is proposed a novel method to approximate the maximum power for a photovoltaic inverter system. It is designed for power systems application and utilities. The proposed Maximum Power Point Tracking(MPPT) control has the advantage to provide a new simple way to approximate the optimal or rated voltage, the optimal or rated current and maximum power rating produced by a solar panel and the photovoltaic inverter. And this straightforward method will be named linear reoriented coordinates method(LRCM) with the advantage that Pmax and $V_{op}$ can be approximated using the same variable as the dynamic model without using complicate approximations or Taylor series. This paper is proposed MPPT using LRMC method using weather condition of domestic moderate program technique. This paper is proposed the experimental results to verify the effectiveness of the new methods.

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