• Honam Mathematical Journal
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• v.31 no.3
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• pp.437-449
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• 2009

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

• Journal of the Korean Geotechnical Society
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• v.26 no.8
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• pp.67-75
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• 2010

In this study, a series of 1 g shaking table tests were carried out for a single pile in soft clay with various input acceleration amplitudes and frequencies. Based on the results, dynamic p-y curves were drawn and, in turn, the dynamic p-y backbone curve was formed by connecting the peak points, corresponding to the maximum soil resistance, of the dynamic p-y curves. In order to represent the p-y backbone curve numerically, Matlock's p-y formulations for clay was used to find the initial stiffness ($k_{ini}$) and the ultimate capacity ($p_u$) of the clay, both of which are required to formulate the p-y backbone curve as a hyperbolic function. The suggested p-y backbone curve was verified through comparisons with currently available p-y curves as well as other researchers' centrifuge test results and numerical analysis results.

• Journal of the Korean Geotechnical Society
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• v.34 no.7
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• pp.51-58
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• 2018

In this study a series of centrifuge tests were carried out in dry sand to analyze the comparison of lateral pile behavior for static loading and dynamic loading condition. In case of static loading condition, the lateral displacement was applied up to 50% of pile diameter by deflection control method. And the input sine wave of 0.1 g~0.4 g amplitude and 1 Hz frequency was applied at the base of the soil box using shaking table for dynamic loading condition. From comparison of experimental static p-y curve obtained from static loading tests with API p-y curves, API p-y curves can predict well within 20% error the ultimate subgrade reaction force of static loading condition. The ultimate subgrade reaction force of experimental dynamic p-y curve is 5 times larger than that of API p-y curves and experimental static p-y curves. Therefore, pseudo-static analysis applied to existing p-y curve for seismic design could greatly underestimate the soil resistance at non-linear domain and cause overly conservative design.

• Transactions of the Korean Society of Pressure Vessels and Piping
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• v.15 no.2
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• pp.1-8
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• 2019

The integrity of the Reactor Pressure Vessel (RPV) is affected by the neutrons bombarding the vessel wall leading to embrittlement. This irradiation-induced embrittlement leads to reduction in the fracture toughness of RPV materials. This paper presents a comparative study of typical Optimized Power Reactor (OPR)1000 reactor pressure-temperature (P-T) limit curves using the pre-2006 American Society of Mechanical Engineers (ASME) editions used in the power plant and the current ASME edition of 2010. The current ASME Code utilizes critical reference stress intensity factor based on the lower bound of static, while the Pre-2006 ASME editions are based the critical reference stress intensity factor based on the lower bound of static, dynamic and crack arrest. Model-Based Systems Engineering approach was used to evaluate ASME Code Section XI Appendix G for generating the P-T limit curves. The results obtained from this analysis indicate decrease in conservatism in P-T limit curves constructed using the current 2017 ASME code, which can potentially increase operational flexibility and plant safety. Hence it is recommended to use ASME code edition after 2006 be used in all operating nuclear power plants (NPPs) to establish P-T limit curve.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.31-37
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• 2003

In this paper, we calculate the number of points on elliptic curves y$^2$ = x$^3$ + cx over F$_p$ mod 8.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.29-38
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• 2000

In this paper, we consider a criterion on primitive roots modulo p where p is the prime of the form $p=2^kq+1$, q odd prime. For such p we also consider the least primitive root modulo p. Also, we deal with certain isomorphism classes of elliptic curves over finite fields.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.93-101
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• 2012

Let $E_A^B$ denote the elliptic curve $E_A^B:y^2=x^3+Ax+B$. In this paper, we calculate the number of points on elliptic curves $E_A^0:y^2=x^3+Ax$ over $\mathbb{F}_p$ mod 24. For example, if $p{\equiv}1$ (mod 24) is a prime, $3t^2{\equiv}1$ (mod p) and A(-1 + 2t) is a quartic residue modulo p, then the number of points in $E_A^0:y^2=x^3+Ax$ is congruent to 0 modulo 24.

• Geomechanics and Engineering
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• v.28 no.1
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• pp.11-23
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• 2022

The response of pile foundations under lateral loads are usually analyzed using beam-on-nonlinear-Winkler-foundation (BNWF) model framework employing various forms of empirically derived p-y curves and p-multipliers. In practice, the p-y curve presented by the American Petroleum Institute (API) is most often utilized for piles in granular soils, although its shortcomings are recognized. The objective of this study is to evaluate the performance of the BNWF model and to quantify the error in the estimated pile response compared to a rigorous numerical model. BNWF analyses are performed using three sets of p-y curves to evaluate reliability of the procedure. The BNWF model outputs are compared with results of 3D nonlinear finite element (FE) analysis, which are validated via field load test measurements. The BNWF model using API p-y curve produces higher load-displacement curve and peak bending moment compared with the results of the FE model, because empirical p-y curve overestimates the stiffness and underestimates ultimate resistance up to a depth equivalent to four times the pile diameter. The BNWF model overestimates the peak bending moment by approximately 20-30% using both the API and Reese curves. The p-multipliers are revealed to be sensitive on the p-y curve used as input. These results highlight a need to develop updated p-y curves and p-multipliers for improved prediction of the pile response under lateral loading.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.11 s.254
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• pp.1417-1424
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• 2006

In order to evaluate variation of fatigue life of mechanical components including engineering plastics, it is important to estimate probabilistic strain-life curves to accurately define the variation of fatigue characteristics. This paper intends to provide new assessment of P-$\varepsilon$-N (probabilistic strain-life curves) for considering the variation of fatigue characteristics in polyacetal. The fatigue strain controlled tests were conducted under constant 50% humidity and room temperature condition by a universal testing machine at strain ratio, R=0. A practical procedure is introduced to evaluate probabilistic strain-life curves. Three probabilistic distributions were used for generating P-$\varepsilon$-N curves such as normal, 2-parameter and 3-parameter Weibull. In this study, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue characteristic were examined using chi-square and Kolmogorov-Smirnov test. The more appropriate P-$\varepsilon$-N curves for these materials are generated by the proposed method considering 3-parameter Weibull distribution.

• Journal of the Korean Geotechnical Society
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• v.23 no.3
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• pp.141-147
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• 2007

Various approaches have been developed for the dynamic response analysis of piles. In one of the approaches, the soil-pile interaction is approximated by using parallel nonlinear springs, namely the p-y curves. Currently available p-y curve recommendations are based on static and cyclic lateral load tests. Other researchers have attempted to extend the p-y curves by incorporating the effects of liquefaction on soil-pile interaction and derived scaling factors of p-y curves to account fur the liquefaction. However, opinions on the scaling factors vary. In this study, the sealing factors, which reflect the variation of the elastic moduli of surrounding soils, were established combining the relationship between excess pore pressures and the natural frequencies of a soil-pile system obtained from Ig shaking table tests and the relationship between the elastic moduli of surrounding soils and the natural frequencies of a soil-pile system obtained from numerical analyses. As a result, the scaling factors were presented in an exponential function.