• Title/Summary/Keyword: second-order expansion

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SOLVING SECOND ORDER SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH LAYER BEHAVIOR VIA INITIAL VALUE METHOD

  • GEBEYAW, WONDWOSEN;ANDARGIE, AWOKE;ADAMU, GETACHEW
    • Journal of applied mathematics & informatics
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    • v.36 no.3_4
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    • pp.331-348
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    • 2018
  • In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

Development of Refrigeration Equipment for Tuna Long Liner (참치 어선 냉동장치의 개발에 관한 연구)

  • 오후규;정재천;김성규;구학근
    • Journal of Advanced Marine Engineering and Technology
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    • v.16 no.4
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    • pp.78-87
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    • 1992
  • The experimental study and theoretical analysis are made in order to investigate a new refrigeration system, R-22 and R-502 or R-13 cascade compressor with panel type cooler, for tuna long liner. The experimental apparatus consists with the cascade unit, 1.5 HP R-502 compressor in the first stage and 1 HP R-22 compressor in the second stage, and 3 $m^2$ cold storage room with a direct expansion panel type cooler. The main result are as follows: 1. The energy saving and C.O.P. of the R-22 and R-502 or R-22 and R-13 cascade are improved much higher than two stage compressor. 2. For the point of simplicity of design, installation, and running cost, the panel type cooler is much better than traditional hair pin coil type cooler. 3. From the experimental data and analysis, the R-22 and R-502, or R-22 and R-13 cascade compressor with panel type cooler is recommended for a new refrigeration equipment of the tuna long liner.

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Rural Residents' Satisfaction of Living Environment and Social Service (농촌 주민의 생활환경 및 사회서비스 만족도)

  • Choi, Yoon-Ji;Hwang, Jeong-Im
    • Journal of Agricultural Extension & Community Development
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    • v.17 no.4
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    • pp.685-716
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    • 2010
  • The purposes of this study were to exploring the rural residents' satisfaction of living environment and social service. For these purpose we collected the data from the residents in rural area(1,000). The major findings of this study were as follows : First, the total satisfaction score is 58.9. The highest score group is housing and environment(69.9). And the lowest score group is cultural life and leisure environment. Various welfare services have been carried out for low income people, disabled people, old people, children and rural women within the social service system. But many respondents did not have chances to use social service because it was not efficiently provided many social services. So most of the residents in village wanted more welfare services. Second, the qualitative enhancement is more important than physical infrastructure expansion in order to improve rural settlement condition(housing quality, water supply and drainage, road and traffic system, medical care etc.)

A SUPERLINEAR $\mathcal{VU}$ SPACE-DECOMPOSITION ALGORITHM FOR SEMI-INFINITE CONSTRAINED PROGRAMMING

  • Huang, Ming;Pang, Li-Ping;Lu, Yuan;Xia, Zun-Quan
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.759-772
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    • 2012
  • In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

Non-Planar Non-Linear Vibration Phenomenon on the One to One Resonance of the Circular Cantilever Beam (원형 외팔보의 일대일 공진에서의 비평면 비선형 진동현상)

  • Park Chul-Hui;Cho Chongdu;Kim Myoung-Gu
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.2 s.245
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    • pp.171-178
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    • 2006
  • Experimental and theoretical study of the non-planar response motions of a circular cantilever beam subject to base harmonic excitation has been presented in this paper work. Theoretical research is conducted using two non-linear coupled integral-differential equations of motion. These equations contain cubic linearities due do curvature term and inertial term. A combination of the Galerkin procedure and the method of multiple scales are used to construct a first-order uniform expansion for the case of one-to-one resonance. The results show that the non-linear geometric terms are very important for the low-frequency modes of the first and second mode. The non-linear inertia terms are also important for the high-frequency modes. We present the quantitative and qualitative results for non-planar motions of the dynamic behavior.

