• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.171-182
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• 2005

An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures, the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the non-homogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.931-936
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• 1993

Optimal model following control scheme is to design the controller which makes the response of real system follow that of desirable model. This kind of design scheme is developed for first order system. We extends the scheme for second order system regarding the characteristics of mechanical second order system for vibration suppression of flexible structures. The model of mechanical second order system is obtained using suitable damping ratios and natural frequencies. Using this scheme, we can design the good controller which uses the characteristic of second order system. Numerical examples are presented which were used optimal model following control scheme.

• Bulletin of the Korean Chemical Society
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• v.17 no.1
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• pp.61-65
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• 1996

The semiempirical time-dependent Hartree-Fock PM3 calculations have been performed on three polyene systems. In order to study the nonlinear optical properties, we calculated the frequency-dependent first-, second-, and third-order polarizabilities of thiophene-, furan-, pyrrole-nitro polyene systems. The PM3 predicted average and longitudinal polarizabilties increase in the order: thiophene- > pyrrole- > furan-nitro polyene systems. The PM3 predicted limiting average second-order polarizabilities show the order: pyrrole- > furan- > thiophene-nitro polyene systems. The average and longitudinal third-order polarizabilties have the following order: pyrrole- > thiophene- > furan-nitro polyene systems. In these trends, we sugest that pyrrole group is the best donor group among the three polyene systems.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.11
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• pp.16-21
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• 1992

The validity of the application of the second-order Born equation to the ultrasound tomography algorithm is studied by comparing the scattered fields computed using the first-order Born equation, the first-order Rytove equation, and the second-order Born equation. The second-order Born equation turns out to provide more desirable results than the other two equations for a certain group of test objects. Phantom images with resolutions upto 1 pixel$\times$1 pixel are satisfactorily reconstructed using the second-order Born equation. It is shown that when the view angle is limited, good resonstruction results are also obtained using multi-frequency incident fields.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.75-93
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• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• Progress in Superconductivity and Cryogenics
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• v.3 no.2
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• pp.69-76
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• 2001

Unsteady components of the second-order axial velocity and temperature within a tapered pulse tube were obtained by using a novel hybrid method of solution which combines an analytical solution with a numerical solution. The effects of operating frequency, taper angle and cold eng temperature on the unsteady components of the second-order axial velocity and temperature were shown. The unsteady component of the second-order mass flux had the amplitude of the same order as the steady component when the velocities at the ends of the pulse tube have only first-order components.

• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.780-786
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• 2013

In the reliability-based design optimization of electromagnetic devices, the accurate and efficient reliability assessment method is very essential. The first-order sensitivity-assisted Monte Carlo Simulation is proposed in the former research. In order to improve its accuracy for wide application, in this paper, the second-order sensitivity analysis is presented by using the hybrid direct differentiation-adjoint variable method incorporated with the finite element method. By combining the second-order sensitivity with the Monte Carlo Simulation method, the second-order sensitivity-assisted Monte Carlo Simulation algorithm is proposed to implement reliability calculation. Through application to one superconductor magnetic energy storage system, its accuracy is validated by comparing calculation results with other methods.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.91-103
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• 2006

Yun (2005) introduced an estimator of the second order parameter characterizing the tail behavior of probability distributions and proved its consistency. In this paper we prove its asymptotic normality under a third order condition.