• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1549-1559
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• 2008

In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.33-44
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• 1998

This paper is concerned with the existence of mutiple positive solution of (equation omitted) with Dirichlet boundary condition.

• Journal of the Korean Operations Research and Management Science Society
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• v.35 no.3
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• pp.25-43
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• 2010

We consider a multi-objective balancing and sequencing problem in mixed model assembly lines, which is important for an efficient use of the assembly lines. In this paper, we present a neighborhood symbiotic evolutionary algorithm to simultaneously solve the two problems of balancing and model sequencing under multiple objectives. We aim to find a set of well-distributed solutions close to the true Pareto optimal solutions for decision makers. The proposed algorithm has a two-leveled structure. At Level 1, two populations are operated : One consists of individuals each of which represents a partial solution to the balancing problem and the other consists of individuals for the sequencing problem. Level 2, which is an upper level, works one population whose individuals represent the combined entire solutions to the two problems. The process of Level 1 imitates a neighborhood symbiotic evolution and that of Level 2 simulates an endosymbiotic evolution together with an elitist strategy to promote the capability of solution search. The performance of the proposed algorithm is compared with those of the existing algorithms in convergence, diversity and computation time of nondominated solutions. The experimental results show that the proposed algorithm is superior to the compared algorithms in all the three performance measures.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.445-454
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• 2011

In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.89-91
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• 1995

This paper describes an extension or a pair or multiple load flow solutions and nose curve method developed for voltage stability analysis or AC power systems to AC/DC systems. In this approach the converters are regarded as voltage dependent loads. Assuming that the converters at the unstable (-mode) solution consume the same power equal to the power at the stable (+mode) solution, the unstable solutions or the nose curves arc determined. This method is very efficient since estimating voltage collapse point and voltage stability margin arc determined by a few iterations of multiple load flow solutions. Also the method has the advantages that since the structure or Jacobian matrix is same with that of AC load flow, modal analysis or voltage stability is readily applicable if desired.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.279-292
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• 2011

In this paper, we consider anti-periodic solutions of the following BAM neural networks with multiple delays on time scales: $$\{{x^\Delta_i(t)=-a_i(t)e_i(x_i(t))+{\sum\limits^m_{j=1}}c_{ji}(t)f_j(y_j(t-{\tau}_{ji}))+I_i(t),\atop y^\Delta_j(t)=-b_j(t)h_j(y_j(t))+{\sum\limits^n_{i=1}}d_{ij}(t)g_i(x_i(t-{\delta}_{ij}))+J_j(t),}\$$ where i = 1, 2, ..., n,j = 1, 2, ..., m. Using some analysis skills and Lyapunov method, some sufficient conditions on the existence and exponential stability of the anti-periodic solution to the above system are established.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

• Research in Mathematical Education
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• v.13 no.3
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• pp.197-216
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• 2009

The purpose of this study was to investigate middle and high school mathematics teachers' levels and multiple approaches in United States practicing their abstraction levels and, different strategies and method of solutions towards given number theory problems. The mathematics teachers taking part in this study are consisted of 25 members of online graduate and undergraduate course (MAE 5641 and MAE 4813) delivered through Online Learning System called as the Blackboard (http://www.blackboard.com). Data collection methods include journal entries, written solutions to problems, the teachers' reflections on said problems, and post interviews. Data analysis was done based on [Hazzan, O. & Zazkis, R. (2005). Reducing abstraction: The case of school mathematics. Educ. Stud. Math. 58(1), 101-119]. Analysis of students' written solutions revealed that transitions among the solution methods have major effect on abstraction levels. Elevation and reducing abstraction is a dynamic process.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.911-926
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• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).