• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.5
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• pp.499-508
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• 2004

An efficient method of moments(MoM), which can lead to the analytical evaluation of the matrix elements, is proposed to analyze microstrip structures. The present method is formulated in conjunction with use of a new closed-form spatial-domain Green's functions which are derived by use of the integral formula for semi-infinite integrals of Bessel functions. It is observed that the computational efficiency such as the amount of calculation and computation speed has been improved due to the present MoM scheme by a factor of about 4 in comparison with the previous method. To validate the proposed method, several numerical examples are presented.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.151-160
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• 1993

This paper is concerned with formulations of the hierarchical $C^{\circ}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element based on Integrals of Legendre shape functions is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method are proposed to verify the superior convergence and algorithmic efficiency with the help of the simply supported L-shaped plate problems.

• Structural Engineering and Mechanics
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• v.21 no.4
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• pp.437-450
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• 2005

In this study, a complete analysis of soil-structure interaction problems is presented which includes a modelling of the near surrounding of the building (near-field) and a special description of the wave propagation process in larger distances (far-field). In order to reduce the computational effort which can be very high for time domain analysis of wave propagation problems, a special approach based on similarity transformation of the infinite domain on the near-field/far-field interface is applied for the wave radiation of the far-field. The near-field is discretised with standard Finite Elements, which also allows to introduce non-linear material behaviour. In this paper, a new approach to calculate the involved convolution integrals is presented. This approximation in time leads to a dramatically reduced computational effort for long simulation times, while the accuracy of the method is not affected. Finally, some benchmark examples are presented, which are compared to a coupled Finite Element/Boundary Element approach. The results are in excellent agreement with those of the coupled Finite Element/Boundary Element procedure, while the accuracy is not reduced. Furthermore, the presented approach is easy to incorporate in any Finite Element code, so the practical relevance is high.

• Journal of the Korean Chemical Society
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• v.26 no.4
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• pp.211-217
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• 1982

Assuming krypton molecules adsorbed on the graphite surface as a two-dimensional (2D) gas, 4th virial coefficient of the virial equation is calculated by the use of cluster integrals. The Henry's law constant, and 2nd and 3rd virial coefficients are also calculated. Adsorption isotherms calculated from this virial equation agree very satisfactorily with experimental results. The interaction energy of Kr-graphite surface is calculated assuming the pairwise additivity of Lennard-Jones(12,6) potential, and parametars therein are taken as; ${\varepsilon}_{gs}$/k = 71.1 K, ${\varepsilon}_{gg}$/k = 170 K, ${\sigma}_{gs}$ = 354 pm, and ${\sigma}_{gg}$ = 368 pm.

• Nuclear Engineering and Technology
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• v.31 no.4
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• pp.401-407
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• 1999

We have performed two experiments in the fast critical assembly BFS to measure the effective delayed neutron fraction $\beta$$_{eff}$ values and compared the results to validate the $\beta$$_{eff}$ computation code, BETA-K. Measurements of $\beta$$_{eff}$ were carried out in a metallic plutonium core and a metallic uranium core with Cf$^{252}$ source pseudo-reactivity method. Fission integrals and correction factors, which were used to obtain the experimental $\beta$$_{eff}$ values, were calculated by using the LMR core design computation code system of KAERI. BETA-K has been developed consistently with the hexagonal Nodal Expansion Method (NEM) and it used delayed neutron data of ENDF/B-VI. By comparing the computed $\beta$$_{eff}$ values with the measured ones, we found that the results from BETA-K agreed with the experimental values within the experimental error bound.ror bound.

• Journal for History of Mathematics
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• v.28 no.2
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• pp.85-102
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• 2015

Elliptic curves are a common theme among various fields of mathematics, such as number theory, algebraic geometry, complex analysis, cryptography, and mathematical physics. In the history of elliptic curves, we can find number theoretic problems on the one hand, and complex function theoretic ones on the other. The elliptic curve theory is a synthesis of those two indeed. As an overview of the history of elliptic curves, we survey the Diophantine equations of 3rd degree and the congruent number problem as some of number theoretic trails of elliptic curves. We discuss elliptic integrals and elliptic functions, from which we get a glimpse of idea where the name 'elliptic curve' came from. We explain how the solution of Diophantine equations of 3rd degree and elliptic functions are related. Finally we outline the BSD conjecture, one of the 7 millennium problems proposed by the Clay Math Institute, as an important problem concerning elliptic curves.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.307-320
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• 2001

Traditionally, there are many inherent restrictions in highschool mathematics textbooks. They are restricted in its contents and inevitably resorted to reader's ability of intuition. So they are usually lacked logical precisions and have various differences in expressions. We are mainly concerned with the definite integral and its applications in current highschool mathematics II textbooks according to 6th curriculum. We choose 6 of them arbitrarily and survey by comparison to deduce some controversial topics among them as follows. 1) absurd metaphors in formula process 2) confusions in important notations and too much choices in terms and statements. 3) lack of precisions in - teaching hierarchy (between some contents of Physics and the applications of definite integral) - introducing a proof of theorem (fundamental theorem of Calculus I) - introducing the methods (integral substitutions 1, ll) 4) adopting small topics such as - mean value theorem of integral - integrals with variable limits. In coming 7th curriculum, highschool students in Korea are supposed to choose calculus as a whole, independent course. So we hope that the suggested controversial topics are to be referred by authors to improve the preceding Mathematics ll textbooks and for teachers to use them for better mathematics education.

• Transactions of Materials Processing
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• v.15 no.8 s.89
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• pp.550-555
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• 2006

In this study, effects of forming angle and friction coefficient on a initiation of the Mannesmann hole defect were analyzed by using a response surface method. The maximum effective plastic strain at center point of specimen is utilized for the prediction of the starting point of crack occurrence, which is suggested by the comparison of integrals of four different ductile fracture models between the histories of the effective plastic strain at center point. It was revealed that the principal stress at the center is the dominant element to the increase of the effective plastic strain. It was also verified by the simulation results from the comparison of experiment and simulation. It is provided that the forming angle of 25 degrees and the spreading angle of 1 degree can be a proper design condition without an occurrence of internal hole defect and an excessive slip.

• Aerospace Engineering and Technology
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• v.11 no.1
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• pp.169-177
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• 2012

This paper considers the explicit guidance algorithm to determine the closed-loop guidance law applicable to upper stages of a given space launch vehicle. It has the advantage of very simple forms derived from the flat earth assumption, which is appropriate for its on-board application. However the simple time-to-go prediction equation produces the degraded guidance performance of the launcher because of its inaccuracy. To overcome the problem, the elaborate prediction equations, which have been employed in Saturn and H-II, are attempted here. Finally, the simulation results show that the simple guidance approach requires the more accurate time-to-go prediction and gravity integrals for its broad application.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.1-8
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• 1992

This paper presents a p-version finite element approach for modeling the stress distribution around a circular hole in a finite strip subjected to membrane and flexural behaviors. Also, same problem with a crack emanating from a perforated tension strip was solved by virtual crack extension method. The p-version of the finite element method based on integrals of Legendre polynomials is shown to perform very well for modeling geometries with very steep stress gradients in the vicinity of a circular cutout. Here, the transfinite mapping technique for circular boundaries was used to avoid the discretization errors. The numerical results from the proposed scheme have a good comparison with those by Nisida, Howland, Newman etc. and the conventional finite element approach.