• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.5
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• pp.46-55
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• 2006

In general, 3-dimensional point-mass equation has been widely used for the trajectory optimization of the fixed-wing aircraft and reentry vehicle. But it should be modified and represent target vehicle's own characteristics. For a lighter-than-air vehicle such as an airship, there exists different and peculiar flight characteristics compared with the aircraft. The first part of this paper is to derive the dynamic equation of motion for the mid-altitude unmanned airship and the second part is to obtain the optimal trajectories under the minimal time flight given constraints. The trajectory optimization problem is converted into the nonlinear programming problem using Sequential Quadratic Programming approach. Finally numerical solutions are presented in the last part of the paper.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.660-662
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• 2000

The most important problem in traget tracking can be said to be modeling the tracking system correctly. Although the simple linear dynamic equation for this model has used until now, the satisfactory performance could not be obtained owing to uncertainties of the real systems in the case of designing the filters based on the dynamic equations. In this paper, we propose the extended robust Kalman filter(ERKF) which can be applied to the real target tracking system with the parameter uncertainties. To solve the robust nonlinear fettering problem, we derive the extended robust Kalman filter equation using the Krein space approach and sum quadratic constraint. We show the proposed filter has better performance than the existing extended Kalman filter(EKF) via 3-dimensional target example.

• Structural Engineering and Mechanics
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• v.20 no.3
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• pp.313-334
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• 2005

The paper presents a new approach for the analysis of slope stability that is based on the numerical solution of a differential equation, which describes the thrust force distribution within the potential sliding mass. It is based on the evaluation of the thrust force value at the endpoint of the slip line. A coupled approximation of the slip and thrust lines is applied. The model is based on subdivision of the sliding mass into slices that are normal to the slip line and the equilibrium differential equation is obtained as the slice width approaches zero. Opposed to common iterative limit equilibrium procedures the present method is straightforward and gives an estimate of slope stability at the value of the safety factor prescribed in advance by standard requirements. Considering the location of the thrust line within the soil mass above the trial slip line eliminates the possible development of a tensile thrust force in the stable and critical states of the slope. The location of the upper boundary point of the thrust line is determined by the equilibrium of the upper triangular slice. The method can be applied to any smooth shape of a slip line, i.e., to a slip line without break points. An approximation of the slip and thrust lines by quadratic parabolas is used in the numerical examples for a series of slopes.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1267-1269
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• 1999

This paper studies on arrangement of load correlation coefficient for advanced load management. To accurate load correlation coefficient, we used two real factors, electrical energy(kWh) and peak load current of pole transformers, acquired by measuring instrument. Out of several correlation equations, we find that the quadratic equation is the most accurate to express peak load current and working electrical energy. If the data is located in the outside of ${\pm}3{\sigma}$ it is discarded. For load management, we rearranged load correlation coefficient considering +2${\sigma}$ at load correlation equation. Comparing conventional load correlation coefficient with rearranged one, we can get the result of error reduced and it is adjacent to the actual data. It will be used peak load forecasting from working electrical energy and we are able to prevent from the damaging of pole transformer due to overload.

• Nuclear Engineering and Technology
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• v.24 no.3
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• pp.319-328
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• 1992

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation.

• Korean Journal of Optics and Photonics
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• v.6 no.2
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• pp.156-164
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• 1995

Based on the scalar wave equation of optical fibers, the dispersion characteristics of arbitrarily profiled fibers were analyzed. We used the I-D FEM employing quadratic interpolation fucntions to solve the scalar wave equation. We simulated the DC optical fibers as objects, and searched for the refractive index distribution to minimize the total dispersion. In DC fibers, we found the design parameters for which the total dispersion was almost zero at $\lambda=1.3{\mu}m and 1.55{\mu}m$ simultaneously. We also found the design parameters where the dispersion was flattened, less than 1.0 ps/km.nm for$\lambda=1.4~1.7{\mu}m$1. and the dispersion was as low as 0.65 ps/km.nm at $\lambda=1.55{\mu}m$..

• Journal of the Korean Society of Tobacco Science
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• v.2 no.2
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• pp.44-50
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• 1980

The growth of flue-cured tobacco was analyzed with the mathematical treatment. The results are summarized as followings: 1. The growth curve was fitted to the quadratic polynomial equation in improved-mulching cultivation, blot to the Gompertz equation in the other cultivations. 2. The initial point of the maximum growth phase for dry weight was about 50 days after transplanting in improved-mulching cultivation, but about 40 days in the other cultivations, and the maximum growth period was for 25 days in all cultivations. 3. The growth rate of the maximum growth period in dry weight decreased in the order of improved-mulching cultivation, mulching cultivation, and non-mulching cultivation. 4. A relative growth amount in the maximum growth period was higher in later sowing. 5. The length of maximum growth was 5 days shorter in leaf area than in dry weight. The maximum growth phase was 7 days earlier in leaf area than in dry weight.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• Journal of the Optical Society of Korea
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• v.13 no.3
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• pp.379-385
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• 2009

The vergence control of binocular stereoscopic camera is the most essential factor for acquiring high quality stereoscopic images. In this paper, we proposed a binocular stereoscopic camera vergence control method using disparity information by the simple image processing and estimate the quantity of vergence control using the Lagrange interpolation equation. The method of extracting disparity information through image processing is as follows: first the key-object in left & right images was extracted through labeling of the central area of the image, and then a simple method was used for calculating the disparity value of the same key-object in the labeled left and right images. The vergence control method uses disparity information and keeps the convergence distance of left & right cameras and the distance of the key-object the same. According to the proposed method, variance in the distance of the key-object and application of calculated disparity information of obtained left & right images to the quadratic Lagrange interpolation equation could estimate the quantity of vergence control, which confirmed that the method of stereoscopic camera vergence control can be simplified through experiments on various key-objects and other convergence distance.

• Steel and Composite Structures
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• v.17 no.5
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• pp.753-776
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• 2014

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.