• Carbon letters
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• 제22권
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• pp.14-24
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• 2017

Carboxylated multi-wall carbon nanotubes (MWCNTs-COOH) have been used as efficient adsorbents for the removal of picric acid from aqueous solutions under stirring and ultrasound conditions. Batch experiments were conducted to study the influence of the different parameters such as pH, amount of adsorbents, contact time and concentration of picric acid on the adsorption process. The kinetic data were fitted with pseudo-first order, pseudo-second-order, Elovich and intra-particle diffusion models. The kinetic studies were well described by the pseudo-second-order kinetic model for both methods. In addition, the adsorption isotherms of picric acid from aqueous solutions on the MWCNTs were investigated using six two-parameter models (Langmuir, Freundlich, Tempkin, Halsey, Harkins-Jura, Fowler-Guggenheim), four three-parameter models (Redlich-Peterson, Khan, Radke-Prausnitz, and Toth), two four-parameter equations (Fritz-Schlunder and Baudu) and one five-parameter equation (Fritz-Schlunder). Three error analysis methods, correlation coefficient, chi-square test and average relative errors, were applied to determine the best fit isotherm. The error analysis showed that the models with more than two parameters better described the picric acid sorption data compared to the two-parameter models. In particular, the Baudu equation provided the best model for the picric acid sorption data for both methods.

• Journal of Advanced Marine Engineering and Technology
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• 제31권3호
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• pp.293-300
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• 2007

The aim of this paper is to design a speed controller of a DC motor by selection of a PID parameters using genetic algorithm. The model of a DC motor is considered as a typical non-oscillatory, second-order system, And this paper compares three kinds of tuning methods of parameter for PID controller. One is the controller design by the genetic algorithm. second is the controller design by the model matching method third is the controller design by Ziegler and Nichols method. It was found that the proposed PID parameters adjustment by the genetic algorithm is better than the Ziegler & Nickels' method. And also found that the results of the method by the genetic algorithm is nearly same as the model matching method which is analytical method. The proposed method could be applied to the higher order system which is not easy to use the model matching method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.83-104
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• 1997

This paper studies parameter estimation for a first-order hyperbolic integro-differential equation modelling one-sex population dynamics. A second-order finite difference scheme is used to estimate parameters such as the age-specific death-rate and the age-specific fertility from fully discrete observations on the population. The function space parameter estimation convergence of this scheme is proved. Also, numerical simulations are performed.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.903-917
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• 2023

This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.495-508
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• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• 대한수학회지
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• 제41권3호
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• pp.435-459
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• 2004

Identification problems for the system governed by abstract nonlinear damped second order evolution equations are studied. Since unknown parameters are included in the diffusion operator, we can not simply identify them by using the usual optimal control theories. In this paper we present how to solve our identification problems via the method of transposition.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.649-662
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• 2021

Recently the author studied a one-parameter family of divergences and considered the related median minimization problem of finite points over these divergences in general symmetric cones. In this article, to utilize the results practically, we deal with a special symmetric cone called second order cone, which is important in optimization fields. To be more specific, concrete computations of divergences with its gradients and the unique minimizer of the median minimization problem of two points are provided skillfully.

• Earthquakes and Structures
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• 제11권2호
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• pp.297-313
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• 2016

A virtual parameter is introduced into the formulation of the previously published integration method to improve its stability properties. It seems that the numerical properties of this integration method are almost unaffected by this parameter except for the stability property. As a result, it can have second order accuracy, explicit formulation and controllable numerical dissipation in addition to the enhanced stability property. In fact, it can have unconditional stability for the system with the instantaneous degree of nonlinearity less than or equal to the specified value of the virtual parameter for the modes of interest for each time step.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.45-60
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• 2008

Here we consider the evaluation of the the dynamic component of the second order force due to wave diffraction by a circular cylinder analytically and numerically. The cylinder is fixed, vertical, surface piercing in water of finite uniform depth. The formulation of the wave-structure interaction is based on the assumption of a homogeneous, ideal, incompressible, and inviscid fluid. The nonlinearity in the wave-structure interaction problem arises from the free surface boundary conditions, namely, dynamic and kinematic free surface boundary conditions. We expand the velocity potential and free surface elevation functions in terms of a small parameter and then consider the second order diffraction problem. After deriving the pressure using Bernoulli's equation, we obtain the analytical expression for the dynamic component of the second order force on the cylinder by integrating the pressure over the wetted surface. The computation of the dynamic force component requires only the first order velocity potential. Numerical results for the dynamic force component are presented.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.