• Journal of the Computational Structural Engineering Institute of Korea
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• v.35 no.5
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• pp.267-275
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• 2022

Using a nonconforming mesh in enrichment methods results in several numerical issues induced by discontinuities and singularities found within the solution spaces, including the computational overhead during integration. In this study, we present a novel enrichment technique based on the selective expansion technique of moment fitting (Düster and Allix, 2020). In particular, two modifications are proposed to address the inefficiency during the integration process. First, a feedforward artificial neural network is introduced to correlate the implicit functions and integration moments. Through numerical examples, it is shown that the efficiency of the method is greatly improved when compared with existing expansion techniques, whereas the solution accuracy is maintained. Additionally, the finite element and domain representation grids are separated, which in turn improves the solution accuracy even for coarse mesh conditions.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.199-230
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• 2018

In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

• East Asian mathematical journal
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• v.27 no.1
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.1
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• pp.100-106
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• 2013

This paper describes an integrated optimization design using multilevel decomposition technique on the base of the parametric distribution and independent axiom at the stages of lower level. Based on Pareto optimum solution, the detailed parameters at the lower level can be defined into the independent axiom. The suspension design is used as the simulation example.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.193-202
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• 2010

We investigate the estimation of the moisture transfer coefficients in porous media by optimization technique which minimizes the functional defined by the squares error of the numerical solution of an inverse diffusion problem from their experimental values of the moisture content at the some time-steps. In this paper, we solve a diffusion equation numerically by the control volume finite element methods.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.177-198
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• 1994

We consider an algorithm for the Crew Scheduling Problem (CSP) based on the Transportation Problem approach. The main flows of the algorithm are arranged in three steps. First we propose a heuristic algorithm of the greedy principle to obtain an initial feasible solution. Secondary we present a method of formulating CSP into a Modified Transportation Problem format. Lastly the procedures of network search to get the optimal solution are presented. This algorithm can be applied to the general GSP and also to most combinatorial problems like the Vehicle Routing Problems. The computational results show that the large size CSP's could be tackled.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.295-309
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• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Structural Engineering and Mechanics
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• v.6 no.5
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• pp.517-527
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• 1998

This paper describes an exact method of analysis for natural vibration of diagonal networks by considering an equivalent cyclic periodic structure and adopting the double U-transformation technique. Both a lumped mass system and a distributed mass system are considered to investigate the diagonal networks. The exact solution for the frequency equations and the natural modes of the networks can be derived. As numerical examples, square diagonal cable networks with different meshes are worked out.