• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.593-610
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• 2023

In view of Nevanlinna theory, we investigate the meromorphic solutions of q-difference differential equations and our results give the estimates about counting function and proximity function of meromorphic solutions to these equations. In addition, some interesting results are obtained for two general equations and a class of system of q-difference differential equations.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.201-208
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• 2015

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.869-880
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• 1998

In this paper, we show that the weak solutions of the time-dependent Magnetohydrodynamics equations in 3 dimensional periodic domain belong to L(equation omitted)(0, T; V$_{r}$) following the method of Foias-Guillope-Temam for Navier-Stokes equations.s.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.668-671
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• 1996

Two expressions for the inertial navigation system error equations are derived using a perturbation method; one in navigation frame, and the other in geographic frame. The equivalence between two expressions is shown by explicit equations and computer simulation.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.81-88
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• 2009

In this paper, we investigate h-stability for the nonlinear Volterra integro-differential equations and the functional integro-differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.541-545
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• 2013

In this paper, we explain how to get defining equations of the modular curves $X_1(2,2N)$ which show the moduli problems and present defining equations of $X_1(2,2N)$ for $N=2,3,{\ldots},8$.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.373-388
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• 2010

We introduce mixed cubic-quartic functional equations. And using the fixed point method, we prove the generalized Hyers-Ulam stability of cubic-quartic functional equations on random normed spaces.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.555-561
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• 2019

In this paper we consider degenerate compressible Navier-Stokes equations giving rise to a variety of mathematical problems in many areas. We study the long time behavior for the degenerate compressible Navier-Stokes equations with damping.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.869-882
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• 2023

In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.836-839
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• 2005

The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.