• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.14 no.8
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• pp.640-646
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• 2001

The electrical stability for DC stress of Pr$_{6}$O$_{11}$-based ZnO varistos consisting of ZnO-Pr$_{6}$O$_{11}$-CoO-Cr$_2$O$_3$-Er$_2$O$_3$-based ceramics were investigated with sintering temperature in the range of 1325~1345$^{\circ}C$. A the sintering temperature is raised, the nonlinear exponent of varistors was decreased, whereas the stability was markedly improved. The density of ceramics was found to greatly affect the electrical stability for DC stress. The varistors sintered at 13$25^{\circ}C$ were completely degraded because of thermal runaway attributing to low density. The varistors sintered at 1335$^{\circ}C$ exhibited the highest nonlinearity, with a nonlinear exponent of 70.53 and a leakage current of 1.92$\mu$A, whereas they did not exhibit relatively high stability. On the contrary, the varistors sintered at >134$0^{\circ}C$ exhibited not only a high nonlinearity marking the nonlinear exponent above 50 and the leakage current below 3$\mu$A, but also a high stability marking the variation rate of the varistor voltage below 2%, even under DC stress such as (0.80V$_{1mA}$/9$0^{\circ}C$/12h)+(0.85V$_{1mA}$/115$^{\circ}C$/12h)+(0.90V$_{1mA}$/12$0^{\circ}C$/12h)+(0.95V$_{1mA}$/1$25^{\circ}C$/12h)+(0.95V$_{1mA}$/15$0^{\circ}C$/12h). In particular, ti was found that the varistors sintered at 134$0^{\circ}C$ were more nonlinear and more stable, compared with that of 1345$^{\circ}C$.EX>.}C$.EX>.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.8
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• pp.1211-1216
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• 1989

To enhance the breakdown properties of low voltage-oriented ZnO varistor, sample were fabricated with additive oxides and sintering conditions. Addition of TiO2 lowered breakdown voltage` nonlinear resistances were lowered about 10V/mm and nonlinear exponents were not lowered with respect to it with the basic composition. To the samples added TiO2, V2ko5, and Cr2O3, microstructures were observed by SEM, moreover Ti was detected at grainboundaries and within the grain by EDS. Addition of Si-oxides and Sb2O3 increased nonlinear exponent and also increased nonlinear resistance, by addition of TiO2 to these samples at the sintering conditions of 1250\ulcorner and 1 hour we could fabricate low voltage-oriented ZnO varistors with nonlinear exponent of 30 or more and with real breakdown voltage of 30V/mm.

• Proceedings of the IEEK Conference
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• 2009.05a
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• pp.79-81
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• 2009

In this paper, we design a dynamic state feedback smooth stabilizer for a nonlinear system whose Jacobian linearization may have uncontrollable because its eigenvalues are on the right half-plane. After designing an augmented system, a dynamic exponent scaling and backstepping enable one to explicitly design a smooth stabilizer and a continuously differentiable Lyapunov function which is positive definite and proper.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.771-783
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• 2018

This paper, we investigate a strongly damped nonlinear Klein-Gordon equation with nonlinearities of variable exponent type $$u_{tt}-{\Delta}u-{\Delta}u_t+m^2u+{\mid}u_t{\mid}^{p(x)-2}u_t={\mid}u{\mid}^{q(x)-2}u$$ associated with initial and Dirichlet boundary conditions in a bounded domain. We obtain a nonexistence of solutions if variable exponents p (.), q (.) and initial data satisfy some conditions.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.07a
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• pp.415-418
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• 2001

The I-V characteristics and its stability of ZPCCL-based ceramic varistors doped with La$_2$O$_3$in the range of 0.0~4.0 mol% were investigated. The density of ceramics was increased in the range of 4.7~5.8 g/cm$^3$ with increasing La$_2$O$_3$content. As La$_2$O$_3$content is increased, the varistor voltage was decreased in the range of 503.49-9.42 V/mm up to 2.0 mol%, whereas increasing La$_2$O$_3$content further caused it to increase. The ZPCCL-based varistors were characterized by nonlinearity, in which the nonlinear exponent is in the range of 3.05~82.43 and leakage current is in the range of 0.24-100.22 $\mu$A. Among ZPCCL-based varistors, 0.5 mol% added-varistors exhibited an excellent nonlinearity, in which the nonlinear exponent is 82.43 and the leakage current is 0.24 $\mu$A. Furthermore, they exhibited a high stability, in which the variation rate of the varistor voltage and the nonlinear exponent was -1.11% and -6.72%, respectively, under DC stress, such as (0.80 V$_{1mA}$9$0^{\circ}C$/12h)+(0.85 V$_{1mA}$115$^{\circ}C$//12h) +(0.90 V$_{1mA}$12$0^{\circ}C$//12h)+(0.95 V$_{1mA}$1$25^{\circ}C$//12h)+(0.95 V$_{1mA}$15$0^{\circ}C$//12h). Consequently, it was estimated that ZPCCL-based ceramics will be applied to development of Pr$_{6}$O$_{11}$ based ZnO varistors having a high performance.e.rformance.e.

