• Tunnel and Underground Space
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• v.31 no.6
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• pp.480-493
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• 2021

Since the generalized Hoek-Brown criterion (GHB) provides an efficient way of identifying its strength parameter values with the consideration of in-situ rock mass condition via Geological Strength Index (GSI), this criterion is recognized as one of the standard rock mass failure criteria in rock mechanics community. However, the nonlinear form of the GHB criterion makes its mathematical treatment inconvenient and limits the scope of its application. As an effort to overcome this disadvantage of the GHB criterion, the explicit approximate analytical equations for the minimum principal stress, which is associated with the maximum principal stress at failure, are formulated based on the Taylor polynomial approximation of the original GHB criterion. The accuracy of the derived approximate formula for the minimum principal stress is verified by comparing the resulting approximate minimum principal stress with the numerically calculated exact values. To provide an application example of the approximate formulation, the equivalent friction angle and cohesion for the expected plastic zone around a circular tunnel in a GHB rock mass are calculated by incorporating the formula for the approximate minimum principal stress. It is found that the simultaneous consideration of the values of mi, GSI and far-field stress is important for the accurate calculation of equivalent Mohr-Coulomb parameter values of the plastic zone.

• Journal of the Korea institute for structural maintenance and inspection
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• v.25 no.5
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• pp.60-67
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• 2021

According to the 「Guidelines of Structural Design for Piloti Building」 of the Ministry of Land, Infrastructure and Transport (2018), the natural period of middle and low rise building of upper-walled lower frame type, such as the domestic multiplex house in piloti style, is suggested for safety to apply the existing code formula of the wall structure. However, the current code formula of the wall structure was provided based on actual measurement of high-rise wall-type structures that mainly exhibit bending behavior. So it is considered that it is not suitable for a piloti-type house with four stories or less, where the wall behaves in shear. See also Park et al. (2000) confirmed that the effect of the lower frame part is greater than that of the upper wall part in the natural period of complex structures with 10 or more floors through analytical studies. Therefore, in this study, in order to examine the effect of the lower frame on the natural period of the middle and low-rise piloti structure, the estimation of natural period by the finite element analysis, approximation formula and ccurrent code formula was performed for the target structures with the shear and flexural stiffness of the upper wall and the shear stiffness of the lower frame as variables. As result, it was found that the change in the shear stiffness of the lower frame had a greater effect on the natural period of the whole building than the change in the bending or shear stiffness of the upper wall.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.493-506
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• 2000

Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7], They use the well-known fact that the solution of such problem has a singular representation, deduced a well-posed new variational problem for a regular part of solution and an extraction formula for the so-called stress intensity factor using tow cut-off functions. They use Fredholm alternative an Garding's inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for mesh h theoretically. although the numerical experiments shows the convergence for every reasonable h with reasonable size y imposing a restriction to the support of the extra cut-off function without using Garding's inequality. We also give error analysis with similar results.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.671-682
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• 1999

Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration $E\;\longrightarrow\;B$. The construction works for any commutative ring R with unit and is denoted by $R_f(E)\;l\ongrightarrow\;B$. For any pointed space B let $G_I(B)\;\longrightarrow\;B$ be the i-th Ganea fibration. Defining $M_R-cat(B):= inf{i\midR_f(G_i(B))\longrihghtarrow\;B$ admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then $M_Q$-cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1858-1863
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• 1991

The theory of stock option pricing has, recently, attracted attention of many researchers interested not only in finance but also in statistics and control theory. In this field, the problem of estimating stock return volatility is, above all, of great importance in calculating actual stock option value. In this paper, we assume that the stock market is represented by the stochastic volatility model which is the same as that of Hull and White. Then, we propose an approximation function of option value. It is a type of Black-Sholes option formula in which the first and the second order moments of logarithmic stock value are modified in a special form from the original model. Finally, an algorithm of estimating the parameters of the stochastic volatility model is given, and parameters are estimated by using Nikkei 225 index option data.

• Journal of the Korean Vacuum Society
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• v.8 no.3B
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• pp.308-314
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• 1999

We used the photoreflectance spectroscopy for characterization of the infrared photodetector structure we GaAs/$Al_{0.3}Ga_{0.7}As$ multi-quantum well (MQW) structures grown by molecular beam epitaxy (MBE) method. Energy gap related transitions in GaAS and AlGaAs were observed. The Al composition(x) was determined b Sek's composition formula. MQW related transition energies were identify the transitions, the experimentally observed energies were compare with results of the envelope function approximation for a rectangular quantum well.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.48 no.2
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• pp.141-146
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• 1999

The eigenvalue equations of multiple waveguides with step-index profile are derived by using the WKB theory. Phase changes unique to step-index discontinuity areintroduced when applying the WKB connection formula to turning points. The transfer matrix method is employed for the analysis of multiple structure and the derived eigenvalue equation are represented in the recursive form. The results by the WKB are compared with those by the FEM for a three-waveguide coupler.

• Journal of IKEEE
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• v.8 no.1 s.14
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• pp.121-127
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• 2004

We performed the spectrum analysis of arrayed waveguide grating using Fresnel Kirchhoff diffraction formula and its approximated Fraunhofer diffraction equation and applied both methods to 16 channel and 40 channel models. We presented the spectra and found out the limitations of Fraunhofer diffraction in analysis of arrayed waveguide grating and compared the errors coming from Fraunhofer diffraction approximation and due to imperfection during the fabrication process.

• Journal of electromagnetic engineering and science
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• v.7 no.3
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• pp.109-115
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• 2007

The performances of M-ary PSK(MPSK) systems using L-branch maximum ratio combining(MRC) diversity reception in frequency-nonselective slow Rician fading channels are derived theoretically. Especially we investigate the effect of number of symbols on the difference between the approximation to bit error probability and the exact bit error rate(BER) in evaluating the performance of MPSK signals through numerical analyses. On the other hand, when M-ary DPSK(MDPSK) signals experience the Rician fading channels, the general formula for evaluating BER of MDPSK signals in the independent branch diversity system is presented using the integral-form expressions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.238-266
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• 2013

The Interaction Picture (IP) method is a valuable alternative to Split-step methods for solving certain types of partial differential equations such as the nonlinear Schr$\ddot{o}$dinger equation or the Gross-Pitaevskii equation. Although very similar to the Symmetric Split-step (SS) method in its inner computational structure, the IP method results from a change of unknown and therefore do not involve approximation such as the one resulting from the use of a splitting formula. In its standard form the IP method such as the SS method is used in conjunction with the classical 4th order Runge-Kutta (RK) scheme. However it appears to be relevant to look for RK scheme of higher order so as to improve the accuracy of the IP method. In this paper we investigate 5th order Embedded Runge-Kutta schemes suited to be used in conjunction with the IP method and designed to deliver a local error estimation for adaptive step size control.