• East Asian mathematical journal
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• v.29 no.3
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• pp.349-353
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• 2013

In this paper, we study equations over nilpotent groups of class 2. We show that there are some overgroups which contains solutions of equations with exponent sum 1 over nilpotent groups of class 2. As known, equations over a field has a solution in an extension field which contains a copy of the given field. But it is not easy to find that a solution of equations over groups. In many cases, even if equations over groups has a solution, the overgroup is not concrete but very Here we find the concrete overgroups in case of nilpotent groups.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.167-174
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• 2013

The main goal in the present paper is to obtain a solution of Einstein's unified field equations for the third class in $X_4$.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.4
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• pp.21-27
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• 1998

In the case of existing in free-edge delaminations of composite laminates which are symmetry with respect to mid-plane in laminates also, in the case of asymmetry and anti-symmetry, the generalized quasi-three dimensional displacement field equations developed from quasi-three dimensional displacement field equations can be applied to solve above cases. We introduce three paramenters in this paper, which have not been used in quasi-three dimensional displacement field equations until now. To the laminate subjected to the axial extension strain $\varepsilon$0(C1) in $\chi$-direction, the bending deformation $\chi$$\chi$(C$_2$) around у-direction, the bending deformation w$\chi$(C$_4$) around z-direction and the twisting deformation $\chi$$\chi$y(C$_3$) around $\chi$-direction .The generalized quasi-three dimensional displacement field equations are able to be analyzed efectively.

• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.17-28
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• 2017

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.401-411
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• 2023

The effects of longitudinal velocity dusty fluid flow in a weak magnetic field are investigated in this paper. An external uniform magnetic field parallel to the flow of dusty fluid influences the flow of dusty fluid. Besides that, the problem under investigation is completely defined in terms of identifying parameters such as longitudinal velocity (u), Hartmann number (M), dust particle interactions β, stock resistance γ, Reynolds number (Re) and magnetic Reynolds number (Rm). While using suitable transformations of resemblance, The governing partial differential equations are transformed into a system of ordinary differential equations. The Hankel Transformation is used to solve these equations numerically. The effects of representing parameters on the fluid phase and particle phase velocity flow are investigated in this analysis. The magnitude of the fluid particle is reduced significantly. The result indicates the magnitude of the particle reduced significantly. Although some of our numerical solutions agree with some of the available results in the literature review, other results differs because of the effect of the introduced magnetic field.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1131-1145
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• 2021

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p ∈ (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.

• Advances in concrete construction
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• v.11 no.4
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• pp.315-321
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• 2021

In this article, an analytical solution of the dynamical behavior in an orthotropic non-homogeneity elastic material using for elastodynamics equations is investigated. The effects of the magnetic field, the initial stress, and the non-homogeneity on the radial displacement and the corresponding stresses in an orthotropic material are investigated. The analytical solution for the elastodynamic equations has solved regarding displacements. The variation of the stresses, the displacement, and the perturbation magnetic field have shown graphically. Comparisons are made with the previous results in the absence of the magnetic field, the initial stress, and the non-homogeneity. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.681-688
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• 2011

Structural model of laminated composite plates based on the first order shear deformable plate theory and subjected to a combination of magnetic and thermal fields is developed. Coupled equations of motion are derived via Hamilton's principle on the basis of electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. In order to obtain the implications of a number of geometrical and physical features of the model, one special case is investigated, that is, free vibration of a composite plate immersed in a transversal magnetic field. Special coupling effects between the magnetic and elastic fields are revealed in this paper.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1047-1053
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• 1996

In this paper, we obtain a solution of Einstein's unified field equations on a generalized n-dimensional Riemannian manifold $X_n$.