• Korean Journal of Mathematics
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• 제23권1호
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• Tribology and Lubricants
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• 제28권5호
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• pp.218-232
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• 2012

In a spool valve analysis, the Reynolds equation is commonly used to investigate the lubrication characteristics. However, the validity of the Reynolds equation is questionable in a spool valve analysis because cavitation often occurs in the groove and the depth of the groove is much higher than the clearance in most cases. Therefore, the validity of the Reynolds equation in a spool valve analysis is investigated by comparing the results obtained from the Reynolds equation and the Navier-Stokes equation. Dimensionless parameters are determined from a nondimensional form of the governing equations. The differences between the lateral force, friction force, and volume flow rate (leakage) obtained by the Reynolds equation and those obtained by the Navier-Stokes equation are discussed. It is shown that there is little difference (less than 10%), except in the case of a spool valve with many grooves where no cavitation occurs in the grooves. In most cases, the Reynolds equation is effective for a spool valve analysis under a no cavitation condition.

• Bulletin of the Korean Chemical Society
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• 제33권8호
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• pp.2699-2702
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• 2012

Gold-polypyrrole segment nanowires prepared using anodized aluminum oxide templates can be assembled into a curved superstructure that shows stimuli-induced contraction and expansion. The radius of the superstructures can be predicted using the simple equation suggested by J. K. Lim et al. (Nano Lett. 8, 4441 (2008)). The suggested equation, however, is valid only within the limiting condition in that the length of the polypyrrole segment is comparable to, or much longer than the gold segment. In this study, the original equation was modified to a new equation that is valid for all length scales of polypyrrole segments. The radius of the superstructures calculated using the modified equation was compared with the result calculated by the original equation, and the validity of the modified equation is discussed.

• 대한수학회논문집
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• 제35권2호
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• pp.685-695
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• 2020

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

• 한국소음진동공학회논문집
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• 제23권8호
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• pp.734-741
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• 2013

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

• 한국농공학회지
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• 제24권4호
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• pp.80-91
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• 1982

To precict the suspended sediments which are 80% of total sediments in a flood disch- arge, an equation representing vertical distribution of sediment concentration was derived based upon the diffusion theory and the logalithmic velocity distribution function in the tubulent flow mechanism. The hypothesis that the uniform mass transfer is occurred at upper part along the center line of water depth, was established as a preconition to solve the problem. The theorecal and the observed values were compared. And the theoretical equation was modified to be fit the theoretical values the observed values. Observed results are as follow; 1) Equation 12) is the theoretical equation representing the vertical concentration distri- bution of suspended sedimenta 2) Rous&exonential type vertical concentration distribution equation shows signification errors near the water surface. But the equation 12) shows substation cocentration values near the water surface. 3) Equation 15) is the modified theoretical equation which is possible to predict the vertical concentration distribution of suspended sediments.

• 대한전기학회논문지
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• 제43권2호
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• pp.285-295
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• 1994

Double Injection(DI) switching devices consist of PS0+T and nS0+T contact separated by a nearly intrinsic semiconductor region containing deep trap. The equation set for DI switching device simulation by FEM is proposed. The existance of deep trap requires the modification of conventional equation set. So recombination rate equation is modified and a new equation is included in the equation set which conventionally consists op Poisson equation and current continuity equation. Consequently, the modeling equation set, which is proposed in this paper, can be applied to other semiconductor devices with trap.

• 한국공간구조학회논문집
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• 제24권1호
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• pp.65-72
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• 2024

This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

• 대한수학회지
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• 제35권4호
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• pp.903-931
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• 1998

Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

• 한국지반신소재학회논문집
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• 제14권1호
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• pp.59-65
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• 2015

TDR을 이용한 흙의 건조밀도와 함수비의 새로운 보정 방정식을 검증하기 위해 본 연구를 수행하였다. 기존의 보정 방정식이 제안되고 몇몇 연구자들에 의해 새로운 보정 방정식을 개발하는 연구가 진행되고 있다. 기존의 보정 방정식이 함수비가 높은 세립토와 느슨한 토질에서는 적용되기 어려워 새로운 보정 방정식을 개발하였다. 이에 따라 본 연구에서는 새로운 보정 방정식을 소개하고 기존의 실험과 비교해 새로운 보정방정식의 국내지반과의 적용성을 검토를 수행하였다. 그 결과 함수비의 보정방정식에 오차가 발생하여 함수비의 새로운 보정방정식을 개발하였고, 개발한 보정방정식을 검토한 결과 95%이상의 정확도를 보여준다.