• Journal of Internet Computing and Services
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• v.25 no.2
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• pp.93-99
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• 2024

In this paper, we derive the Partial Differential Bond Price Equation (PDBPE) by using Ito's Lemma to determine the pricing of bond on term-structure of interest rate (TSIR) model with jump. From PDBPE, the Maclaurin series (MS) and the moment-generating function (MGF) for the exponential function are used to obtain a numerical solution (NS) of the bond prices. And an algorithm for determining bond prices using Monte Carlo Simulation (MCS) techniques is proposed, and the pricing of bond is determined through the simulation process. Comparing the results of the implementation of the above two pricing methods, the relative error (RE) is obtained, which means the ratio of NS and MCS. From the results, we can confirm that the RE is less than around 2.2%, which means that the pricing of bond can be predicted very accurately using the proposed algorithms as well as numerical analysis. Moreover, it was confirmed that the bond price obtained using the MS has a relatively smaller error than the pricing of bond obtained by using the MGF.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.7
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• pp.607-615
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• 2020

The purpose of this study was to analyze the research status and trends related to the industrial mathematics based on text mining techniques with a sample of 4910 papers collected in the SIAM Journal on Applied Mathematics from 1970 to 2019. The R program was used to collect titles, abstracts, and key words from the papers and to analyze topic modeling techniques based on LDA algorithm. As a result of the coherence score on the collected papers, 20 topics were determined optimally using the Gibbs sampling methods. The main results were as follows. First, studies on industrial mathematics were conducted in a variety of mathematics fields, including computational mathematics, geometry, mathematical modeling, topology, discrete mathematics, probability and statistics, with a focus on analysis and algebra. Second, 5 hot topics (mathematical biology, nonlinear partial differential equation, discrete mathematics, statistics, topology) and 1 cold topic (probability theory) were found based on time series regression analysis. Third, among the fields that were not reflected in the 2015 revised mathematics curriculum, numeral system, matrix, vector in space, and complex numbers were extracted as the contents to be covered in the high school mathematical curriculum. Finally, this study suggested strategies to activate industrial mathematics in Korea, described the study limitations, and proposed directions for future research.

• Journal of Internet Computing and Services
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• v.15 no.6
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• pp.15-26
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• 2014

This study focus on a economic value of the Big Data technologies by real options model using big data technology company's stock price to determine the price of the economic value of incremental assessed value. For estimating stochastic process of company's stock price by big data technology to extract the incremental shares, Generalized Moments Method (GMM) are used. Option value for Black-Scholes partial differential equation was derived, in which finite difference numerical methods to obtain the Big Data technology was introduced to estimate the economic value. As a result, a option value of big data technology investment is 38.5 billion under assumption which investment cost is 50 million won and time value is a about 1 million, respectively. Thus, introduction of big data technology to create a substantial effect on corporate profits, is valuable and there are an effects on the additional time value. Sensitivity analysis of lower underlying asset value appear decreased options value and the lower investment cost showed increased options value. A volatility are not sensitive on the option value due to the big data technological characteristics which are low stock volatility and introduction periods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.1-8
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• 2010

The Fourier series uses a vibrating wave that possesses an amplitude that is like the one of the sine curve. Therefore, the functions used in the Fourier series do not change due to the value of the frequency and that set a limit to express irregular signals with rapid oscillations or with discontinuities in localized regions. However, the wavelet series analysis(WSA) method supplements these limits of the Fourier series by a linear combination of a suitable number of wavelets. By using the wavelet that is focused on time, it is able to give changes to the range in the cycle. Also, this enables to express a signal more efficiently that has singular configuration and that is flowing. The main objective of this study is to propose a scheme called wavelet series analysis for the application of wavelet theory to one-dimensional problems represented by the second-order elliptic equation and to evaluate theperformance of proposed scheme comparing with the finite element analysis. After a through evaluation of different types of wavelets, the HAT wavelet system is chosen as a wavelet function as well as a scaling function. It can be stated that the WSA method is as efficient as the FEA method in the case of axial bars with distributed loads, but the WSA method is more accurate than the FEA method at the singular points and its computation time is less.

