• Korean Journal of Mathematics
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• v.28 no.2
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• pp.295-309
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• 2020

In this paper we study the growth of solutions of some non-linear complex differential equations in connection to Brück conjecture using the theory of complex differential equation.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.739-744
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• 2002

Recently we have discovered that sediments should be separated from lithosphere, and soil should be separated from biosphere, both sediment and soil will be mixed sediments-soil-sphere (Seso-sphere), which is using particulate mechanics to be solved. Erosion and sediment both are moving by particulate matter with water or wind. But ancient sediments will be erosion same to soil. Nowadays, real soil has already reduced much more. Many places have only remained sediments that have ploughed artificial farming layer. Thus it means sediments-soil-sphere. This paper discusses sediments-soil-sphere erosion modeling. In fact sediments-soil-sphere erosion is including water erosion, wind erosion, melt-water erosion, gravitational water erosion, and mixed erosion. We have established geographical remote sensing information modeling (RSIM) for different erosion that was using remote sensing digital images with geographical ground truth water stations and meteorological observatories data by remote sensing digital images processing and geographical information system (GIS). All of those RSIM will be a geographical multidimensional gray non-linear equation using mathematics equation (non-dimension analysis) and mathematics statistics. The mixed erosion equation is more complex that is a geographical polynomial gray non-linear equation that must use time-space fuzzy condition equations to be solved. RSIM is digital image modeling that has separated physical factors and geographical parameters. There are a lot of geographical analogous criterions that are non-dimensional factor groups. The geographical RSIM could be automatic to change them analogous criterions to be fixed difference scale maps. For example, if smaller scale maps (1:1000 000) that then will be one or two analogous criterions and if larger scale map (1:10 000) that then will be four or five analogous criterions. And the geographical parameters that are including coefficient and indexes will change too with images. The geographical RSIM has higher precision more than mathematics modeling even mathematical equation or mathematical statistics modeling.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.65-73
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• 2021

In this paper, we investigate the growth properties of solutions of the non-homogeneous linear complex differential equation L(f) = b (z) f + c (z), where L(f) is a linear differential polynomial and b (z), c (z) are entire functions and give some of its applications on sharing value problems.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.229-241
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• 2020

For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.819-829
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• 2016

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.289-295
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• 2012

We research the properties of solutions of general higher order non-homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.205-209
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• 2005

In this paper we discuss on the uniquenss of the solution of partial differential equations: (1) $${\frac{{\partial}w}{{\partial}{\bar{z}}}}=F(z,\;w,\;{\frac{{\partial}w}{{\partial}z}}}+G(z,\;w.{\bar{w})$$ in the sobolev space $W_{1,p}(D)$.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.5
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• pp.83-83
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• 2004

The analysis of relative pose(position and rotation) between stereo cameras is very important to determine the solution that provides three-dimensional information for an arbitrary moving target with respect to robot-end. In the space of free camera-model, the rotational parameters act on non-linear factors acquiring a kinematical solution. In this paper the general solution of active stereo that gives a three-dimensional pose of moving object is presented. The focus is to achieve a derivation of linear equation between a robot′s end and active stereo cameras. The equation is consistently derived from the vector of quaternion space. The calibration of cameras is also derived in this space. Computer simulation and the results of error-sensitivity demonstrate the successful operation of the solution. The suggested solution can also be applied to the more complex real time tracking and quite general and are applicable in various stereo fields.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.5
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• pp.89-90
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• 2004

The analysis of relative pose(position and rotation) between stereo cameras is very important to determine the solution that provides three-dimensional information for an arbitrary moving target with respect to robot-end. In the space of free camera-model, the rotational parameters act on non-linear factors acquiring a kinematical solution. In this paper the general solution of active stereo that gives a three-dimensional pose of moving object is presented. The focus is to achieve a derivation of linear equation between a robot's end and active stereo cameras. The equation is consistently derived from the vector of quaternion space. The calibration of cameras is also derived in this space. Computer simulation and the results of error-sensitivity demonstrate the successful operation of the solution. The suggested solution can also be applied to the more complex real time tracking and quite general and are applicable in various stereo fields.