• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.123-132
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• 2008

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend the result of L. Z. Yang by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. We also consider the nonhomogeneous linear differential equations.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.797-803
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• 2020

The Brück conjecture is still open for an entire function f with hyper order of no less than 1/2, which is not an integer. In this paper, it is proved that the hyper order of solutions of a linear complex differential equation that is related to the Brüuck Conjecture is infinite. The results show that the conjecture holds in a special case when the hyper order of f is 1/2.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.179-191
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• 2021

In this paper we introduce generalised logarithmic proximate order, generalised logarithmic proximate type of an entire function and prove the corresponding existence theorems. Also we investigate some theorems on the application of generalised logarithmic proximate order.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.175-189
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• 2012

This paper presents an algorithm for structural reliability with the response surface method. For this aim, an approach with three stages is proposed named as improved response surface method. In the algorithm, firstly, a quadratic approximate function is formed and design point is determined with First Order Reliability Method. Secondly, a point close to the exact limit state function is searched using the design point. Lastly, vector projected method is used to generate the sample points and Second Order Reliability Method is performed to obtain reliability index and probability of failure. Five numerical examples are selected to illustrate the proposed algorithm. The limit state functions of three examples (cantilever beam, highly nonlinear limit state function and dynamic response of an oscillator) are defined explicitly and the others (frame and truss structures) are defined implicitly. ANSYS finite element program is utilized to obtain the response of the structures which are needed in the reliability analysis of implicit limit state functions. The results (reliability index, probability of failure and limit state function evaluations) obtained from the improved response surface are compared with those of Monte Carlo Simulation, First Order Reliability Method, Second Order Reliability Method and Classical Response Surface Method. According to the results, proposed algorithm gives better results for both reliability index and limit state function evaluations.

• Structural Engineering and Mechanics
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• v.20 no.6
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• pp.713-726
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• 2005

Based on the improved first order Taylor interval expansion, a new interval analysis method for the static or dynamic response of the structures with interval parameters is presented. In the improved first order Taylor interval expansion, the first order derivative terms of the function are also considered to be intervals. Combining the improved first order Taylor series expansion and the interval extension of function, the new interval analysis method is derived. The present method is implemented for a continuous beam and a frame structure. The numerical results show that the method is more accurate than the one based on the conventional first order Taylor expansion.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.111-114
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• 1996

This paper proposes a robust control method using Universal Learning Network(U.L.N.) and second order derivatives of U.L.N.. Robust control considered here is defined as follows. Even if external input (equal to reference input in this paper) to the system at control stage changes awfully from that at learning stage, the system can be controlled so as to maintain a good performance. In order to realize such a robust control, a new term concerning the perturbation is added to a usual criterion function. And parameter variables are adjusted so as to minimize the above mentioned criterion function using the second order derivative of the criterion function with respect to the parameters.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.491-497
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• 2015

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.1
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• pp.12-21
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• 2016

In this paper, the $2^{nd}$ order hydrodynamic force effect of heaving submerged circular cylinder is considered, with the linear potential theory. Boundary value problem (BVP) is expanded up to the $2^{nd}$ order by using of the perturbation method and the $2^{nd}$ order velocity potential is calculated by means of integral equation technique using the classical Green's function expressed in cylindrical coordinates. The method of solving BVP is based on eigenfunction expansions. With different cylinder heights and heaving frequencies, graphical results are presented. As a result of the study, the cause of oscillatory force pattern is analyzed with the occurrence of negative added mass when a top of the cylinder gets closer to the free surface.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.302-304
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• 1992

This paper presents the method to reduce the order of high-order linear time invarient system via Walsh function. It is based on the matrix pseudoinverse algorithm to determine the parameters of the reduced model which minimize the sum of the squares of the errors between the reponses of the high-order system and a reduced model to a given input. This proposed method can be conveniently implemented with a computer. They will be very useful in the study of control system via Walsh function.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.271-274
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• 1998

This paper describes a new method for separation of the Volterra kernels which are identified by use of M-sequence. One of the authors has proposed a method for identification of Volterra kernels of nonlinear systems using M-sequence and correlation technique. When M-sequence are applied to a nonlinear systems, the cross-correlation function between the input and the output of the nonlinear systems includes cross-sections of high-order Volterra kernels. However, if various order Volterra kernels exixt on the obtained cross-correlation function, it is difficult to separate the Volterra kernels. In this paper, the authors show that the magnitude of Volterra kernels is maginified by the amplitude of M-sequence according to the order of Volterra kernels. By use of this property, each order Volterra kernels is obtained by solving linear equations. Simulations are carried out for some nonlinear systems. The results show that Volterra kernels can be separated in each order successfully by the proposed method.