• Title/Summary/Keyword: s equations

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GENERALIZED FORMS OF SWIATAK'S FUNCTIONAL EQUATIONS WITH INVOLUTION

  • Wang, Zhihua
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.779-787
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    • 2019
  • In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

A New Approach for Motion Control of Constrained Mechanical Systems: Using Udwadia-Kalaba′s Equations of Motion

  • Joongseon Joh
    • International Journal of Precision Engineering and Manufacturing
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    • v.2 no.4
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    • pp.61-68
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    • 2001
  • A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

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Statistical Evaluation of Sigmoidal and First-Order Kinetic Equations for Simulating Methane Production from Solid Wastes (폐기물로부터 메탄발생량 예측을 위한 Sigmoidal 식과 1차 반응식의 통계학적 평가)

  • Lee, Nam-Hoon;Park, Jin-Kyu;Jeong, Sae-Rom;Kang, Jeong-Hee;Kim, Kyung
    • Journal of the Korea Organic Resources Recycling Association
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    • v.21 no.2
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    • pp.88-96
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    • 2013
  • The objective of this research was to evaluate the suitability of sigmoidal and firstorder kinetic equations for simulating the methane production from solid wastes. The sigmoidal kinetic equations used were modified Gompertz and Logistic equations. Statistical criteria used to evaluate equation performance were analysis of goodness-of-fit (Residual sum of squares, Root mean squared error and Akaike's Information Criterion). Akaike's Information Criterion (AIC) was employed to compare goodness-of-fit of equations with same and different numbers of parameters. RSS and RMSE were decreased for first-order kinetic equation with lag-phase time, compared to the first-order kinetic equation without lag-phase time. However, first-order kinetic equations had relatively higher AIC than the sigmoidal kinetic equations. It seemed that the sigmoidal kinetic equations had better goodness-of-fit than the first-order kinetic equations in order to simulate the methane production.

On the Limitation of Telegrapher′s Equations for Analysis of Nonuniform Transmission Lines

  • Kim, Se-Yun
    • Journal of electromagnetic engineering and science
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    • v.4 no.2
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    • pp.68-71
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    • 2004
  • The limitation of telegrapher's equations for analysis of nonuniform transmission lines is investigated here. It is shown theoretically that the input impedance of a nonuniform transmission line cannot be derived uniquely from the Riccati equation only except for the exponential transmission line of a particular frequency-dependent taper. As an example, the input impedance of an angled two-plate transmission line is calculated by solving the telegrapher's equations numerically. The numerical results suffer from larger deviation from its rigorous solution as the plate angle increases.

LOCAL WELL-POSEDNESS OF DIRAC EQUATIONS WITH NONLINEARITY DERIVED FROM HONEYCOMB STRUCTURE IN 2 DIMENSIONS

  • Lee, Kiyeon
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1445-1461
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    • 2021
  • The aim of this paper is to show the local well-posedness of 2 dimensional Dirac equations with power type and Hartree type nonlin-earity derived from honeycomb structure in Hs for s > $\frac{7}{8}$ and s > $\frac{3}{8}$, respectively. We also provide the smoothness failure of flows of Dirac equations.

General Derivation of Two-Fluid Model (2상 유동 모델의 일반적인 유도)

  • Hee Cheon No
    • Nuclear Engineering and Technology
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    • v.16 no.1
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    • pp.1-10
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    • 1984
  • General time-volume averaged conservation equations and jump conditions for two-phase flows are derived here. The time-averaged equations for a single phase region in two-phase flow are obtained from local instant balance equations by a technique often used for single phase turbulent flow equations. The results obtained by integrating the time averaged equations over a flow volume are spatially averaged twice; first, they are averaged over a single phase region of the k-th phase and then averaged over the total volume of the k-th phase, in a flow volume. The mass, momentum, and energy conservation equations are obtained from the general time-volume averaged equations. The advantages of the present model are explained by comparing it with Ishii's model (1) and Banerjee's model (2). Finally, the assumptions and approximate terms of the equations of the THERMIT-6S are clarified.

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Hamilton제s Principle for the Free Surface Waves of Finite Depth (유한수심 자유표면파 문제에 적용된 해밀톤원리)

  • 김도영
    • Journal of Ocean Engineering and Technology
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    • v.10 no.3
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    • pp.96-104
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    • 1996
  • Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

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ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS

  • Simeonov, P.S.;Bainov, D.D.
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.1-14
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    • 1994
  • In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.

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FRACTIONAL NONLOCAL INTEGRODIFFERENTIAL EQUATIONS AND ITS OPTIMAL CONTROL IN BANACH SPACES

  • Wang, Jinrong;Wei, W.;Yang, Y.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.14 no.2
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    • pp.79-91
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    • 2010
  • In this paper, a class of fractional integrodifferential equations of mixed type with nonlocal conditions is considered. First, using contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. Second, the existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with nonlocal conditions is also presented.