• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.597-610
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• 2024

Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

• Journal of Korea Water Resources Association
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• v.38 no.7 s.156
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• pp.527-535
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• 2005

The computation of normal depth is very important for the design of channel and the analysis of water flow. Drainage pipe generally has the shape of curvature like circular or U-type, which is different from artificial triangular or rectangular channel. In this case, the computation of normal depth or the derivation of equations is very difficult because the change of hydraulic radius and area versus depth is not simple. If the ratio of the area to the diameter, or the hydraulic radius to the diameter of pipe is expressed as the water depth to the diameter of pipe by power law, however, the process of computing normal depth becomes relatively simple, and explicit equations can be obtained. In the present study, developed are the explicit normal depth equations for circular and U-type pipes, and the normal depth equation associated with Hagen (Manning) equation and friction factor equation of smooth turbulent flow by power law is also proposed because of its wide usage in engineering design.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.723-738
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• 2015

In this paper, the prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument

• Korea-Australia Rheology Journal
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• v.11 no.3
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• pp.225-232
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• 1999

This study presents 1-dimensional simple model for sheet casting or rectangular fiber spinning process. In order to achieve this goal, we introduce the concept of force flux balance at the die exit, which assigns for the extensional flow outside the die the initial condition containing the information of shear flow history inside the die. With the Leonov constitutive equation that predicts non-vanishing second normal stress difference in shear flow, we are able to describe the anisotropic swelling behavior of the extrudate at least qualitatively. In other words, the negative value of the second normal stress difference causes thickness swelling much higher than width of extrudate. This result implies the importance of choosing the rheological model in the analysis of polymer processing operations, since the constitutive equation with the vanishing second normal stress difference is shown to exhibit the characteristic of isotropic swelling, that is, the thickness swell ratio always equal to the ratio in width direction.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.443-454
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• 2010

In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation $f^{(n)}+A_{n-2}(z)f^{(n-2)}+{\cdots}+A_1(z)f'+A_0(z)f=0(n{\geq}2)$ in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.81-93
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• 2009

Bifurcation method of dynamical systems is employed to investigate exact solitary wave solutions and kink wave solutions in the generalized modified Boussinesq equation. Under some parameter conditions, their explicit expressions are obtained. Some previous results are extended.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.861-870
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• 2007

In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.61-88
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• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

• East Asian mathematical journal
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• v.17 no.2
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.565-571
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• 2006

In this paper, we present the explicit formula of the generalized inverse $A^{(2)}_{T,S}$, and we apply this result to solve restricted linear equation $Ax+y=b$, $x{\in}T$, $y{\in}S$ and $Ax+By=b$, $x{\in}T$, $y{\in}S$.