• 충청수학회지
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• 제20권4호
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• pp.551-560
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• 2007

We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condition $$\{^{-{\Delta}^2u-c{\Delta}u+{\gamma}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega},\;}_{-{\Delta}^2u-c{\Delta}u+{\delta}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega}}$$, where $u^+$ = max{u, 0}, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition.

• Korean Journal of Mathematics
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• 제15권1호
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• pp.51-57
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• 2007

We prove the existence of a positive solution for the system of the following nonlinear biharmonic equations with Dirichlet boundary condition $$\{{\Delta}^2u+c{\Delta}u+av^+=s_1{\phi}_1+{\epsilon}_1h_1(x)\;in\;{\Omega},\\{\Delta}^2v+c{\Delta}v+bu^+=s_2{\phi}_1+{\epsilon}_2h_2(x)\;in\;{\Omega},$$ where $u^+= max\{u,0\}$, $c{\in}R$, $s{\in}R$, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition. Here ${\epsilon}_1$, ${\epsilon}_2$ are small numbers and $h_1(x)$, $h_2(x)$ are bounded.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.135-143
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• 2008

We investigate the existence of nontrivial solutions of the nonlinear biharmonic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\Delta}^2{\xi}+c{\Delta}{\xi}={\mu}h({\xi}+{\eta})\;in{\Omega},\\{\Delta}^2{\eta}+c{\Delta}{\eta}={\nu}h({\xi}+{\eta})\;in{\Omega},\end{array}$$ where $c{\in}R$ and ${\Delta}^2$ denote the biharmonic operator.

• 충청수학회지
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• 제20권1호
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• pp.81-95
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• 2007

We are concerned with the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=g(u)$, in ${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show that there exists at least three solutions of the above problem under the suitable condition of g(u).

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 E
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• pp.2392-2395
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• 1999

This paper describes to access the insulation deterioration condition of the stator windings in six high voltage motors. Nondestructive tests have been carried out on stand-still motors. These tests include ac current increase rate($\Delta$I), delta tan delta(${\Delta}tan{\delta}$), and maximum partial discharge(PD). AC current and $tan{\delta}$ were measured by Schering bridge. The measurement of PD patterns were conducted using digital partial discharge detector. PD patterns were observed treeing and internal discharges in Motor 1 and 2. The stator windings of two motors were found to be in a poor condition and their were recommended to rewind. The stator. windings of four motors were judged to be in serviceable condition.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.205-215
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• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.473-487
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• 2010

We investigate the existence of multiple nontrivial solutions (${\xi}$, ${\eta}$) for perturbations $g_1$, $g_2$ of the harmonic system with Dirichlet boundary condition $${\Delta}^2{\xi}+c{\Delta}{\xi}=g_1(2{\xi}+3{\eta})\;in\;{\Omega}\\{\Delta}^2{\eta}+c{\Delta}{\eta}=g_2(2{\xi}+3{\eta})\;in\;{\Omega}$$ where we assume that ${\lambda}_1$ < $c$ < ${\lambda}_2$, $g^{\prime}_1({\infty})$, $g^{\prime}_2({\infty})$ are finite. We prove that the system has at least three solutions under some condition on $g$.

• Journal of Electrical Engineering and Technology
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• 제6권3호
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• pp.384-390
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• 2011

To evaluate the condition of stator winding insulation in generators that have been operated for a long period of time, diagnostic tests were performed on the stator bars of a 500 MW, 22 kV generator under accelerated thermal and electrical aging procedures. The tests included measurements of AC current (${\Delta}I$), dissipation factor ($tan{\delta}$), partial discharge (PD) magnitude, and capacitance (C). In addition, the AC current test was performed on the stator winding of a 350 MW, 24 kV generator under operation to confirm insulation deterioration. The values of ${\Delta}I$, ${\Delta}tan{\delta}$, and PD magnitude in one stator bar indicated serious insulation deterioration. In another stator bar, the ${\Delta}I$ measurements showed that the insulation was in good condition, whereas the values of ${\Delta}tan{\delta}$ and PD magnitude indicated an incipient stage of insulation deterioration. Measurements of ${\Delta}I$ and PD magnitude in all three phases (A, B, C) of the remaining generator stator windings showed that they were in good condition, although the ${\Delta}tan{\delta}$ measurements suggested that the condition of the insulation should be monitored carefully. Overall analysis of the results suggested that the generator stator windings were in good condition. The patterns of PD magnitude in all three phases (A, B, C) were attributed to internal discharge.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 E
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• pp.2093-2096
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• 1999

This paper describes to access the insulation deterioration condition of the stator windings in three large turbine generators. Nondestructive tests have been carried out on stand-still generators which have been in service for 2 to 30 years. In most cases these tests include ac current increase rate($\Delta$I), delta tan delta( ${\Delta}tan{\delta}$), and maximum partial discharge(Qm). Gen. 2 show that the $tan{\delta}$ is higher than other two generators in the $tan{\delta}$-voltage curve. Partial discharge(PD) patterns were observed internal, corona and treeing discharges in large turbine generators. The PD tests were confirmed the correlation between discharge patterns and the kinds of defects.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.165-172
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• 2008

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.