Improved component mode synthesis method using experimental obtained modal data (실험모달데이터를 사용한 구분모두 합성법의 개선)

  • 장경진;지태한;박영필
    • Journal of KSNVE
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    • v.6 no.1
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    • pp.97-106
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    • 1996
  • This paper presents systematic study of the experimental application of a free-interfaced component mode synthesis method. In the free-interfaced component mode synthesis method, an error the to truncated higher modes and neglected ineria loadings on a component from the connected component is inherent. Also, it is difficult to directly use experimental modal data in a modal synthesis method which links experimental model to finite-element model because of many inconsistencies between experimentally obtained and analytically obtained modal vectors and missing degrees-of-freedom (DOFs) such as rotational DOFs. In order to solve these problems, three methods, the first one based on attaching auxiliary weights to the connection points, the second one utillizing the normalization of experimental modal vector, and the third one generating smoothed and expanded experimental mode shapes, are studied in this paper. Finally, the study is illustrated for a flat-plate structure by using simulated and measured experimental data.

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Supersonic Axisymmetric Minimum Length Nozzle Conception at High Temperature with Application for Air

  • Zebbiche, Toufik
    • International Journal of Aeronautical and Space Sciences
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    • v.9 no.1
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    • pp.1-30
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    • 2008
  • When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect; its state equation remains always valid, except, it is named in more by calorically imperfect gas. The aim of this work is to trace the profiles of the supersonic axisymmetric Minimum Length Nozzle to have a uniform and parallel flow at the exit section, when the stagnation temperature is taken into account, lower than the dissociation threshold of the molecules, and to have for each exit Mach number and stagnation temperature shape of nozzle. The method of characteristics is used with the algorithm of the second order finite differences method. The form of the nozzle has a point of deflection and an initial angle of expansion. The comparison is made with the calorically perfect gas. The application is for air.

Improving the Safety Regulation For Self Contained Breathing Apparatus (특정소방대상물의 공기호흡기 안전규제 개선방안)

  • Lee, Sang-Pal
    • Fire Science and Engineering
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    • v.24 no.3
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    • pp.45-51
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    • 2010
  • The objective of this study to analyse the cause and pattern of failing to use in Self Contained Breathing Apparatus using by government regulation for producer and client. Regulation for producer is related to legal and institution of safety inspectiontest of SCBA. Rregulation for client is preventive maintenance. Improving fail in use of SCBA are following. First, expansion of ad hoc collection inspection and safety checking is required. Second, the strict application of the law for monitoring and auditing disposal procedure in low performance SCBA is required.

Analysis of the Three Phase Inductor-Converter Bridge Circuit by Means of State-Space Averaging Method. (상태변수 평균화법에 의한 삼상 ICB회로 해석)

  • Park, Min-Ho;Hong, Soon-Chan;Choy, Ick;Oh, Soo-Hong
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.38 no.9
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    • pp.701-709
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    • 1989
  • The time-averaged behavior of the three-phase Inductor-Converter Bridge (ICB) circuit has been analyzed by using the state-space averaging method. Especially, a second order approximation in the matrix expansion makes the analysis possible. The results are in a closed form which is quite different from the conventional solution obtained by using the Fourier Series. Therefore, the computational difficulties in evaluating the infinite Fourier series can be avoided and the results derived in this paper are available expecially in real time control. By comparing with the Fourier result, it has been verified that the analysis by means of the state-space averaging method is more accurate and simple. The digital simulation and the equivalent experiments have also been carried out to confirm the theoretical results.

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Numerical Analysis for Under- or Over- Expanded Supersonic Turbulence Jet Flow (초음속 불완전 팽창 난류 제트 유동에 관한 수치적 연구)

  • Kim Jae-Soo
    • 한국전산유체공학회:학술대회논문집
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    • 1999.05a
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    • pp.85-89
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    • 1999
  • Numerical Analysis has been done for the supersonic off-design jet flow due to the pressure difference between the jet and the ambient fluid. The difference of pressure generates an oblique shock or an expansion wave at the nozzle exit, The waves reflect repeatedly at the center axis and on the sonic surface in the shear layer, and the pressure difference is resolved across these waves interacted with the turbulence mixing layer. In this paper, the axi-symmetric Navier-Stokes equation has been used with two equation $k-{\varepsilon}$ turbulence closure model. The second order TVD scheme with flux limiters, based on the flux vector split by the smooth eigenvalue split, has been used to capture internal shocks and other discontinuities. The correction term for the compressible flow and the damping function are used in the turbulence model. Numerical calculations have been done to analyze the off-design jet flow due to the pressure difference. The variation of pressure along the flow axis is compared with an experimental result and other numerical result. The characteristics of the interaction between the shock cell and the turbulence mixing layer have been analyzed.

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