• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.215-222
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• 2021

We explore an optimal consumption/portfolio and retirement problem with a CARA utility function of consumption. The relevant Bellman equation for the value function is transformed into a linear equation and the optimal strategies are obtained explicitly.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.495-506
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• 2004

Some oscillation criteria are given for second order nonlinear differential equations by means of integral averaging technique.

• Steel and Composite Structures
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• v.24 no.2
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• pp.141-149
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• 2017

In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones.

• Journal of Advanced Marine Engineering and Technology
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• v.15 no.4
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1360-1365
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• 2007

A linear compressor used in a refrigerator has higher energy efficiency than other compressors. On the other hand, its vibration level has still been much severe. Changing the characteristics of connecting parts may reduce the vibration level of linear compressor. The piston, body and shell are assumed to be rigid. These rigid bodies are connected by coil springs and flexible loop pipe. This paper derived the mathematical model by combining the equation of motion of rigid parts and flexible parts. The variation of vibration level according to the change of connecting parts was investigated.

• International Journal of Aeronautical and Space Sciences
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• v.11 no.3
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• pp.206-220
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• 2010

This paper proposes optimal control techniques for determining translational and rotational maneuvers that facilitate proximity operations and docking. Two candidate controllers that provide translational motion are compared. A state-dependent Riccati equation controller is formulated from nonlinear relative motion dynamics, and a linear quadratic tracking controller is formulated from linearized relative motion. A linear quadratic Gaussian controller using star trackers to provide quaternion measurements is designed for precision attitude maneuvering. The attitude maneuvers are evaluated for different final axis alignment geometries that depend on the approach distance. A six degrees-of-freedom simulation demonstrates that the controllers successfully perform proximity operations that meet the conditions for docking.

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.881_882
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• 2009

The purpose of this paper is Characteristics Analysis according to thickness of Secondary Conductor in Tubular Linear Induction Motor(TLIM). Linear motors make good used of several applications as pumps and linear actuator. Characteristic equations of TLIM are obtained form voltage equation. And parameters of voltage equation are calculated.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.10
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• pp.1166-1172
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• 1988

This paper presents an efficient method of analyzing linear time-varying systems via Taylor polynomials. While the approach suggested by Sparis and Mouroutsos gives an implicit form for unknown state vector and requires to solve a linear algebraic equation with large dimension when the number of terms increases, the method proposed in this paper shows an explicit form and has no need to solve any linear algebraic equation.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems, to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original non-linear BSDE in two different cases.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.73-76
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• 1988

In this paper, the governing equation of the three phase linear induction motor is induced by the method that current in the primary winding is assumed as a current sheet. The steady state flux and the flux that is produced by end effect are mathematically analysed by electromagnetic equation. Each thrust of these flux is respectively induced. So in this paper, it is proved that linear motor is highly affected by end effect at high speed and speed-thrust characteristics of three phase linear induction motor are shown by frequency variation in the actual model.