• Journal of the Korean Society of Manufacturing Process Engineers
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• v.18 no.8
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• pp.82-90
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• 2019

We propose an equivalent model of a sintered metal mesh filter calculated by Ergun's equation and polynomial regression for the CFD analysis of breakaway devices at a hydrogen fueling station. CFD analysis of filters that cause high pressure loss is essential because breakaway devices in high-pressure hydrogen conditions require low pressure loss. A differential pressure experiment with a filter was performed in a low-pressure air condition considering similarities. An equivalent model was developed by deriving the resistance value by the polynomial regression using the experimental results. The results of CFD analysis using the equivalent model show that there was almost no error in the operating condition of the breakaway device compared to the experimental results. Through this work, we believe that the proposed equivalent model of a filter can be applied to the analysis of breakaway devices in hydrogen fueling stations. We will study how to optimize the shape and position of the filter in breakaway devices using the developed equivalent model.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1145-1166
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• 2022

In this paper, for a transcendental meromorphic function f and α ∈ ℂ, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: $$f^n+{\alpha}f^{n-2}f^{\prime}+P_d(z,f)={\sum\limits_{i=1}^{k}}{p_i(z)e^{{\alpha}_i(z)},$$ where P_d(z, f) is a differential polynomial of f, p_i's and α_i's are non-vanishing rational functions and non-constant polynomials, respectively. When α = 0, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case α ≠ 0 has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.603-611
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• 2020

In this manuscript, we discuss the relationship between prime rings and automorphisms satisfying differential identities involving commutators and anti-commutators on Lie ideals. In addition, we provide an example which shows that we cannot expect the same conclusion in case of semiprime rings.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.52.2-52
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• 2002

In this paper we consider an approach to a formal linearization for time-variant nonlinear systems. A time-variant nonlinear sysetm is assumed to be described by a time-variant nonlinear differential equation. For this system, we introduce a coordinate transformation function which is composed of the Chebyshev polynomials. Using Chebyshev expansion to the state variable and Laguerre expansion to the time variable, the time-variant nonlinear sysetm is transformed into the time-variant linear one with respect to the above transformation function. As an application, we synthesize a time-variant nonlinear observer. Numerical experiments are included to demonstrate the validity of...

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.675-682
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• 2009

In this paper, we study the uniqueness problems on entire functions sharing one value. We improve and generalize some previous results of Zhang and Lin [11]. On the one hand, we consider the case for some more general differential polynomials $[f^nP(f)]^{(k)}$ where $P({\omega})$ is a polynomial; on the other hand, we relax the nature of sharing value from CM to IM.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.451-464
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• 2016

In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R. $Br{\ddot{u}}ck$.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.767-779
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• 2003

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $h^{3/2}$ in the case of piecewise linear polynomial space.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.657-670
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• 2015

In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.935-950
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• 1997

When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.