• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.763-779
• /
• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.143-152
• /
• 2010

Based on the Exp-function method and a suitable transformation, new generalized solitonary solutions including free parameters of the MDI and Sawada-Kotera equations with variable coefficients are obtained, form which solitary wave solutions and periodic solutions including some known solutions reported in open literature are derived as special cases. The free parameters in the obtained generalized solitonary solutions might imply some meaningful results in the physical models. It is shown that the Exp-function method provides a very effective and important new method for nonlinear evolution equations with variable coefficients.

• Tunnel and Underground Space
• /
• v.3 no.1
• /
• pp.80-95
• /
• 1993

Convergence measurements play very important role in the assessment of stability of a tunnel and of the economics of rock reinforcements. The characteristics of convergences are both due to the face advance effect and the time-dependent behaviour of rocks. As the convergence law can be modeled as a specific function of two variables of distance and time, we can determine the type of function and the related parameters from the field measurements. By using the regression method based on the Levengberg-Marquardt algorithm, an analysis of convergence of two different tunnels and one numerical example is described. It is shown that the convergence can be modeled as following function, C(x)=a{1-exp(-bx)} or C(t)=a{1-exp(-bt)} in case of a tunnel excavated in elastic rocks, in case of elasto-plastic or over stressed rocks.

• Communications of the Korean Mathematical Society
• /
• v.17 no.2
• /
• pp.363-370
• /
• 2002

We show that G(x) = $e^{(x}$(1-x))/ -1 is the exponential generating function for the labeled digraphs whose weak components are transitive tournaments and derive both a recursive formula and an explicit formula for the number of them on n vertices. Moreover, we investigate the asymptotic behavior for the coefficients of G(x) using Hayman's method.d.

• Bulletin of the Korean Chemical Society
• /
• v.11 no.6
• /
• pp.497-505
• /
• 1990

The function exp$(x^2)$erfc(x), which is often encountered in studies of electrode kinetics, is evaluated to an extended precision with 32 significant decimal digits in order to find theoretical relationships used in derivative polarography/voltammetry for a chemically-coupled electrode process. Computations with a lower precision are not successful. Evaluation of the function is accomplished by using three types of expansions for the function. Best ranges of arguments are selected for each equation for particular precisions for efficiencies. The method is successfully applied to calculate higher-order derivatives of the current-potential curves in all potential ranges for a reversible electron transfer reaction coupled with a prior chemical equilibrium (i.e., a CE type process). Various parameters that characterize the peak asymmetry (such as ratios of peak-heights, ratios of half-peak-widths, and separations in peak-potentials) are analyzed to find how kinetic and thermodynamic parameters influence shapes of the derivatives. The results from the CE process is compared with those from an EC process in which a reversible electron transfer is coupled with a follow-up homogeneous chemical reaction. The two processes exibit quite contrasting differences for values of the parameters.

• Journal of the Mineralogical Society of Korea
• /
• v.16 no.1
• /
• pp.65-73
• /
• 2003

In this study we have derived the two correction methods of hydrogen bonding distance. In case of the intermediate or long hydrogen bond(＞2.5 $\AA$), hydrogen bonding distances can be corrected by using the function d(O-H)=exp((2.173-d(O…O))/0.138)+0.958 obtained by least- squares fit to the data from the neutron diffraction at low temperatures. The valence-least-squares method is effective for the distance correction of very short hydrogen bond(<2.5 $\AA$). The distance correction is necessary for the long intermolecular hydrogen bond obtained from X-ray diffraction analysis.