• Journal of the Korean Ceramic Society
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• v.42 no.7 s.278
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• pp.490-496
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• 2005

The electrical properties and stability of the varistors composed of ZnO-Pr$_{6}$O$_{11}$-CoO-Cr$_{2}$O$_{3}$-Dy$_{2}$O$_{3}$ system were investigated with sintering time in the range of 1$\~$3 h at 1350$^{\circ}C$ . As the sintering time was increased, the varistor voltage and leakage current increased, but the nonlinear exponent decreased. The varistors sintered for 1 h exhibited excellent nonlinearity, with a nonlinear exponent of 55.3 and a leakage current of 0.1 $\mu$A, whereas presented relatively low stability. The varistors sintered for 2 h exhibited not only high nonlinear exponent of 46.3, low leakage current of 0.3 $\mu$A, low dielectric dissipation factor of 0.0431, but also the highest stability, in which the variation rates of varistor voltage, nonlinear exponent, leakage current, dielectric constant, and dielectric dissipation factor were -3.0$\%$, -4.1$\%$, +3056.2$\%$, +5.1$\%$, and -12.5$\%$, respectively, after DC accelerated aging stress state of 0.95 V$_{1ma}$/150$^{\circ}C$/24 h. On the whole, the nonlinearity and stability of these varistors are greatly affected by the sintering time.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.05b
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• pp.190-195
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• 2000

The electrical properties and stability of ZPCE varistors consisted of $ZnO-Pr_6O_{11}-CoO-Er_2O_3$ ceramics were investigated. $ZnO-Pr_6O_{11}-CoO-Er_2O_3$ based ceramics were sintered at $1300^{\circ}C$ and $1350^{\circ}C$, respectively, without and with 0.5 mol% $Er_2O_3$. The varistors sintered at $1300^{\circ}C$ exhibited a better nonlinearity than that $1350^{\circ}C$. The varistors with $Er_2O_3$ of 0.5 mol% exhibited a high nonlinear exponent of 52.8. However, they easily degraded due to the low density below 85% of TD. On the other hand, the varistors sintered at $1350^{\circ}C$ without $Er_2O_3$ exhibited an extremely poor nonlinearity, but the varistors with $Er_2O_3$ of 0.5 mol% exhibited a relatively good nonlinearity, which the nonlinear exponent is 34.8 and the leakage current is $7.4\;{\mu}A$ Morever, they exhibited a very high stability, which the variation rate of varistor voltage, nonlinear exponent, and leakage current are -0.9%, -2.9%, and +2.7%, respectively, under the third stress $(0.80 V_{1mA}/90^{\circ}C/12h)$ + $(0.85 V_{1mA}/115^{\circ}C/12h)$ + $(0.90 V_{1mA}/120^{\circ}C/12h)$. Consequently, it was estimated that $ZnO-Pr_6O_{11}-CoO-Er_2O_3$ ceramics will be usefully applied to develop the advanced $Pr_6O_{11}$-based ZnO varistors.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.21 no.7
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• pp.652-659
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• 2008

The nonlinear electrical properties and aging characteristics against surge stress of ZPCCL-based varistors were investigated for different sintering temperatures of the range $1240-1300^{\circ}C$. As the sintering temperature increased, the varistor voltage decreased from 732.2 to 53.8 V/mm, the nonlinear exponent decreased from 58.5 to 4.1, and the leakage current increased from $0.38{\mu}A$ to $46.5{\mu}A$. The varistors sintered at $1250^{\circ}C$ and $1260^{\circ}C$ exhibited the high stability against multiple surge, $150A/cm^2(8{\times}20{\mu}s)$. On the whole, the variation rate of electrical characteristics against impulse current stress was gradually increased in order of varistor voltage$\rightarrow$nonlinear exponent$\rightarrow$dissipation facto$\rightarrow$leakage current.

• Transactions on Electrical and Electronic Materials
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• v.6 no.4
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• pp.144-148
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• 2005

The microstructure and electrical properties of varistor ceramics, which are composed of Zn-Pr­Co-Cr-Dy-oxide system, were investigated at various dysprosia $(Dy_2O_3)$ addition contents. The $DY_2O_3$ microstructurally played the role of inhibition for the densification and grain growth. As the $DY_2O_3$ content increased, the density decreased in the range of $5.51-4.90 g/cm^3$, reaching maximum at $0.5 mol\%$ and the average ZnO grain size decreased in the range of $17.7-6.0{\mu}m$. The incorporation of $DY_2O_3$ significantly improved the nonlinear properties of varistors, above 30 in nonlinear exponent, compared with that without $DY_2O_3$. The varistors with the best performance of nonlinear properties was obtained $DY_2O_3$ content of $1.0 mol\%$, 49 in nonlinear exponent and $0.5{\mu}A$ in leakage current.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.419-434
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• 2024

This paper is devoted to the existence of solutions for Kirchhoff type equations with singular nonlinearities, sub-critical and critical exponent. By using the Nehari manifold and Maximum principle theorem, the existence of at least two distinct positive solutions is obtained.