• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.3
• /
• pp.163-173
• /
• 2010

In this work, we consider a nonlinear budworm model by a system of three ordinary differential equations originally created by Ludwig et al. in 1978. The nonlinear system describes the dynamics of the interaction between a budworm and a fir forest. We introduce stability techniques to analyze the dynamical behavior of this nonlinear system. Then we use constant effort harvesting techniques to control the budworm population. We also give numerical simulations of the population model with harvest and without harvest.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.4
• /
• pp.275-284
• /
• 2010

Deliberate self-harm (DSH) is the act of deliberately harming your own body, such as cutting or burning yourself, without suicidal intent. It has especially become a problem among adolescents and college-age students in institutional settings such as boarding schools, Greek houses, detention centers and hospitals. We focus on contagion of DSH among adolescents and young adults by creating a deterministic epidemiological model. We study the impact of actual peer pressure, virtual peer pressure (the Internet) and treatment analytically in terms of a basic reproduction number through stability analysis of a system of ordinary differential equations. All parameters are approximated and results are also explored by simulations. The model shows that DSH is present in an endemic state in the population considered, and the control strategies are discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.1
• /
• pp.66-73
• /
• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

• Journal of the Korean Mathematical Society
• /
• v.44 no.6
• /
• pp.1313-1327
• /
• 2007

We review the algebraic structure of $\mathbb{H}{\sharp}$ and show that $\mathbb{H}{\sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${\mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $\mathbb{H}{\sharp}$ determines a rotation $R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${\mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.31-48
• /
• 2010

In this article, we consider singularly perturbed Boundary Value Problems(BVPs) for second order Ordinary Differential Equations (ODEs) with Neumann boundary condition and discontinuous source term. A parameter-uniform error bound for the solution is established using the Streamline-Diffusion Finite Element Method (SDFEM) on a piecewise uniform meshes. We prove that the method is almost second order of convergence in the maximum norm, independently of the perturbation parameter. Further we derive superconvergence results for scaled derivatives of solution of the same problem. Numerical results are provided to substantiate the theoretical results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.977-981
• /
• 2002

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effect of shear deformation as well as the effects of vertical, rotatory and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported, with and without the effect of shear deformation, as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio and the stiffness parameter.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.3
• /
• pp.269-277
• /
• 2014

A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.

• Journal of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.229-241
• /
• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10b
• /
• pp.1185-1188
• /
• 1996

In this paper we present a genetic approach for trajectory control algorithm of balancing weight for IWR biped walking robot. The biped walking robot, IWR that was made by Automatic Control Lab. of Inha University has a trunk which stabilizes its walking by generating compensation moment. Trunk is composed of a revolute and a prismatic joint which roles balancing weight. The motion of balancing weight is determined by the gait of legs and represented by two linear second order ordinary differential equations. The solution of this equation must satisfy some constraints simultaneously to have a physical meaning. Genetic algorithm search for this feasible motion of balancing weight under some constraints. Simulation results show that feasible motion of balancing weight can be obtained by genetic algorithm.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.9
• /
• pp.2312-2321
• /
• 1994

In this work the dynamics of an electromagnetic levitation system is described by a set of three first order nonlinear ordinary differential equations. The objective is to design a digital linear controller which takes the inherent instability of the uncontrolled system and the disturbing force into consideration. The controller is made by employing digital linear quadratic(LQ) design methodology and the unknown state variables are estimated by the kalman filter. The state estimation is performed using not only an air gap sensor but also both an air gap sensor and a piezoelectric accelerometer. The design scheme resulted in a digital linear controller having good stability and performance robustness in spite of various modelling errors. In case of using both a gap sensor and an accelerometer for the state estimation, the control input was rather stable than that in a system with gap sensor only and the controller dealt with the disturbing force more effectively.