• Proceedings of the KIEE Conference
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• 1991.11a
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• pp.27-30
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• 1991

Recently, the phenomena of voltage instability have become major concern in power system, these phenomena are closely related to what are called multiple load flow solutions and calculation methods on these solutions have developed. The multiple solutions concerned with phenomena are pair solutions in heavy loaded contion. But conventional methods require much run time to find this pair solutions and unusual generation patten in the condition of multiple solutions. In this paper, by using concept of existence condition of multiple solutions, calculation method on the multiple load flow solutions is presented which find the pair solutions in light loaded condintion.

• School Mathematics
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• v.19 no.3
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• pp.481-494
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• 2017

Tasks of multiple solutions have been said to be suitable for the cultivation of mathematical creativity. However, studies on the fact that multiple solutions presented by students are useful or meaningful, and students' thoughts while finding multiple solutions are very short. In this study, we set goals to confirm the qualitative differences among the multiple solutions presented by the students and, if present, from the viewpoint of mathematical creativity. For this reason, after presenting the set of tasks of the two versions to eight mathematically gifted students of the second-grade middle school, we analyzed qualitative differences that appeared among the solutions. In the study, there was a difference among the solution presented first and the solutions presented later, and qualitatively substantial differences in terms of flexibility and creativity. In this regard, it was concluded that the need to account for such qualitative differences in designing and applying multiple solutions should be considered.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.925-934
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• 2012

In this work the sine-Gordon equation will be examined for multiple soliton solutions. The higher dimensional sine-Gordon equations will be studied for multiple soliton solutions as well. The simplified form of the Hirota's method will be employed to conduct this analytic study.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.158-161
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• 1990

Recently, the phenomena of voltage instability have become major concern in power system. These phenomena are closely related to what are called multiple load flow solutions and calculation methods on these solutions have developed. But conventional methods require much run time. In this paper, by using sign of |J| and weighting factor considering system configuration, fast calculation method on the multiple load flow solutions is presented.

• Journal of computational fluids engineering
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• v.21 no.3
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• pp.64-70
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• 2016

Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.556-558
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• 1995

This paper presents a new simplified method for finding the multiple load flow solutions and through their solutions the voltage stability can be evaluated. Line flow($P_{ij}$, $Q_{ij}$) may be formulated with the second-order equations for $V_{i}^{2}$ in polar coordinates or two circle equations for $e_{i}$ and $f_{i}$ in rectangular coordinates. Based on this feature, multiple load flow solutions are calculated with simple works, results of multiple load flow solutions are used for sensitivity analysis of voltage stability. Also, in the case that reactive power sources is considered, method of evaluating the voltage stability is introduced. The proposed method was validated to 2-bus and IEEE 6-bus system.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.691-699
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• 2009

In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.

• East Asian mathematical journal
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• v.30 no.3
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• pp.335-353
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• 2014

We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.847-858
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• 2011

We make use of the simplified Hirota's bilinear method with computer symbolic computation to study a variety of coupled potential KdV (pKdV) equations. Each coupled equation is completely integrable and gives multiple soliton solutions and multiple singular soliton solutions. The phase shifts for all coupled pKdV equations are identical whereas the coefficients of the obtained solitons are not identical. The four coupled pKdV equations are resonance free.