• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.491-511
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• 2006

The existence of the admissible solution for conservation laws of trilinear type occurring material sciences was proved by Abeyaratne and Knowles. LeFloch proved the existence of admissible solutions of conservation laws of this type via Glimm's method. In this paper we introduce a front tracking solution and prove the existence of the front tracking solution. We also investigate the admissibility of solutions via the Front Tracking Method.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.95-112
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• 2005

This work concerns the stabilization of uninfected steady state of an ordinary differential equation system modeling the interaction of the HIV virus and the immune system of the human body. The control variable is the drug dose, which, in turn, affects the rate of infection of $CD4^{+}$ T cells by HIV virus. The feedback controller is constructed by a variant of the receding horizon control (RHC) method. Simulation results are discussed.

• School Mathematics
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• v.1 no.2
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• pp.513-528
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• 1999

The primary purpose of the constructivist teaching experiment is to experience and construct models of students' mathematical teaming and reasoning. The constraints the teacher experience in teaching experiment constitute a basis for understanding students' mathematics. The constructivist teaching experiment that includes a dynamic interaction process between teacher and students and between students and students, is the most hopeful research method in mathematics education. In this paper, I introduced the constructivist teaching experiment and showed several examples of applications that were used in the previous research.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.238-266
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• 2013

The Interaction Picture (IP) method is a valuable alternative to Split-step methods for solving certain types of partial differential equations such as the nonlinear Schr$\ddot{o}$dinger equation or the Gross-Pitaevskii equation. Although very similar to the Symmetric Split-step (SS) method in its inner computational structure, the IP method results from a change of unknown and therefore do not involve approximation such as the one resulting from the use of a splitting formula. In its standard form the IP method such as the SS method is used in conjunction with the classical 4th order Runge-Kutta (RK) scheme. However it appears to be relevant to look for RK scheme of higher order so as to improve the accuracy of the IP method. In this paper we investigate 5th order Embedded Runge-Kutta schemes suited to be used in conjunction with the IP method and designed to deliver a local error estimation for adaptive step size control.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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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.

• Interaction and multiscale mechanics
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• v.4 no.1
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• pp.1-16
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• 2011

The inverse problem about the theoretical analysis of a drill string bending in a channel of an inclined bore-hole with localized geometrical imperfections is studied. The system of ordinary differential equations is first derived based on the theory of curvilinear flexible elastic rods. One can then use these equations to investigate the quasi-static effects of the drill string bending that may occur in the process of raising, lowering and rotation of the string inside the bore-hole. The method for numerical solution of the constructed equations is described. With the proposed method, the phenomenon of the drill column movement, its contact interaction with the bore-hole surface, and the frictional seizure can be simulated for different combinations of velocities, directions of rotation and axial motion of the string. Geometrical imperfections in the shape of localized smoothed breaks of the bore-hole axis line are considered. Some numerical examples are presented to illustrate the applicability of the method proposed.

• Journal of The Korean Association For Science Education
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• v.22 no.1
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• pp.141-157
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• 2002

The purpose of this study was to analyze teacher's teaching-learning strategies and young children's concepts related to mathematics and science in integrated mathematics and science education activities. To achieve this purpose, actual class episodes were analyzed. The episodes were derived from 7 sessions of interaction between teacher and 4 kindergartners in integrated mathematics and science education activities. As a result of the study, children's concepts related to mathematics and science in integrated mathematics and science education activities occurred three factors: the relationship between weight, shape and movement, the relationship between weight and size, and the concept of measurement. In teacher's teaching-learning strategies, three factors were revealed: teacher's questioning, use of teaching materials, and children grouping.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.61-70
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• 2001

Certain elliptic interacting system involving symbiotic is considered. The sufficient conditions for the existence of positive solutions of system is provided for four different types of interaction among three species by using the method of decomposing operator.

• Advances in nano research
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• v.10 no.3
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• pp.263-270
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• 2021

The present manuscript focuses the effects of suction on the flow of the dusty fluid along permeable exponentially stretching cylinder. Derived PDEs for this work are changed into ODEs by adopting right transformations. Numerical procedure is carried out for the obtained resultant equations by Shooting Technique in accordance with Runge-Kutta (RK-6) technique. Obtained results for the parameters namely, particle interaction parameter, suction parameter and Reynold number parameters are probed thoroughly. Some salient points are: (a) Fluid velocity decreases and the dust phase velocity rises for the higher values of particle interaction parameter; (b) more suction produces retarding velocities for both the phases; (c) high Reynold number slows down the fluid velocity while the speed of dust phase and (d) skin friction coefficient goes high for all these parameters.

• Steel and Composite Structures
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• v.48 no.6
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• pp.611-623
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• 2023

This work considered an optimal control formulation in the sense of Caputo derivatives. The optimality of the fractional optimal control problem. The tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. In addiltion, existence and local stability of fixed points are investigated for discrete model. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Our technique likewise allows the advancement of results, such as return time to baseline that are unrealistic with current model solvers.