• Journal of Environmental Impact Assessment
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• v.29 no.6
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• pp.403-413
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• 2020

A mathematical model comprised with eight simultaneous quasi-linear partial differential equations was suggested to provide optimal chlorination strategy. Upstream weighted finite element method was employed to construct multidimensional numerical code. The code was verified against measured concentrations in three type of reactors. Boundary conditions and reaction rate were calibrated for the sixteen cases of experimental results to regenerate the measured values. Eight reaction rate coefficients were estimated from the modeling result. The reaction rate coefficients were expressed in terms of pH and temperature. Automatic optimal algorithm was invented to estimate the reaction rate coefficients by minimizing the sum of squares of the numerical errors and combined with the model. In order to minimize the concentration of chlorine and pollutants at the final usage sites, a real-time predictive control system is imperative which can predict the water quality variables from the chlorine disinfection process at the water purification plant to the customer by means of a model and operate the disinfection process according to the influent water quality. This model can be used to build such a system in water treatment plants.

• Geophysics and Geophysical Exploration
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• v.11 no.2
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• pp.85-92
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• 2008

Magnetotelluric (MT) methods are widely applied as an effective exploration technique to geothermal surveys. Two-dimensional (2-D) analysis is frequently used to investigate a complicated subsurface structure in a geothermal region. A 2-D finite-element method (FEM) is usually applied to the MT analysis, but we must pay attention to the accuracy of so-called auxiliary fields. Rodi (1976) proposed an algorithm of improving the accuracy of auxiliary fields, and named it as the MOM method. Because it introduces zeros into the diagonal elements of coefficient matrix of the FEM total equation, a pivoting procedure applied to the symmetrical band matrix makes the numerical solution far less efficient. The MOM method was devised mainly for the inversion analysis, in which partial derivatives of both electric and magnetic fields with respect to model parameters are required. In the case of forward modeling, however, we do not have to resort to the MOM method; there is no need of modifying the coefficient matrix, and the auxiliary fields can be elicited from the regular FEM solution. The computational efficiency of the MOM method, however, can be greatly improved through a sophisticated rearrangement of the total equation.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.3
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• pp.189-198
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• 2019

In photogrammetry, single photo resection is a method of determining exterior orientation parameters corresponding to a position and an attitude of a camera at the time of taking a photograph using known interior orientation parameters, ground coordinates, and image coordinates. In this study, we proposed a single photo resection algorithm that determines the exterior orientation parameters of the camera using cosine law and linear equation-based three-dimensional coordinate transformation. The proposed algorithm first calculated the scale between the ground coordinates and the corresponding normalized coordinates using the cosine law. Then, the exterior orientation parameters were determined by applying linear equation-based three-dimensional coordinate transformation using normalized coordinates and ground coordinates considering the calculated scale. The proposed algorithm was not sensitive to the initial values by using the method of dividing the longest distance among the combinations of the ground coordinates and dividing each ground coordinates, although the partial derivative was required for the nonlinear equation. In addition, since the exterior orientation parameters can be determined by using three points, there was a stable advantage in the geometrical arrangement of the control points.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.2
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• pp.161-170
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• 2012

There are many factors to consider when attempting to improve the efficiency of fuel cell operation, such as the operation temperature, humidity, stoichiometry, operation pressure, geometric features, etc. In this paper, the effects of the operation pressure were investigated to find the current density and water saturation behavior on a cross section designated by the design geometry. A two-dimensional geometric model was established with a gas channel that can provide $H_2$ to the anode and $O_2$ and water vapor to the cathode gas diffusion layer (GDL). The results from this numerical modeling revealed that higher operation pressures would produce a higher current density than lower ones, and the water saturation behavior was different at operation pressures of 2 atm and 3 atm in the cathode GDL. In particular, the water saturation ratios are higher directly below the collector than in other areas. In addition, this paper presents the dependence of the velocity behavior in the cathode on pressure changes, and the velocity fluctuations through the GDL are higher in the output area than in inlet area. This conclusion will be utilized to design more efficient fuel cell modeling of real fuel cell operation.