• Title/Summary/Keyword: fourth order

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AN ASYMPTOTIC FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE WITH DISCONTINUOUS SOURCE TERM

  • Babu, A. Ramesh;Ramanujam, N.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1057-1069
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    • 2008
  • We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

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A Possible Detection of a Secondary Light-Time Orbit of the Massive Early type Eclipsing Binary Star AH Cephei

  • Kim, Chun-Hwey;Nha, Il-Seong;Jerzy M. Kreiner
    • Bulletin of the Korean Space Science Society
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    • 2003.10a
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    • pp.75-75
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    • 2003
  • All published and newly observed times of minimum light of the massive, early-type eclipsing binary star AH Cep were analyzed. After subtracting the light time effect due to the well-known third body from the residuals of the observed times of minimum light, it was found that the second-order Ο-C residuals varied in a cyclical way. It was assumed that the secondary oscillations were produced by a light time effect due to a fourth body so all the times of minimum light were reanalyzed with a differential least-squares scheme in order to obtain the light time orbits due to both the third and fourth bodies. The periods, eccentricities, semi-amplitudes of the light time orbits for the third and fourth-bodies were derived as : P$\_$3/=68.$\^$y/3 and P$\_$4/=9.$\^$y/3, e$_3$=0.53 and e$_4$=0.83, K$_3$=0.$\^$d/0585 and K$_4$=0.$\^$d/0045, respectively. The analysis of the radial velocities of AH Cep published so far, do not conflict with the hypothesis of the multiplicity of the system but their accuracies are not high enough to be useful to support the interpretation. Other properties of the distant bodies are discussed for assorted possible inclinations of their orbits.

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A Complimentary Direction of the Fourth Industrial Revolution and the Department of Military Science in Universities (제4차 산업혁명과 민간대학 군사학과 교육체계 보완방향)

  • Kim, Yeon-Jun
    • Journal of National Security and Military Science
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    • s.15
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    • pp.31-55
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    • 2018
  • It has been fifteen years since military science was introduced into private and public universities since 2004. The department focuses on the improvements of the South Korean Army quality based on the Korean Army's traits including: an increase of power in the armed force and operations through research, development, and the expansion of a cooperation between the public (civilians) and military. Approximately, four hundred students from various universities in the military science department graduate in order to become an officer. The fourth industrial revolution causes structural transformation to our lives. Through the use of Artificial Intelligence (AI,) war and the military as a whole will be altered significantly particularly with regard to efficiency. Nevertheless, it is important for us to train officers in creative ways so that they can deal with situations where machines will be unable to handle situations. Considering this change in our lives, it is necessary for the military science departments to change the way to teach and train their students. In order to accomplish this goal, we need to introduce a method called "Flipped Learning" and during the process all the members need to participate and communicate in an interactive way. By doing this, the military science departments will play an important role by improving human resource in terms of military and national security.

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An O(h6 ) Quinltic Spline Interpolation for Quintic Spline Collocation Method

  • Chung, Seiyoung
    • Journal of the Chungcheong Mathematical Society
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    • v.7 no.1
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    • pp.237-242
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    • 1994
  • An quintic spline interpolate to a function in $C^{10}$[a, b] and its O($h^6$) error behavior are presented when its fourth derivative satisfies some kind of end conditions. The O($h^6$) relations between its derivatives up to fourth order and the m-th derivatives of the given function are also given at the nodes.

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Low-power DWT filter bank design using comb filter and fourth-order polynomial (Comb 필터와 4차 다항식을 사용한 저전력 DWT 필터뱅크 설계)

  • Jang Young-Beom;Lee Won-Sang
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.42 no.1
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    • pp.87-94
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    • 2005
  • In this paper a low-power DWT(Discrete Wavelet Transform) design technique is proposed. As basic low-pass filter for analysis bank, comb filter is utilized, and in order to improve frequency response for the comb filter, a fourth order polynomial is also proposed. Another filters are designed by using perfect reconstruction conditions. The lowpass filter coefficients of the analysis filter bank are optimized based on the cost function and perfect reconstruction condition. The number of the multiplications and MSE(Mean Squared Error) performance of the proposed DWT filter bank are compared with those of the JPEG2000 (9, 7) filter bank. It is shown that number of multiplications of the proposed filter bank are saved with 33.3%, and MSE values of the proposed filter bank are also superior to those of the JPEG2000 (9, 7) filter bank.

2.5 GHZ SECOND-AND FOURTH-ORDER INDUCTORLESS RF BANDPASS FILTERS

  • Thanachayanont, Apinunt
    • Proceedings of the IEEK Conference
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    • 2002.07a
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    • pp.86-89
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    • 2002
  • A new design approach for realising low-power low-voltage high-Q high-order RE bandpass filter is proposed. Based on the gyrator-C inductor topology, a 2$\^$nd/-order biquadratic bandpass filter can be realised by adding a series capacitor to the input port of the gyrator. High-Q 2$\^$nd/-order and 4$\^$th/-order fully differential RF bandpass filters operating in the 2.4-㎓ ISM (Industrial, scientific and medical) frequency band under a 2-V single power supply voltage with low power dissipation are reported.

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A Study on the Syllable Recognition Using Neural Network Predictive HMM

  • Kim, Soo-Hoon;Kim, Sang-Berm;Koh, Si-Young;Hur, Kang-In
    • The Journal of the Acoustical Society of Korea
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    • v.17 no.2E
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    • pp.26-30
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    • 1998
  • In this paper, we compose neural network predictive HMM(NNPHMM) to provide the dynamic feature of the speech pattern for the HMM. The NNPHMM is the hybrid network of neura network and the HMM. The NNPHMM trained to predict the future vector, varies each time. It is used instead of the mean vector in the HMM. In the experiment, we compared the recognition abilities of the one hundred Korean syllables according to the variation of hidden layer, state number and prediction orders of the NNPHMM. The hidden layer of NNPHMM increased from 10 dimensions to 30 dimensions, the state number increased from 4 to 6 and the prediction orders increased from 10 dimensions to 30 dimension, the state number increased from 4 to 6 and the prediction orders increased from the second oder to the fourth order. The NNPHMM in the experiment is composed of multi-layer perceptron with one hidden layer and CMHMM. As a result of the experiment, the case of prediction order is the second, the average recognition rate increased 3.5% when the state number is changed from 4 to 5. The case of prediction order is the third, the recognition rate increased 4.0%, and the case of prediction order is fourth, the recognition rate increased 3.2%. But the recognition rate decreased when the state number is changed from 5 to 6.

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Eulerian-Lagrangian Split-Operator Method for the Longitudinal Dispersion Equation (종확산 방정식에 대한 Eulerian-Lagrangian 연산자 분리방법)

  • Jun, Kyung Soo;Lee, Kil Seong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.1
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    • pp.131-141
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    • 1994
  • Three characteristics-based split-operator methods were applied to a longitudinal pollutant dispersion problem, and the results were compared with those of several Eulerian schemes. The split-operator methods consisted of generalized upwind, two-point fourth-order and sixth-order Holly-Preissmann schemes, respectively, for the advection calculation, and the Crank-Nicholson scheme for the diffusion calculation. Compared with the Eulerian schemes tested, split-operator methods using the Holly-Preissmann schemes gave much more accurate computational results. Eulerian schemes using centered difference approximations for the advection term resulted in numerical oscillations, and those using backward difference resulted in numerical diffusion, both of which were more severe for smaller value of the longitudinal dispersion coefficient.

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