• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.387-395
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• 1991

Large deflection behavior of cylindrically orthotropic thin circular plates is investigated by the numerical technique of differential quadrature. Governing equations are derived in terms of transverse deflection and stress function and a Newton-Raphson technique is used to solve the nonlinear systems of equations. For small values of degree of differential quadrature (N.leq.13), as the degree of differential quadrature increases, the center deflection converges. However, as N increases further, the center deflection diverges by ill-conditioning in the weighting coefficients. As the orthotropic parameter increases, the center deflection decreases and behaves linear for the loads. At center, the stress is affected mainly by orthotropic parameter, while the stress is affected mainly by boundary condition at edge.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.786-789
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• 1989

A nonlinear self-tuning regulator for a neutralization process of a weak acid and strong base system is proposed. Rearranging the state equation of the process model, we first obtain equations which are linear for a manipulated variable or unknown parameters. Then to these equations we apply the standard procedure used in designing linear self-tuning regulators. Simulation results show that the regulator provides very good performances for various realistic situations and traces variations of the unknown parameters. Since computations are simple and additional measurements except the effluent pH value are only flow rates of influent streams, it can be easily applied to real processes such as a waste water treatment process.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.67-80
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• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.511-526
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• 2008

In this paper, we consider an elliptic system of three equations using the minimax theorem. We prove the existence of two solutions for suitable forcing terms, under a condition on the linear part which prevents resonance with eigenvalues of the operator.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.45-48
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• 1986

In this paper, time optimal positioning control of the robotic manipulator is discussed. The equations for dynamic model of the robotic manipulator are nonolinear, and each link is highly coupled. A feedback linearizing and decoupling transformation makes the dynamic model linearized and decoupled, and optimal control input for the linear and decoupled system is derived.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.81-84
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• 1996

We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.2
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• pp.935-949
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• 2016

In this paper, we present a novel authenticated group key distribution scheme for large and dynamic multicast groups without employing traditional symmetric and asymmetric cryptographic operations. The security of our scheme is mainly based on the basic theories for solving linear equations. In our scheme, a large group is divided into many subgroups, where each subgroup is managed by a subgroup key manager (SGKM) and a group key generation center (GKGC) further manages all SGKMs. The group key is generated by the GKGC and then propagated to all group members through the SGKMs, such that only authorized group members can recover the group key but unauthorized users cannot. In addition, all authorized group members can verify the authenticity of group keys by a public one-way function. The analysis results show that our scheme is secure and efficient, and especially it is very appropriate for secure multicast communications in large and dynamic client-server networks.