• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.231-249
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• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.159-168
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• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

• Journal of Electrical Engineering and Technology
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• v.6 no.2
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• pp.174-181
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• 2011

This paper proposes a novel binary ant colony optimization (NBACO) method. The proposed NBACO is based on the concept and principles of ant colony optimization (ACO), and developed to solve the binary and combinatorial optimization problems. The concept of conventional ACO is similar to Heuristic Dynamic Programming. Thereby ACO has the merit that it can consider all possible solution sets, but also has the demerit that it may need a big memory space and a long execution time to solve a large problem. To reduce this demerit, the NBACO adopts the state probability matrix and the pheromone intensity matrix. And the NBACO presents new updating rule for local and global search. The proposed NBACO is applied to test power systems of up to 100-unit along with 24-hour load demands.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.11-23
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• 2020

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.194-199
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• 2003

Data are an expression of the language or numerical values that show some features. And the information is extracted from data for the specific purposes. The knowledge is utilized as information to construct rules that recognize patterns or make a decision. Today, knowledge extraction and application of that are broadly accomplished for the easy comprehension and the performance improvement of systems in the several industrial fields. The knowledge extraction can be achieved by some steps that include the knowledge acquisition, expression, and implementation. Such extracted knowledge is drawn by rules with data mining techniques. Clustering (CL), input space partition (ISP), neuro-fuzzy (NF), neural network (NN), extension matrix (EM), etc. are employed for the knowledge expression based upon rules. In this paper, the various approaches of the knowledge extraction are surveyed and categorized by methodologies and applied industrial fields. Also, the trend and examples of each approaches are shown in the tables and graphes using the categories such as CL, ISP, NF, NN, EM, and so on.

• Journal of Korean Society for Atmospheric Environment
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• v.6 no.1
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• pp.11-21
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• 1990

To quantitatively estimate the effect of yellow sand(loess) fromt he Northern China, various soil sources having similar chemical compositions to yellow sands should be separated and identified. After that, mass contribution for yellow sand can be calculated. The study showed that it was impossible to solve this problem by the traditional bulk analyses. However, particle-by-particle analysis by a CCSEM (computer controlled scanning electron microscope) gave enormous potentials to solve it. To perform this study, seven soil source data analyzed by CCSEM were obtained from Texas, U.S.A. Initially, each soil date was classified into two groups, coarse and fine particle groups since the particle number distribution showed a minimum occurring at 5.2$\mu$m of aerodynamic diameter. Particles in each group were then classified into one of the 283 homogeneous particle classes by the universal classification rule which had been built by an expert system in the early study. Further, mass fractions and their uncertainties for each class in each source were calculated by the Jackknife method, and then source profile matrix for the 7 soil sources was created. To use the profile matrix in the study of source contribution, it is necessary to test the degree of collinearity among sources. The profiles were tested by the singular value decomposition method. As a result, each soil source characterized by artificially created variables was totally independent each other and is ready to use in source contribution studies as a receptor model.

• Journal of Korea Foundry Society
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• v.13 no.4
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• pp.359-368
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• 1993

Mg-9wt.%Al and Mg-9wt.%-1.6wt%Zn/SiCp(particle size $40{\mu}m$) metal-matrix-composite specimens were manufactured by rheo-compocasting method, known for its effect of improving the wettability. The ceramic reinforcement particles(SiCp) were dispersed in the semi-solid magnesium alloy matrix slurry being vigorously stirred in a high frequency induction furnace under inert atmosphere. A microstructural study of the dispersed particles in the specimens, prepared under different conditions as regards the time(10min, 20min, 30min) and temperature of the stirring, was made with the aid of optical microscope and SEM. The effect of superheating was also observed. It is revealed that 30 minutes' stirring time of the semi-solid at 40% solid fraction temperature(Mg-9wt.%Al : $590^{\circ}C$, AZ91 : $576^{\circ}C$), as determined by the lever rule, gives a satisfactorily uniform distribution of the particles. The superheating is observed to enhance further the uniformity.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.515-531
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• 2008

The visual cryptography scheme is a simple method which can be decoded directly the secret information in human visual system without performing any cryptographic computations. For some secret of image type, we scatter them to random n images and if any threshold (or more) of them are stacked together then original image is visible. In this paper we consider (2,n) visual cryptography scheme and show a construction method of the sample matrix using the rule of binomial coefficients $_nC_2$. This scheme can contribute interesting and effectiveness to the study of mathematics.

• Smart Structures and Systems
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• v.30 no.2
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• pp.135-143
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• 2022

The object of this paper is to investigate the free vibration behavior under the effect of carbon nanotube distribution in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) by using higher-order shear deformation theories. In this work, we present a novel distribution method for carbon nanotubes in the polymer matrix by using a new exponential power law distribution of carbon nanotube volume fraction. It is assumed that the SWCNTs are aligned along the beam axial direction and the distribution of the SWCNTs may vary through the thickness of the beam with different patterns of reinforcement. The rule of mixtures is used in order to obtain material properties of the CNTRC beams. Hamilton's principle is used in deriving the equations of motion. The validity of the free Vibration results is examined by comparing them with those of the known data in the literature. The results that obtained indicate that the carbon nanotube volume fraction distribution play a very important role on the free vibrations characteristics of the CNTRC beam.

• Advances in nano research
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• v.16 no.1
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• pp.11-26
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• 2024

In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.