• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.763-777
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• 2000

We investigate the existence of group invariant solutions of the Emden-Fowler equation, - u=$\mid$x$\mid$$\sigma$$\mid$u$\mid$p-1u in B, u=0 on B and u(gx)=u(x) in B for g G. Here B is the unit ball in n 2, 1$\sigma$ 0 and G is a closed subgrop of the orthogonal group. A soultion of the problem is called a G in variant solution. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.369-380
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• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.23 no.10
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• pp.782-787
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• 2010

Recently the solution-based thin film technology has often been treated in the field of device fabrication owing to easy process and convenience for the development of various semiconductor devices and sensors. We deposited on glass substrate single-walled carbon nanotubes (SWNTs)/silane hybrid thin films by multiple spray-coating which is one of solution-based processes, and examined their electrical response for humidity. Generally silane binders which are often mixed in carbon nanotube (CNT) solution to adhere CNTs to substrate well form easily each own functionalized group on the surface of CNTs after they are hardened by way of the hydrolysis reaction. In this work, we investigated how silane binders (TEOS (tetraethoxy silane), MTMS (methyltrimethoxysilane) and VTMS (vinyltrimethoxysilane)) in CNT thin films make effect to their electrical response on humidity. As the result, we found that the resistance in the samples using TEOS was changed dramatically while it was almost invariant in the samples using MTMS and VTMS for increasing humidity.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2010.06a
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• pp.196-196
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• 2010

In this work, we deposited SWNTs/silane hybrid thin films by multiple spray-coating on glass substrate, and examined their electrical response for humidity. Generally silane binders which are often used in CNT solution to adhere CNTs to substrate well can be easily functionalized to each own group on the surface of CNTs after they are hardened by way of the hydrolysis reaction. We investigated how silane binders (TEOS,, MTMS and VTMS) in SWNTs hybrid thin films make effect to their electrical response on humidity. As the result, we observed that the resistance in the sample using TEOS was changed dramatically while it was almost invariant in the samples using MTMS and VTMS for increasing humidity.