• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.10
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• pp.77-84
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• 1997

The refractive index changes due to the electroptic effect are discussed when external electric fields $E_x, E_y, E_2$ are applied on $LiNbO_3$, a typical anisotropic material. Derived are approximate equations for principal axis' rotations and index changes, results of which are compared with exact results by te computer simulations. In each useful application of $LiNbO_3$substrate, the results of the approximate equations are confirmed to agree with exact solutions.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.1-8
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• 2011

The approximate controllability for the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator is studied. The existence, uniqueness and a variation of solutions of the system are also given.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.213-230
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• 2002

We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the mere general Lipschitz continuity of nonlinear operator f from $R\;\times\;V$ to H. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.18 no.3
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• pp.74-81
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• 2019

Herein, we performed a comparative study on approximate multi-objective design optimization, to realize a structural design to improve the weight and vibration performances of the knuckle - a car suspension component - considering various load conditions and vibration characteristics. In the approximate multi-objective optimization process, a regression meta-model was generated using the response surfaces method (RSM), while Kriging and back-propagation neural network (BPN) methods were applied for interpolation meta-modeling. The Pareto solutions, multi-objective optimal solutions, were derived using the non-dominated sorting genetic algorithm (NSGA-II). In terms of the knuckle design considered in this study, the characteristics and influence of the meta-model on multi-objective optimization were reviewed through a comparison of the approximate optimization results with the meta-models and the actual optimization.

• Tribology and Lubricants
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• v.35 no.5
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• pp.310-316
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• 2019

This paper presents two methods for designing a high-speed air spindle operated over the rotational speed of 50,000 rpm. The first method is an approximate method, which assumes a symmetric spindle shape even though it is not symmetric in reality. The second is an analysis of rotordynamics using beam and solid models. The approximate method can be used to calculate the bearing load capacities, stiffness and damping coefficients, stability of the shaft system, and response of the forced excitation from the unbalanced mass. Designers can use this method to determine the dimensions of the desired spindle at the first stage of the design. The more detailed behavior of the spindle can be calculated using the rotordynamics theory using beam and solid models based on the Finite Element Method. In this paper, a spindle, with two air bearings, one motor at the end, and two air thrust bearings, is newly developed. The solutions from the two rotordynamics theories are compared with the solution obtained using the approximate method. The three calculations are in agreement, and the procedure for the design of a spindle system, supported on the externally pressurized air bearings, ispresented and discussed.

• Steel and Composite Structures
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• v.44 no.4
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• pp.531-543
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• 2022

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1059-1068
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• 2015

The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1549-1556
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• 2011

In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{\infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${\varphi}$ defined on ($-{\infty}$, 0] with norm ${\parallel}{\varphi}{\parallel}={\sup}_{-{\infty}<{\theta}{\leq}0}{\mid}{\varphi}({\theta}){\mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.793-809
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• 2008

The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the RK-eight stage seventh order limiting formulas. The parameters governing the arm model of a robot control problem have also been discussed through RK-eight stage seventh order limiting algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. Based on the numerical results a thorough comparison is carried out between the numerical algorithms.