• Journal of the korean Society of Automotive Engineers
• /
• v.13 no.5
• /
• pp.51-64
• /
• 1991

In this paper, an attempt is made to analyze the impulsive stress directly underneath the concentrated impact point for a supported square plate by using the three-dimensional dynamic theory of elasticity and the potential theory of displacement (stress function) on the supposition that the load, F$_{*}$0 sin .omega.t, acted on the central part of it. The results obtained from this study are as follows: 1. The impulsive stress cannot be analyzed directly underneath the acting point of concenrated impact load in privious theories, but can be analyzed by using the three-dimensional dynamic theory of elasticity and the potential theory of displacement. 2. Theorically, with increasing the pulse width of applied load, it was possible to clarify that the amount of stress in the point of concentrated impact load was increased and that of stress per unit impulse was decreased. 3. The numerical inversion of laplace transformation by the use of the F.F.T algorithm contributes the reduction of C.P.U time and the improvement of the accuracy or results. 4. In this paper recommended, it is found that the approximate equation of impact load function P (.tau.) = A.tau. exp (-B.tau.), and P (.tau.) =0.85A exp (-B.tau.) sinC.tau. could actually apply to all impact problem. In compared with the experimental results, the propriety of the analytical method is reasonable.

• Journal of Positioning, Navigation, and Timing
• /
• v.4 no.2
• /
• pp.79-85
• /
• 2015

Existing Differential GPS (DGPS) pseudorange correction (PRC) generation techniques based on a virtual reference station cannot effectively assign a weighting factor if the baseline distance between a user and a reference station is not long enough. In this study, a virtual reference station DGPS PRC generation technique was developed based on an enhanced inverse distance weighting method using an exponential function that can maximize a small baseline distance difference due to the dense arrangement of DGPS reference stations in South Korea, and its positioning performance was validated. For the performance verification, the performance of the model developed in this study (EIDW) was compared with those of typical inverse distance weighting (IDW), first- and second-order multiple linear regression analyses (Planar 1 and 2), the model of Abousalem (1996) (Ab_EXP), and the model of Kim (2013) (Kim_EXP). The model developed in the present study had a horizontal accuracy of 53 cm, and the positioning based on the second-order multiple linear regression analysis that showed the highest positioning accuracy among the existing models had a horizontal accuracy of 51 cm, indicating that they have similar levels of performance. Also, when positioning was performed using five reference stations, the horizontal accuracy of the developed model improved by 8 ~ 42% compared to those of the existing models. In particular, the bias was improved by up to 27 cm.

• Tunnel and Underground Space
• /
• v.13 no.2
• /
• pp.77-86
• /
• 2003

The finite element method and statistics of the convergence measurement are useful method of the stability analysis of the tunnel adjacent to the pier. It is the purpose of the this case study to certificate of validity of the application of those methods. The safety of the pilot tunnel method and LW pre-grouting has been evaluated from the FEM analysis. The three-dimensional finite element method is carried out for the decision of the level of stress redistribution at the two-dimensional numerical analysis. An analysis of the convergence is carried out by the estimation of preceding convergence at tunnel excavation. F-examination is applied for this estimation. As results of that analysis, The F-value is from 10.81 to 158.74 and the coefficient of determination is from 0.82 to 0.99. An analysis of convergence is carried out by using regression analysis. Consequently, it is shown that the convergence can be modeled as following function C(t)=a[1-exp(-bt)].

• Journal of the Korean Geophysical Society
• /
• v.7 no.4
• /
• pp.313-324
• /
• 2004

The finite element method and statistics of the convergence measurement are useful method of the stability analysis of the tunnel adjacent to the pier. It is the purpose of the this case study to certificate of validity of the application of those methods. The safety of the pilot tunnel method and LW pre-grouting has been evaluated from the FEM analysis. The three-dimensional finite element method is carried out for the decision of the level of stress redistribution at the two-dimensional numerical analysis. An analysis of the convergence is carried out by the estimation of preceding convergence at tunnel excavation. F-examination is applied for this estimation. As results of that analysis, The F-value is from 10.81 to 158.74 and the coefficient of determination is from 0.82 to 0.99. An analysis of convergence is carried out by using regression analysis. Consequently, it is shown that the convergence can be modeled as following function C(t) = a[1-exp(-bt)].