• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.19-30
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• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• Water for future
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• v.11 no.2
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• pp.54-61
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• 1978

An attemption of synthesizing and forecasting of monthly river flow has been made by employing a linear stochastic difference equation model. As one of the linear stochestic difference equation model, an ARIMA Type is tested to find the suitability of the model to the monthly river flows. On the assumption of the stationary covariacne of differenced monthly river flows the model is identrfield and is evaluated so that the residuale have the minimum variance. Finally a test is performed to finld the residerals beings White noise. Monthly river flows at six stations in Han River Basin are applied for case studies. It was found that the difference operator is a good measure of forecasting the monthly river flow.

• Journal of the Korean School Mathematics Society
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• v.18 no.3
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• pp.259-279
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• 2015

In this paper, we study the recognition and fallacy of middle school students about the concepts of liner equations and liner functions. We chose 163 8th grade students and 103 9th grade students in M city and investigate their recognition and fallacy about the concepts of liner equations and liner functions. We found following facts. First, middle school students recognize an equation with respect to x as an equation, but do not recognize an equation with respect to y as an equation. Second, middle school students tend to recognize a linear function as a constant function y=p. Third, middle school students tend to distinguish an equation and a function according to the form of an algebraic expression. Finally, middle school students discern the difference between an equation and a function using their concepts in textbooks.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

• Journal of Korean Society on Water Environment
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• v.23 no.3
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• pp.385-390
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• 2007

Reliable flow measurement for dry season is very important to set up the in-stream flow exactly and total maximum daily load control program in the basin. Especially, in the points which tidal current effects are dominant because reliability of the low measurement decrease. The reliable measuring methods are needed. In this study, we analysis the water surface elevation difference of water surface elevation. Quantity relationship to consider tidal currents in these regions. It is known that tidal current effects from Nakdong river barrage are dominant in Samrangjin measuring station. We developed multiple regression equation with water surface elevation, quantity, and difference of water surface elevation and compared these results water measured rating curve. All of these regression equation including linear regression equation and log regression equation fits better measured data them existing water surface elevation quantity line and Among three equations, the log regression equation is best to represent the measured the rating curve in Samrangjin point. The log regression equation is useful method to obtain the quantity in the regions which tidal currents are dominant.

• Korean Journal of Remote Sensing
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• v.33 no.4
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• pp.401-410
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• 2017

Estimation of snow depth using optical image is conducted by using correlation with Snow Cover Fraction (SCF). Various algorithms have been proposed for the estimation of snow cover fraction based on Normalized Difference Snow Index (NDSI). In this study we tested linear, quadratic, and exponential equations for the generation of snow cover fraction maps using data from the Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua satellite in order to evaluate their applicability to the complex terrain of South Korea and to search for improvements to the estimation of snow depth on this landscape. The results were validated by comparison with in-situ snowfall data from weather stations, with Root Mean Square Error (RMSE) calculated as 3.43, 2.37, and 3.99 cm for the linear, quadratic, and exponential approaches, respectively. Although quadratic results showed the best RMSE, this was due to the limitations of the data used in the study; there are few number of in-situ data recorded on the station at the time of image acquisition and even the data is mostly recorded on low snowfall. So, we conclude that linear-based algorithms are better suited for use in South Korea. However, in the case of using the linear equation, the SCF with a negative value can be calculated, so it should be corrected. Since the coefficients of the equation are not optimized for this area, further regression analysis is needed. In addition, if more variables such as Normalized Difference Vegetation Index (NDVI), land cover, etc. are considered, it could be possible that estimation of national-scale snow depth with higher accuracy.

• Journal of Korean Society of Forest Science
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• v.90 no.2
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• pp.210-216
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• 2001

Pinus densiflora S. et Z. has widely been distributed, and is one of the important main foret resources in Korea. Diameter and height growth patterns were estimated using non-linear algebraic difference equation, which requires two-measurement times $T_1$ and $T_2$. To maximize data use, all possible measurement interval data were derived using Lag and Put statements in the SAS. In results, of the algebraic difference equations applied, the Schumacher and the Gompertz polymorphic equations for diameter and height, respectively showed the higher precision of the fitting. In order to allow more precise estimation of growth than those of the basic Schumacher and the Gompertz, further refinement that combine biological realism as input into the equation would be necessary.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.33 no.1
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• pp.68-75
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• 1997

In this paper, we propose the improved initial image estimation method for a fast fractal image decoding. When the correlation between a domain and a range is given as the linear equation, the value of initial image estimation using the conventional method is the intersection between its linear equation and y=x. If the gradient of linear equation is large, that the difference of the value between each adjacent pixels is large, the conventional method has disadvantage which has the impossibility of exact estimation. The method of the proposed initial image estimation performs well by two steps. he first step can improve the disadvantage of the conventional method. The second step upgrades the range value which was found previous step by referring information of its domain. Though the computational complexity for the initial image estimation increses slightly, the total computational complexity decreases by 30% than that of the conventional method because of diminishing in the number of iterations.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.739-744
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• 2002

Recently we have discovered that sediments should be separated from lithosphere, and soil should be separated from biosphere, both sediment and soil will be mixed sediments-soil-sphere (Seso-sphere), which is using particulate mechanics to be solved. Erosion and sediment both are moving by particulate matter with water or wind. But ancient sediments will be erosion same to soil. Nowadays, real soil has already reduced much more. Many places have only remained sediments that have ploughed artificial farming layer. Thus it means sediments-soil-sphere. This paper discusses sediments-soil-sphere erosion modeling. In fact sediments-soil-sphere erosion is including water erosion, wind erosion, melt-water erosion, gravitational water erosion, and mixed erosion. We have established geographical remote sensing information modeling (RSIM) for different erosion that was using remote sensing digital images with geographical ground truth water stations and meteorological observatories data by remote sensing digital images processing and geographical information system (GIS). All of those RSIM will be a geographical multidimensional gray non-linear equation using mathematics equation (non-dimension analysis) and mathematics statistics. The mixed erosion equation is more complex that is a geographical polynomial gray non-linear equation that must use time-space fuzzy condition equations to be solved. RSIM is digital image modeling that has separated physical factors and geographical parameters. There are a lot of geographical analogous criterions that are non-dimensional factor groups. The geographical RSIM could be automatic to change them analogous criterions to be fixed difference scale maps. For example, if smaller scale maps (1:1000 000) that then will be one or two analogous criterions and if larger scale map (1:10 000) that then will be four or five analogous criterions. And the geographical parameters that are including coefficient and indexes will change too with images. The geographical RSIM has higher precision more than mathematics modeling even mathematical equation or mathematical statistics modeling.