• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1185-1199
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• 2015

This paper is concerned with the optimal control problem for the viscous weakly dispersive Benjamin-Bona-Mahony (BBM) equation. We prove the existence and uniqueness of weak solution to the equation. The optimal control problem for the viscous weakly dispersive BBM equation is introduced, and then the existence of optimal control to the problem is proved.

• East Asian mathematical journal
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• v.33 no.5
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• pp.495-509
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• 2017

With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.351-367
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• 2011

In this article, we construct exact traveling wave solutions for nonlinear PDEs in mathematical physics via the (1+1)- dimensional combined Korteweg- de Vries and modified Korteweg- de Vries (KdV-mKdV) equation, the (1+1)- dimensional compouned Korteweg- de Vries Burgers (KdVB) equation, the (2+1)- dimensional cubic Klien- Gordon (cKG) equation, the Generalized Zakharov- Kuznetsov- Bonjanmin- Bona Mahony (GZK-BBM) equation and the modified Korteweg- de Vries - Zakharov- Kuznetsov (mKdV-ZK) equation, by using the (($\frac{G'}{G}$) -expansion method combined with the Riccati equation, where G = $G({\xi})$ satisfies the Riccati equation $G'({\xi})=A+BG^2$ and A, B are arbitrary constants.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.2
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• pp.231-241
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• 2021

The purpose of this study is to apply Structural equation modeling (SEM) analysis with Generalized Structured Component Analysis (GSCA) and translate the effect of Spiritual Marketing and Entrepreneurial Orientation on Sustainable Competitive Advantage with Marketing Capabilities as Mediation, especially for General BBM marketing at PT. Pertamina (Persero). The quantitative approach in this study uses a survey method by taking samples from the population. The survey was conducted by distributing questionnaires to respondents. Data analysis was performed using SEM and analyzed using the GSCA model. The population of this study consisted of 3,207 workers in central and regional marketing offices (Marketing Operation Region (MOR) spread throughout Indonesia. Therefore, a sample of 356 respondents was taken according to the Slovin formula. Spiritual marketing and entrepreneurial orientation directly influence the ability to improve Innovation which directly influences sustainable competitive advantage. Therefore, to develop a sustainable competitive advantage in marketing Pertamina's General BBM, it is necessary to implement spiritual marketing and improve entrepreneurial orientation. The novelty in this study lies in the unprecedented research on the role and position of spiritual marketing towards marketing capabilities and sustainable competitive advantage, combined with entrepreneurial orientation variables.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.247-259
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• 2011

In this paper, the $(\frac{G'}{G})$-expansion method is used to construct new exact travelling wave solutions of some nonlinear evolution equations. The travelling wave solutions in general form are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, as a result many previously known solitary waves are recovered as special cases. The $(\frac{G'}{G})$-expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.

• Composites Research
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• v.16 no.5
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• pp.28-38
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• 2003

In this study, the analytical investigation of orthotropic rectangular plate is presented. The loaded edges are assumed to be simply supported and the unloaded edges could have elastically restrained boundary conditions including the extreme boundary condition such as simple, fixed, and free. Using the closed-form solutions, the buckling analyses of orthotropic plate with arbitrary boundary conditions are performed. Based on the data obtained by conducting numerical analysis, the simplified form of equation for finding the buckling coefficient of plate with elastically restrained boundary conditions at the unloaded edges is suggested as a function of aspect ratio, elastic restraint. and material properties of the plate. The results of buckling analyses by closed-form solution and simplified form of solution are compared for various orthotropic material properties. It is confirmed that the difference of results is less than 1.5%.