• Bulletin of the Korean Chemical Society
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• v.19 no.3
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• pp.299-307
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• 1998

PM3 semiempirical calculations were carried out to study the frequency-dependent nonlinear optical properties of thiophene, furan, pyrrole, (1,2,4)-triazole, (1,3,4)-oxadiazole, and (1,3,4)-thiadiazole monomers and oligomers. The longitudinal component, αxx, is the largest of three principle components. On the other hand, the out-of-plane component, αzz, is the smallest. Moreover, the out-of-plane component (αzz) of thiophene, furan, pyrrole, (1,2,4)-triazole, (1,3,4)-oxadiazole, and (1,3,4)-thiadiazole monomers show constant changes with increasing optical frequencies. The frequency-dependent first- order polarizabilities increase in the order: thiophene > (1,2,4)-triazole > pyrrole > furan > (1,3,4)-thiadiazole > (1,3,4)-oxa-diazole monomers and oligomers. The effects of β(-2ω;ω,ω) (SHG) shows a larger dispersion compared with (-ω;ω,0) (EOPE) and β(0;-ω,ω) (OR). The second- order polarizabilities of thiophene, furan, pyrrole, (1,2,4)-triazole, (1,3,4)-thiadiazole, and (1,3,4)-oxadiazole monomers for the various second- order effects have the order: β(-2ω;ω,ω) (SHG) > β(-ω;ω,0) (EOPE) > β(0;-ω,ω) (OR) and thiophene > pyrrole > (1,2,4)-triazole > furan > 1,3,4-thiadiazole > 1,3,4-oxadiazole monomers. The third- order polarizabilities for the various third- order effects have the following order: γ(-3ω;ω',ω,ω) (THG) > γ(-2ω;0,ω,ω) (EFISHG) > γ(-ω;ω',-ω,ω) (IDRI) > γ(-ω;0,0,ω) (OKE). The effects of THG increase rapidly with increasing optical frequencies compared with the other effects. In particular, OKE effects increase most slowly with increasing optical frequencies. Also, the effects of THG for thiophene, furan, pyrrole, (1,2,4)-triazole, (1,3,4)-thiadiazole, and (1,3,4)-oxadiazole oligomers show the order thiophene > (1,2,4)-triazole > furan > pyrrole > (1,3,4)-thiadiazole > (1,3,4)-oxadiazole oligomers. In particular, the third- order polarizabilities of thiophene and (1,3,4)-thiadiazole oligomers are about four and three times larger than those of (1,3,4)-oxadiazole and (1,2,4)-triazole oligomer, respectively.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.977-984
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• 2006

Generally main girders and steel piers of temporary bridges form the steel rahmen structure. In this study, the rational stability design procedure for main members of temporary bridges is presented using 3D system buckling analysis and second-order elastic analysis. 2 types of temporary bridges, which are possible to be designed and fabricated in reality, are chosen and the buckling design for them is performed considering load combinations of dead and live loads, thermal load, and wind load. Effective buckling length of steel piers, effects of live loads on effective length of main members, transition of ~id buckling modes, and effects of second-order analysis are investigated through case study of 2 temporary bridges.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.993-1000
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• 2006

Practical stability design method of main members of cable-stayed bridges is proposed and discussed through a design example. For this purpose, initial tensions of stay cables and axial forces of main members are firstly determined using initial shaping analysis of bridges under dead loads. And then the effective buckling length using system elastic/inelastic buckling analysis and bending moments considering $P-{\delta}-{\Delta}$ effect by second-order elastic analysis are calculated for main girder and pylon members subjected to both axial forces and moments, respectively. Particularly, load combinations of dead and live loads, in which maximum load effects due to live loads are obtained, are taken into account and effects of live loads on effective buckling lengths are investigated.

• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.262-266
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• 1986

A multi-reference many-body perturbation theory (MRMBPT) method is critically tested in second order by comparing with the corresponding configuration interaction (CI) calculations. Excitation energies of the four-valence-electron states of transition metal atoms and ions are used for the comparison. The agreement between the second order MRMBPT and CI calculations is very reasonable, confirming the reliability of the second order MRMBPT method. The reliability of calculations with the present second order MRMBPT method was only been inferred empirically in the past since most results have been gauged by the agreement with experiment and/or with other MRMBPT calculations based upon different sets of orbitals and configuration spaces. The present MRMBPT method appears to be an efficient ab initio multi-reference method for the calculation of electron correlation effects in atoms and molecules, and it is shown how MRMBPT can be used to estimate core-core and core-valence correlation effects which are often omitted in CI calculations because too many configurations and correlating electrons are involved.

• Genomics & Informatics
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• v.20 no.1
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• pp.9.1-9.6
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• 2022

Mendelian randomization (MR) uses genetic variation as a natural experiment to investigate the causal effects of modifiable risk factors (exposures) on outcomes. Two-sample Mendelian randomization (2SMR) is widely used to measure causal effects between exposures and outcomes via genome-wide association studies. 2SMR can increase statistical power by utilizing summary statistics from large consortia such as the UK Biobank. However, the first-order term approximation of standard error is commonly used when applying 2SMR. This approximation can underestimate the variance of causal effects in MR, which can lead to an increased false-positive rate. An alternative is to use the second-order approximation of the standard error, which can considerably correct for the deviation of the first-order approximation. In this study, we simulated MR to show the degree to which the first-order approximation underestimates the variance. We show that depending on the specific situation, the first-order approximation can underestimate the variance almost by half when compared to the true variance, whereas the second-order approximation is robust and accurate.

• Structural Engineering and Mechanics
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• v.25 no.1
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• pp.53-73
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• 2007

In this study, an effective load increment method for multi modal adaptive non-linear static (pushover) analysis (NSA) for building type structures is presented. In the method, lumped plastisicity approach is adopted and geometrical non-linearties (second-order effects) are included. Non-linear yield conditions of column elements and geometrical non-linearity effects between successive plastic sections are linearized. Thus, load increment needed for formation of plastic sections can be determined directly (without applying iteration or step-by-step techniques) by using linearized yield conditions. After formation of each plastic section, the higher mode effects are considered by utilizing the essentials of traditional response spectrum analysis at linearized regions between plastic sections. Changing dynamic properties due to plastification in the system are used on the calculation of modal lateral loads. Thus, the effects of stiffness changes and local mechanism at the system on lateral load distribution are included. By using the proposed method, solution can be obtained effectively for multi-mode whereby the properties change due to plastifications in the system. In the study, a new procedure for determination of modal lateral loads is also proposed. In order to evaluate the proposed method, a 20 story RC frame building is analyzed and compared with Non-linear Dynamic Analysis (NDA) results and FEMA 356 Non-linear Static Analysis (NSA) procedures using fixed loads distributions (first mode, SRSS and uniform distribution) in terms of different parameters. Second-order effects on response quantities and periods are also investigated. When the NDA results are taken as reference, it is seen that proposed method yield generally better results than all FEMA 356 procedures for all investigated response quantities.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.1000-1013
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• 2014

This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM) based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.19-25
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• 2001

Random effects models which describe the dependence via random effects in various correlated data have recently received considerable attention in the biomedical literature. They include mixed linear models (MLMs), generatized linear mixed models (GLMMS) and hierarchical generalized linear models (HGLMs). For the inference Lee and Nelder (2000) proposed the first-and second-order REML (restricted maximum likelihood) methods based on hierarchical-likelihood of tee and Welder (1996). In this paper, for Poisson-gamma HGLMs the new methods are theoretically compared with marginal likelihood methods and both methods are illustrated by two practical examples.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.157-173
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• 2007

In this article it is considered that how the slope-rotatability property of a second order design for response surface model is affected by block effects and how the design points are assigned into the blocks so that the blocked design may have the property of slope-rotatability. If an unblocked design is blocked properly, it could be a slope-rotatable design with block effects and this property is named as block slope-rotatability. We approach this problem from the moment matrix of the blocked design, which plays an important role to get the variances of the estimates, and suggest conditions of block slope-rotatability.