• 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.

• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.727-746
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• 1998

Finite element models and numerical results are presented for bending and natural vibration using the unified third-order plate theory developed in Part 1 of this paper. The unified third-order theory contains the classical, first-order, and other third-order plate theories as special cases. Analytical solutions are developed using the Navier and L$\acute{e}$vy solution procedures (see Part 1 of the paper). Displacement finite element models of the unified third-order theory are developed herein. The finite element models are based on $C^0$ interpolation of the inplane displacements and rotation functions and $C^1$ interpolation of the transverse deflection. Numerical results of bending and natural vibration are presented to evaluate the accuracy of various plate theories.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.877-882
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• 2010

In this paper, a third-order three-point boundary value problem on time scales is considered. We establish criteria for the existence of a solution and a positive solution by using the Leray-Schauder fixed point theorem. An example is also given to illustrate our results.

• Steel and Composite Structures
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• v.25 no.1
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• pp.67-78
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• 2017

In this study, free vibration of functionally graded (FG) micro/nanobeams based on nonlocal third-order shear deformation theory and under different boundary conditions is investigated by applying the differential quadrature method. Third-order shear deformation theory can consider the both small-scale effects and quadratic variation of shear strain and hence shear stress along the FG nanobeam thickness. The governing equations are obtained by using the Hamilton's principle, based on third-order shear deformation beam theory. The differential quadrature (DQ) method is used to discretize the model and attain the natural frequencies and mode shapes. The properties of FG micro/nanobeam are assumed to be chanfged along the thickness direction based on the simple power law distribution. The effects of various parameters such as the nonlocal parameter, gradient index, boundary conditions and mode number on the vibration characteristics of FG micro/nanobeams are discussed in detail.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.04a
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• pp.208-212
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• 1993

Third order correlation function is to be advantageous to detect unique features embedded in various random signals that are undtectable with second order correlation or power spectrum. In order paper, we will introduce a real time third order correlator which consists of a laser light source, an acousto-optical modulator with signal controlling circuitry, and a CCD camera connected to computer for image processing. With this correlator, the third order correlation pattern of a signal can be immediately obtained at the camera due to parallelnature of optical computing.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.206-213
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• 1996

Third order correlation funciton is to be advantageous to detect unique features embedded in various random signals that are undetectable with second order correlation or power spectrum. In this paper, we will introduce optical modulator which consists of a laser light source, 2-dimensional ultrasonic diffractor cell with signal controlling circuitry, and a CCD camera connected to personal computer for image processing. With this modulator, the third order correlaiton pattern of signal can be immediately obtained at the camera due to parallel nature of optical computing.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.5
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• pp.707-714
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• 2000

In this paper, using third-order system of the PLL we'll analyze the aspect of flicker noise appearing troubles in the low frequency band. Since it is difficult to analyze mathematically flicker noise in the third-order system of the PLL, introducing the concept of pseudo-damping factor using the optimized second-filter has made an ease of the access of the flicker-noise variance. we'll show a numerical formula of flicker variance in the third-order system of the PLL which is compared with that of 1/f noise variance in the second-order system of the PLL.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.11a
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• pp.230-235
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• 1999

In this paper, Using third-order system of the PLL we analyze the aspect of flicker noise appearing troubles In the low frequency band. Since i. Is difficult to analyze mathematically flirter noise In the third-order system of the PLL, introducing the concept of pseudo-damping factor using the optimized second-filter makes an ease of the access of the flicker-noise variance. we'll show a numerical formula of flicker variance in the third-order system of the PLL which is compared with that of 1/f-noise variance in the second-order system of the PLL.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.37 no.1
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• pp.44-51
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• 2000

We have analyzed optical matched filters considering the third order signals in the optical code division multiple access (CDMA) system based on optical series coupler access encoder (SCAE) and series coupler access decoder (SCAD). In previous studies, the performance evaluation of the optical CDMA system using SCAE and SCAD was not sufficiently accurate because they analyzed system performance only considering the first order signals. Since optical SCAE and SCAD intrinsically have high order signals of various patterns as the number of coupler increases, they change auto- and cross-correlation intensities. Thus, it is necessary to investigate properties of the third order signals so that we may analyze the exact performance of system. In this paper, we mathematically interpret the optical signals up to the third order, and analyzed the effects of th third order signals on auto- and cross-correlation intensities. In result, as ${\alpha}$(coupling coefficient) value increases, the intensity of the third order signals increases. It is found that the peak to side-lobe ratio considering the third order signals is degraded by 3.75 dB at N(coupler number)=5 and ${\alpha}$=0.5. Also if threshold value in receiver is set by main-lobe peak of the first order signals, it is found that the number of users in an optical CDMA system is limited because the intensity peak of side-lobes is raised by the third order signals.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.623-637
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• 1999

This paper presents a four-noded quadrilateral $C^0$ strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the $C^1$-continuity formulation, the present plate element is of $C^0$-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.